Design Optimization of a Mechatronic Device in the Presenceof Quantitative and Qualitative Design Criteria and MultipleObjectivesbyLucas FalchBSc, Technische Universität München, 2014MSc, Technische Universität München, 2015a thesis submitted in partial fulfillmentof the requirements for the degree ofDoctor of Philosophyinthe faculty of graduate and postdoctoral studies(Mechanical Engineering)The University of British Columbia(Vancouver)December 2019c© Lucas Falch, 2019The following individuals certify that they have read, and recommend to the Faculty of Graduateand Postdoctoral Studies for acceptance, the dissertation entitled:“Design Optimization of a Mechatronic Device in the Presence of Quantitative and QualitativeDesign Criteria and Multiple Objectives.”submitted by Lucas Falch in partial fulfillment of the requirements for the degree of Doctor ofPhilosophy in Mechanical Engineering.Examining Committee:Prof. Clarence W. de SilvaDepartment of Mechanical Engineering, University of British ColumbiaSupervisorProf. Ryozo NagamuneDepartment of Mechanical Engineering, University of British ColumbiaSupervisory Committee MemberProf. Septimiu SalcudeanDepartment of Electrical and Computer Engineering, University of British ColumbiaUniversity ExaminerProf. Anasavarapu Srikantha PhaniDepartment of Mechanical Engineering, University of British ColumbiaUniversity ExaminerAdditional Committee Members:Prof. Nariman SepehriDepartment of Mechanical and Manufacturing Engineering, University of ManitobaExternal ExamineriiAbstractMechatronic devices and multi-domain (multi-physics) systems are widely used in modern indus-try and other engineering applications. Mechatronic engineering focuses on developing a designsolution that integrates multiple domains, particularly electrical and mechanical systems. Fora successful product, these systems require to be accurate, fast, reliable, flexible, minimalist,easy to use and cost effective. Such design demands are diverse, can interact with each other,and might be characterized quantitatively, qualitatively, or both. This might require differentscales, units, and physical representations between multiple criteria or objectives. Interactingcriteria or objectives might be conflicting, e.g., improving one requirement might deteriorateanother requirement. This requires reaching a compromise between objectives, a trade-off deci-sion. The present dissertation addresses the multi-objective design optimization problem thatinvolves quantitative and qualitative design criteria and objectives, in a mechatronic system.The methods developed in this thesis are applied to the design of a wearable sleep monitoringsystem. For the benefit of that application, a design optimization framework is proposed forsensor placement on a human body to improve the wearablity and reliability of a monitoringsystem that contains the sensors. The developed framework assists the designer in selectingthe type and location of the sensors, and the pertinent wiring. The framework uses fuzzy setsand numbers to reduce the subjectivity that arises with qualitative criteria. To describe thequalitative objective comfort, fuzzy measures and the Choquet integral are used, particularlyfor combining multiple criteria and handling model interactions. Furthermore, fuzzy measureswith the Choquet integral and the decision-making method VIKOR are introduced to make arelatively less subjective trade-off decision between conflicting objectives. Finally, a compari-son is made between an improved VIKOR method and a fuzzy measure and Choquet integralapproach, related to their optimization trade-off decisions. This study leads to a synthesis of allpresented results and concludes that the proposed methods provide comparable results and areeffective strategies for trade-off decisions. In this manner, the present investigation significantlycontributes to the development of a more effective approach for solving a multi-objective designproblem with quantitative and qualitative design criteria.iiiLay SummaryThe design of a product or device typically requires the consideration of multiple design cri-teria. Such a design must be accurate, reliable, esthetically appealing and cost effective to beacceptable for the consumer. Some of these objectives can be represented as numerical functionsor quantities, while others may be “qualitative” and only be described over linguistic terms.When considering or improving multiple design objectives at the same time, conflicts couldarise. For example, the improvement of one objective might make another one worse. Thisdissertation seeks to improve a multi-objective design of a mechatronic system, by consideringboth qualitative and quantitative design criteria simultaneously, by incorporating not only nu-merical functions but also linguistic methods, in a less subjective manner. Furthermore, twomethods are proposed to make a more effective trade-off decision when design objectives areconflicting. In this manner, the present thesis contributes to designing a mechatronic productmore effectively.ivPrefaceThis thesis is original work completed by Lucas Falch in the Industrial Automation Laboratory(IAL) at The University of British Columbia, Vancouver campus, under direct supervision andguidance of Dr. Clarence W. de Silva, Professor of Mechanical Engineering, The University ofBritish Columbia. Dr. de Silva proposed and supervised the overall research project, acquiredfunding and resources for the project, suggested the topic of the thesis, suggested concepts andmethodologies in addressing problems in the topic, provided research facilities, continuously su-pervised the progress of the research, and revised the thesis presentation. This thesis includestwo published manuscripts, and in addition two other manuscripts submitted. Because parts ofthe thesis have been published individually, there is some cross-over among different chapters,in particular in the introductory sections.Chronologically, the first paper (Chapter 2) has been published in the Sensors Journal byauthors Lucas Falch (first author) and Clarence W. de Silva. Lucas Falch was responsible for allmajor areas of concept formulation, algorithm development and contribution to the manuscript.Clarence W. de Silva was the supervisory author on this work and was involved throughout theproject in concept revisions and manuscript composition.The second paper (Chapter 3) has been published and presented at the 2018 IEEE 9th An-nual Information Technology, Electronics and Mobile Communication Conference (IEMCON)by authors Lucas Falch (first author) and Clarence W. de Silva. Clarence W. de Silva suggestedthe concept of fuzzy measures, which Lucas Falch applied as a decision making framework fora design optimization problem. Lucas Falch was responsible for major areas of concept formu-lation, algorithm development and contribution to the manuscript. Clarence W. de Silva wasthe supervisory author and was involved throughout the work in concept revisions, guidance,and manuscript composition.The third paper (Chapter 4) has been submitted to an appropriate journal by authors LucasFalch (first author) and Clarence W. de Silva. Lucas Falch was responsible for all major areasof concept formation, questionnaire formulation, execution of questionnaire study, algorithmdevelopment, experiment validation, as well as manuscript composition. Clarence W. de Silvawas the supervisory author and was involved throughout the work in concept revisions, guidanceand editing the manuscript.Chapter 5 has been submitted to an appropriate journal by authors Lucas Falch (firstvauthor) and Clarence W. de Silva. Lucas Falch discovered the shortcomings in an existingdecision making method, improved them and used the improved decision making method forcomparison with the fuzzy measure approach. Clarence W. de Silva provided scientific guidanceand suggestions, and is the supervisory author.List of publications from this thesis:Chapter 2:L. Falch and C. W. de Silva, “An Approach to Optimize Multiple Design Objectives WithQualitative and Quantitative Criteria for a Wearable Body Sensor System,” in IEEE SensorsJournal, vol. 18, no. 23, pp. 9708-9717, December, 2018. doi: 10.1109/JSEN.2018.2871676Chapter 3:L. Falch and C. W. de Silva, “Fuzzy Techniques to Reduce Subjectivity and Combine Qualitativeand Quantitative Criteria in a Multi-objective Design Problem,” IEEE 9th Annual InformationTechnology, Electronics and Mobile Communication Conference (IEMCON), Vancouver, BC,Canada, 2018, pp. 42-48. doi:10.1109/IEMCON.2018.8614996List of submitted paper from this thesis:Chapter 4:L. Falch and C. W. de Silva, “Incorporating the Qualitative Variable Comfort into the Designof a Wearable Body Sensor System”Chapter 5:L. Falch and C. W. de Silva, “Decision Making in a Multi-objective Design Problem”viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Acronyms and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . xivAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Wearable Sleep Monitoring System . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.1 Polysomnography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 Portable Sleep Monitoring Systems . . . . . . . . . . . . . . . . . . . . . . 51.2.3 EEG/EOG Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3.1 Dealing with Qualitative Measures . . . . . . . . . . . . . . . . . . . . . . 71.3.2 Design Optimization of Product Style . . . . . . . . . . . . . . . . . . . . 91.3.3 Design Optimization of Wearable Body Sensor Network . . . . . . . . . . 101.4 Research Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.5 Contributions and Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Optimization of Multiple Design Objectives with Qualitative and Quanti-tative Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14vii2.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3 Design Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.4 Fuzzy Sets and Fuzzy Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.5 EEG/EOG Body Sensors in Sleep Monitoring . . . . . . . . . . . . . . . . . . . . 212.6 Multi-objective Design Optimization for EEG/EOG Monitoring . . . . . . . . . . 222.7 Design Optimization Using Linear Programing and Minimum Spanning Tree(MST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.7.1 EEG/EOG Monitoring Design Optimization Using Linear Programingand MST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.7.2 Results of an EEG/EOG Monitoring Design . . . . . . . . . . . . . . . . . 262.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Design Optimization Using Fuzzy Sets and Fuzzy Measures . . . . . . . . . 323.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3 Multi-Criteria Decision Aiding (MCDA) . . . . . . . . . . . . . . . . . . . . . . . 343.3.1 Capacities/Fuzzy Measures . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3.2 Choquet Integral as an Aggregation Operator . . . . . . . . . . . . . . . . 353.3.3 Determination of Fuzzy Measures . . . . . . . . . . . . . . . . . . . . . . . 373.4 Classification of Utility Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.5 Identifications of Fuzzy Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.6 Final Design Stage for EEG/EOG Electrode Placement . . . . . . . . . . . . . . 413.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424 Incorporating Comfort into the Design . . . . . . . . . . . . . . . . . . . . . . 434.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3 Comfort as a Design Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.4 Determination of Fuzzy Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.5 Modeling Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.6 Comfort Model for a Wearable Body Sensor System . . . . . . . . . . . . . . . . 504.6.1 Comfort Questionnaire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.6.2 Determination of Comfort Model . . . . . . . . . . . . . . . . . . . . . . . 514.6.3 Validation of the Comfort Model . . . . . . . . . . . . . . . . . . . . . . . 534.7 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 Decision Making in Multi-objective Design . . . . . . . . . . . . . . . . . . . 565.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57viii5.3 VIKOR Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.3.1 VIKOR Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.3.2 Shortcomings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.4 Modified VIKOR-method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.4.1 Modified Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.4.2 Modified VIKOR Weight Margins . . . . . . . . . . . . . . . . . . . . . . 625.4.3 Weight Margin Using a Range of Objectives Values . . . . . . . . . . . . . 635.5 Design Optimization Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.5.1 Design of a Wireless Sleep Monitoring System . . . . . . . . . . . . . . . . 645.5.2 Design of an EEG Electrode . . . . . . . . . . . . . . . . . . . . . . . . . . 705.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756 Comparison of Decision Making Methods . . . . . . . . . . . . . . . . . . . . 766.1 Comparison of Chapter 2 Decision Making Method with VIKOR . . . . . . . . . 766.2 An Example Comparison of Fuzzy Measures/Choquet Integral with VIKOR . . . 776.3 Another Comparison of Fuzzy Measures/Choquet Integral with VIKOR . . . . . 796.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837.2 Possible Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86ixList of TablesTable 2.1 Fuzzy weights for linguistic variables . . . . . . . . . . . . . . . . . . . . . . . 22Table 2.2 Fuzzy weight assignment for electrode locations. Column 1 presents the elec-trode locations according to the 10-20 EEG system (see Figure 2.1). xi arebinary variables for placing an electrode at that particular location. The lasttwo columns are the fuzzy weights assigned to each electrode location. . . . . 23Table 2.3 Fuzzy weight assignment for electrodes. . . . . . . . . . . . . . . . . . . . . . . 25Table 2.4 Comparison matrix with given length and fuzzy weightings for electrode con-nection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Table 3.1 Utility values for discomfort, reliability and power consumption. The numbersin brackets are the normalized utility values. . . . . . . . . . . . . . . . . . . . 39Table 3.2 Fuzzy measures m and Shapley indices φSh . . . . . . . . . . . . . . . . . . . . 40Table 3.3 Interaction indices between the three criteria. . . . . . . . . . . . . . . . . . . 41Table 3.4 Sorted Choquet integral values and the corresponding electrode placements.The version in column 3 corresponds to the electrode arrangements in Figure 2.1 41Table 4.1 Normalized utility values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Table 4.2 Shapley index of MR method and LS method. . . . . . . . . . . . . . . . . . . 52Table 4.3 Shapley indices of MR and LS methods. . . . . . . . . . . . . . . . . . . . . . 53Table 4.4 Interaction indices between criteria for MR method and LS method. . . . . . 53Table 4.5 Shapley indices of the MR method and LS method. . . . . . . . . . . . . . . . 53Table 4.6 Normalized root mean square deviation (NRMSD). . . . . . . . . . . . . . . 54Table 4.7 Locations sorted from the most comfortable to the least comfortable. . . . . . 54Table 5.1 Example 1, where ai are design alternatives, xi are the objective functions,WS is the weighted sum, S is the maximum group utility in the VIKORmethod, R is the minimum individual regret in the VIKOR method, and Qis the aggregated value of S and R in the VIKOR method. . . . . . . . . . . . 59xTable 5.2 Example 2, where ai are design alternatives, xi are the objective functions,S is the maximum group utility in the VIKOR method, R is the minimumindividual regret in the VIKOR method, and Q is the aggregated value of Sand R in the VIKOR method. . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Table 5.3 Notations and numerical values in energy consumption optimization. . . . . . 67Table 5.4 Three objectives and utility values for the design of a wireless sleep monitoringsystem (The maximum utility value for each objective is highlighted in bold). 68Table 5.5 Modified VIKOR weight margin for comfort (w1), energy consumption (w2)and signal interference (w3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Table 5.6 Parameters in the multi-objective optimization of EEG electrode (four typesof polymer are considered). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Table 5.7 Weight margins for conductivity (w1), durability (w2) and flexibility (w3) . . . 73Table 5.8 Weight margins for conductivity (w1), durability (w2) and flexibility (w3) . . . 74Table 6.1 Fuzzy measures m in Möbius representation and Shapley indices φSh . . . . . 78Table 6.2 Utility values of the VIKOR method for two different weightings. . . . . . . . 81xiList of FiguresFigure 1.1 The figure shows a typical Polysomnography setup with the typical sensorsthat a patient has to wear to monitor sleep in order to detect potential sleepdiseases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Figure 1.2 The figure shows the necessary sleep monitoring sensors and their locationon a human body. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Figure 2.1 Possible electrode locations for EEG and EOG in sleep monitoring. . . . . . . 22Figure 2.2 Triangular fuzzy membership function. . . . . . . . . . . . . . . . . . . . . . . 23Figure 2.3 Pareto front for electrodes with trade-off solutions of non-reliability and non-wearability. The red circle indicates the chosen trade-off solution. Each solu-tion on the Pareto front corresponds to a particular EEG/EOG electrode ar-rangement with reliability and wearability values according to equations (2.9)and (2.10). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Figure 2.4 The bars in the bar plots indicate number of times a location is part ofindividual non-dominated solutions. . . . . . . . . . . . . . . . . . . . . . . . 29Figure 2.5 An EEG/EOG design. Electrodes on the forehead are connected in paralleland have a common supply connection. . . . . . . . . . . . . . . . . . . . . . 30Figure 3.1 Sensitivity of the δ value. The plot shows the fuzzy measures as a functionof δ. A too high δ value will violate the preference rankings (equation (3.12)). 40Figure 4.1 Box plot of comfort questionnaire data. The red horizontal line representsthe median and the red plus signs show the outliers. The lines extendingabove and below each box are the whiskers (see box-and-whisker plot formore detail). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Figure 4.2 Normalized root mean square deviation (NRMSD) for various criteria. . . . 52Figure 5.1 Sensor nodes i and candidate sites zj for a wireless sleep monitoring system. 65Figure 5.2 TDMA frame structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66xiiFigure 5.3 Green square: most preferred solution determined over the modified VIKORmethod; Red star: determined through the original VIKOR method. Theusage of all alternatives or only the non-dominated solutions change slightlyin the original VIKOR method. . . . . . . . . . . . . . . . . . . . . . . . . . . 69Figure 5.4 Non-dominated solutions of polymer 1 with marked preferred design solutionof original and modified VIKOR method. . . . . . . . . . . . . . . . . . . . . 72Figure 5.5 Non-dominated solutions of polymer 1 with marked preferred design solutionof original and modified VIKOR method. The conductivity constraint isapplied to the Pareto front. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 5.6 Discontinuous Pareto front of four types of polymer. . . . . . . . . . . . . . . 74Figure 6.1 Comparison of Chapter 2 result with the proposed decision making methodof Chapter 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Figure 6.2 Comparison of fuzzy measures/Choquet integral decision making with VIKORmethod in the example of Chapter 3. . . . . . . . . . . . . . . . . . . . . . . . 79Figure 6.3 Comparison of fuzzy measures/Choquet integral decision making with VIKORmethod using the example in Chapter 5. . . . . . . . . . . . . . . . . . . . . . 80xiiiList of Acronyms and AbbreviationsAcronym /AbbreviationDefinitionAASM American Academy of Sleep MedicineAHP Analytic Hierarchy ProcessCAD Computer Aided DesignCB Carbon BlackCFP Contention Free PeriodCS Candidate SiteCSA Central Sleep ApneaECG ElectrocardiogramEEG ElectroencephalographyELECTRE ELimination Et Choix Traduisant la REalité(Elimination and Choice Expressing Reality)EMG ElectromyographyEOG ElectrooclugraphyFAHP Fuzzy Analytic Hierarchy ProcessFDA Food and Drug AdministrationGRA Gray Relation AnalysisGTS Guaranteed Time SlotIMU Inertial Measurement UnitIP Inactive PeriodLS Least-SquaresMAV T Multi-Attribute Value TheoryMCDA Multi-Criteria Decision AidingMR Marichal and Roubens methodMSLT Multiple Sleep Latency TestsMST Minimum Spanning TreeNRMSD Normalized Root Mean Square DeviationNSGA Non-dominated Sorting Genetic AlgorithmOSA Obstructive Sleep ApneaxivPROMETHEE Preference Ranking Organization Method forEnrichment of EvaluationsPSG PolysomnographyQFD Quality Function DeploymentREM Rapid Eye MovementRMSD Root Mean Square DeviationSPEA Strength Pareto Evolutionary AlgorithmTDMA Time Division Muliple AccessTOPSIS Technique for Order of Preference by Similarity toIdeal SolutionsV IKOR from Serbian: VIseKriterijumska Optimizacija IKompromisno Resenje, meaning: Multi-criteriaOptimization and Compromise SolutionWBSN Wireless Body Sensor NetworkxvAcknowledgmentsSeveral people have helped me in one way or another during the course of my PhD research,and deserve my gratitude. I would like to thank my supervisor, Dr. Clarence W. de Silva forhis continuous enthusiasm, encouragement, valuable advice, guidance and support throughout.Thanks also to my supervisory committee, Dr. Mu Chiao, Dr. Ryozo Nagamune and Dr.Patrick Kirchen for their guidance and encouragement.I also acknowledge the funding I received throughout my PhD from the Natural Sciencesand Engineering Research Council of Canada, Project STPGP 493908, with Dr. Clarence W.de Silva as the Principal Investigator of the grant.I would also thank all my colleagues in the Industrial Automation Laboratory and the SleepMonitoring group for their support and fruitful discussions.Thanks also to my friends I met throughout my stay in Vancouver. Boris, who was alwaysgood for having a discussion about the university, but also personal matters and life. Myroommates Deb, Ryan and Todd. Veronika and Karo for baking a cake once in a while andgiving me input to improving my writing skills. Also thanks to my climbing partners and peoplein other social activities; Juan, Flo, Mike, British, Tomas, Lili and Swapna. Special thanks aredeserved by Anna, because she supported me considerably, whether it was in brainstorming,listening to my problems, editing my papers, or making my life better in Vancouver.Danke natürlich an all meine Lieben zu Hause, meine Eltern die mich in meinen Entschei-dungen und während meines Studiums immer unterstützt haben, meine Schwester Sarah mitClara und Benni, Onkel und Tanten. Babsi, Jacopo und Nadine die mich von zu Hause aus mo-tiviert und mich in Vancouver besucht haben. Danke auch für den Besuch vom Waffenhändler,Paul und Lukas. Eva und Günne für die Oster und Weihnachtsgeschenke. Ohne Abenteur undInspiration hätte ich mir das alles gar nicht ausdenken können.xviDedicationTo my friends and family, who were always there for me –and the mountains that gave me the best views after a hard climb.xviiChapter 1IntroductionThis dissertation is based on two published papers (Chapters 2 and 3) and two paper submitted(Chapter 4 and 5). The present introductory chapter provides the motivation of the researchand rationale, organization of the dissertation, and some relevant background material. In theformat of a complete paper, each chapter includes a detailed introduction to the specific issuethat it addresses, pertinent developments, results, and a discussion.1.1 MotivationEvery engineering device is assessed by its properties, characteristics and the functional pur-pose. A mechatronic device, in particular, contains both mechanical and electrical parts, andits development requires the involvement of different fields of knowledge, such as controls andcomputer engineering, mechanics and electronics [1]. Traditionally, electro-mechanical systemswere designed or selected separately in a sequential manner and combined with other compo-nents, hardware and software in later steps. In a mechatronic approach, the complete electro-mechanical system is handled as a whole in an integrated manner that incorporates multipledomains (e.g., electrical, mechanical, thermal, and fluid). A multi-domain (or, multi-physics)device requires a mechatronic approach, which is integrated, unified, systematic and unique.This is the extended and more generalized definition for a mechatronic device, as proposed byde Silva [2], which goes beyond the previous definition involving only electro-mechanical sys-tems an integrated design. In this definition, “unified” means similar or analogous techniques tohandle different domains, using the corresponding across-variables and through-variables. Next,“unique” result is achieved through optimization of the development according the pertinentperformance indices and constraints. It can be argued that, a mechatronic product that is de-veloped through this approach will be more efficient and cost effective, precise, reliable, flexible,functional and mechanically less complex than a non-mechatronic product with a comparablelevel development effort and expenditure.A mechatronic system consist of many different types of interconnected components and el-ements. Various properties and characteristics have to be considered during the design process1of the device. Product design can be a time-consuming, complex, and costly task. Many designtools, such as Computer Aided Design (CAD) and simulation software, are available to reducethe time to bring a product to the market. Properties and design specifications of a device arediverse and have different characteristics. A “unique” engineering design is realized throughdesign optimization, which may use a mathematical formulation of the design problem to sup-port the selection of the “optimal” (or “unique”) design from many alternatives. The designoptimization procedure involves various types of objective functions, which may incorporatesuch attributes as performance, quality, cost, speed, ease of operation, safety, and environmen-tal impact of the designed product or system, which involve both quantitative and qualitativeaspects, in general. The involvement of these various properties will generally require manydecisions, which suggests that the task of design can be viewed as a decision-making process[3]. A design optimization problem involves design variables, describing the design alternatives;design objectives, which are functional combinations of variables to be maximized or mini-mized; and constraints that must be satisfied by the acceptable alternatives. When solving amechatronic design problem that incorporates a number of objectives, multi-disciplinary designoptimization allows the designer to consider all relevant factors simultaneously to improve thedesign and reduce the time and cost of the design cycle. Furthermore, the solution to a mul-tidisciplinary (or, mechatronic) design optimization problem will have to consider interactionsbetween different aspects and domains, and is therefore more desirable than the optimizationof each aspect individually [4]. Also, limits of the objectives (constraints) are not necessar-ily known, particularly when qualitative objectives are treated as constraints. Therefore, it isdesirable to optimize the design objectives simultaneously, using a multi-objective optimiza-tion formulation. Multi-objective design optimization was initially developed for and is stillwidely used in aerospace engineering, such as aircraft and spacecraft design [5–7] in view of thecomplex and multi-domain nature of the design of such systems. DeWispelare [8] presentedin his PhD research a process algorithms for multiobjective optimization theory and multipleattribute utility theory with application in a defense system problem, specifically for electronicretrofit of warfare aircraft. Multi-objective design optimization has been extended to a numberof fields, including automobile design [9] and building design [10].The optimization of multiple-objective functions often requires a trade-off, because an im-provement in one objective might downgrade another one. Designing a new mechatronic devicesometimes requires the construction of a few models or prototypes to gain knowledge and ex-perience. However, each model or prototype might have its advantages and disadvantages,making it difficult to chose the optimal design. A simple way to make the selection might be tocount the number of advantages and pick the one with the highest count. However, advantagescan be of qualitative nature and they can be as important, if not more than, the quantitativeadvantages. Qualitative objectives in a design process are often not known in the beginning.An example of a mechatronic device for which qualitative design criteria are important is ahealthcare monitoring device. Kasabach et al. [11] sought to design an accurate and comfort-2able wearable body monitoring system. To find a good mounting location on the human body,they created three prototypes and tested them on subjects to select the best location. This isa reasonable approach; however, resources are not always available to build several prototypesand conduct a study. Instead, an analytical approach is desirable, and a tool that facilitatesoptimal design decisions would save time and money. Kasabach et al. [11] make their design de-cision for the device location based on arguments rather than through an efficient and analyticalstudy. This leads to subjective decisions, does not consider possible differences in importanceof arguments, and is almost impossible to validate. Therefore, a more powerful and analyticalapproach is needed to incorporate qualitative design objectives as well as quantitative and makeless subjective design decisions.In this backdrop, the main challenges associated with the design of a mechatronic productinclude: (i) Incorporating qualitative design criteria (e.g., the level of comfort of a wearablebody sensor network) into the design process, (ii) Evaluation of a design trade-off by consideringmultiple design objectives.When considering multiple design objectives, the design space contains several possiblealternatives. The best alternative would be the one that has the highest satisfactory valuein each criterion, but in reality an alternative in which all criteria dominate may not exist.Solutions in a multi-objective optimization problem that are not dominated by other solutionsare called Pareto optimal solutions [12]. Determination of non-dominated solutions reducesthe set of possible design alternatives, and a decision that considers various importance valuesfor criteria is required to choose one of them. Out of this set of solutions, the one with thehighest satisfaction value for the overall design requires a decision by an expert or the designer.A more effective multi-criteria decision making method that incorporates the importance andinteractions between criteria in a non-subjective way is a helpful tool for designing a mechatronicdevice.The present research addresses the development, implementation, and evaluation of a prac-tical and effective approach that incorporates qualitative design objectives directly into thedesign process that also has quantitative design objectives. The developed methods within thisresearch are applied to the design of a portable sleep monitoring system. The following sectionspresent an overview and the importance of a wearable sleep monitoring system and indicatethe need to design a highly functional, comfortable and reliable sleep monitoring system.1.2 Wearable Sleep Monitoring SystemPoor-quality sleep over a long period of time can lead to adverse effects such as hypertension,cardiovascular pathologies, obesity and diabetes, and it can affect the immune system [13].Often, poor-quality sleep is caused by sleep disorders, which affect nearly 27% of the worldpopulation [14]. Lack of sleep can harm the economy due to the resulting loss of productivity.The costs are estimated to be about $18 billion globally [15]. There are numerous methodsto evaluate sleep in a clinical laboratory. These include overnight Polysomnography (PSG),3multiple sleep latency tests (MSLT), and Video-PSG. However, a clinical environment is costlyto maintain because of the necessary facilities and staff. Long delay in getting an appointmentat a sleep clinic is another concern. Furthermore, the sleep condition at a clinic, typically,is quite different from that at the familiar home environment. Hence, the monitored resultsmay not be quite representative. Consequently, there is a high interest in developing portabledevices that can perform comprehensive monitoring of sleep in a home environment. Theexisting home monitoring devices do not record adequate data (in both type and duration) toproperly diagnose sleep apnea and other sleep disorders. A comprehensive yet portable sleepmonitoring device will cater to a large portion of the population at a lower cost.1.2.1 PolysomnographyPolysomnography (PSG) is the current gold standard in sleep monitoring and takes place ina clinical environment. It is an effective, precise, and comprehensive sleep monitoring methodto diagnose diverse sleep disorders like obstructive sleep apnea (OSA), central sleep apnea(CSA) and insomnia. OSA is a disease where the upper airway is obstructed during sleep [16].The throat muscles relax and close the pharynx and as a result the airway is partially orcompletely blocked. OSA is usually associated with a reduction in the blood oxygen and causesawakening from sleep. In CSA the breathing intermittently stops and starts during sleep andthis occurs because the brain does not send proper signals to the muscles that control thebreathing [17]. This is different from OSA and can cause heart failure and structural damageto the central nervous system. Therefore it is important to diagnose such sleep disorders toperform appropriate treatment. Figure 1.1 shows a typical PSG setup with a range of sensorsto diagnose the mentioned sleep diseases.Figure 1.1: The figure shows a typical Polysomnography setup with the typical sensorsthat a patient has to wear to monitor sleep in order to detect potential sleepdiseases.With PSG it is possible to detect different sleep stages like REM sleep and non-REM sleep,and record periodic limb movements during sleep, like restless legs syndrome [18]. While PSG4provides extensive information, the unfamiliar sleep environment and the single night moni-toring can lead to unacceptable results. Many people have variations in their daily sleep ordifferent symptoms over several nights, weeks or months, which might be related to caffeine, al-cohol consumption, medication, stress or daily exercising. These conditions cannot be analyzedand diagnosed with just a single night of sleep monitoring. Further drawbacks of PSG include,for example, the non-standardized protocols in laboratories, the clinical conditions of equip-ment and personnel, and the long duration of monitoring and analysis and the related costsand other hardships. These shortcomings can be improved with comprehensive, yet portablesleep monitoring devices.1.2.2 Portable Sleep Monitoring SystemsThe American Academy of Sleep Medicine (AASM) divides portable monitoring devices intofour types [17]:• Type 1: Full attended polysomnography (≥ 7 channels) in a laboratory setting• Type 2: Full unattended polysomnography (≥ 7 channels)• Type 3: Modified portable sleep apnea testing (minimum 4 channels)• Type 4: Continuous single or dual bio parameter recording, usually using oximetry as oneof the parametersMostly, type 3 devices are available at present. The existing portable monitoring devices areonly suitable for people with a high probability of moderate to severe OSA. However, with moresensors and improved technology of portable devices, sleep monitoring for the home environ-ment could be made comparable to clinical sleep monitoring. With portable monitoring devices,more people can be monitored at lower cost, because there is no need for special facilities withall the sophisticated equipment and staff. However, current portable monitoring devices donot contain all the needed sensors for comprehensive PSG. A comprehensive sleep monitoringdevice must record at least the airflow, respiratory effort, blood oximetry, electrocardiography,electroencephalography (EEG), electrooculography (EOG) and electromyography (EMG). Non-invasive sensors such as cameras are not suitable to detect the mentioned sleep diseases suchas OSA or CSA. Cameras would only monitor the sleeping behavior, but it is not possible todetect OSA or CSA by using them. According to the current AASM standards, a certified sleepspecialist or a person that satisfies the criteria for sleep medicine examination must evaluate theraw data from the monitoring process and make a statement about an eventual sleep disorder[19]. The first portable monitoring test was published in 1994, which promised to reduce theunacceptable delays in accessing PSG. However, its acceptance and success were limited.A portable monitoring device is accepted as a diagnostic tool only if it follows the AASM-accredited criteria, the United States Food and Drug Administration (FDA) guidelines, and ISO13485 for Europe and Canada. The certification pathways in the United States at present arethrough the American Board of Sleep Medicine and the American Board of Medical Specialties.5The currently used technologies in portable sleep monitoring devices include:• Electroencephalography (EEG): Records the electrical activity of the brain trough elec-trodes on the scalp• Electrooculogram (EOG): Records the cornea-retinal potential between front and back ofthe eye, detecting eye movements• Electromyogram (EMG) for chin: Measures the electrical activity of the muscles to detectbruxism• Electromyogram (EMG) for leg: Measures the electrical activity of the muscles, to detectmovement related disorders• Airflow signals: Measure the flow of air through the nose and/or mouth. Such sensors aspressure sensor and thermistor may be used• Respiratory effort (RE) signals: Record the movement of the chest and the abdomen dueto respiration, using elastics band with a strain sensor• Oxygen saturation: Measures the concentration of oxygen in the blood.• Body position: The position of the body during sleep (spine, lateral recumbent, etc.)• Electrocardiogram (ECG): Records the electrical activity of the heart using electrodesFigure 1.2 shows the arrangement of the listed sensors on a human.Figure 1.2: The figure shows the necessary sleep monitoring sensors and their locationon a human body.The demand for portable home sleep monitoring devices is high. Currently there are just afew such devices on the market and many of them do not fulfill the requirements for accuratemedical monitoring. With most of the portable monitoring devices, it is only possible todiagnose specific sleep disorders. The sensors that are missing in current portable monitoringsystems include Electroencephalography (EEG) and Electrooculography (EOG).61.2.3 EEG/EOG MonitoringAn important sensor system that is not commonly available in the present home-based sleepmonitoring devices is Electroencephalography (EEG). EEG records the change in human brainsignals [20]. For monitoring the eye movement for sleep stage detection, Electrooculography(EOG) measures the electrical potential between the cornea and the retina.Evaluating sleep stages is one part in a sleep study and can be precisely done with theanalysis of brain wave patterns. Observing the EEG signals in sleep monitoring requires onlya portion of the electrodes used in clinical applications. A minimum of three EEG channels isrequired to classify sleep stages. Section 2.5 provides further details on EEG/EOG in portablesleep monitoring.1.3 Related Work1.3.1 Dealing with Qualitative MeasuresMany methods are available to assign importance weightings to design variables or factors. Acommon technique to compute the importance of a qualitative criterion or a linguistic variable isby using an analytic hierarchy process (AHP) [21]. AHP provides a comprehensive and rationalframework for structuring a decision by creating a comparison matrix where alternatives arecompared with respect to criteria. Decision makers or experts give ratings of importance, andby using the principal right eigenvector (e.g., [22]) or the geometric mean of rows (e.g., [23]) ofthe matrix, utility values for all the criteria are determined.In order to reduce the subjectivity of the design decision in a multi-objective optimizationalgorithm, a group of researchers [22] used a fuzzy analytic hierarchy process (FAHP). Theyused triangular fuzzy numbers, α-cuts and the lower and upper bounds of the α-cut to quantifythe importance weights determined by AHP.Another method for dealing with qualitative measures is given in the study of Babbar etal. [24], where they considered qualitative and quantitative criteria to select a set of suppliers.They determined the quantity of an order to reduce costs, and considered environmental impactsas well. To assign weights and thereby rank the suppliers, they developed a quality functiondeployment (QFD) model. QFD is based on the opinion of decision makers and is thereforesensitive to the number of experts used in the study and their level of experience. In theirapproach, three experts rated a product based on such customer considerations as price andquality. Babbar, et al. [24] used trapezoidal fuzzy numbers to reduce subjectivity in the rantingsby experts. The overall weight of each product property is computed using fuzzy arithmetic.With this method, experts rated if a supplier can satisfy customer needs and specific predefinedcharacteristics of the supplier. The fuzzy weights as determined through expert ratings werequantified using the mean of the four trapezoid fuzzy parameters and were normalized withinthe range 0 and 1. They formulated a multi-objective optimization problem that was based on7the previously mentioned supplier weights and on quantitative parameters such as the unit costof a product. The problem was solved using three different methods: (i) weighted sum method,(ii) weighted-constraint method, and (iii) distance method.A more standardized technique to quantify qualitative design criteria is quantification theorytype 1, which was developed in the 50’s by Hayashi [25]. It makes use of linear regression andis expressed as:Yk =m∑i=1n∑j=1βijxij + k (1.1)where Yk is the observed value or the response, usually rated by volunteers or experts; βijis the parameter of the model or the weight of a level or category; and xij is the level or thecategory variable (dummy). The least square algorithm minimizes the prediction error k.Hsiao et al. [23] applied quantification theory type 1 to measure the perception of home-pages. Human perceptions are thought to be non-quantifiable, subjective and affect-based, andare difficult to objectively measure using conventional methods. They used qualitative factorslike proximity and similarity to describe human perception. Diverse homepage samples wereevaluated by volunteers over a set of linguistic variables. Ratings given by experts or decisionmakers are highly subjective. To reduce subjectivity in the evaluation of homepage design,Hsiao et al. [23] used triangular fuzzy membership functions with seven linguistic importancejudgments of qualitative factors. To quantify the linguistic importance judgments of qualita-tive factors, they used α-cuts and center-of-gravity method. Fuzzy entropy was then used as ameasure for human perception. A higher fuzzy entropy indicated a higher human perceptionof a single homepage. Fuzzy entropy indicated the fuzziness of the fuzzy set. In this manner,their approach addressed and weakened the subjectivity of human-based decisions.Mohsenzadeh et al. [26] presented a method to rate appliances based on a predicted elec-tricity usage costs and the occupant comfort in the household. A fuzzy-logic technique wasused to model these two objectives. Their goal was to minimize the utility cost and maximizethe comfort. A normal distribution curve, a rectangular curve, or a trapezoidal curve, was useddepending on the appliance in order to model the comfort profile of the device.A different approach to make a model by capturing subjective and qualitative measures, wasdeveloped by Grabisch et al. [27]. They used fuzzy measures and integrals to model discomfortfor subjects sitting for a long period of time (such as when driving a car). Subjects filled outa questionnaire to express their experiences during an experiment that used different car seatsunder various conditions. Based on this approach, an overall comfort value was determined andfuzzy measures were identified by minimizing the squared error of the overall comfort. However,inferring the overall comfort value from a questionnaire is subjective and requires a prototypedesign to conduct the experiment. Despite these concerns, it is a common approach and hasbeen applied by various researchers (e.g., [28], [29], [30]).81.3.2 Design Optimization of Product StyleOther applications that require the quantification of qualitative variables is in the field ofproduct style design. To assess and select a product design Hsiao et al. [31] collected productstyles and used morphological analysis theory to form different styles for various parts of acoffee maker. To obtain a score for each part (casing, water compartment, etc.) and category(funneled, spheroid, etc.,) the researchers applied quantification theory type 1. Specifically,they used a questionnaire, in which the subjects rated 26 representative samples based onseven linguistic variables. In order to obtain an optimal design solution for a coffee maker,they applied a genetic algorithm. The fitness function for the optimization process was formedby the weight of each linguistic variable and the individual score for the styles. The methodused in their work requires a generation of representative designs. This is possible when amodel representation (such as a CAD drawing) exists. However, it considers qualitative designcriteria only based on the appearance of the product and is highly dependent on the surveygroup. A similar approach to optimize the form and shape of a product was used by Shieh etal. [22], where the main difference lies with regard to the optimization method. Hsiao et al.[31] created a single objective function with a score for each category and a weighting for thelinguistic descriptive variables, whereas Shieh et al. [22] created one objective function for eachlinguistic variable and applied a multi-objective optimization algorithm. Their algorithm [22]was applied to the form design of a car. In describing and judging design variables, they usedfactor analysis to pick the main factors such as modern, rounded, and simple. A questionnairewas created where 60 participants rated 27 sample designs using a scoring scale from 1 to 7 basedon linguistic factors. Each linguistic factor was represented in an objective function, and theyused the multi-objective optimization algorithm NSGA-II in order to optimize the mentionedfactors (modern, rounded, etc.,). The multi-objective optimization algorithm delivered thenon-dominated solutions. To select a solution and make a final design decision, they appliedfuzzy analytic hierarchy process (FAHP). This provided a weight for each factor, which gave aperformance value as the product of each Pareto solution vector and the weight. The highestperformance value represented the final and optimal solution.Xue et al. [32] presented an approach to develop a product design using Gray RelationalAnalysis (GRA). GRA defines situations with no information as black and those with perfectinformation as white, whereas information in between is classified as gray. The input andoutput in their approach were linguistic variables that were determined based on fuzzy theory.Morphological analysis extracted the product from the design elements of experimental samples.Subjects rated these samples on a seven point scale, which provided a numerical database ofthe product image to construct fuzzy rules. In their work, a train seat design served as a casestudy, and Computer Aided Design (CAD) was used to build 3-D models.The study of Brintrup et al. [33] emphasizes the importance of combining qualitative andquantitative criteria in a design process. They developed an interactive genetic algorithm formultiple objectives and tested it on the design of an office chair. Their method was based on9multi-criteria decision making and user-interactive evolutionary optimization techniques. Forinteractive evolutionary optimization, subjective evaluation by humans was integrated into thefitness function. This implied that the designer acted as a qualitative fitness function withinthe genetic algorithm and gave ratings for qualitative objectives. Therefore, the human himselfwas not a model, but was incorporated into the algorithm and produced subjective input intothe design. This publication presented three methods: (i) a parallel, (ii) a sequential, and (iii) amulti-objective interactive genetic algorithm. In (i), the offspring population was created fromthe qualitative and quantitative fitness functions in parallel by migrating them. In (ii), an initialqualitative run created the parent population for the sequential quantitative run. Method (iii)was based on the usual non-domination techniques and used elitism to combine parent andoffspring populations before sorting them for non-domination and creating a set of solutions.The connection between the qualitative and quantitative aspects lied within the optimizationalgorithm itself, and the fitness function for qualitative objectives was the design expert. Thisstep induced human evaluation after each run into the process which adds subjectivity, mightbe inconsistent and vary depending on the person or experience.1.3.3 Design Optimization of Wearable Body Sensor NetworkDesigning a wearable body sensor network requires the consideration of multiple factors suchas comfort. Even a well-functioning and reliable wearable body sensor network might not beaccepted by the end user, if it is uncomfortable or distracting. Comfort is a highly subjectiveand qualitative measure. It can be a physical sensation, a psychological state, or both simul-taneously. Several authors have previously tried to optimize comfort or wearability. Anliker etal. [34] sought to optimize multiple objectives of a wearable architecture. Their work presentsa systematic way to choose and attach devices to a human body. The design space includedbattery life, system functionality, and wearability. For battery life they used the average powerconsumption of the system, and considered a variety of computing devices. A specific comput-ing device was able to perform different tasks like image encoding and zip decoding at variousbody locations. For each task they used an average computing power in order to optimize thebattery life. In addition, the power consumption for connecting the devices was considered,since it varied depending on the connection channel (USB, I2C, Bluetooth, etc.). To quantifythe functionality of the system, they used the execution and communication delay betweendevices. The wearability objective was based on the weight vectors assigned to different bodylocations. The wearability factors also depended on the size, weight, and wired or wirelessconnections. The weights given for the wearability factors were not explained in their paper,and it was left for treatment through ergonomic research and social acceptability to determinethese weights. The underlying design challenge was addressed by considering a multi-objectiveoptimization problem and using the evolutionary SPEA2 algorithm. It created a Pareto frontwith a set of trade-off solutions.In a follow-up paper [35], the authors additionally considered sensors that could be attached10to a human body. The sensor selection was based on the trade-off parameters: power consump-tion and recognition performance. Recognition quality was quantified using a theory based onmutual information. Mutual information is a measure of the information that a sensor (e.g.,accelerometer, air pressure sensor) provides about a recognition class such as the user activities.It was computed using experimental data, and joint probability functions were estimated. An-liker et al. [35] used a genetic algorithm to derive a set of Pareto optimal system configurationsand optimize the two objective functions.Other researchers in the field of wearable sensor systems, such as Tabares et al. [36], at-tempted to optimize the same objective functions, wearability and functionality, as mentionedbefore ([34], [35]). Here, they considered state-of-the-art platforms in order to build theirobjective functions. Their product was an ergonomic clothing article with an integrated elec-trocardiogram system. The design variables were x1 = skin contact quality, x2 = size, x3 =weight, x4 = fluid repellency and x5 = magnetic protection. They formulated a simple objectivefunction f for functionality, as:f = (x21 + x2 + x3 + x4 + x5)/5 (1.2)The impact of each design variable (quadratic or linear) was based on the intuition and availableinformation. They did not perform actual quantification of the design variables. Results wereexpressed as percentages; for example, the skin contact quality = 69.45% or size = 33.03%.Such values may be interpreted as importance factors. However, because of the intuitive natureof the objective function and seemingly random choice of a solution from the Pareto front, thesolution presents some caveats.In a subsequent paper, the same researchers [37] used a different approach to address someof these caveats and attempted to model the objective functions through multivariate regres-sion. They studied a linear regression model and a nonlinear regression model with real andcategorical values. Their specific application was an electrocardiogram system. The researchersmade 160 measurements from 12 volunteers for various body locations, with different rotationangles and pressure levels. The volunteers provided information on the device comfort for eachmeasurement. To gain information about the functionality, they correlated their measured sig-nal with a reference signal. A higher correlation meant higher functionality. The conflictingobjective functions wearability and functionality were fitted using regression and then optimizedthrough a genetic algorithm and represented as a Pareto set (non-dominated solutions). Thisapproach helped to select a good location for the rotation and the pressure level of an electro-cardiogram system. Yet, in designing a wearable system or a mechatronic device in general, itmight not be always possible to conduct experiments at first. Even if an experiment producesrepresentable results, different types of parameters such as different electrodes can skew theoutcome.In the field of powered lower-limb prostheses design, Sahoo et al. [38] optimized the powerconsumption of the input motor by maximizing the ratio of maximum knee torque to maxi-11mum torque for a gait cycle. Their goal was to achieve low power consumption, low weight,fast response and compactness for the prostheses. Laschowski et al. [39] reviewed the elec-tromechanical design and optimization of lower-limb devices and discussed design optimizationobjectives such as electrical energy regeneration, mechanical power transmission, electromag-netic machine, electrical drive, mass and moment of inertia and energy storage. Consideredobjectives were quantitative aspects and they did not consider qualitative objectives such ascomfort, which also plays a role in lower-limb prostheses.1.4 Research IssuesThe following section highlights the questions addressed in this thesis. In particular it addresseshow it contributes to solving a design problem, motivated by the design optimization of wearablesleep monitoring systems (Section 1.2).Design problems often times have a range of objectives to be considered. Focusing on thefield of medical devices, a wearable device does not only have to function properly, it also hasto be comfortable to wear, should not distract the person while performing daily tasks, andshould consume little power. These properties are diverse, some of them are quantitative orquantifiable and others are rather qualitative. The difficulties that come with such design prop-erties are different scales and units between objectives. These objectives need to be consideredsimultaneously, taking into account existing interactions. Multiple criteria or objectives can beconflicting and by improving one, another one might degrade, which leads to the situation inwhich a trade-off decision needs to be made. Qualitative criteria or objectives are subjective, aswell as the trade-off decision that is necessary to pick one final design. Taking all this into ac-count is a challenging task for the design and development of a mechatronic device. A strategyis required to perform such a complex design task. This thesis applies the developed conceptsto a wearable body sensor network, specifically a sleep monitoring device. It thus contributesto the team effort in developing such a device within our research group. However, developedconcepts can of course be applied on a much broader scale which is reflected in the followingresearch questions:• How to include and handle qualitative design requirements?• How to incorporate quantitative and qualitative design criteria or objectives simultane-ously and handle different scales and units?• How to reduce subjectivity associated with qualitative criteria or objectives?• How to make a trade-off decision, when criteria or objectives are conflicting?1.5 Contributions and Thesis OverviewBy addressing the indicated research issue, the present thesis makes important contributions tothe state of the art of the focus area. The main contributions and an overview of the present12dissertation are given next.1. Chapter 2 presents a design optimization framework for the sensor placement on a humanbody with specific application to an EEG/EOG device for sleep monitoring. The quan-titative optimization method uses pre-chosen qualitative metrics to improve wearabilityand reliability and assists the designer in the selection of type, location and wiring of thedevices. Fuzzy weights express the qualitative metrics. In the application of EEG/EOGmonitoring, the approach provides solutions for various types of electrodes instead ofjust one. The design space is reduced through this approach. A simple decision makingmethod with equal importance for both objectives is presented as an illustrative examplein the case study.2. In the present work, two decision making methods are improved and introduced to mecha-tronic design optimization. One method is based on fuzzy measures and the Choquetintegral with the ability to model interactions, as developed in Chapter 3.3. How to describe the qualitative design objective comfort among multiple criteria is demon-strated in Chapter 4. Criteria describing comfort are combined with fuzzy measures andthe Choquet integral. The improvement and comparison between two fuzzy measuredetermination techniques is another important contribution of the dissertation. The out-come of this work is a comfort model for a wearable body sensor network, which isdetermined through a questionnaire study and validated using test samples. This makesthe determination of the qualitative objective comfort less subjective.4. The information needed to make a trade-off decision is based on preferences of some alter-natives. As the second decision making approach that is developed in the present work,an existing method with clear shortcomings is improved, to overcome these deficiencies,in Chapter 5.5. Finally, the two introduced methods are compared with each other in Chapter 6. Thedeveloped decision making methods reduce subjectivity in the design trade-off selection.13Chapter 2Optimization of Multiple DesignObjectives with Qualitative andQuantitative CriteriaThe material in this chapter has been published in the IEEE Sensors Journal (L. Falch andC. W. de Silva, “An Approach to Optimize Multiple Design Objectives with Qualitative andQuantitative Criteria for a Wearable Body Sensor System,” in IEEE Sensors Journal, vol. 18,no. 23, pp. 9708-9717, 1 Dec.1, 2018. doi: 10.1109/JSEN.2018.2871676)2.1 SummaryThis chapter presents an approach to optimize multiple design objectives that have qualitativeand quantitative design variables, with specific application for a wearable body sensor system.The methodology incorporates a way to group the qualitative and quantitative design variablesand the design objectives that are present in the problem and the establishment of the domainsthat exist in such a design problem. Design indices are the objective functions that representthe qualitative design goals. The design space is systematically reduced thereby making iteasier to decide on an optimal design solution, specifically to pick a good solution from thenon-dominated solutions. A technique of fuzzy logic is used to assign weights to the subjectiveand non-crisp design criteria. With the method presented in this chapter it is illustrated howto design a wearable body sensor network with respect to comfort and reliability. Specifically,the design of an EEG/EOG monitoring system for sleep monitoring is considered, where thepresented approach provides a systematic way to find an appropriate number and type ofcomponents, their locations, and how they are connected and arranged.142.2 IntroductionA wearable body sensor system is assessed through their features, properties, characteristics,and the functional purpose. All these aspects have to be considered during the design processof the system. However, the system properties and design specifications can be quite diverseand have different characteristics. For example, the weight, size and the cost of the device aretypically represented by real numbers, whereas functionality, comfort, complexity and aesthet-ics are complex attributes that are rather subjective and of qualitative nature. An experienceddesigner might be able to handle both qualitative and quantitative design objectives in a mean-ingful way in the design process. Even with many years of design experience, however, a humandesigner may not be able to directly and completely apply the previous experience for a newdevice in a different field. Therefore, a systematic and algorithmic approach to incorporatequalitative and quantitative design parameters and optimize multiple design objectives is ben-eficial, particularly with regard to the efficiency, effectiveness, flexibility, speed, and cost ofthe design. It will enable the industries to design reliable and well-functioning devices in asystematic manner. This is a key focus of the present research.Researchers have sought to optimize a variety of devices with respect to qualitative andquantitative aspects. To assess and select a product design Hsiao et al. [31] collected productstyles and used morphological analysis theory to form different styles for various parts of acoffee maker. To obtain a score for each part (casing, water compartment, etc.,) and category(funneled, spheroid, etc.,) the researchers applied quantification theory type 1: They used aquestionnaire, where subjects rated 26 representative samples based on seven linguistic vari-ables. In quantification theory type 1, the degree of influence of the target variable on eachcategory of items is computed by multiple regression. They used Analytic Hierarchy Process(AHP) to compute the importance of each linguistic variable. In AHP, as developed by Saaty[21], a decision maker judges the importance by pairwise comparison of each factor. The rel-ative scale measurement is presented as a matrix and the weights are calculated through themethod of normalization of the geometric mean of rows. To obtain an optimal design solutionfor a coffee maker they applied a genetic algorithm. The fitness function for the optimizationprocess was formed by the weight of each linguistic variable and the individual score for thestyles. The method used in their work required a generation of representative designs. This ispossible when a model representation (such as a CAD drawing) exists. However, it consideredqualitative design criteria only based on the appearance of the product and was highly depen-dent on the survey group. The method did not consider other objectives such as functionality,reliability, and power consumption.A similar approach to optimize the form and shape of a product is used by Shieh et al. [22],where the main difference lies with regard to the optimization method. Hsiao et al. [31] createda single objective function with a score for each category and a weighting for the linguisticdescriptive variables whereas Shieh et al. [22] created one objective function for each linguisticvariable and applied a multi-objective optimization algorithm. Their algorithm [22] was applied15to the form design of a car. Through morphological analysis they selected representative designvariables with the help of experts. To describe and judge these design variables they usedfactor analysis to pick the main factors such as modern, rounded, and simple. A questionnairewas created where 60 participants rated 27 sample designs using a scoring scale from 1 to 7based on linguistic factors. To quantify and build a model, the researchers used quantificationtheory analysis 1. Each linguistic factor was represented in an objective function, and theyused the multi-objective optimization algorithm NSGA-II in order to optimize the mentionedfactors (modern, rounded, etc.). The multi-objective optimization algorithm delivered the non-dominated Pareto solutions. In order to select a solution and make a final design decision, theyapplied fuzzy analytic hierarchy process (FAHP). Because AHP is subjective, the researchersused triangular fuzzy membership functions to judge the comparison. This provided a weightfor each factor. The highest utility value computed by the weighted sum was their optimalsolution.Brintrup et al. [33] developed an interactive genetic algorithm for multiple objectives withqualitative and quantitative criteria for a chair design. Their method was based on multi-criteriadecision making and user-interactive evolutionary optimization techniques. For interactive evo-lutionary optimization, subjective evaluation by humans was integrated into the fitness function.This implied that the designer acted as a qualitative fitness function within the genetic algo-rithm and gave ratings for qualitative objectives. Therefore, the human themselves was nota model, but incorporated into the algorithm and produced subjective input into the design.Their paper presented three methods: (i) a parallel, (ii) a sequential, and (iii) a multi-objectiveinteractive genetic algorithm. In (i), the offspring population was created from the qualitativeand quantitative fitness functions in parallel by migrating them. In (ii), an initial qualitativerun created the parent population for the sequential quantitative run. Method (iii) was basedon the usual non-domination techniques and used elitism to combine parent and offspring pop-ulations before sorting them for non-domination and creating a set of solutions. The connectionbetween the qualitative and quantitative aspects was within the optimization algorithm itself,and the fitness function for qualitative objectives was the design expert, which required humanevaluation after each run, which is subjective. The human evaluation might even be inconsistentand vary depending on the group/person or experience.The work in [23] applied quantification theory type 1 to measure the perception of home-pages. Quantification theory type 1 has been developed in the 50’s by Hayashi [25] and thatwork made use of linear regression. Human perceptions are thought to be non-quantifiable,subjective and affect-based experiences, and are difficult to objectively measure using conven-tional methods. Their paper used triangular fuzzy membership functions with seven linguisticimportance judgments of qualitative factors. They applied the method to homepage design andused qualitative factors like proximity and similarity. Diverse homepage samples were evalu-ated by volunteers using a set of linguistic variables. In order to quantify each factor, theyused α-cuts and the center-of-gravity method. Fuzzy entropy was then used as a measure for16human perception. Fuzzy entropy indicates the fuzziness of a fuzzy set. In this manner, theirapproach addressed and weakened the subjectivity of human-based decisions. A higher fuzzyentropy indicated a greater human perception of a single homepage. Other applications thatrequire the quantification of qualitative variables is in the design of the product style.Mohsenzadeh et al. [26] presented a method to rate appliances based on predicted electricityusage costs and the occupant comfort in the household. A fuzzy-logic technique was used tomodel these two objectives. Their goal was to minimize the utility cost and maximize thecomfort. A normal distribution curve, a rectangular curve, or a trapezoidal curve, was useddepending on the appliance in order to model the comfort profile of the device.Babbar et al. [24] considered qualitative and quantitative criteria to select a set of suppliers,determine the quantity of an order to reduce costs, and consider environmental impact. Toassign weights and thereby rank the suppliers, they developed a quality function deployment(QFD) model. QFD is based on the opinion of decision makers and is therefore sensitive to theused number of experts and their level of experience. In their approach, three experts rateda product based on such customer considerations as price and quality. The rating scale wasa trapezoidal fuzzy number, and the rating was weighted depending on the expertise of thedecision maker. The weight was also a trapezoid fuzzy number. The overall weight of eachproduct property was computed using fuzzy arithmetic. With this method, experts rate if asupplier can satisfy customer needs and specific predefined characteristics of the supplier. Thefuzzy weights as determined through expert ratings were quantified using the mean of the fourtrapezoid fuzzy parameters and were normalized within the range 0 and 1. They formulateda multi-objective optimization problem that was based on the previously mentioned supplierweights and on such quantitative parameters as the unit cost of a product. The problem wassolved using three different methods: (i) weighted sum method, (ii) weighted-constraint method,and (iii) distance method. An underlying issue in the existing studies was the lack of a cleardefinition for “qualitative” design objectives and the weight assignment for qualitative designvariables.In the field of wearable body sensor systems, Anliker et al. [34] sought to optimize multipleobjectives of a wearable architecture. Their work presented a systematic way to choose andattach devices to a human body. The design space included battery life, system functionality,and wearability. For battery life they used the average power consumption of the system, andconsidered a variety of computing devices. A specific computing device was able to performdifferent tasks like image encoding and zip decode at various body locations. For each task theyused an average computing power in order to optimize the battery life. Also, the power con-sumption for connecting the devices was considered, since it varied depending on the connectionchannel (USB, I2C, Bluetooth, etc.,). To quantify the functionality of the system they usedthe execution and communication delay between devices. The wearability objective was basedon the weight vectors assigned to different body locations. The wearability factors also dependon the size, weight, and wired or wireless connections. The weights given for the wearability17factors were not explained in their paper, and it was left for treatment through ergonomic re-search and social acceptability. The underlying design challenge was addressed by considering amulti-objective optimization problem and using the evolutionary SPEA2 algorithm. It createda Pareto front with a set of trade-off solutions.In a follow-up paper [35] the authors additionally considered sensors that could be attachedto a human body. The sensor selection was based on the trade-off parameters: power consump-tion and recognition performance. Recognition quality was quantified using a theory based onmutual information. Mutual information is a measure of the information that a sensor (e.g.,accelerometer, air pressure sensor) provides about a recognition class such as user activities.Mutual information was computed using experimental data, and joint probability functionswere estimated. They used a genetic algorithm to derive a set of Pareto optimal system con-figurations and optimized the two objective functions.Other researchers in the field of wearable sensor systems, such as Tabares et al. [36], at-tempted to optimize the same objective functions, wearability and functionality, as mentionedbefore ([34], [35]). Here, they considered state-of-the-art platforms in order to build theirobjective functions. Their product was an ergonomic clothing article with an integrated elec-trocardiogram system. The impact of each design variable was mainly based on intuition. Theydid not perform actual quantification of the design variables. Because of the intuitive natureof the objective function and seemingly random choice of a solution from the Pareto front, thesame researchers [37] used a different approach to address some of these caveats and attemptedto model the objective functions through multivariate regression. They studied a linear and anonlinear regression model with real and categorical values. Their specific application was anelectrocardiogram system. The researchers made 160 measurements from 12 volunteers for var-ious body locations, with different rotation angles and pressure levels. The volunteers providedinformation on the device comfort for each measurement. To gain information about the func-tionality, they correlated their measured signal with a reference signal. A higher correlationmeant higher functionality. The conflicting objective functions wearability and functionalitywere fitted using regression and then optimized through a genetic algorithm and represented asa Pareto set (non-dominated solutions). This approach helped to select a good location for therotation and the pressure level of an electrocardiogram system. Yet, in designing a wearablesystem or a mechatronic device in general, it might not be always possible to conduct experi-ments. Even if an experiment produces representable results, different types of parameters suchas different electrodes can skew the outcome.The literature here, which deal with optimization of a mechatronic design, does not considerboth qualitative and quantitative design variables. To improve the time and cost of designingand developing a good product, the production of prototypes during the design process mustbe minimized. Therefore, it is important to include qualitative design aspects such as comfortas well in the design process, to quickly attain an optimal and user-accepted design. In order toincorporate subjectivity in the optimization process with respect to qualitative variables, fuzzy18logic is used in the present work to represent the associated non-crisp boundaries. Further, tosatisfy several aspects of the design, multiple objectives are considered in solving the designoptimization problem. The literature reviewed here show some shortcomings and hence callfor combined approaches in order to tackle a variety of optimization problems and efficientlydesign products. All these are considerations in the present research.2.3 Design VariablesThe first key step of designing a mechatronic device is the identification of the relevant designvariables/parameters and objective functions. Typically, more than one design variable may beneeded to define a design objective, and more than one design objective may be needed as well.In the design process, the designer needs to define the objectives of the designed system, whichdepend on the application of the system. Functionality is an important design criterion, butin case of a wearable body sensor system, comfort also plays an important role. Even a highlyfunctional and quality product might not be accepted by the customer, if the comfort level ofthe product is not adequate. Therefore, it is necessary to include such qualitative objectiveswithin the set of design objectives. The next step consists of characterizing the design variablesby sorting them into relevant domains. The following list shows examples of domains where adesign variable is quantitative or qualitative:• Quantitative– ∈ R Real numbers (cost, weight, lifetime, ...)– ∈ Z Integer numbers (number of components, ...)– ∈ FD Finite domain (design possibilities, component locations, ...)– ∈ P Probability distribution (failure rate, probability of fault/malfunction, ...)• Qualitative– ∈ QS Sortable in decreasing or increasing order of value (comfort, drive-ability, ...)– ∈NO Subjective and with no order of value (aesthetics, appearance, ...)Some design variables like the monetary cost, size, and weight are quantitative measures andcan be represented by real numbers. Number of components; e.g., number of screws and numberof IMUs, are integer values. However, these design variables are also indicators of qualitativemeasures. The comfort level of a wearable product depends on the number of components in theproduct, but also on the location where a component such as a sensor is attached to the bodyof the wearer. Possible locations to place sensors are finite and are an important criterion inoptimizing the user comfort (some locations on the human body are less sensitive than others).Some design criteria may be representable as probability functions.Qualitative measures may be grouped into two categories, namely qualitative sortable (QS)and non-sortable (NO). For example, if comfort is related to pain, it is a qualitative aspect since19humans have different comfort zones and thresholds of pain tolerance. However, the ratingsof locations/devices with respect to the user comfort can be sorted based on the anatomy.However, aesthetics or appearance may depend on an individual’s taste or level of maturity. Itmight be possible to rate devices or the style of a product for a specific group of people havingsimilar tastes or backgrounds, but the resulting ratings would be biased. When including non-sortable design aspects in the design process it is important to factor in the characteristics ofthe group of people who use the device. The present work considers sortable design aspectsonly and does not focus on a specific group of people. However, qualitative design criteriaare still subjective, and in order to deal with subjectivity and the lack of crisp boundaries forqualitative measures, the use of fuzzy set theory is appropriate.2.4 Fuzzy Sets and Fuzzy NumbersTo approximate subjective and qualitative knowledge, Zadeh [40] introduced the concept offuzzy sets and related it to fuzzy logic, in the mid-1960s. The theory has been widely used to dealwith subjectivity and qualitative measures, and applied to many practical situations. A fuzzyset is defined by its membership function, which indicates the grade (degree) of membershipof an element (member) within the set. The membership value is defined in the interval [0, 1],and the membership function is expressed as µM : X → [0, 1] [41, 42]. For analytical purposes,a fuzzy set may be represented by a group of crisp sets called α-cuts [42]. The α-cut of a fuzzyset is the crisp set that includes all the members of the fuzzy set whose membership values aregreater than or equal to α. If the elements of this crisp set are in the interval [m,n], then thecorresponding α-cut can be expressed as Mα = [m,n].Any fuzzy set can be completely defined by its set of α-cuts [42, 43] and therefore it is possibleto limit arithmetic operations to its interval, provided that they are continuous membershipfunctions. It is clear from the above definition that the sum and the multiplication of α-cutsare given by:Mα +Nα = [m1,m2] + [n1,n2]= [m1 + n1,m2 + n2] (2.1)MαNα = [m1,m2] · [n1,n2]= [min(m1n1,m1n2,m2n1,m2n2), max(m1n1,m1n2,m2n1,m2n2)] (2.2)Here M and N are two fuzzy sets, and Mα and Nα are their respective α-cuts. Obviously,the result of the α-cut summation is a crisp set because the α-cuts themselves are crisp sets.The defuzzification of a fuzzy set may be done using the center-of-gravity method. Specifi-cally:µM (x) =∫x · µ(x)dx∫µ(x)dx(2.3)20Further details on fuzzy logic and soft computing are found in [41], [42] and [43].2.5 EEG/EOG Body Sensors in Sleep MonitoringThe methods investigated and developed in the next sections will be applied to the design ofan Electroencephalography (EEG) and Electrooculography (EOG) device for sleep monitoring.As mentioned in Chapter 1 Electroencephalography (EEG) records the change in humanbrain signals [20]. Observing EEG signals in sleep monitoring does not require all the electrodesthat are used in clinical applications. A minimum of three EEG channels is required to classifysleep stages [44]. The analysis of brain wave patterns is an important step of evaluating sleepstages. Electrooculography (EOG) is also important in the detection of sleep stages. EOGmeasures the electrical potential between cornea and retina. In the process, electrodes recordvertical eye movements (such as blinking) and horizontal eye movements simultaneously.The American Academy of Sleep Medicine (AASM) manual [17] suggests different electrodemounting locations and combinations for sleep monitoring. Four acceptable versions and loca-tions of the placement of EEG and EOG electrodes are listed below and shown in Figure 2.1.• EEG– Version1: F4-M1, C4-M1, O2-M1– Version2: F3-M2, C3-M2, O1-M2– Version3: Fz-Cz, Cz-Oz, C4-M1– Version4: Fpz-Cz, Cz/C3-O1, C4/C3-M2• EOG– E1-M1/M2/Fpz– E2-M1/M2/FpzIn the figure, circles indicate EOG electrodes. Electrode locations marked in red representversion 1 of the acceptable positions for EEG monitoring in a sleep study [17]. Green, blueand purple correspond to version 2, 3 and 4, respectively. A combination of the four versions isalso possible. Specifically, combining the four versions of electrode arrays will give 15 possibleelectrode arrangements.21F4C4O2M1F3 FzFpzC3O1M2CzOzC4M1 CzO1M2C3E1 E2M2FpzEOGEEGEEGVersion1: F4-M1, C4-M1, O2-M1 (recommended)Version2 :F3-M2, C3-M2, O1-M2 (backup)Version3: Fz-Cz, Cz-Oz, C4-M1Version4: Fpz-Cz, Cz/C3-O1, C4/C3-M2EOGE1-M1/M2/FpzE2-M1/M2/FpzFigure 2.1: Possible electrode locations for EEG and EOG in sleep monitoring.2.6 Multi-objective Design Optimization for EEG/EOGMonitoringThis section demonstrates the design optimization of an EEG/EOG system for sleep monitoring.The goal here is to find comfortable and reliable locations in a human body for EEG/EOGmonitoring. For different locations, type of devices and connection channels, it is possible toassign linguistic fuzzy numbers such as those shown in Table 2.1. Here, comfort and reliabilityare rated ranging from unreliable/uncomfortable to reliable/comfortable, in five categories, andintervals of fuzzy numbers are assigned for each linguistic variable. The membership function istriangular (Figure 2.2). The assignment of a fuzzy membership function reduces the subjectivityand, after defuzzification, a numerical value for the reliability and comfort of the objectives isprovided.Table 2.1: Fuzzy weights for linguistic variablesLinguistic variable Interval of triangular fuzzy numberUnreliable (UR) [0, 0.333]Uncomfortable (U)Moderate Unreliable (MUR) [0.167, 0.5]Moderate Uncomfortable (MU)Moderate (M) [0.333, 0.667]Moderate (M)Moderate Reliable (MR) [0.5, 0.833]Moderate Comfortable (MC)Reliable (R) [0.667, 1]Comfortable (C)22x00.5µ(x)100.167 0.333 0.5 0.667 0.833UR MUR M MR RFigure 2.2: Triangular fuzzy membership function.The possible locations and the combinations of the connections for the electrodes representan extensive design space. Therefore, an approach to find an optimal design is needed. Thefuzzy weightings that characterize each location for comfort and reliability are given in Table 2.2.Table 2.2: Fuzzy weight assignment for electrode locations. Column 1 presents the elec-trode locations according to the 10-20 EEG system (see Figure 2.1). xi are binaryvariables for placing an electrode at that particular location. The last two columnsare the fuzzy weights assigned to each electrode location.Electrode Design Fuzzy weightvariable Comfort ReliabilityE1 x1 C RE2 x2 C RFpz x3 C RF3 x4 C MRFz x5 MC RF4 x6 C MRM1 x7 U MRC3 x8 MU MURCz x9 M MC4 x10 MU MURM2 x11 U MRO1 x12 U UROz x13 U URO2 x14 U URThe assigned weights are intuitive and therefore subjective, yet they are derived by consid-ering the human anatomy and sleeping behavior. The majority of people sleep on the side [45]and in order to breath while sleeping, the forehead and the upper part of the head should nottouch the pillow. Considering this aspect, it is more comfortable and reliable to place electrodeson the forehead, and the lack of hair at such locations is an added advantage. Furthermore,the back or the side of the head is more likely to touch the pillow and the additional appliedpressure through the attached electrodes causes further discomfort. These areas are also con-sidered more unreliable, since movements at night can lead to detachment of the electrodes.However, to assign fuzzy weights more precisely and less intuitively, a survey or questionnaireis suggested. For demonstration purposes of the theory, these intuitively assigned weights areemployed.232.7 Design Optimization Using Linear Programing andMinimum Spanning Tree (MST)This section presents an approach to design a wearable body sensor system by consideringtwo qualitative objective functions: wearability and reliability. Previous approaches (e.g., [34],[36], [37]) attempted to model wearability and reliability as two separate objective functions.In their approach, they encountered problems in the combination of design variables havingdifferent units and incomparable magnitudes. The approach presented in this chapter, however,overcomes this problem by finding an appropriate number of devices with respect to the twospecific objective functions. Afterwards a minimum spanning tree algorithm is applied, wherethe inputs are the combined weightings of the two objective functions and the connection lengthof the electrodes. This approach ensures that the electrodes are associated with the smallestpossible weightings. In order to optimize wearability, the number of devices attached to the bodyshould be minimized. On the other hand, by increasing the number of devices, the reliabilitycan improve, as well as the functionality. The latter aspect is not considered in the presentwork. An increase in the number of components would lead to degraded reliability when thecomponents are connected in series. However, here only parallel connections (backup/redundantdevices) are considered. Each device has its own connection, but the wires can be in the samecable channel. The present method that addresses the described problem is detailed now.Wearability: min # devices =n∑i=1ˆ(ct) t xi (2.4)Reliability: max # devices =n∑i=1ˆ(rt) t xi (2.5)min tree of graph G with edges cij (2.6)subject to xi ∈ {0, 1}t ∈ {available devices}cij ∈ {0, 1}cij ≤ xi · xj , ∀ij connections (2.7)cij =1 if ˆ(cr)ij 6max ˆ(cr)−min ˆ(cr)20 otherwise(2.8)Here xi are the locations at which a device/sensor can be placed, as represented by a binaryvalue (1 for present and 0 for absent); n is the number of locations that are available to placea device/sensor. The available type of devices/sensors to be placed at particular locations isdenoted by t. Each device and location gets a fuzzy weighting (see Table 2.2) depending on thecorresponding comfort and reliability. The combined weighting of comfort/reliability and thetype of device, ˆ(ct) and ˆ(rt) is computed using fuzzy arithmetic (equation (2.2)) and defuzzifiedby the center-of-gravity method, as given by equation (2.3).24The selected locations xi, which are suitable for mounting a device or sensor, are the nodesin a graph G [46] and cij denotes the possible connections (edges in graph G). If a location xior xj is not selected, cij does not exist, as expressed in equation (2.7). The weightings ˆ(cr)ij ingraph G are computed using wearability and reliability fuzzy weightings by equation (2.2) and(2.3) and also the length lij to connect the nodes. To optimize wearability and reliability, therequired length to connect devices must be minimized, and comfortable and reliable connectionsshould be preferred (equation (2.6)) as the minimum spanning tree of graph G. It is necessaryto supply devices/sensors. It is possible to have a single power supply for each sensor/device (allcij = 0), which will make the system more reliable, because sensors are connected independently.On the other hand, a common power supply, which is the connection of several devices/sensors(cij 6= 0) would make the system more comfortable. Therefore, not every connection cij in theminimum spanning tree will be chosen. This is implemented using equation (2.8). The presentwork considers a connection as valid if the weighting of the connection lies in the middle of theminimum and maximum of all possible weightings of the minimum spanning tree, because thepresent work assigns equal importance for wearability and reliability. Hence, equation (2.8) isonly true for this case. The proposed approach is applied to design an EEG/EOG monitoringsystem for sleep monitoring, as presented next.2.7.1 EEG/EOG Monitoring Design Optimization Using LinearPrograming and MSTThis section presents the design optimization of a monitoring system that has the sensingcapabilities of EEG and EOG.Acceptable versions and locations of the EEG and EOG electrodes are listed in Section 2.5and shown in Figure 2.1. They take into consideration that at minimum 3 EEG electrodesare required to classify sleep stages, as suggested by the American Academy of Sleep Medicine(AASM) [17].Fuzzy weightings characterizing comfortable and reliable locations are given in Table 2.2,in the previous section. This approach also considers the type of electrodes. The fuzzy weightsfor three different types of electrodes are listed in Table 2.3. The weight assignment is intuitiveand based on personal experience.Table 2.3: Fuzzy weight assignment for electrodes.Type of Fuzzy weightelectrode Comfort Reliability(A) Capacitive M MUR(B) Spiky contact U M(C) Microneedle C MURIn total, there are 14 locations for electrodes. The resulting multi-objective optimizationproblem aiming to find a comfortable and reliable number of electrodes may be expressed as25Wearability: min # electrodes =n∑i=1ˆ(ct) t xi (2.9)Reliability: max # electrodes =n∑i=1ˆ(rt) t xi (2.10)subject to xi ∈ {0, 1}t ∈ {available electrodes}x1 + x2 ≥ 2 (2.11)x6 + x7 + x10 + x14 ≥ 4−M(1− y1) (2.12)x4 + x8 + x12 + x11 ≥ 4−M(1− y2) (2.13)x5 + x7 + x9 + x10 + x13 ≥ 5−M(1− y3) (2.14)x3 + x8 + x9 + x11 + x12 ≥ 5−M(1− y4) (2.15)y1 + y2 + y3 + y4 ≥ 1 (2.16)yi ∈ {0, 1},M is chosen sufficiently largen ... number of locations (n = 14)Equations (2.9) and (2.10) are the two objective functions that have to be optimized. Electrodesx1 and x2 have to be a part of the system in order to form an EOG-monitoring system. Thisis specified in the constraint equation (2.11). Equations (2.12) to (2.15) are the possible com-binations, for a sleep disorder EEG-monitoring system (specified in the AASM manual [17]).Equation (2.16) ensures that at least one possible EEG-combination is selected. The minimiza-tion of the wiring length and choosing comfortable and reliable connections is implementedusing the minimum spanning tree algorithm and described in equation (2.6). The wiring lengthand the fuzzy weightings for each connection are presented in Table 2.4. The wiring length ischosen based on the 10/20 EEG positioning system and average head size dimensions [47].2.7.2 Results of an EEG/EOG Monitoring DesignThe approach proposed in the previous section optimizes the objective functions simultaneously.The optimization of multiple-criteria requires a trade-off between the objective functions. How-ever, in the case of two objective functions, there is a set of solutions that optimize bothobjective functions simultaneously, which are called non-dominated solutions or Pareto opti-mal solutions [48]. In order to obtain the non-dominated solutions, it is common to use anevolutionary algorithm (e.g., NSGA-II [49], SPEA2 [50]). In the present research, the chosenalgorithm has to handle binary variables and linear constraints. However, in the EEG/EOGdesign, the design space is sufficiently small to go through all the possibilities without a dedi-cated algorithm. Therefore, the present research does not have to deal with local minima. Theresulting Pareto front is shown in Figure 2.3.26Table 2.4: Comparison matrix with given length and fuzzy weightings for electrode con-nection.x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14x1L [cm] 5.9 3 3.8C C C CR R R Rx2L [cm] 5.9 3 3.8C C C CR R R Rx3L [cm] 3 3 5.5 2.3 5.5C C C MC C MCR R R R R Rx4L [cm] 3.8 5.5 5.1 6.1 7 8.6 12.4C C MC MC M MC MU MUR R R R M MR R MRx5L [cm] 2.3 5.1 5.1 8.6 7 8.6C C MC MC MC MU MCR R R R MR R MRx6L [cm] 3.8 5.5 5.1 12.4 8.6 5.1 6.1C C MC MC MU MU MC MR R R R R R MR Mx7L [cm] 6.1 3.2 6.0C M M MUR M M MURx8L [cm] 7.0 8.6 12.4 3.2 5.1 6.3 8.1 12C MC MC MU M M M MU UR MR MR MR M MR M R Mx9L [cm] 8.6 7.0 8.6 5.1 5.1 8.1 6.3 8.1C MU MU MU M M MU M MUR R R R MR MR R MR Rx10L [cm] 12.4 8.6 5.1 5.1 3.2 12 8.1 6.3C MU MC MC M M U MU MR MR MR MR MR M M R Mx11L [cm] 6.1 3.2 6.0C M M MUR M M MURx12L [cm] 6.0 6.3 8.1 12 5.1C MU M MU U UR MUR M R M URx13L [cm] 8.1 6.3 8.1 5.1 5.1C MU M MU U UR R MR R UR URx14L [cm] 12.0 8.1 6.3 6.0 5.1C U MU M MU UR M R M MUR URFinding a suitable number of electrodes and acceptable locations to place the electrodesrequires a trade-off between reliability and wearability. Fewer electrodes lead to improvedwearability, but will degrade the reliability, because additional electrodes are considered asbackup electrodes (parallel connections). However, after finding the non-dominated solutions,the decision space is reduced and it is then easier to pick a suitable solution.270 1 2 3 4 5 6-7-6-5-4-3-2-10(C) Micro Needle(B) Spiky contact(A) CapacitiveFigure 2.3: Pareto front for electrodes with trade-off solutions of non-reliability and non-wearability. The red circle indicates the chosen trade-off solution. Each solutionon the Pareto front corresponds to a particular EEG/EOG electrode arrangementwith reliability and wearability values according to equations (2.9) and (2.10).The Pareto front is divided into three parts as highlighted in Figure 2.3. Each part correspondsto a particular electrode type. Microneedles are known to be the most comfortable electrodes.Hence, solutions with microneedles are in the Pareto front located with low non-wearabilitybut high non-reliability. It is observed that capacitive electrodes are actually dominated bymicroneedle electrodes, because the microneedle is better or same in both objectives, namelycomfort and reliability (see Table 2.3). However, mounting capacitive electrodes at locationswith different wearbility and reliability weightings can make them also non-dominant. This isdue to the nonlinearity of fuzzy relations, which would not be possible to model with conven-tional weight multiplication.Indeed, the Pareto front is a reduced design space, yet a decision is needed to pick asolution out of the Pareto front. Note that Figure 2.3 presents the combinations of electrodelocations that should be used to monitor sleep at the highest level of wearability and reliability.However, a trade-off is required. One way to achieve this is to count how often a combinationof electrode locations is selected for non-dominance. Four combinations of electrode locationsare non-dominant solutions for all three types of electrodes. This means these combinationsare comfortable and reliable locations for all types of electrodes and rather independent on thetype of electrode. In the current implementation it was only possible to select one type forall locations, and mixed types of electrodes for various locations was not feasible (e.g., a mixof type (A) and type (C) electrodes). The next step is to select one solution out of the fourcombinations of electrode locations. Therefore, how often a location itself is part of the non-dominated solutions is counted (Figure 2.4). Locations chosen more often for non-dominanceare both, comfortable and reliable. The electrode locations with most comfortable and reliable28locations from Figure 2.4 are selected as the final solution.x1 x2 x6 x3 x4 x5 x10 x11 x7 x14 x8 x12 x9 x130510x1 x2 x3 x4 x6 x5 x11 x8 x7 x10 x9 x12 x14 x130510x1 x2 x6 x5 x3 x10 x4 x11 x14 x7 x8 x9 x12 x130510x1 x2 x6 x3 x5 x4 x11 x10 x7 x14 x8 x9 x12 x130102030Figure 2.4: The bars in the bar plots indicate number of times a location is part ofindividual non-dominated solutions.Equal importance of wearability and reliability leads to a solution in the middle of the Paretofront and therefore to electrode type (A)-capacitive. The selected solution from the Pareto frontin Figure 2.3 is marked by a red dot. The mounting locations of electrodes in the design ofa wearable and reliable EEG/EOG monitoring system are x1,x2,x3,x4,x5,x6,x7,x10,x11 andx14 (Figure 2.5).After selecting an adequate amount of electrodes and appropriate locations, it is necessaryto find the most suitable way to supply them with power and read the EEG/EOG signals. Theapplied minimum spanning tree algorithm in equation (2.6) provides a spanning tree whosesum of edge weights is as small as possible. However, to strike a good trade-off betweenhaving a common power and signal connection and possibly supply electrodes individuallyresults in the solution of connecting electrodes x1,x2,x3,x4,x5 and x6 and supply them together(implemented using equation (2.8)). Electrodes x10 and x14 are connected and electrode x7 andelectrode x11 are individually supplied (see Figure 2.5). The reason for this is that more supplyconnections make the device more uncomfortable, while they create improved independencebetween electrodes and make the system more reliable. If one electrode goes off and is notconnected with another one, it is more likely that it does not affect the others. This strikes agood trade-off between connecting electrodes to have a common supply connection or supplythem separately. The final EEG/EOG design is presented in Figure 2.5. Comfortable andreliable connections in the front are connected through a cable channel and uncomfortable andparticularly unreliable connections get their own supply connection. Hence, it makes sense forthe two reference electrodes M1 and M2 to get higher independence. In the present work it is29assumed that wearability and reliability have the same level of importance. If one or the otherobjective is more important for the design, a different solution has to be picked from the Paretofront.F4C4O2M1F3 FzM2E1 E2FpzEOGEEGF4C4O2M1F3FzE1 E2FpzEOGEEGsupply connectionsupply connectionconnection to group electrodessupply connectionsupply connectionconnection to group electrodesFigure 2.5: An EEG/EOG design. Electrodes on the forehead are connected in paralleland have a common supply connection.2.8 ConclusionThe approach proposed in this chapter provided a systematic way to design a body sensorsystem that is comfortable and reliable wearable. A fuzzy technique was used to reduce thesubjectivity of the assigned weights. The approach was applied to EEG/EOG-monitoring insleep disorder evaluation, and an optimized result for an EEG/EOG monitoring system waspresented. The methodology provides a tool that will assist a designer in the selection of thetype of devices/sensors and good body locations to attach a device/senor, and in deciding howto connect and supply them.The qualitative objective functions in this work were wearability and reliability. To optimizethese two objective functions, the design variables (number of devices) w re considered as fit-ness functions. Thus design variables with various magnitudes and units (dimensions) need notbe combined into one fitness function. The design space is reduced by keeping a non-dominantsolution, thereby easing the design decisions. In the process, combinations of electrode loca-tions and how often a location was selected for non-dominance were counted. Some aspectsof this study were predefined for simplicity but could theoretically be adapted depending onthe application. It was assumed that the two objective functions had the same level of im-portance. If one or the other is more important in the design, a solution further left or righton the Pareto front would result, thereby changing the final design. For the final design, only30components/electrodes of the same type were feasible solutions. A mix of electrodes was notconsidered. This would increase the design space and it would take a longer time to go throughall possible design solutions on a standard personal computer. Also, memory issues have to beaddressed for memory allocation operations. Therefore, a more sophisticated algorithm, such asan evolutionary algorithm would be suitable for optimization in relatively large design spaces.The algorithm must deal with binary variables and linear and nonlinear constraints. Finally,a sensitivity analysis for the weight assignment and the α-value for the quantification of thefuzzy values could help to select a solution from the Pareto front.The next chapter presents a more sophisticated approach to make a design decision. Themethod proposed here will be compared with other methods in Chapter 6.31Chapter 3Design Optimization Using FuzzySets and Fuzzy MeasuresThis chapter includes the research that was published and presented at the IEMCON confer-ence (L. Falch and, C. W. de Silva, “Fuzzy Techniques to Reduce Subjectivity and CombineQualitative and Quantitative Criteria in a Multi-Objective Design Problem”, IEEE 9th An-nual Information Technology, Electronics and Mobile Communication Conference (IEMCON),Vancouver, BC, Canada, 2018, pp. 42-48. doi:10.1109/IEMCON.2018.8614996)3.1 SummaryThe approach in the last chapter assisted the designer in reducing the design space to select asolution quite easily. However, the final design decision could not deal with different importancevalues of the objectives and was not able to consider interactions. This chapter uses fuzzysets and fuzzy numbers to make a less subjective design decision when multiple objectives andqualitative criteria are involved. Through fuzzy measures and the Choquet integral it is possibleto combine multiple qualitative and quantitative criteria into a single numerical value and makea proper design decision. The fuzzy measures, indicators of the importance of single criteriaare determined using a linear program optimization method. The input for the linear programis only a preference order of some of the alternatives. With the verified fuzzy measures it isthen possible to compute a single numerical value for the remaining alternatives. This resultsin an order of preferred design constructions and a recommendation for an optimized design.The theory is applied to EEG/EOG (electroencephalography/electrooculography) electrodeplacement for sleep monitoring by incorporating the criteria: comfort, reliability and powerconsumption.323.2 IntroductionBy considering multiple design criteria, the decision maker, expert or designer has to strike atrade-off to satisfy multiple objectives. The present chapter seeks to reduce the subjectivityand combine qualitative and quantitative objectives in a design problem by incorporating fuzzysets, fuzzy numbers, fuzzy measures and fuzzy integrals. The theory is applied to design anEEG/EOG sensory device for sleep monitoring. The goal is to design a comfortable and reliableEEG/EOG monitoring system with low power consumption. These three objectives are partlyqualitative and partly quantitative, and also subjective to some degree. It may not be possible tooptimize them concurrently, and an acceptable trade-off for different design criteria is required.Many researchers have sought to optimize or make decisions about a design using qualitativeand quantitative design criteria. In the field of wearable body sensor systems, Anliker et al. [34]attempted a systematic way to choose and attach devices to a human body. Their design criteriaincluded battery life, system functionality and wearability. To quantify these criteria, they usedthe average power consumption for battery life and the execution and communication delaybetween devices for functionality. For wearability they assigned intuitive weights to differentbody locations, which is highly subjective. To solve the design problem, the researchers appliedthe multi-objective evolutionary SPEA2 algorithm, which creates a set of solutions. Choosingthe final design out of the solution set required a trade-off between the objectives battery life,functionality and wearability. The trade-off decision in their paper had no mathematical reasonand was rather intuitive.Also in the field of wearable body sensor systems (e.g., [36], [37]), researchers sought todesign a wearable electrocardiogram (ECG) system with high functionality. One approachwas rather intuitive and the other one was based on multivariate regression with real andcategorical variables. To apply the technique of regression, the researchers made measurementsof volunteers by attaching electrocardiogram electrodes at different body locations, in variousrotation angles of the electrodes and with different pressure levels. In this process, the volunteersprovided information about their comfort level. With the collected data the researchers createda model using a regression method and subsequently optimized the model with a multi-objectiveoptimization algorithm, which was a set of solutions. The trade-off decision between the twoobjectives was executed by the researchers.A standard technique to quantify qualitative design criteria, such as the appearance or thecomfort of a product, in the field of wearable sensor systems, is quantification theory type 1[25]. It makes use of linear regression, and volunteers or experts give weights to categories orcriteria. This technique was for example applied to evaluate the design of a coffee maker, in[31] or to assess the design appearance of a car, in [22].A common technique to compute the importance of qualitative criteria or linguistic variablesis presented in the form of analytic hierarchy process (AHP) [21]. A decision maker or expertjudges the importance of criteria by pairwise comparison of the criterion. The relative scalemeasurement is presented as a matrix and the weights are calculated through the method of33normalization of the geometric mean of rows (e.g., [23]) or eigenvectors (e.g., [22]).Fuzzy logic or fuzzy numbers have been used to reduce subjective evaluation of decisionmakers. Hsiao and Chou [23] for example tried to make a model for human perception inhomepage design. They used triangular fuzzy membership functions with linguistic importancejudgments of qualitative factors. Volunteers evaluated a range of homepages and assignedlinguistic weights addressing given design criteria. To quantify the linguistic importance judg-ments, the authors used α-cuts and the center-of-gravity method. Their approach addressedand weakened the subjectivity of human-based decisions.To reduce subjectivity in AHP, researchers in [22] used the fuzzy analytic hierarchy process(FAHP). They used triangular fuzzy numbers, α-cuts and the lower and upper bounds of theα-cuts to quantify the importance weights determined by AHP. FAHP was then applied tomake a design decision in a multi-objective design problem.Grabisch et al. [27] used a different approach to model and capture subjective and qualitativemeasures. With fuzzy measures and integrals they modeled the discomfort levels of subjectssitting in a car seat for a long period of time. Under various conditions while sitting on differentcar seats, subjects expressed their feelings in a questionnaire and provided an overall comfortvalue. To compute the fuzzy measures for particular criteria, they minimized the squared errorof the overall comfort value.Generally speaking, the overall satisfaction of all given criteria for a particular design ishardly possible. Oftentimes, it requires a questionnaire and/or a prototype to find satisfactionvalues.The present chapter uses fuzzy sets and fuzzy numbers to reduce the subjectivity of qual-itative judgments and fuzzy measures and integrals to make a more objective decision aboutthe importance of multiple design criteria. This does not require questionnaires or prototypesand aims to achieve the most acceptable design solution.3.3 Multi-Criteria Decision Aiding (MCDA)Generally, it is not possible to measure a qualitative variable using a measuring device. Thepresent work uses Multi-Criteria Decision Aiding (MCDA) to combine multiple objectives withqualitative design criteria and determine a ranking of preferred design solutions. Multiplecriteria are represented by N = {1, ...,n} as the set of criteria. Elements of a set of alternativesA = {a, b, c, ...} are associated with a utility xa = (xa1, ...,xan) ∈ Rn, where xai is the numericalvalue of a related to criterion i, with xai ∈ Xi ⊆ R, i = 1, ...,n. Note that all xai use a commonscale (Xi = X ∀i).To rank alternatives, or more specifically make a decision of which qualitative variablesare a better choice than others, single criteria are combined into one numerical value using anaggregation operation, specifically the aggregation function [51]. Arguably the most popularmethod to aggregate criteria is the weighted arithmetic mean (weighted sum). However, manydisadvantages of the weighted sum are known, such as the inability to model dependencies34between criteria or its sensitivity to extreme values [52]. In Multi-Attribute Value Theory(MAVT) [53], alternative a is preferred over alternative b (a b), if their aggregated valuescomputed using the aggregation function F : Xn → R with F (xa) = F (xa1, ...,xan) fulfill:a b⇔ F (xa) > F (xb), ∀a, b ∈ A (3.1)In order to model possible interactions between criteria and overcome the drawbacks ofthe weighted sum, a more generalized aggregation operator is necessary. The introduction ofcapacities by Choquet [54] or a similar concept proposed by Sugeno [55] as “fuzzy measures”or later by Schmeidler [56] as “non-additive measures” help to deal with interactions.3.3.1 Capacities/Fuzzy MeasuresA fuzzy measure [55] on N is a mapping of µ : 2N → [0, 1] with the following conditions:i) µ(∅) = 0, µ(N) = 1 (boundary condition)ii) S ⊆ T ⊆ N implies µ(S) ≤ µ(T ) (monotonicity)A fuzzy measure assigns a weight to each subset of criteria. The mapping µ(S), with S ⊆ Nmay be interpreted as the extensive weightings of criteria. For example, if S = {i, j}, the fuzzymeasures µ({i, j}) would describe the combined weighting of criteria i and j. An aggregationoperator that uses capacities (fuzzy measures) is the Choquet integral [54], which is describednext.3.3.2 Choquet Integral as an Aggregation OperatorIf there are no interactions between criteria, then µ(S ∪ T ) = µ(S) + µ(T ), for any S,T ⊆ Nsuch that S ∩ T = ∅. Then the fuzzy measures are said to be additive and consequently thefuzzy measures coincide with the weights of the weighted sum. However, if the fuzzy measuresare non-additive then the weighted sum can be extended to the Choquet integral, which canevaluate 2N values µ(S), with S ⊆ N .Cµ(a) = ya1µ(N) +n∑i=2(yai − yai−1)µ({i, ...,n}) (3.2)where yai are the rearranged utility values xai of the criteria a, such that ya1 ≤ ... ≤ yan.The complexity of fuzzy measures makes their use challenging, because n criteria require 2ncoefficients in [0, 1] to define the fuzzy measure µ of every subset. Even a fuzzy measurethat considers the combined weighting of three criteria, is already challenging to interpret.Furthermore, if this information needs to be provided by a decision maker or expert, it ishardly possible to address more than two criteria. To reduce the complexity of this power set(2n fuzzy measures), Grabisch [57] introduced k-additive fuzzy measures. In order to explain35the concept of k-additive fuzzy measures, it is useful to introduce the Möbius representation offuzzy measure µ. The Möbius representation is a function m : 2N → R and is defined as:µ(S) =∑T⊆Sm(T ) (3.3)where the Möbius representation m(S) is obtained from µ(S) as follows:m(S) =∑T⊆S(−1)|S|−|T |µ(T ) (3.4)The following equation shows the Choquet integral in terms of the Möbius representation:Cm(a) =∑T⊆Nm(T )mini∈Txai (3.5)A fuzzy measure is k-additive, if for |T | > k,m(T ) = 0, with T ⊆ N . Because of thementioned complexity of 2n fuzzy measures, the present study only considers 2-additive mea-sures, which represents the most common scenario in practical applications. This only requiresn+ (n2) = (n(n+ 1))/2 coefficients. A 2-additive fuzzy measure or capacity µ for a set S ⊆ Nis specified with respect to the Möbius representation as follows:µ(S) =∑i∈Sm({i}) +∑{i,j}⊆Sm({i, j}), ∀S ⊆ N (3.6)For the 2-additive case the Choquet integral expressed in terms of the Möbius representationbecomes [57]Cm(a) =∑i∈Nm({i})xai +∑{i,j}⊆Nm({i, j})min(xai ,xaj ) (3.7)One disadvantage of the Choquet integral is that every criterion has to have the same scale.To resolve this problem the utility values are normalized as follows:xai =xai −min(xi)max(xi)−min(xi) (3.8)The importance of a criterion does not only depend on one single fuzzy measure µ({i}) orm({i}), but also on each contribution of each coalition of criteria. The “importance” indexintroduced in cooperative game theory facilitates the understanding of the meaning of thenumerical value of a fuzzy measure. The importance index, also known as the Shapley index[58] indicates the overall importance of a criterion i ∈ N , not only represented by the fuzzymeasure µ({i}), but also by all µ(S) with i ∈ S. A criterion i is classified as important wheneveri enters a group of criteria T and the difference µ(T ∪ i)− µ(T ) is high. The Shapley indexφSh({i}) is a weighted average of the difference over all possible T ⊆ N \ i. In the 2-additive36case the Shapley index is described asφSh({i}) = m({i}) + 12∑j∈N\{i}m({i, j}) (3.9)To illustrate the degree of interaction of a pair of criteria {i, j} ⊆ N an interaction indexhelps to elucidate the interaction between i and j. In the 2-additive Möbius representation theinteraction I({i, j}) is simply:I({i, j}) = m({i, j}) (3.10)If I({i, j}) is positive then there is a positive interaction or synergy between i and j, whichmeans that the satisfaction of both criteria is more valuable than the satisfaction of themseparately. If it is negative it means that the criteria overlap and the satisfaction of both is notbetter than the satisfaction of one of them. A value of zero means that there is no interactionbetween criteria i and j.To illustrate the concept of the Shapley index consider three workers x1,x2 and x3. Supposethat their fuzzy measures, representing the worker’s productivity, are as follows:• m({x1}) = 0.3, m({x2}) = 0.2, m({x3}) = 0.3• m({x1,x2}) = 0.6, m({x1,x3}) = −0.2, m({x2,x3}) = −0.2By looking at the fuzzy measures of single criterion one can see, that the workers x1 and x3have the same importance for a company when they work alone on a project. However, thecombined fuzzy measure m({x1,x2}) ≥ m({x1}) +m({x2}) indicates that the worker x1 has agreat relationship with the worker x2 and is therefore able to work as a team. The combinedfuzzy measure m({x1,x3}) ≤ m({x1}) +m({x3}), indicates that they have a bad relationshipand the worker x3 is not able to work in a team. Therefore, the worker x1 is more important forthe company, which is represented by the Shapley values (φSh({x1}) = 0.5, φSh({x2}) = 0.4,φSh({x3}) = 0.1).As mentioned before, n+ (n2) parameters are required to compute the Choquet integral ofa 2-additive fuzzy measure. These fuzzy measures have to be determined.3.3.3 Determination of Fuzzy MeasuresA decision maker or expert can decide the importance of a single criterion, but not an exactnumerical value corresponding to it. Grabisch, Kojadinovic and Meyer [59] reviewed usefultechniques to identify fuzzy measures that can achieve this. A commonly used method is basedon the least-square approach. It requires the knowledge of the overall aggregated value ofeach alternative. It can be hard to evaluate this or may be completely unknown. Generally,the overall satisfaction of all given criteria for a particular design is hardly possible. Often,it requires a questionnaire and/or a prototype to obtain the satisfaction values. Therefore,37the least-squares approach is not always acceptable. The approach of Marichal and Roubens[60] based on linear programming is another possible way to determine fuzzy measures. Here,a decision maker or expert provides information on preferences, such as the preferences ofalternatives or criteria. Here, a decision maker or expert ranks solutions (e.g., a preferredoverall design) and also the preference of criteria. The model can be stated as follows:max FMR() = (3.11)subject toCm(a)−Cm(b) > + δ if a A b (3.12)φSh({i})− φSh({j}) > if i N j (3.13)∑i∈Nm({i}) +∑{i,j}⊆NI({i, j}) = 1 (3.14)m({i}) +∑j∈TI({i, j}) > 0, ∀i ∈ N , ∀T ⊆ N \ i (3.15)m({i}) ∈ [0, 1], I({i, j}) ∈ [−1, 1], ∈ [0, 2] (3.16)The principle of this approach is to maximize the minimal difference between the overall ag-gregated alternatives, where the alternatives have been ordered with respect to their preferenceby an expert or a decision maker. Equation (3.12) represents the rankings of the alternatives,which indicates that the aggregated value of alternative a is greater than the aggregated value ofb (Cm(a) > Cm(b)). δ in equation (3.12) guarantees that the difference between two aggregatedvalues is at least δ. A larger δ results in a smaller optimized . Once δ exceeds a threshold valueit can result in no solution at all. It is suggested to compare the solutions for different valuesof δ. Equation (3.13) specifies the preference of criterion i over j and makes criterion i moreimportant than criterion j. Equation (3.15) represents the monotonicity conditions, which are(2n−1 − 1) · n constraints (2n−1, ∀T ⊆ N \ i; −1 for ∅; times n, ∀i ∈ N). Equation (3.16) arethe boundary conditions.In the next sections, the theory of fuzzy measures and integrals is applied to the designoptimization of an EEG/EOG device for sleep monitoring with respect to comfort, reliabilityand power consumption. In order to get the utility values for each electrode location, aspresented previously, the assignment of fuzzy weights is necessary. The relevant fuzzy weightsfor comfort and reliability are listed in Section 2.6, Table 2.2.3.4 Classification of Utility ValuesThere are four possible ways to place electrodes for EEG/EOG monitoring (see Section 2.5).Combinations of these four are possible as well. In order to estimate the overall comfort andreliability of each version, the present work uses fuzzy arithmetic (Section 2.4). The level ofdiscomfort increases when more electrodes are placed on the head. Placing electrodes at loca-tions with high comfort (such as the forehead) minimally impacts the overall discomfort (see38Table 2.1). In order to measure EEG/EOG signals, each electrode is connected with a referenceelectrode (Section 2.5). Therefore, electrodes are connected in parallel; the reliability increaseswhen more electrodes are used because of the increased redundancy. The power consumptionincreases with each additional electrode. Since the electrodes are connected in parallel witha reference electrode, each electrode (except the reference electrode) creates a voltage dropand hence increases the power consumption. Simply, the number of electrodes, excluding thereference electrodes, is proportional to the power consumption. With this information and thetheory of fuzzy arithmetic and defuzzification, utility values for the criteria: comfort, reliabilityand power consumption can be determined for 15 possible electrode placements (Table 3.1). Inorder to compare the three criteria and aggregate them using the Choquet integral, a normal-ization between 0 and 1 is performed (see parentheses in Table 3.1).Table 3.1: Utility values for discomfort, reliability and power consumption. The numbersin brackets are the normalized utility values.Id Version Discomfort Reliability Power consumption(# of electrodes)1 1 2.83 (0.0714) 3.5 (1) 5 (0)2 2 2.83 (0.0714) 3.5 (1) 5 (0)3 3 2.83 (0.0716) 3.83 (0.9189) 5 (0)4 4 2.49 (0) 3.50 (0.9999) 5 (0)5 12 5.33 (0.6071) 5.33 (0.5542) 8 (0.4286)6 13 4.50 (0.4287) 5 (0.6351) 7 (0.2857)7 14 4.99 (0.5357) 5.33 (0.5541) 9 (0.5714)8 23 5.33 (0.6072) 5.66 (0.4728) 9 (0.5714)9 24 3.49 (0.2143) 4.83 (0.6754) 7 (0.2857)10 34 4.50 (0.4287) 5.16 (0.5945) 8 (0.4286)11 123 7.00 (0.9644) 6.83 (0.1893) 11 (0.8571)12 124 5.99 (0.7500) 6.66 (0.2297) 9 (0.5714)13 134 6.16 (0.7858) 6.33 (0.3107) 10 (0.7143)14 234 6.33 (0.8216) 6.66 (0.2297) 9 (0.5714)15 1234 7.16 (1) 7.61 (0) 12 (1)3.5 Identifications of Fuzzy MeasuresTable 3.1 shows that the optimization of the three criteria: comfort, reliability and power con-sumption requires a trade-off. There are 15 possible ways to place the electrodes for EEG/EOGmonitoring. For example, version 14 is the combination of version 1 and 4. Version 4 has thelowest discomfort value and also the lowest power consumption. However, the highest reli-ability is achieved by version 1234. For the described approach to identify fuzzy measures(Section 3.3.3) a preference of some versions over others is needed. A decision maker or expertdecides, for example, that version 1 combined with version 4 (version 14) is preferred over ver-sion 4 and version 4 is preferred over version 3. This can be described as a linear programminginequality constraint, as in equation 3.12:• version 14 version 4 version 3The designer can furthermore decide that comfort and reliability are more important than power39consumption and comfort is more important than reliability. These relations are implementedas inequality constraints as in equation 3.13:• comfort power consumption• reliability power consumption• comfort reliabilityThe MATLAB function linprog determines the fuzzy measures for the preferred alternativesand criteria. Figure 3.1 shows the evolution of the fuzzy measures for comfort, reliability andpower consumption as a function of δ. The δ value changes in a range, and the linear programfinds a solution to maximize . As stated before, the fuzzy measure for comfort appears as themost preferred fuzzy measure µ, followed by reliability and power consumption.0 0.005 0.01 0.015 0.02 0.0250.550.560.570.580.590.60.61{comfort}{reliability}{power-consumption}Figure 3.1: Sensitivity of the δ value. The plot shows the fuzzy measures as a functionof δ. A too high δ value will violate the preference rankings (equation (3.12)).A high δ value makes the linear program infeasible. Therefore, the final solution will bedetermined with a δ value of 0.005, because a smaller δ makes bigger, and the linear programis still feasible. The determined fuzzy measures and Shapley indices are presented in Table 3.2.Table 3.2: Fuzzy measures m and Shapley indices φShComfort Reliability Power consumptionµ({i}) 0.5978 0.5795 0.5612φSh({i}) 0.3172 0.2989 0.7531The order of importance of the fuzzy measures µ coincides with the linear program con-straints. However, the fuzzy measures µ do not necessarily reflect the importance of the criteriaas described earlier. The importance of a single criterion is given by the Shapley index andtherefore power consumption is the most important criterion, followed by comfort and reliabil-ity as the least important ones. The importance values are derived from the preferred orderof alternatives (version 14 version 4 version 3). Table 3.3 presents the interaction indicesbetween the criteria.40Table 3.3: Interaction indices between the three criteria.Comfort Reliability Power consumptionComfort — 0.3839 -0.5612Reliability 0.3839 — -0.5612Power consumption -0.5612 -0.5612 —There is a positive interaction between reliability and comfort. The negative interactionbetween comfort and power consumption indicates that the satisfaction of both criteria is notbetter than satisfying one of them. The negative interaction also means that there is an overlapbetween these two criteria, which is consistent with the results in Table 3.1. The normalizedutility values of discomfort and power consumption tend to increase concurrently. The overlapbetween these two criteria can be explained by the fact that on increasing the number ofelectrodes, the power consumption increases as well as the discomfort. The determined fuzzymeasures are the parameters required to compute the Choquet integral.3.6 Final Design Stage for EEG/EOG Electrode PlacementTable 3.4 presents the sorted Choquet integral values and an order of the preferred versions toattach EEG/EOG electrodes in sleep monitoring. The Choquet integral was computed withthe determined fuzzy measures.Table 3.4: Sorted Choquet integral values and the corresponding electrode placements.The version in column 3 corresponds to the electrode arrangements in Figure 2.1Index Cµ(f ) Version1 0.4815 242 0.5248 343 0.5407 1244 0.5531 235 0.5561 146 0.5794 47 0.5835 2348 0.5947 1349 0.5978 123410 0.6027 311 0.6285 1312 0.6496 113 0.6496 214 0.6526 12315 0.6563 12Version 24 is the most preferred solution, followed by version 34. Note that the solutiondepends on the preference of some versions. However, the advantage of this approach is thatsome experience or limited preferences can help in the determination of the fuzzy measuresand the order or preference of all other unknown options. This leads to less subjective decisionmaking.413.7 ConclusionThe approach presented in this chapter used fuzzy sets and fuzzy numbers to reduce subjectivityof qualitative measures. Fuzzy arithmetic and the center-of-gravity method quantified thequalitative criteria. To combine different criteria with distinct weightings of importance, thepresent work used fuzzy measures and the Choquet integral. Fuzzy measures take into accountthe interaction between criteria and the Choquet integral also considers non-linearities in theaggregation process.The theory was applied to the design of an EEG/EOG device for sleep monitoring. Withthe proposed approach it was possible to combine multiple objectives with quantitative andqualitative criteria and reduce subjectivity in the decision making process to find an appropriatedesign.However, the fuzzy weight assignment for comfort and reliability was still somewhat in-tuitive. The use of fuzzy techniques admittedly reduced subjectivity, but for a more precisesolution the use of a questionnaire would be desirable. The ranking of alternatives over otherswas carried out as an example case. In a real application, an expert would be required to pro-vide the ranking. Furthermore, the design space of 15 alternatives was rather small. A biggerdesign space would require a multi-objective optimization algorithm to determine the Paretooptimal solutions first. The non-dominant solutions could then be considered as a preselection,and further decision making could be handled using the proposed theory. The proposed theoryhowever, will be compared with another decision making method in Chapter 6. The next chap-ter applies the theory of fuzzy measures to determine comfortable locations on the human body.With the help of a questionnaire, the objective comfort used in the present and the previouschapters can be described more meaningfully.42Chapter 4Incorporating Comfort into theDesignThis chapter is based on a paper that has been submitted to an appropriate journal.4.1 SummaryTo demonstrate the approach developed in Chapter 2 and 3, the formulation of qualitativeobjectives was based on rather intuitive aspects. This chapter presents an approach to representa qualitative objective in a systematic and analytic way in the design of a wearable device. Thisis particularly useful when designing a wearable mechatronic device that incorporates sensors,where qualitative design objectives play a significant role in the consumer appeal and success ofthe product. An approach is developed in which the qualitative objective is represented usingmultiple criteria. Those criteria are then combined using fuzzy measures and the Choquetintegral for making design decisions. The particular qualitative variable that is considered inthis chapter is the comfort of a wearable body sensor system. The presented approach evaluatesthe nature and importance of the criteria that describe comfort in a wearable body sensorsystem and determines the most suitable locations where the hardware should be mounted,by taking into consideration those criteria. The fuzzy measures are determined through twodifferent methods. One method uses a least squares algorithm and the other determines fuzzymeasures using a preference ranking of alternatives. Preference rankings are locations, orderedfrom the most comfortable to the least comfortable. This order of locations can be replicatedwith the determined fuzzy measures and Choquet integral, to build a comfort model. An errordescribing the inaccuracy in the order of preferred to non-preferred alternatives is introduced.The comfort model established in this work is validated using a training set and test set. Acomparison between the two methods that determine the fuzzy measures is given.434.2 IntroductionThis chapter addresses the design of a wearable body sensor system. For the design of such asystem one needs to consider qualitative design aspects as well, such as comfort. The optimiza-tion of devices with quantitative and qualitative optimization parameters is a rather complexand challenging process, because qualitative objectives can be highly subjective and difficult todescribe in a mathematical way. An analytical formulation, however, is required in order to in-tegrate qualitative objectives with quantitative objectives. Even for an experienced designer itis difficult to simultaneously include quantitative and qualitative design criteria into the designprocess in a systematic and reliable manner. This chapter presents an analytical approach toincorporate a qualitative design objective into the design process, in a less subjective manner.It shows how to systematically deal with the qualitative objective of comfort. It describes thequalitative design objective using multiple criteria and combines them by using fuzzy measuresand integrals. Two methods to determine the fuzzy measures are developed and compared.The introduction of an error that describes the mismatch of preference rankings of alternativesfacilitates this comparison.In the design of various devices and products it is important to include qualitative designobjectives as well in the design process. Qualitative variables cannot be quantified by abso-lute numerical values and depend on considerations such as intuition, subjectivity, experience,expertise and other “fuzzy” attributes. Incorporation of qualitative variables into the designprocess will require methodologies that are not used in traditional, quantitative design. In par-ticular, qualitative variables may be represented using weights or descriptive terms. A commonapproach that deals with qualitative variables is the analytic hierarchy process (AHP) [21].AHP provides a comprehensive and rational framework for structuring a decision by creatinga comparison matrix where alternatives are compared with respect to some criteria. Deci-sion makers or experts give ratings of importance, and using the principal right eigenvectorof the comparison matrix, utility values for all criteria are determined. For the final decision(|A|+ 1) ·n(n− 1)/2 individual values have to be considered, where n as number of criteria and|A| as the number of alternatives. In the field of product design, Hsiao et al. [31] or Shieh et al.[22] have used AHP to improve the shape and style of a coffee maker and a car, respectively,by evaluating linguistic variables. The linguistic values have been assigned by subjects via aquestionnaire. Azeez et al. [61] applied AHP for selecting a configuration of a transmissionsystem for a winch, and thereby configure the design of a gearbox.In the field of wearable devices Anliker et al. [34] have attempted to systematically chooseand attach devices to desirable locations of the human body. To represent the qualitativeobjective of wearability, they assigned intuitive weighting vectors to different body locations.The weight assignment itself was highly subjective and they have pointed to ergonomic researchand social acceptability considerations for further investigation of wearability.Other work in the field of body sensor systems (e.g., [36], [37]), have attempted to optimizethe design of an electrocardiogram (ECG) with respect to comfort and functionality. Their first44attempt to do so, has been rather intuitive, and a follow up paper used multivariate regressionwith real and categorical variables for this purpose. To apply regression analysis, the researchershave collected measurements by attaching electrocardiogram electrodes to volunteers, and haveused a questionnaire to gain insight into functionality and comfort.Grabisch [27] modeled comfort with fuzzy measures and integrals to represent the discomfortof subjects sitting in a car seat for long periods of time. Subjects expressed their comfort levelunder various conditions by filling out a questionnaire. The fuzzy measures, which describe theimportance and interactions among criteria to some extent, were then identified by minimizingthe squared error of the overall comfort value.A recent paper in the field of product form design also used the technique of fuzzy measuresand integrals [62] to optimize the design of a vase. They used λ-fuzzy measures and determinedthem by assigning numerical values through a decision maker. This of course increased thesubjectivity and lead to a somewhat non-reproducible result.Our previous work [63] used fuzzy weights as qualitative measurements for body worn sen-sors. The method was based on linear programming and considered wearability and reliability.The appropriate hardware locations were then selected based on constraints. That investigationalso provided information on how to attach and wire wearable devices. A case study appliedthe approach to an electroencephalogram (EEG)/electrooculography (EOG) system for sleepmonitoring.Fuzzy measures and integrals have been used in our previous work [64] to make a moresophisticated design decision. The considered objective functions were comfort, reliability andpower consumption. The method was again applied to an EEG/EOG design for sleep moni-toring. The comfort and reliability values were rather intuitively assigned using fuzzy weights,and the power consumption had a proportional relation to the number of attached electrodes.An important qualitative design objective in the field of wearable body sensor systems iscomfort. Kasabach et al. [11] have attempted to design an accurate and comfortable bodysensor system. To determine a good mounting location on the human body, they developedthree prototypes and tested them on subjects to decide on the mounting locations. This isa reasonable approach; however, resources are not always available to build prototypes andconduct experimental studies. Alternatively, a software tool that facilitates optimal designdecisions will save time and money. Furthermore, Kasabach et al. [11], made their designdecision for the device location based on human reasoning. This results in a subjective decision,does not consider relative importance of the arguments, and it is difficult to validate a particulardecision. The existing wearable body sensor systems have not included comfort as an objectivein a mathematical or analytical way into the design process. Past research has only evaluatedcomfort through questionnaires, using an experimental prototype or an already manufactureddevice [29], [30].The present chapter revisits the qualitative criterion comfort, which is highly subjectiveand depends on many factors. In fact, Knight et al. [29] identified 92 comfort terms to45describe a wearable body sensor system and they reduced them into 6 main groups (emotions,attachment, harm, perceived change, movement, and anxiety). Many design variables such asattachment methods, materials, and so on, are challenging to incorporate into a comfort model.Therefore, the present study does not seek to determine the most comfortable setup for thesensors themselves, but rather find a location at which the device can be most comfortablyattached. In order to do that, this research study describes comfort using multiple criteria suchas pressure pain threshold, motion impedance, social acceptability, touch sensitivity, and painsensitivity. Data sets and utility values are available to describe these criteria. Specifically,the paper by Zeagler [65] summarizes the literature over the past 20 years that considers thesecriteria. However, up to this point it is unclear how important these criteria are, how theyinteract with each other, and how they can describe comfort for a wearable body sensor systemin an analytical way. The present chapter considers these aspects of designing a wearable device.4.3 Comfort as a Design ObjectiveProducing a successful product that achieves wide acceptance from the consumer requires theconsideration of the locations where various hardware components are placed. Here, comfortis described using multiple criteria. Comfort is a very broad term, and depending on theapplication different criteria may be considered. In order to compare the comfort of devicelocations, various aspects such as the type of attachment, the material used to attach hardwareand the attachment force have to be considered. The considered attachment for the comfortmodel that is used here is a belt wrapped around a specific body location. The criteria andthe corresponding data that describe comfort at various body locations have been summarizedby Zeagler [65], on considering functional, technical and social aspects of body locations forwearable technology in the past 20 years. The present paper uses criteria and definitions givenby Zeagler [65]. Some pertinent terminology is given now.• Proxemics (Prox) is the perception of the self-size of a human. The self-size is themaximum distance a device can extend from the body while it is still naturally consideredas part of the human body, through self-size cognition [66].• Pressure Pain Threshold (PPT) is the amount of weight or pressure that can beapplied before it is perceived as discomfort. It is defined by Weber-Fechner’s law [67],which states that a sensation is proportional to the logarithm of the stimulus.• Motion Impedance (MI) describes the opposite of the ability to move freely [65].Regions that are not restricted by a mounted device provide the least level of body motionimpedance.• Social Acceptability (SA) areas on the body are associated with sexual sensation orexcretion of body waste [65].• Touch Sensitivity is perceived through mechanoreceptors, which are sensors in the skinthat respond to mechanical pressure or distortion [68].46• Pain Sensitivity Webster’s on-line dictionary [69] defines comfort as a “state of beingrelaxed and feeling no pain.” Several studies address pain and touch sensations (e.g., [70],[71]) and give information about the body locations that are sensitive to varying degree.• Tissue Volume Amount of tissue and/or muscles at a particular body location. Onengaging the tissue, such as a muscle or the lungs, the volume increases and therefore theattachment would feel tighter. For the present study, the muscle volume was collectedfrom the past work [72], [73], [74] and [75]. The following are the tissues/muscles used forthis criterion.– Forearm: brachioradialis, pronator teres, flexor carpi radialis, flexor carpi ulnaris,palmaris longus, flexor digitorum superficcialis, extensor carpi radialis brevis, exten-sor carpi radialis longus, extensor digitorum communis, extensor carpi ulnaris– Upper Arm: biceps femoris long head, semimembranosus, brachialis, biceps brachii,triceps brachii long head, triceps brachii– Shoulder: deltoid, subscapularis– Chest: pectoralis major sternocostal, pectoralis major, lung, heart, rhomboid major,trapezius, infraspinaturs, subscapularis, supraspinatus, rhomboid minor– Abdomen: external obliques, rectus abdominus, internal obliques, jejunum, colon,latissimus dorsi– Hip: gluteus maximus, gluteus medius, gluteus minimus, illiopsoas– Thigh: vastus intermedius, adductor longus, satorius, adductor magnus, quadricepsfemoris, biceps femoris, vastus lateralis, vastus medialis, rectus femoris, sartorius,semitendinosus, semimembranosus– Calf: soleus, medial gastrocnemius, lateral gastrocnemius, tibialis anterior– Locations such as the wrist or the ankle are assumed to have no tissue volume.The data used in this research are presented in Table 4.1. The values are normalized between0 and 1. The reason to do so is because of the Choquet integral and is explained in Section 3.3.2and the corresponding operation is given by equation (3.8). A value of 0 means it is the worstlocation to attach hardware in terms of the specific criterion. A value of 1 for tissue volumemeans there is no tissue at all and it is therefore ranked highest in terms of the tissue volume.The degree of comfort does not necessarily increase additively between two criteria. There-fore, interactions are considered using the theory of fuzzy measures and integrals to developa model for the qualitative objective comfort. It is then possible to decide on the most com-fortable location and get a better understanding of the criteria that play a role in designing acomfortable wearable body sensor system.47Table 4.1: Normalized utility valuesLocation Prox PPT MI SA Touch Pain Tissue1 Wrist 0.000 0.013 0.361 1.000 0.391 0.409 1.0002 Forearm 0.045 0.013 1.000 1.000 0.435 0.455 0.9603 Elbow 0.636 0.000 0.023 1.000 0.609 0.682 1.0004 Upper Arm 0.455 0.093 0.776 1.000 0.696 0.773 0.8595 Shoulder 0.636 0.360 0.361 1.000 0.696 0.091 0.9806 Forehead 0.045 0.000 0.877 1.000 0.000 0.000 1.0007 Chest 0.455 0.360 0.530 1.000 0.739 0.818 0.2498 Abdomen 0.455 0.573 0.639 0.500 0.913 1.000 0.0009 Hip 1.000 1.000 0.598 0.000 0.478 0.636 0.96210 Upper Thigh 0.455 0.360 0.868 0.500 0.565 0.818 0.67711 Lower Thigh 0.455 0.053 0.708 1.000 0.565 0.818 0.70712 Knee 0.455 0.573 0.000 1.000 0.522 0.682 1.00013 Calf 0.182 0.053 0.986 1.000 1.000 1.000 0.87814 Ankle 0.182 0.173 0.562 1.000 0.870 0.955 1.000One reason that the technique of fuzzy measures is suitable in the present methodology isthe monotonicity condition. Through monotonicity it is guaranteed that if an alternative, inthis case a location, is the best in each criterion, (e.g., lowest motion impedance, lowest touch,pain sensitivity), another alternative cannot be preferred. Hence, it is ensured that the usedcriteria describe the objective. The theory of fuzzy measures and the Choquet integral wasdescribed in the previous chapter in Sections 3.3.1 and 3.3.2. However, the determination offuzzy measures is extended here and it is compared with a least squares approach.4.4 Determination of Fuzzy MeasuresAs mentioned in the previous chapter, a commonly used method is based on the least-squareapproach. It requires the knowledge of the overall aggregated value da of each alternative.In this chapter, the comfort value for each location is used for this purpose. The data froma survey questionnaire are used to compute this value. The least squares approach may beformulated as follows:minm12∑A||Cm(a)− da||22 (4.1)subject toBoundMonCond.BoundMonCond. are the same boundary and monotonicity conditions as in Section 3.3.3:∑i∈Nm({i}) +∑{i,j}⊆NI({i, j}) = 1 (4.2)m({i}) +∑j∈TI({i, j}) > 0, ∀i ∈ N , ∀T ⊆ N \ i (4.3)m({i}) ∈ [0, 1], I({i, j}) ∈ [−1, 1] (4.4)The explanation of the constraints is provided in Section 3.3.3.The approach of Marichal and Roubens [60] based on linear programming, which is also used48in the previous chapter, is improved here. A decision maker or expert provides information onpreferences, such as the preferences of alternatives or criteria. As before, the necessary datafor the computation of the preferences are again provided through a survey questionnaire. Thetwo approaches of determining the fuzzy measures differ as follows: The least square approachseeks to minimize the sum of errors between Cm(a) and da, whereas Marichal and Roubensapproach tries to accomplish the same preference ranking as from the questionnaire (orderingof locations from the most comfortable to the least comfortable). The linear programmingproblem is extended to a mixed integer linear program:max FMR() = +p∑k=1wk · yk (4.5)subject toCm(a)−Cm(b) > −M(1− yk) + δ if a A b (4.6)φSh({i})− φSh({j}) > if i N j (4.7)BoundMonCond.p number of rankings,M is positive large numberyk ∈ {0, 1}, ∈ [0, 2] (4.8)Equation (4.6) represents the rankings of the alternatives, which indicates that the ag-gregated value of alternative a is greater than the aggregated value of b (Cm(a) > Cm(b)).Sometimes it is not possible to fulfill all rankings of alternatives with the given data, and thenthe linear program would not be able to find a solution with the given constraints. Therefore,the binary values yk are introduced to achieve as many rankings as possible. Similar overallcomfort values for locations, get a low ranking wk because this ranking does not necessarilyhas to be accepted, and the ranking can be switched. δ in equation (4.6) guarantees that thedifference between two aggregated comfort values is at least δ. The linear program maximizesthe difference () between the two aggregated values. This will make sure that there is cleardistinction between the two alternatives. Equation (4.7) specifies the preference of criterion iover j and makes criterion i more important than criterion j.4.5 Modeling ErrorIn the least squares parameter estimation, the residual is used to describe the difference betweenthe overall determined model value and the actual data value. However, when a questionnaireis used to collect data, the actual overall data value might not be precise. Also, in makinga decision on the most comfortable location, the ranking is more important than the overallnumerical comfort value. To accomplish this, this study introduces a ranking error. Throughthe questionnaire data, a ranking of locations from the most comfortable to the least comfortableis established. By determining the fuzzy measures, the Choquet integral can be computed. The49ranking error describes how far an alternative (in this case a location) moved from its originalranked position. The root mean square ranking deviation is defined as,RMSDrank =√√√√√∑A (iˆ− i)2|A| (4.9)where, iˆ is the index of the ranked alternative established through fuzzy measures, i is theindex of an alternative determined through the questionnaire data and |A| is the cardinalityof the set of alternatives A. For a fair comparison the RMSD is normalized, by dividingthe maximum possible index an alternative can move from one position to another minus theminimum position an alternative can move. Here, the maximum position is |A| − 1 and theminimum possible is 0. Therefore,NRMSDrank =RMSDrank|A| − 1 (4.10)Additionally, the study uses the standard root mean square deviation RMSD of the resid-uals.4.6 Comfort Model for a Wearable Body Sensor SystemTo determine a comfort model with low subjectivity, the present work first conducts a survey(using a questionnaire) and then determines the fuzzy measures.4.6.1 Comfort QuestionnaireThe data for the overall comfort value has been determined through a questionnaire. To comparethe individual locations with each other in a fair manner, the type of attachment and theattachment force must be the same. A belt, more specifically a blood pressure cuff, has beenused for the experiment. The blood pressure cuff is a belt that can be inflated with air.The belt is attached to the 14 body locations listed in Table 4.1 and then inflated to equalpressure (20 mmHg). For wider body locations such as the chest, the blood pressure belt wasextended as appropriate. 20 males participated in the experiment and gave a comfort ratingfrom 1 corresponding to very comfortable to 5, which corresponds to not comfortable, foreach body location. The outcome was normalized between 0 and 1. The results are shownin Figure 4.1. The blue boxes in the plot describe the middle 50% of all the values for thatlocation. The red horizontal line represents the median and the red plus signs show the outliers.The lines extending above and below each box are the whiskers (see box-and-whisker plot formore details).501 2 3 4 5 6 7 8 9 10 11 12 13 1400.20.40.60.81MeanFigure 4.1: Box plot of comfort questionnaire data. The red horizontal line representsthe median and the red plus signs show the outliers. The lines extending aboveand below each box are the whiskers (see box-and-whisker plot for more detail).4.6.2 Determination of Comfort ModelTo obtain the comfort model, the fuzzy measures are determined via the least squares (LS)method and the Marichal and Roubens [60] (MR) method. All seven criteria are used. Tocheck if the criteria can generally model comfort, we check the following condition:a b→ ∃i ∈ N : xai > xbi (4.11)This means, if an alternative a (location) ranked better (more comfortable) than an alter-native b, then there has to be at least one utility value xai bigger than the utility value of thesame criterion of alternative b. If this is not the case the monotonicity condition describedin Section 3.3.1 is violated and the given criteria do not describe comfort. Potentially, morecriteria are necessary to describe comfort.By optimizing the objective FMR() of MR method two preference rankings cannot befulfilled, which can be seen from the binary variable yk. The violated preference rankings are,location 2 more comfortable than location 13, and location 11 more comfortable than location4. However, Figure 4.1 shows that the mean of the location 2 and 13, and locations 4 and 11are similar (within 8% and 1%, respectively).Table 4.2 provides the importance values φSh({i}) for each criterion. The importance ofTouch sensitivity is 0, and therefore does not contribute to describing comfort when attaching51a belt to a body. As usual, the fuzzy measures are determined by leaving out touch sensitivity.Also, proximics has 0 importance for the LS approach and a really small level of importancewith theMR method. The criteria for the model are reduced and the corresponding normalizedroot mean square deviations (NRMSD) are represented in Figure 4.2.Table 4.2: Shapley index of MR method and LS method.Prox PPT MI SA Touch Pain TissueφSh({i})MR 0.023 0.013 0.596 0.142 0.000 0.095 0.130φSh({i})LS 0.000 0.041 0.612 0.047 0.000 0.136 0.164Prox,PPT,MI,SA,T,P,TissProx,PPT,MI,SA,P,TissProx,MI,SA,P,TissMI,SA,P,TissMI,P,Tiss00.10.2Prox,PPT,MI,SA,T,P,TissProx,PPT,MI,SA,P,TissProx,MI,SA,P,TissMI,SA,P,TissMI,P,Tiss00.050.1Prox,PPT,MI,SA,T,P,TissProx,PPT,MI,SA,P,TissProx,MI,SA,P,TissMI,SA,P,TissMI,P,Tiss00.020.040.06Prox,PPT,MI,SA,T,P,TissProx,PPT,MI,SA,P,TissProx,MI,SA,P,TissMI,SA,P,TissMI,P,Tiss00.050.1Figure 4.2: Normalized root mean square deviation (NRMSD) for various criteria.The NRMSD of the MR method is bigger than that of the LS method. However, theNRMSDrank is smaller for the MR method. This is because the MR method attemptsto keep the order of the alternatives, in this case the order of most comfortable location tothe least comfortable location. By reducing the number of unimportant criteria, determinedthrough the Shapley index, the NRMSD does not become too large until only 3 criteria areleft. By examining the NRMSD, it is seen that the criteria Motion Impedance (MI), SocialAcceptability (SA), Pain Sensitivity (P) and Tissue Volume (Tiss) are the determined criteriathat describe comfort most accurately. Table 4.3 and Table 4.4 list the fuzzy measures andinteraction indices, respectively. Generally, there is low interaction between the criteria.52With the fuzzy measures and the Choquet integral it is now possible to compute the comfortvalues for a wearable body sensor system that attaches a device using a belt. The Shapleyvalue shows that motion impedance (MI) is the most important criterion when designing acomfortable wearble body sensor system. Also, the high correlation between MI and the overallcomfort value of the questionnaire demonstrates the importance of this criterion. Unimportanceof proxemics also makes sense, because the blood pressure cuff used in the survey using thequestionnaire was still part of the perceived human self-size (see Section 4.3).Table 4.3: Shapley indices of MR and LS methods.MI SA Pain Tissuem({i})MR 0.7694 0.1999 0.0704 0.1669φSh({i})MR 0.6399 0.1262 0.1243 0.1096m({i})LS 0.4599 0.0000 0.0000 0.0536φSh({i})LS 0.6448 0.0583 0.1366 0.1603Table 4.4: Interaction indices between criteria for MR method and LS method.I({i, j}) MI SA Pain TissueMI MR — -0.199 0.108 -0.167LS — 0.000 0.273 0.097SA MR -0.199 — 0.000 0.052LS 0.0000 — 0.000 0.117Pain MR 0.108 0.000 — 0.000LS 0.273 0.000 — 0.000Tissue MR -0.167 0.052 0.000 —LS 0.097 0.117 0.000 —4.6.3 Validation of the Comfort ModelFor validating the fuzzy measures and the model, only 10 locations are used to determine thefuzzy measures and compute the overall comfort value of the rest of the locations through thefuzzy measures and the Choquet integral. Table 4.5 presents the Shapley indices computedover the 10 locations. It is seen that the Shapley index of the LS approach hardly changes, andthe change in the MR approach is slightly larger.Table 4.5: Shapley indices of the MR method and LS method.MI SA Pain TissueφSh({i})MR 0.5627 0.0885 0.1663 0.1825φSh({i})LS 0.6399 0.0637 0.1400 0.1564Table 4.6 lists the normalized root mean square deviation (NRMSD). The column “Prev” isthe error previously computed (Figure 4.2 third bar: MI, SA, P, Tiss). Column “Test” describesthe NRMSD only computed with the locations not used to compute the fuzzy measures. The“Total” column lists the NRMSD computed with all 14 locations. Compared to the previouserror (“Prev” column), the NRMSD hardly changes. This confirms a valid description of thequalitative objective comfort via the computed fuzzy measures and therefore the model.53Table 4.6: Normalized root mean square deviation (NRMSD).Prev Test Total Prev Test TotalNRMSD−MR 0.187 0.270 0.229 NRMSDrank −MR 0.050 0.168 0.096NRMSD−LS 0.087 0.075 0.088 NRMSDrank −LS 0.087 0.067 0.087Table 4.7 lists the locations sorted from the most comfortable to the least comfortable. Theoutcome of the questionnaire would suggest forearm as the most comfortable location. However,through the criteria describing comfort and the determined fuzzy measures the calf would bethe most comfortable location to mount hardware using a belt. This is absolutely possible,since the outcome of the survey questionnaire (Figure 4.1) shows a similar mean for forearm(location #2) and calf (location #13). Similarly, this is true for other locations that do notcorrespond to the questionnaire data. Therefore, backing up the data through a questionnairewith a model makes it less subjective, and reduces uncertainties in the questionnaire study.Furthermore, the model will help in the design process, because it gives a deeper understandingas to which criteria are more important than others and where improvements can be made.Table 4.7: Locations sorted from the most comfortable to the least comfortable.Questionnaire MR LSForearm Calf CalfCalf Forearm ForearmUpper Thigh Upper Thigh Upper ArmLower Thigh Upper Arm Upper ThighUpper Arm Lower Thigh Lower ThighAnkle Ankle ForeheadForehead Forehead AnkleWrist Wrist HipAbdomen Abdomen WristHip Hip AbdomenShoulder Chest ChestChest Shoulder ShoulderElbow Elbow ElbowKnee Knee KneeFinally, this paragraph compares the two methods for determining the fuzzy measures. Themethod of Marichal and Roubens requires only the ranking of alternatives (locations). It mightbe the case that no solution for the given alternative ranking could be found through the linearprogram. However, a solution that describes the ranking as accurately as possible can be foundwith the introduced binary variable (see Section 4.4). This converts the linear program into amixed integer program. If it is not possible to find a solution for the provided ranking, thensome preferences would be violated and the binary variable would become 0 in the mixed integerprogram. For example, if one preference ranking at the end (e.g., least comfortable) is violatedit can happen that it moves all the way to the front (most comfortable). In order to preventthis, it must be specified that, for example, an alternative in the front is preferred over everysingle alternative that comes after. For example, c a b, automatically specifies that c b.However, if in the algorithm c a cannot be fulfilled, the constraint c b also does not holdand b can be preferred over c, even though it would be possible to keep the order of c b.54Consequently, instead of (n− 1) preference rankings, n · (n− 1)/2 preference rankings have tobe fed into the algorithm. This vastly increases the number of constraints and the algorithmwill become slow if it has to deal with a high number of alternatives. However, if the overallvalue is not known, from the ranking of the alternatives it is possible to still determine thefuzzy measures. The least squares approach can definitively handle more alternatives with amuch shorter computing time and is also easier to implement. However, the approach needs anoverall numerical value, and simple ranking is not sufficient.4.7 Discussion and ConclusionThis chapter presented a systematic approach on how to analytically and mathematically handlea qualitative design objective. Specifically, it used fuzzy measures and the Choquet integralto describe comfort. The determined fuzzy measures were evaluated through training dataand test data. A modeling error was introduced that described the error of the preferenceorder of alternatives. Uncertainties in the outcome of a survey using a questionnaire couldbe reduced using the presented method, because the objective was described through multiplecriteria based on data sets. The reduction of uncertainties also reduced the subjectivity thatcame with qualitative variables. For the design of a product it is beneficial to have a betterunderstanding of a qualitative objective and which criteria really matter to make the necessarychanges to the design. In contrast to a machine learning approach, this method does not need ahuge amount of data, and through an importance index (Shapley index), it is easy to interpretthe relevance of variable criteria. The present chapter provided much insight into comfort,specifically addressing wearable body sensor systems and attaching hardware through a belt.The developed method did not consider uncertainties in the utility values themselves. Forexample, the utility value for the criteria tissue volume was created through the muscle andthe tissue volume of a human body. Future work is planning to handle these uncertainties byusing fuzzy sets and fuzzy numbers for the utility values themselves. In order to do so, theChoquet integral must be fuzzyfied in order to operate with fuzzy sets and fuzzy numbers. Fordoing so, the fuzzy measure determination methods (Least Square and Marichal and Roubens)have to be able to handle fuzzy sets and fuzzy numbers as well. The method should then beapplied to another qualitative design objective to increase its validity. The objective comfort, asconsidered in the present chapter, will be included in a multi-objective design decision problemin the next chapter.55Chapter 5Decision Making in Multi-objectiveDesignThis chapter is based on a paper that has been submitted to an appropriate journal.5.1 SummaryThe objective function comfort determined in Chapter 4 is used as one of the objectives inthe design problem of the present chapter. Chapter 3 introduced fuzzy measures and theChoquet integral as decision making method for situations with multiple design objectives. Forcomparison, the present chapter introduces another decision making method .For the design process of mechatronic devices, which typically incorporate mechanical andelectrical domains, it is often necessary to consider multiple objectives/criteria. The designproblem can then be formulated as a multi-objective optimization problem. Multiple objectivescan be conflicting and to pick a design solution a trade-off between those is required. A goodtrade-off is important for a successful product. Different decision making methods are availableaiming towards a successful design trade-off; a commonly used way is the VIKOR method (fromSerbian: VIseKriterijumska Optimizacija I Kompromisno Resenje, meaning: Multi-criteria Op-timization and Compromise Solution). This chapter focuses on the aspects of this method andreveals some weaknesses. Then, a different normalization method is introduced that overcomesthese weaknesses. Next, a minimum weight margin is established that gives information aboutthe stability of a design solution that is generated by the VIKOR method. The weight marginis helpful for elucidating the decision maker’s uncertainty in the original weight assignment.The modified VIKOR method is then applied to the design of a wearable body sensor networkand the design of an EEG electrode. The two design examples show the strength of the newmodified VIKOR method of the present chapter, which resolves the shortcomings of the originalVIKOR method.565.2 IntroductionOne challenging and subjective task in a multi-objective design problem is the final designdecision. Most multi-objective optimization problems do not have a single solution, becausethe objectives can be conflicting. Hence, a trade-off between objectives is unavoidable in theselection of the final design. Multi-objective optimization identifies non-dominated solutions.A solution is called non-dominated or Pareto optimal if none of the objective functions canbe improved in value without degrading some of the other objective values [12]. The trade-offbetween objectives should be a good compromise and should follow a clear strategy. There arenumerous methods to select a final solution out of the non-dominated solutions. The Techniquefor Order of Preference by Similarity to Ideal Solution (TOPSIS) originally developed by Hwanget al. [76] is based on the concept that the compromise solution should have the shortestdistance from the ideal solution. Other common decision making methods are ELECTRE [77],an outranking method which depends on comparison of pairs of alternatives; PROMETHEE[78] that helps decision makers to find the alternative that best suits their goal and the VIKOR[79] method. Opricovic developed the basic idea of the VIKOR method in his PhD dissertationand a first application was published one year later in 1980 [80]. The VIKOR method combinesthe maximum “group utility” and a minimum individual regret of criteria. Opricovic’s paperin 2004 [79] contributed to the recognition of the importance of the VIKOR method. Sincethen the VIKOR method has been used in numerous decision making applications across arange of fields. For example, Jahan et al. [81] used the VIKOR method for selecting materialswith different properties in biomedical implants, where implant materials should have similarcharacteristics to the human tissues. Kiani et al. [82] applied the VIKOR method in thefield of civil engineering to select the best repair material for concrete structures. They usedthree different methods to assign the importance weights to the individual criteria within theVIKOR method and performed a sensitivity analysis for the weight assignment. Garcia-Seguraet al. [83] used analytic hierarchy process (AHP) for the weight determination of individualcriteria within the VIKOR method. Ren et al. [84] suggested a group decision making methodto determine the weights in the VIKOR method. Fei et al. [85] used the VIKOR method forsupplier selection and introduced Dempster-Shafer evidence theory for handling the uncertainweight assignment by the decision maker.This chapter first demonstrates some shortcomings of the VIKOR method and resolvesthem by introducing a modified version of the VIKOR method. The modified version providesa weight margin, which informs the decision maker how sensitive the provided weights areto the determined compromise solution. The modified VIKOR method is then applied to twodesign examples. The examples demonstrate the advantage of the new method over the originalVIKOR method. The procedure of the original VIKOR method is presented in the next section.575.3 VIKOR Method5.3.1 VIKOR ProcedureThe VIKOR method is a multi-criteria decision making method, which has been developed formulti-criteria/objective optimization [79]. The criteria or objectives in an optimization problemusually conflict with each other. Alternatives that are not dominated by other alternatives arethe non-dominated solutions or Pareto optimal solutions [86]. The VIKOR method enablesranking of these conflicting alternatives and selecting a good (compromise) alternative out ofthe Pareto optimal solutions. The Lp-metric is used as an aggregating function and elementai is part of a set of alternatives A = {a1, a2, ..., am}. It is assigned with a utility valuexi = (xi1, ...,xin) ∈ Rn, where n is the number of criteria which are represented by the setN = {1, ...,n}.The steps of the traditional VIKOR method are as follows [79, 87]:i) Determine the best x∗j and the worst x−j values of all criteria j ∈ Nx∗j = maxixij , x−j = mini xij ,if the j-th objective represents a benefit;x∗j = minixij , x−j = maxi xij ,if the j-th function represents a cost.ii) Compute the values Si and Ri, i = 1, ...,m, by relationsSi =n∑j=1wj(x∗j − xij)/(x∗j − x−j )Ri = maxj{wj(x∗j − xij)/(x∗j − x−j )},where wj are the weights of criteria/objectives, expressing the decision maker’s preference.The solution obtained by Si is the maximum group utility and the solution obtained byRi is the minimum individual regret of the “opponent”.iii) Compute the values Qi, i = 1, ...,m using the relationQi = ν(Si − S∗)/(S− − S∗) + (1− ν)(Ri −R∗)/(R− −R∗),where S∗ = miniSi, S− = maxiSi, R∗ = miniRi, R− = maxiRi; ν is the weight for thestrategy of maximum group utility, and (1− ν) is the weight of the individual regret.iv) Rank the alternatives by sorting the values of S,R and Q. The results provide threeranking lists.v) The minimum value of the sorted Q is the proposed compromise solution of alternativea∗ = a(1) if the following conditions (C1 and C2) are satisfied:C1 Acceptable advantage:Q(a(2))−Q(a(1)) > DQ, where a(2) is the alternative ranked on second position inthe ranking list Q and DQ = 1/(m− 1)58C2 Acceptable stability in decision making: Alternative a(1) also has to be best rankedby S or/and R.If one of the conditions is not satisfied, then a set of compromise solution is proposed:• Alternatives a(1) and a(2) if only condition C2 is not satisfied or• Alternatives a(1), a(2), ..., a(M) if condition C1 is not satisfied; a(M) is determined bythe relation Q(a(M))−Q(a(1)) < DQ for maximum M (the positions of alternativesare “in closeness”)vi) Determine a weight stability interval [wLj ,wUj ] for each j-th criterion/objective, separately,with the initial given weights from the decision maker. The weight of each criterion isincreased or decreased from the initial value wj by λ (w′j = λ · wj). The weights arenormalized so that ∑nj=1wj = 1. The other weights keep their initial ratios: w′k = ϕwk,k 6= j, k = 1, ...,n. ϕ(λ) is obtained by the equation λwj + ϕ∑k 6=j wk = 1 and cantherefore be transformed into: ϕ = (1−λwj)/(1−wj). The parameter λ can vary between0 6 λ 6 1/wj . The VIKOR method is applied with different values of parameter λ(searching) to find the interval λ1 6 λ 6 λ2, where the same compromise solution isobtained. The weight stability interval for the j-th criterion is: wLj 6 w′j 6 wUj , wherewLj = λ1wj and wUj = λ2wjThe weight stability intervals are determined for each criterion j = 1, ...,n, with the giveninitial values of weights.5.3.2 ShortcomingsVIKOR is a helpful decision making tool, given a problem with conflicting alternatives and non-commensurable (having different units or non-comparable magnitudes) criteria. The methodaims to select a solution that is the closest to the ideal one. The next few examples demonstratesome shortcomings of the VIKOR method. As Example 1 (Table 5.1 from Huang et al. [88]),consider two criteria and three alternatives:Table 5.1: Example 1, where ai are design alternatives, xi are the objective functions,WS is the weighted sum, S is the maximum group utility in the VIKOR method, Ris the minimum individual regret in the VIKOR method, and Q is the aggregatedvalue of S and R in the VIKOR method.A x1 x2 WS S R Qa1 0.8 0.5 0.65 0.375 0.375 0.000a2 0.6 0.8 0.70 0.500 0.500 0.667a3 0.7 0.4 0.55 0.750 0.500 1.000Weight 0.5 0.5The preference ranking based on the Q-value is a1 a2 a3. S is computed using aweighted sum, where the utility values are normalized between 0 and 1. The highest valuecorresponds to 0 and the lowest to 1. Normalization is required so that non-commensurable59(different units and non-comparable magnitudes) criteria can be aggregated together. However,in this example, the criteria are already on a common scale, and computing the weighted sumresults in a preference ranking of a2 a1 a3. This is not consistent with the ranking of S,which is the same as the ranking of Q. As second example consider (Table 5.2):Table 5.2: Example 2, where ai are design alternatives, xi are the objective functions, Sis the maximum group utility in the VIKOR method, R is the minimum individualregret in the VIKOR method, and Q is the aggregated value of S and R in theVIKOR method.A x1 x2 S R Qa1 90 10 0.50 0.50 0.5a2 85 15 0.72 0.47 0.5a3 80 90 0.50 0.50 0.5Weight 0.5 0.5In this example the VIKOR method does not deliver a solution at all, because all Q valuesare the same. However, one can see that alternative a3 has a high value in both criteria x31and x32 and should be preferred over the alternatives a1 and a2. The problem lies again innormalizing the maximum value to 0 and the minimum value to 1. As third example, considerthe case where, there is a 4-th alternative a4 with x41 = 10 and x42 = 95. Then the alternativea3 with the lowest Q value, would be the clear favorite with Q(a1) = 0.99, Q(a2) = 0.97,Q(a3) = 0.00 and Q(a4) = 0.99. One problem in the normalization method when optimizing abenefit, is that a minimum value is not always available, as in Example 2.Applying the VIKOR method to either the entire set of alternatives or only the non-dominated alternatives should not change the outcome of the decision. However, with thecurrent normalization, this is not necessarily the case (see Section 5.5.1, Figure 5.3). Thisis possible because the minimum value, if the objective is a benefit, or the maximum value,if the objective is a cost, in the normalization is different when using all alternatives or thenon-dominated set.Also, in a multi-objective design problem it might happen that a constraint is included (seeSection 5.5.2, Figure 5.5). One of the multiple objectives is maximized and has to be biggerthan a specific value in order to realize an acceptable design. The solution determined throughthe VIKOR method might change, depending on the inclusion of the constraint into the multi-objective optimization algorithm prior to the decision making or later to the Pareto optimalsolutions. This is because when maximizing, the minimum that is used for the normalizationprocedure changes. Hence, the method can only be applied to selected cases.The conditions for an acceptable advantage in the original VIKOR method are not es-tablished on a mathematical basis but are rather intuitive (see Section 5.3.1 point v). In amulti-objective optimization algorithm it is possible to specify the number of solutions on thePareto front. This is necessary if the objectives are continuous functions, because then thereare theoretically infinite Pareto solutions. The normalization will fit more alternatives between0 and 1 and the distances between the Qi values get smaller as well as the DQ value. However,60a multi-objective optimization algorithm might not spread the solutions evenly on the Paretofront. Also, if there is a discontinued Pareto front and one part has only a few alternatives andthe other part has much more, then using the number of alternatives to judge an acceptableadvantage might not make sense.The determination of the weight stability margin in Section 5.3.1 point vi, will follow anincrease/decrease of one weight and an equal decrease/increase in all the other weights forthe upper/lower bound, respectively. This however is only one way of how the weights canchange. It is also possible that some weights are unchanged or assume any other possibleincrease/decrease of weights. The only condition that needs to be satisfied is, if one weight isincreasing/decreasing, at least one weight must decrease/increase, because the sum of weightsmust add up to 1 (∑wj = 1). Choosing weights out of the weight margin presented by Opricovicet al. [87] does not guarantee that the suggested solution will still be the most preferred oneafter using weights out of the weight margin. It only applies to one specific case.The research in the present chapter proposes a modified VIKOR method, which addressesabove issues extending and generalizing the applicability of the originally proposed method.The improved VIKOR method is presented in the next section.5.4 Modified VIKOR-methodWhen maximizing multiple objectives (benefits) and determining the non-dominated or Paretooptimal solutions, the maximum value of each criterion is always part of the Pareto optimalsolution. When minimizing an objective (cost) the utility values can be modified by taking thenegative of that particular criterion (min xj = max(−xj)). Because the maximum (benefit) orminimum (cost) value is the important factor in an optimization problem, it is suggested to usethe L∞-norm or maximum norm:||xj ||∞ = max{|x1j |, |x2j |, ..., |xmj |} (5.1)5.4.1 Modified ProcedureThe modified VIKOR method is stated as follows:Si =n∑j=1wjxij||xj ||∞ (5.2)Ri = min{wjxij||xj ||∞}, j = 1, ...,n (5.3)Qi = νSi||S||∞ + (1− ν)Ri||R||∞ (5.4)Here, S and R are not on a common scale. Specifically, R is smaller than S, because itselects the weighted utility value of just one criterion. Therefore, S and R are normalized with61the L∞-norm. Qi is the aggregated value and is sorted in the decreasing order. The highestvalue of Qi is the most preferred solution that is determined by the present modified VIKORmethod.The present research also proposes a modified weight margin in addition to the preferredalternative. The weight margin will inform the decision maker how sensitive the preferredsolution is to given weights, or in other words, how much they can change the weights so thatthe preferred alternative will still be chosen.5.4.2 Modified VIKOR Weight MarginsThe extended VIKORmethod of Opricovic et al. [87] determines a weight stability as mentionedin Section 5.3 point vi. A more helpful weight margin is to provide a margin, in which anycombination of weights will deliver the same compromise solution. More specifically, someweights are increased while some are decreased and some might not change at all. The smallestweight margin guarantees no change in the solution. The sum of all weights however, must addup to 1 (∑wj = 1). A weight can increase minimally, when only one weight decreases and allothers increase. For example, consider three criteria with three weights:i) ϕ1w1 + λ1w2 + λ1w3 = 1ii) λ2w1 + ϕ2w2 + λ2w3 = 1iii) λ3w1 + λ3w2 + ϕ3w3 = 1Here λ represents an increase in weight and ϕ a decrease in weight to find the upper bound.w3 can then be minimally increased, if all the other weights except one are also increased. Thisis because, w3 has to “share” the increase with the other weights. In this example there aretwo possible ways to increase w3 and at least decrease one. The minimum increase in w3 willbe the upper bound for the chosen alternative still to be described as the most preferred one.The algorithm that determines the upper bound for each wj is presented now.62max λk, k = 1, ...,n (5.5)subject to Qnew(a(1)) > Qnew(a(2)) (5.6)...Qnew(a(1)) > Qnew(a(m)) (5.7)Qnew(a(i)) = νSinew||Snew||∞ + (1− ν)Rinew||Rnew||∞ (5.8)Sinew =n∑j=1wnewjxij||xj ||∞ , Rinew = min{wnewjxij||xj ||∞}(5.9)wnew =λkwj , j = 1, ...,n, j 6= kϕkwk (5.10)ϕkwk + λkn∑j=1wj = 1, j 6= k (5.11)ϕk =1− λk(1−wk)wk(5.12)1 6 λk 61∑nj=1wj, j 6= k (5.13)An upper bound that can guarantee that the solution will not change, independent of theweight increase (e.g., increase two, decrease one, increase one, decrease two) is the minimum ofall determined upper bounds:wUpperj = min{λkwj}, k = 1, ...,n, k 6= j (5.14)The lower bound is determined by minimizing λk in equation (5.5) and using the maximumin equation (5.14). The boundary condition in equation (5.13) changes to 0 6 λk 6 1.The presented algorithm can be solved as an optimization problem with nonlinear con-straints or by increasing/decreasing λk by a specific step size until one of the constraints (5.6)to (5.7) is violated.The importance weights assigned by a decision maker are subjective and the provided nu-merical value might not be exact. Thus, slight variations of the provided weights are possible.If the determined weight margin is sufficiently large, a decision maker can be more confidentabout the solution provided by the VIKOR method.5.4.3 Weight Margin Using a Range of Objectives ValuesIn the case of a continuous objective function, it is possible to increase the number of alternativeson the Pareto front. This on the other hand decreases the weight margin. To still decide ifthe weight margin is sufficient, this section introduces a weight margin in which the objectivesshould lie within a certain range. More specifically, this section provides a weight margin in63which the objectives will not change more than a specific amount. The following steps determinethe weight margin.i) Compute Qi with initial weights.ii) Find Q∗, which is the highest value of Qi, and the corresponding utility values xij of theobjectives.iii) Compute or specify the range describing how much the objective values xij can change.iv) Find the alternatives, where the utility values are not within the specified range.v) Compute the weight margin as presented in Section 5.4.2 without the alternatives fallinginto the range identified in iv. Thus, these alternatives are omitted in the constraints ((5.6)to (5.7)).5.5 Design Optimization ExamplesThe following sections apply the modified VIKOR method to some design examples. The firstexample applies the VIKOR method to the design of a wireless sleep monitoring system.5.5.1 Design of a Wireless Sleep Monitoring SystemIn order to monitor the sleep quality and diagnose sleep disorders, portable sleep monitoringdevices should include the following measurements [19]:• Electroencephalography (EEG), records the change in human brain signals [20].• Electrooculography (EOG) measures the electrical potential between cornea and retina,which is important to detect sleep stages.• Measuring the airflow through the nose, is important to score apnea events.• Respiratory effort is measured through the chest movement.• Electrocardiogram (ECG) displays the heart rate and determines the heart’s electricalactivity.• Pulse-Oximetry records the level of oxygen in the blood.• Electromyography (EMG) measures muscle activity and helps determine sleep stages. Italso detects leg movements.More information on the present topic and the functioning of a sleep monitoring system canbe found in Section 1.2 or the American Academy of Sleep Medicine (AASM) manual [17].64A wireless sleep monitoring system or in general a wireless body sensor network (WBSN)connects various medical sensors and appliances that are located on the human body. The setof sensor nodes is denoted by S. Sensor nodes transmit their data to a base station or relaynode. Potential locations for a base station or relay node are indicated as Candidate Sites(zj). The locations for the sensors S are predetermined. In this example, the objectives areto find a location for the base station/coordinator that is comfortable (objective 1), has lowenergy consumption (objective 2), and has low signal interference (objective 3). Figure 5.1shows possible candidate sites for a base station and the necessary sensors for a wireless sleepmonitoring system. In total 14 candidate sites are considered.z8z9z11z12z14z13z10EEG-1EOG-2Respiratory Effort-4ECG-5Airflow-3Pulse-Oxi-6EMG-7Human front-sidez1z2z3z4z5z6z7Figure 5.1: Sensor nodes i and candidate sites zj for a wireless sleep monitoring system.The comfort values for each of these locations have been determined in Chapter 4. Thedetermination of the energy consumption for each possible candidate site is described next.Energy ConsumptionA WBSN needs to record data for a determined amount of time, using the least possible energy.Less energy consumption also leads to a smaller sized WBSN, because needed battery for data65transmission can have a smaller overall size. Consequently, it also makes it more comfortablefor the person wearing the device. Therefore, it is desirable to design a WBSN with low energyconsumption.A widely used channel access method in WBSNs is time-division multiple access (TDMA)governed by the IEEE 802.15.4 and IEEE 802.15.6 standards [89]. A TDMA frame structureis shown in Figure 5.2.GTS1 GTS2 GTSn Inactive PeriodCFP IPSuperframeFigure 5.2: TDMA frame structure.A super-frame has a Contention Free Period (CFP) and an Inactive Period (IP). Each sensornode has its Guaranteed Time Slot (GTS) in a super-frame. All sensors turn off their radiosin the inactive period to save energy. In one super-frame, each sensor transmits data with aspecific transmission power (Pi, i ∈ S) and transmission time (Ti, i ∈ S) to a candidate sitej ∈ CS. The energy consumption for one sensor i in one super-frame is Pi · Ti. Over thelifetime of the WBSN each sensor sends data Li/Tframe times, where Li is the lifetime of asensor i and Tframe the duration of one super-frame. The optimization model of Zhou et al.[90] and Minhas et al. [91] is adopted here, with the difference that the previous work optimizethe lifetime of the WBSN, and the base station is at a predefined position. In their approachthe sensors themselves can vary in position. For a WBSN design however, lifetime is a designrequirement and a function is limited to a specified amount of time, i.e., in the lifetime, theenergy consumption should be as small as possible. The following model minimizes the energyconsumption and determines the transmission power and transmission time for each sensor nodei.minP ,T ,z∑i∈SPi · Ti · LiTframe(5.15)subject to∑i∈STi ≤ Tframe (5.16)∑j∈CSTi · rij · zj ≥ xi · Tframe, ∀i ∈ S (5.17)rij = W · log2(1+ Pi |hij |2Nj)(5.18)PLij = PL(d0) + 10 · n · log10(dijd0)(5.19)Pmin ≤ Pi ≤ Pmax (5.20)∑j∈CSzj = 1, zj ∈ {0, 1} (5.21)66Equation 5.15 gives the total WBSN’s energy consumption to be optimized. The transmis-sion time of all sensors cannot be bigger than the duration of one super-frame (equation 5.16).rij in equation 5.18 is the channel capacity and the upper bound of information transmittedbetween sensor i and base station j. Nj is the power of noise, W is the bandwidth, |hij |2 isthe channel gain between node i and j. For the channel, the present study only considers thepath loss PL (equation 5.19), because the transmitter and receiver gain are not dependent onthe base station’s location. n in equation 5.19 is the path loss exponent, d0 is the referencedistance, PL(d0) is the path loss at the reference location and dij is the distance from sensornode i to candidate site j. Constraint 5.17 states that the generated data xi of a sensor nodei in one super-frame have to be smaller than the channel capacity for guaranteed time slot Ti.zj are the possible Candidate Sites (CS) for the location of a base station. The transmissionpower of each sensor must lie within Pmin and Pmax (equation 5.20). The energy consumptionPi · Ti · Li/Tframe is basically the battery capacity that is needed for one sensor to transmitdata. The described model is validated in Zhou et al. [90] and Minhas et al. [91].Reusens et al. [92] examine an on-body wireless channel and the present work uses theirdata as follows. The path loss at the reference location determined by Reusens et al. [92]is PL(d0) = 35.2 dB, with a reference distance of d0 = 10 cm and the path loss exponentof n = 3.11. The power of noise Nj in equation 5.18 is −174 dBm/Hz. The present workuses a bandwidth of 0.3 MHz and considers an average data generation speed of 40 kbps foreach sensor. The duration of a super-frame Tframe is 400 ms. The minimum transmissionpower is Pmin = −15 dBm and the maximum transmission power is Pmax = 0 dBm. Table 5.3summarizes the notations and the numerical values used for the design optimization of a wirelesssleep monitoring system.Table 5.3: Notations and numerical values in energy consumption optimization.Notation Meaning ValueS Sensor node set 7 sensorsCS Candidate site set 14 CSsLi Lifetime of sensor i 10 hTframe Duration of super-frame 400msNj The power of noise −174 dBm/Hzxi Data generation rate for sensor node i 40 kbpsW Bandwidth 0.3MHzPmin Minimum transmission power −15 dBmPmax Maximum transmission power 0 dBmd0 Reference distance 10 cmn Path loss exponent 3.11PL(d0) Path loss at reference location 35.2 dBAlthough the energy consumption model is available in literature, it still had to be modifiedfor the present application. Also the parameters such as the distances dij from the sensor nodesto the candidate sites are specific to the present application. The optimization problem statedabove is not solved using a mixed integer program, but it is optimized for each candidate site zjseparately. It minimizes the total energy consumption and thereby determines the transmissiontime and the transmission power for each sensor node.67Another feature considered next to the comfort and the energy consumption is the signalinterference, as discussed next.Signal InterferenceNetworking from the body sensor system to an external station through wireless frequenciescan cause signal interference. Zeagler [65] describes areas with the least possibility of signalinterference by the mass of the body. The data provided in Zeagler’s paper [65] directly relateto this problem and can be used with no further changes.Utility ValuesThe utility values of the three objective functions are summarized in Table 5.4. The comfortvalue and the signal interference are already normalized between 0 and 1.Table 5.4: Three objectives and utility values for the design of a wireless sleep monitoringsystem (The maximum utility value for each objective is highlighted in bold).Location Location Comfort Total Energy SignalNumber Value Consumption [J] Interference1 Wrist 0.6125 20.0042 0.33332 Forearm 0.9333 19.7945 0.33333 Elbow 0.2083 19.4907 0.33334 Upper Arm 0.7333 19.2829 0.00005 Shoulder 0.3208 18.8608 0.00006 Forehead 0.6208 18.1051 0.33337 Chest 0.2542 18.4125 1.00008 Abdomen 0.5583 19.0510 1.00009 Hip 0.5417 19.6804 0.666710 Upper Thigh 0.8167 19.8450 0.833311 Lower Thigh 0.7458 20.7547 0.833312 Knee 0.1083 20.5040 0.833313 Calf 0.8542 20.4927 0.833314 Ankle 0.6542 21.2553 1.0000Still, out of all 14 alternatives, it might be unclear to the decision maker as to whichalternative (location) should be chosen in order to satisfy all the objectives in the best possiblemanner and to make a minor trade-off.Design Decision using the modified VIKOR MethodThis section describes finding the most preferred design solution with the modified VIKORmethod and comparing it with the original VIKOR method. No commercial software of theVIKOR method is available at present and therefore the original and modified VIKOR methodare implemented in Matlab. It starts with the assumption that the decision maker places equalimportance on all objectives (w1 = w2 = w3 = 1/3). The weight for maximum group utilityand minimum regret is ν = 0.5. In Figure 5.3 the three objective functions comfort, energyconsumption and signal interference are assigned to one of the axes. Black crosses present all thealternatives. Blue dots are the non-dominated solutions. Red stars are the solutions determinedusing the original VIKOR method, and the green square solution is the one determined using68the modified VIKOR method.-41-18-3-2-10.8-19 0.6-20 0.4-21 0.2-220All alternativesNonDom SolVIKOR with all altmodVIKOR with all alt-41-18-3-2-10.8-19 0.6-20 0.4-21 0.2-220All alternativesNonDom SolVIKOR with NonDom SolmodVIKOR with NonDom SolFigure 5.3: Green square: most preferred solution determined over the modified VIKORmethod; Red star: determined through the original VIKOR method. The usage ofall alternatives or only the non-dominated solutions change slightly in the originalVIKOR method.Figure 5.3 shows that the conditions specified by the original VIKOR method in Section 5.3provide a different solution, depending on the inclusion of all or only non-dominated alternatives.The original VIKOR method suggests two compromise solutions (see Figure 5.3 subplot a) whenusing all alternatives. However, when using only the non-dominated solutions, the numberof alternatives decreases. This is used as a condition in the original VIKOR method, andthe method provides only one alternative as the compromise solution. This undermines theconditions used for the original VIKOR method.Choosing a weight wj within the lower interval in Table 5.5 guarantees that the preferredalternative determined using the modified VIKOR method will remain the most preferred alter-native no matter which direction the weights are changed, and therefore stabilizes the solution.The weight margin states, how much the weight can be changed in general; for example, w1can be changed by 23%. Thus, the margin describes the stability of the solution.69Table 5.5: Modified VIKOR weight margin for comfort (w1), energy consumption (w2)and signal interference (w3).w1 w2 w3wlowerj 0.1723 0.2600 0.2600wupperj 0.4031 0.4031 0.4693Margin 0.2308 0.1431 0.2093The most preferred compromise solution with equal weights for the three objectives in thisexample is the location number 4 (the upper arm). This means the upper arm is a goodcandidate site to mount a coordinator or base station and it has a good trade-off with respectto comfort, energy consumption and signal interference.5.5.2 Design of an EEG ElectrodeElectroencephalography (EEG) records the change in the human brain signals [20]. EEG mon-itoring is an important way to detect sleep apnea (see Section 1.2). The present exampleconsiders the design of an EEG electrode. The EEG electrode should be flexible to adapt tothe shape of the head, which means it should have low stiffness, but at the same time shouldbe durable over a long lifetime. The impedance of the electrode-electrolyte interface shouldbe as small as possible (<10 kΩ). The electrode’s width is 0.0127 m, its length is 0.01 m andthe thickness is 0.003 m. The next sections describe the three objectives used in this designoptimization problem.Conductivity:The conductivity depends on the material characteristics. Different types of polymers aretypically used in EEG manufacturing [93, 94]. To increase the conductivity of the polymer,carbon black can be added. Although the change in conductivity for variable amounts ofcarbon black has not been tested in depth, the present research makes an assumption abouttheir relationship in order to demonstrate the modified VIKOR method. Specifically, a sigmoidfunction is assumed, implying that the conductivity initially increases and saturates after aparticular amount of carbon black.ai1+ e−bi(CB−ci)(5.22)Here, ai, bi and ci are parameters for different polymers, and CB is the amount of carbonblack added to the polymer.Durability:Durability also depends on the polymer and the added amount of carbon black. More carbonblack results in a harder electrode. Durability or toughness can be determined by integratingthe stress-strain curve. Toughness is defined as the energy of mechanical deformation per70unit volume prior to failure. Similar to the above assumptions, the present work makes anassumption about the physical behavior, for the purpose of testing introduced methodology, asfollows:122fiEi(1+CB1/4) (5.23)Here, fi is the strain at failure and Ei is the Young’s modulus of polymer i.Stiffness:In order to make the EEG electrode attachment as comfortable as possible it should be flexible,i.e., the stiffness should be small. The stiffness depends on the cross sectional area, the lengthof the electrode and the Young’s modulus. The Young’s modulus changes when carbon blackis added. For the stiffness, the present analysis assumes the following relation:wtlEi(1+CB1/3) (5.24)where, w is the width of the electrode, t is the thickness of the electrode, l is the length,and Ei is the Young’s modulus of polymer i.Table 5.6 lists 4 assumed polymers with different parameters for the formulated functions.These functions and parameters are used for the multi-objective optimization of an EEG elec-trode.Table 5.6: Parameters in the multi-objective optimization of EEG electrode (four typesof polymer are considered).1 2 3 4ai 0.0049 0.0054 0.0051 0.005bi 0.9023 2.5937 1.965 1.122ci 26 18 18 19fi 0.18 0.11 0.21 0.09Ei 1 130 169 876Pa 1 062 723 524Pa 560 096 882.8Pa 2 129 910 110PaMulti-objective Optimization and Design DecisionThe three objective functions are optimized simultaneously with a multi-objective evolutionaryalgorithm [95]. The resulting Pareto front of polymer 1 is plotted in Figure 5.4. All objectiveshave the same importance value with w1 = w2 = w3 = 1/3 and ν = 0.5. The originaland modified VIKOR method provide the same most preferred solution. The original VIKORmethod however, provides multiple compromise solutions due to the conditions in Section 5.3.1point v.To record brain waves with the electrode, the impedance must be <10 kΩ, which withthe electrode dimensions, corresponds to a conductivity greater than 2.4× 10−3 S/m. Thisconstraint can be directly applied to the Pareto front or added as a constraint in the multi-objective optimization algorithm, leading to a reduced number of possible alternatives from71Figure 5.4 compared with Figure 5.5.24-2.55-2-1.5107-14 107-0.53 610-3 2 1 08Non-dominated solutionsOriginal VIKOR methodModified VIKOR methodFigure 5.4: Non-dominated solutions of polymer 1 with marked preferred design solutionof original and modified VIKOR method.Now the preferred solution determined by the original VIKORmethod moves down. Becauseonly a conductivity of 2.4× 10−3 S/m is necessary in order to design a well-functioning EEGelectrode, it would be sufficient to choose a solution with the minimum value of conductivityin the constraint Pareto front. On examining the Pareto front in more detail, one can see thatby increasing conductivity, flexibility does not decrease up to a certain point when the curvefalls off. The same is true for durability, and therefore, the trade-off made by increasing theconductivity with respect to the other objectives is rather small. The chosen solution by themodified VIKOR method therefore intuitively makes sense. However, the chosen compromisesolution by the original VIKOR method results in a large trade-off that greatly affects flexibilityand durability.7266.5-2.5-2.45-2.3-2.2-2.1-2107-1.9-1.87 107-1.74.8 4.610-3 7.54.4 4.28Non-dominated solutionsOriginal VIKOR methodModified VIKOR methodFigure 5.5: Non-dominated solutions of polymer 1 with marked preferred design solutionof original and modified VIKOR method. The conductivity constraint is appliedto the Pareto front.This again shows that, on introducing a constraint into the design problem, the solution in themodified VIKOR method does not change, and demonstrates its advantage over the originalmethod. Any combination out of the weight margin presented in Table 5.7 will result in thesame compromise solution provided by the modified VIKOR method.Table 5.7: Weight margins for conductivity (w1), durability (w2) and flexibility (w3)w1 w2 w3wlowerj 0.2422 0.2422 0.1584wupperj 0.5000 0.4347 0.4347Margin 0.2578 0.1925 0.2763A bigger weight margin means the solution is more stable and a decision maker can be moreconfident about the provided solution.Figure 5.6 presents the Pareto front of the four different polymers. The more complexa Pareto front gets, the more challenging it is to find a good compromise solution. Thisdemonstrates the need for a method that helps a designer to choose one solution.Again, equal weights are used to determine a compromise solution. The different curves onthe overall Pareto front represent different types of material (Table 5.6).7302-2.56-2-1.5-11075-0.54 10704 310-3 62 1 80Non-dominated solutionsOriginal VIKOR methodModified VIKOR methodOjectives Range <10%Figure 5.6: Discontinuous Pareto front of four types of polymer.The modified VIKOR method chooses the same solution as before. The original VIKORmethod chooses the same polymer but a different solution. This is because the durability ofone of the polymers that was added to the design space can be much higher, but at the sametime the flexibility is also much lower for the same material. However, as discussed before, itmakes sense to choose the solution provided by the modified VIKOR method, because goingdown the trade-off in this part of the Pareto front increases drastically, for flexibility.Figure 5.6 presents the compromise solutions in green square, where the objectives canchange within a predefined range (in this case 10%). Therefore, the weight margins for theincreased range of alternatives are determined according to Section 5.4.3. The weight marginspresented in Table 5.8, in which the objectives can change within 10% (range of alternatives),is bigger than that for a single alternative (Table 5.8 one alternative).Table 5.8: Weight margins for conductivity (w1), durability (w2) and flexibility (w3)w1 w2 w3wlowerjOne alternative 0.2379 0.2379 0.0921Range of alternatives 0.2379 0.2379 0.0733wupperjOne alternative 0.5000 0.4862 0.4862Range of alternatives 0.5000 0.4862 0.4862Margin One alternative 0.2621 0.2483 0.3942Range of alternatives 0.2621 0.2483 0.4129The difference in this case is rather small however (only w3 has a higher margin). One reason74for this is that the upper weight margin for w1 is already at its maximum. For example, whendecreasing one of the weights except w1 and two weights are increasing at the same time (eitherw1 and w2 or w1 and w3), then the highest possible increase is 0.5. That is, if one goes downto 0 from 1/3, the other ones can only increase by 1/6. This weight margin however, is theworst case scenario, and by providing this value it is guaranteed that by choosing a weightwithin the weight margin the same compromise solution would be picked. Clearly, there aremany more possibilities how to change the weights (e.g., one weight unchanged, one increased,one decreased; one increased, two decreased). Therefore, it makes sense to provide the lowestweight margin, as opposed to the highest possible weight margin (Opricovic et al. [87]).5.6 ConclusionThis chapter revealed some shortcomings of the VIKOR decision making method and proposedimprovements to the originally proposed method. With the use of the L∞-norm, a designdecision is not affected by the inclusion of only the reduced set of non-dominated solutionsversus a complete set of alternatives. The solution also does not change when introducing adesign constraint into a multi-objective design problem. Within an introduced minimum weightmargin, it guarantees that the final design solution will not change on changing the weights inany direction. This is an important information for the decision maker, because they might beuncertain in their weight assignment, and the present approach therefore assesses the stabilityof the solution. If the decision maker’s uncertainty lies within the weight margin they can beconfident about the provided compromise solution. The shortcomings of the original VIKORmethod were demonstrated and it was shown that the conditions for a stable solution providedby the original VIKOR method were rather intuitive.The modified VIKOR method was applied to two design examples. The first design exam-ple was applied to an existing problem that had been addressed in part in Chapter 2 of thethesis. In that chapter a solution was selected based on intuition while acknowledging that amore sophisticated approach would be desirable. The present chapter revisited the problem.The application of the modified VIKOR method helped to objectively select a body locationfor a wearable body sensor network while taking into account the objectives comfort, energyconsumption and signal interference. The second design example concerned the design of anEEG electrode with high conductivity, durability and flexibility.The weight assignment to individual objectives/criteria was illustrated in these examples.Techniques such as AHP or group decision making methods as in [84] could be used for furtherimproving the developed method, to less subjectively assign the weight importance values toobjectives. The next chapter will compare the VIKOR method improved in the present chapterwith the methods used in Chapter 2 and 3.75Chapter 6Comparison of Decision MakingMethodsChapter 2 provided an approach to include qualitative objectives in a less subjective way. Whenconsidering multiple-objectives, some of the objectives might be conflicting and a trade-off isinevitable. The technique proposed in Chapter 2 to make a trade-off decision or in other wordsto pick a solution out of the Pareto front was rather simple. Therefore, a more refined strat-egy to make this design decision was introduced in Chapter 3. Since the qualitative objectivecomfort used in Chapter 2 and Chapter 3 was rather intuitively formulated, Chapter 4 furtherinvestigated this objective. For enhanced validation and further comparison, Chapter 5 intro-duced another decision making method. The next section compares the technique developed inChapter 2 with the more effective technique proposed in Chapter 5.6.1 Comparison of Chapter 2 Decision Making Method withVIKORThe method used in Chapter 2 chose a solution based on the number of times locations werepicked as Pareto optimal in the multi-objective optimization algorithm. This was a ratherintuitive way to make a trade-off. In addition, the method was applied only to the examplein Chapter 2. Therefore, the trade-off decision is compared now with the more effective andbroadly applicable VIKOR method, which was developed in Chapter 5. Figure 6.1 presentsthe result from the method used in Chapter 2 and the VIKOR approach. As can be seen fromthe figure, the VIKOR method and also the modified VIKOR method proposed in Chapter 5select a slightly different solution on the Pareto front. Importance values are the same forboth objectives. Since the threshold value used in Chapter 2 to select a solution was ratherintuitive, it is suggested to use the solution provided by the VIKOR method. Chapter 3 usesthe technique of fuzzy measures and the Choquet integral to improve the trade-off decisiontechnique of Chapter 2. The next section will compare the decision making technique of fuzzymeasures and Choquet integral used in Chapter 3 with the method proposed in Chapter 5.76-7 -6 -5 -4 -3 -2 -1 001234567Non-dominated solutionsSolution Chapter 2VIKORmodVIKOR methodFigure 6.1: Comparison of Chapter 2 result with the proposed decision making methodof Chapter 5.6.2 An Example Comparison of Fuzzy Measures/ChoquetIntegral with VIKORThe VIKOR method introduced in Chapter 5 is based on the maximum “group utility” and“minimal regret.” The Choquet integral in terms of the Möbius representation and the VIKORmethod are similar in taking the “minimum regret”. The Choquet integral however, takes the“minimum regret” of the whole power set of criteria/objectives. For easier comparison theVIKOR method and the Choquet integral in terms of the Möbius representation are presentedhere, again.Cm(ai) =∑T⊆Nm(T )minj∈Txij (6.1)Si =n∑j=1wjxij||xj ||∞ , j = 1, ...,n (6.2)Ri = min{wjxij||xj ||∞}, j = 1, ...,n (6.3)Qi = νSi||S||∞ + (1− ν)Ri||R||∞ (6.4)Making it more specific, considering only three criteria and omitting index i of alternatives, theChoquet integral and VIKOR method appear as follows:77Cm(a) = m1x1 +m2x2 +m3x3+ (6.5)m12 min{x1,x2}+m13 min{x1,x3}+m23 min{x2,x3}+m123 min{x1,x2,x3}Q =ν||S||∞ (w1x1 +w2x2 +w3x3) +1− ν||R||∞ min{w1x1,w2x2,w3x3} (6.6)Here, mj are the fuzzy measures in Möbius representation and wj are the weights for singlecriteria. As seen in the equations above, the first part of the Chouet integral and the firstpart of the VIKOR aggregation are essentially the same with an additional weighting of theweighted sum for the VIKOR method. The Choquet integral takes the minimum regret of eachcombination of criteria, whereas the VIKOR method takes the minimum regret of all criteria.The Choquet integral uses an importance value (fuzzy measure) for each “minimum regret”without a weighting applied to the criteria. By setting fuzzy measures mT with |T | < |N | tozero, only the “minimum regret” of all criteria is considered in the Choquet integral.To compare the technique of fuzzy measures/Choquet integral with the VIKOR methodof Chapter 5, the objectives and utility values from Chapter 3 (see Table 3.1) are used. Thefuzzy measures are determined using the algorithm in Chapter 3 with the following preferencerankings:• version 4 version 3; version 24 version 14; version 124 version 1234• comfort reliability power consumptionTable 6.1 shows the fuzzy measures and Shapley index through these preferences.Table 6.1: Fuzzy measures m in Möbius representation and Shapley indices φShComfort Reliability Power consumptionm({i}) 0.4534 0.0 0.4534φSh({i}) 0.5000 0.2733 0.2267Comfort — 0.5466 -0.4534Reliability 0.5466 — 0.0000Power consumption -0.4534 0.0000 —The Shapley values are then used as importance weightings for the VIKOR method with a νvalue of 0.5.Figure 6.2 shows that the preferred alternative determined through fuzzy measures andChoquet integral coincide with the VIKOR method. This may be due the similarities of thetwo methods.78-12-118 -2-10-9-8-7-6-57-46 5-64-83Non-dominated solutionsFuzzy-M Choquet-IVIKORmodVIKOR methodFigure 6.2: Comparison of fuzzy measures/Choquet integral decision making withVIKOR method in the example of Chapter 3.6.3 Another Comparison of Fuzzy Measures/Choquet Integralwith VIKORThis section compares fuzzy measures/Choquet integral with VIKOR using the example inChapter 5 (for utility values see Table 5.4). This example uses equal importance values for allobjectives (w1 = w2 = w3 = 1/3) in the VIKOR method and equal weightings for the 2-additivefuzzy measures (m1 = m2 = m3 = m12 = m13 = m23 = 1/6). The fuzzy measures/Choquetintegral approach shows the same preferred alternative as the VIKOR method (Figure 6.3).This demonstrates the similarities between the two methods again. However, the ranking errordefined by equations 4.9 and 4.10 in Chapter 4 shows that the order of ranked alternativesdiffers slightly (NRMSDrank = 0.1007).By further comparing the two methods, one can see that the VIKOR method cannot modelinteractions. Consider the following example:A x1 x2a1 26 30a2 28 28a3 30 2679-4-3.5-18 1-3-2.5-2-1.5-10.8-19 0.6-20 0.4-21 0.2-220All alternativesNon-dominated solutionsFuzzyM ChoquetImodVIKOR methodFigure 6.3: Comparison of fuzzy measures/Choquet integral decision making withVIKOR method using the example in Chapter 5.Using the VIKOR method it is not possible to prefer an alternative with a high utility valuein either of the two criteria over an alternative with two medium utility values (a1 a2 anda3 a2). This is because the ν value weighting the maximum group utility (Si) and minimumindividual regret (Ri) is a positive number. More specifically:Q1 =ν||S∞||w126+w230+1− ν||R∞|| min{w126,w230} (6.7)Q2 =ν||S∞||w128+w228+1− ν||R∞|| min{w128,w228} (6.8)Q3 =ν||S∞||w130+w226+1− ν||R∞|| min{w130,w226} (6.9)There is no w1,w2 so that Q1 > Q2 and Q3 > Q2. In contrast, the Choquet integral with fuzzymeasures:Cm(a1) = m126+m230+m12 min{26, 30} (6.10)Cm(a2) = m128+m228+m12 min{28, 28} (6.11)Cm(a3) = m130+m226+m12 min{30, 26} (6.12)and for example,m1 = m2 = 1;m12 = −1 provides a Choquet integral of Cm(a1) = 30,Cm(a2) =28,Cm(a3) = 30 and therefore a1 a2 and a3 a2.It is important to note that the VIKOR method can become confusing when a decision80maker increases the weight in one objective and observes the opposite effect of what he/sheexpects. This is the case in Table 6.2, where by increasing the weight of w1 alternative a3should get the highest Qi value, because it also has the highest value in x1 = 30. On theother hand, it is the case when observing the Si values. However, because the minimum regretof a1 is higher than those in the other alternatives, a1 will be preferred. This might lead tomisinterpretation. An increase in the importance value ν makes Ri less important and a3 willbe the most preferred solution.Table 6.2: Utility values of the VIKOR method for two different weightings.A x1 x2 Si Ri Qi Si Ri Qia1 26 30 0.933 0.433 0.964 0.880 0.100 0.946a2 28 28 0.933 0.467 1.000 0.933 0.093 0.940a3 30 26 0.933 0.433 0.964 0.987 0.087 0.933wj w1 = 0.5,w2 = 0.5 w1 = 0.9,w2 = 0.1The advantage of the VIKOR method lies in its simplicity. A decision maker or expertonly has to provide a linear set of weightings, whereas for the Choquet integral 2n − 2 fuzzymeasures or in case of the 2-additive case n(n+ 1)/2 fuzzy measures have to be provided ordetermined.6.4 ConclusionThis chapter compared the VIKOR method with the theory of fuzzy measures and Choquetintegral approach and demonstrated the advantages and disadvantages. The two decision mak-ing methods provided comparable results. Both methods used similar aggregation functions,although the concepts behind them were different. The VIKOR method’s concept is based onmaximum group utility and individual regret, whereas the main purpose of the fuzzy measureand Choquet integral approach is the consideration of interactions. Solely fuzzy measures inthe Möbius representation show similarities among their methods of aggregation. The VIKORmethod is simpler to apply, because only a linear set of weights is necessary. However, prefer-ence rankings that are more complicated can be modeled with the fuzzy measure approach. Theapplication itself determines the use of the appropriate decision making method. Chapters 3and 4 of this dissertation provided methods to determine fuzzy measures; however, additionalinformation is needed. Techniques such as AHP or group decision making methods as in [84] canbe used to assign the importance values in the VIKOR method. The next chapter summarizesand concludes the present dissertation and presents possible future work.81Chapter 7Discussion and ConclusionThis thesis covered several aspects of the design optimization of a mechatronic system or device.The methods developed in this thesis were mainly applied to a wearable sleep monitoring system.In the design of such a system, multiple features and objectives need to be considered. Someof these features are of quantitative nature, while others are qualitative. When consideringmultiple conflicting objectives, a trade-off is required. Decision making methods help to makebetter trade-offs depending on the application and preferences. However, it involves subjectivity,it depends on the decision maker providing the importance values and also on the group of peoplethe product is designed for (customers). This leads to different trade-offs, and a validation forthe best trade-off method is hardly possible. If the design trade-off decision was satisfactory,still it would not be clear if it was the best trade-off decision. In addition, it is challenging tovalidate a wrong trade-off decision because the decision making framework could have led to thewrong decision or the assigned weights within the decision making framework. Furthermore,how to measure a good trade-off decision is not quite clear. One measure might be the profit acompany makes with the designed product; however, that also depends on the current economicsituation and therefore it is uncertain if another trade-off would have provided a higher profit.However, a methodology that includes design preferences helps to make trade-off decisions andit will potentially lead to a better design. While a full validation of the decision making methodmight not be possible and the present research is limited to make improvements and comparingthem, following a systematic validation strategy is more desirable than choosing a randomsolution. The methods developed in the present dissertation help the designer in the designprocess. First the design space is reduced to a set of non-dominated solutions by includingquantitative and qualitative aspects. Qualitative objectives are modeled using multiple criteriaand the criteria describing the qualitative objective are aggregated to one representative value.The criteria itself can be quantitative or qualitative. The introduced and enhanced decisionmaking methods lead to less subjective trade-off decisions when the objectives are conflicting.827.1 SummaryThis thesis significantly contributes to resolving the question of how to include qualitativecriteria in a less subjective way. In Chapter 2, this was done by using fuzzy sets and fuzzynumbers. The defuzzified fuzzy numbers were the numerical representation of the qualitativecriteria used in Chapter 2. That chapter optimized comfort and wearability simultaneously.It presented a systematic way to design a comfortable and reliable body sensor system. Themethod presented was then applied to a potential design of EEG/EOG for sleep monitoring.However, Chapter 2 did not provide the most comfortable and reliable EEG/EOG system, butrather implemented a method that would assist a designer in the selection of the type of devices,location on the body and how the devices are wired.In Chapter 3 the same exemplary utility values were used to make a more effective designdecision, by using the technique of fuzzy measures and Choquet integral.To obtain more realistic values for the objective functions, Chapter 4 developed a comfortmodel for a wearable body sensor network based on fuzzy measures and the Choquet integral.With fuzzy measures it is possible to model interactions between objectives. This ability ofinteraction modeling described the qualitative objective comfort in a refined way, by usingmultiple criteria to describe comfort. The comfort model was validated through a trainingset and test set with the help of a comfort questionnaire study. The solutions discoveredin Chapter 4 showed how to incorporate a qualitative objective into a multi-objective designproblem with quantitative and qualitative design criteria. When designing a wearable bodysensor system it is helpful to know the importance of comfort and the criteria for describing it,in order to better adjust the design.Chapter 5 described an improved version of the VIKOR decision making method in which asensitivity analysis in terms of a stability weight margin extended the original VIKOR method.The improved method was then applied to two design examples in the field of wearable bodysensor networks, focusing on a portable sleep monitoring system.Chapter 6 provided a comparison of the improved VIKOR method to the decision makingmethods enhanced in the previous chapters.7.2 Possible Future WorkThis dissertation advanced the methods to incorporate qualitative criteria or objectives in aless subjective way into a multi-objective design process for a mechatronic system, where itis necessary to make a trade-off decision. The focus application was a comprehensive sensorsystem for sleep monitoring in the familiar home environment. Since none of the sensor sys-tems in the sleep monitoring project are yet ready for testing, the methods developed in thepresent dissertation were applied to potential design optimization problems of a wearable sleepmonitoring system.In a later design stage of the project, these methods can be applied to the actual sleep83monitoring system that is currently developed in the sleep monitoring research group at TheUniversity of British Columbia. The methods are also applicable to other design optimizationproblems of wearable sensor technology. Developed methodologies are therefore of great impor-tance in a variety of fields. This section indicates several next steps to follow the work of thepresent thesis:1. The method that addresses modeling of qualitative objectives (used in Chapter 4) can befurther improved by making the utility values for criteria describing the objective to fuzzynumbers. This is because the utility values are not precise physical quantities, and alsobecause the overall aggregated value determined through a questionnaire is not an exactnumerical value. Therefore, it could help to treat these utility values as fuzzy numbers.In addition, the criteria chosen to represent comfort can be better described throughanalytical models (e.g., mathematical model for motion impedance). Consequently, themodel depends less on a questionnaire study. A further expansion of the presented studyincludes an additional qualitative objective such as complexity, which can be used to fur-ther validate the concepts developed in the present thesis to handle qualitative objectives.The developed methods can be further applied to different design optimization areas, suchas automotive design. Furthermore, techniques such as AHP or group decision makingmethods, as in [84], can be used to determine the importance weightings in the VIKORmethod. To deal with uncertainties in the weight assignment procedure, the Dempster-Shafer evidence theory introduced by Fei et al. [85] may be applied, which will improvethe VIKOR method.2. An application of the VIKOR method was presented in Chapter 5 of the thesis. Prelimi-nary results were obtained in analyzing material properties as the input for the proposedmethodology. Studies regarding relations between carbon black and different polymerswithin the sleep monitoring research will facilitate applications of the proposed methodthere and evaluate an improved trade-off when optimizing for flexibility, durability andconductivity. The VIKOR method applied to the EEG electrode design example can beapplied, when the relationship between carbon black and different polymer is known, forflexibility, durability and conductivity.3. Further validation of the decision making methods developed in this dissertation (Chap-ters 3 and 5) is desirable. It may be carried out by choosing multiple trade-off solutionsout of the same Pareto-front and manufacturing multiple prototypes for the same productpurpose. A group of people in different categories (job, country, gender, etc.,) may ratethese products from best to worst and provide a reason for their rating. If the givenreason coincides with a high importance value for the same criterion in the decision mak-ing method, it strengthens the decision making of the developed method, and vice versa.By going back to the same people who provided the input earlier can partly validatesthe decision. It will enable further evaluation of the developed decision making methods84and will provide more insight into their strengths and weaknesses. There is a need forconceptual and operational validation of the developed methodology through applicationin real world problems.85References[1] C. W. de Silva. Mechatronics: An Integrated Approach. CRC Press, 2005.[2] C. W. de Silva. 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Design optimization of a mechatronic device in the presence of quantitative and qualitative design criteria… Falch, Lucas 2019
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Title | Design optimization of a mechatronic device in the presence of quantitative and qualitative design criteria and multiple objectives |
Creator |
Falch, Lucas |
Publisher | University of British Columbia |
Date Issued | 2019 |
Description | Mechatronic devices and multi-domain (multi-physics) systems are widely used in modern industry and other engineering applications. Mechatronic engineering focuses on developing a design solution that integrates multiple domains, particularly electrical and mechanical systems. For a successful product, these systems require to be accurate, fast, reliable, flexible, minimalist, easy to use and cost effective. Such design demands are diverse, can interact with each other, and might be characterized quantitatively, qualitatively, or both. This might require different scales, units, and physical representations between multiple criteria or objectives. Interacting criteria or objectives might be conflicting, e.g., improving one requirement might deteriorate another requirement. This requires reaching a compromise between objectives, a trade-off decision. The present dissertation addresses the multi-objective design optimization problem that involves quantitative and qualitative design criteria and objectives, in a mechatronic system. The methods developed in this thesis are applied to the design of a wearable sleep monitoring system. For the benefit of that application, a design optimization framework is proposed for sensor placement on a human body to improve the wearablity and reliability of a monitoring system that contains the sensors. The developed framework assists the designer in selecting the type and location of the sensors, and the pertinent wiring. The framework uses fuzzy sets and numbers to reduce the subjectivity that arises with qualitative criteria. To describe the qualitative objective comfort, fuzzy measures and the Choquet integral are used, particularly for combining multiple criteria and handling model interactions. Furthermore, fuzzy measures with the Choquet integral and the decision-making method VIKOR are introduced to make a relatively less subjective trade-off decision between conflicting objectives. Finally, a comparison is made between an improved VIKOR method and a fuzzy measure and Choquet integral approach, related to their optimization trade-off decisions. This study leads to a synthesis of all presented results and concludes that the proposed methods provide comparable results and are effective strategies for trade-off decisions. In this manner, the present investigation significantly contributes to the development of a more effective approach for solving a multi-objective design problem with quantitative and qualitative design criteria. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2019-12-12 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NonCommercial-NoDerivatives 4.0 International |
DOI | 10.14288/1.0387040 |
URI | http://hdl.handle.net/2429/72700 |
Degree |
Doctor of Philosophy - PhD |
Program |
Mechanical Engineering |
Affiliation |
Applied Science, Faculty of Mechanical Engineering, Department of |
Degree Grantor | University of British Columbia |
GraduationDate | 2020-05 |
Campus |
UBCV |
Scholarly Level | Graduate |
Rights URI | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
AggregatedSourceRepository | DSpace |
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