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UBC Theses and Dissertations

A stability monitoring and advisory system for small ships Köse, Ercan 1994

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A STABILITY MONITORING AND ADVISORY SYSTEM FOR SMALL SHIPS By Ercan Kose BSc. , Karadeniz Technical University, Trabzon, Turkey 1983; MSc. Karadeniz Technical University, Trabzon, Turkey 1985; M.Phil. University of Newcastle Upon Tyne, U.K. 1991 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF MECHANICAL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May 1994 © Ercan Kose, 1994 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. (Signature) Department of \[&c\^grs)c^,\ £og i^-w r r[ n « The University of British Columbia Vancouver, Canada Date 'Z$~ fyA - (cJ3£i DE-6 (2/88) A b s t r a c t Considering the loss of lives and money as a result of marine accidents, the importance of reducing or preventing capsizing of small boats is clearly evident. The research described in this thesis addresses the development of a monitoring and advisory system for the safety of fishing vessels. This system uses environmental infor-mation obtained from a number of sensors and proposes corrective action based on a rule-base derived from experiments, theoretical research and human expertise. Improvements in computer technology and the low prices of measurement equipment facilitates the integration of a system based on off-the-shelf devices and subsystems such as a ship's radar system to measure wave properties.The thesis demonstrates that such off-the-shelf devices and subsystems can be used with special purpose software developed to produce a low cost, intelligent safety monitoring and advisory system. This monitoring system is designed based on the following requirements : • The system should measure the minimum amount of data. In order to make system practical and least costly, the equipments already existing onboard should be used. • The system should not interfere with the operation of the ship, since anything interfering with operation is expected to be discarded by the captain or crew. In view of the need for the evaluation of wave parameters at a fast rate, in the order of 30 - 60 seconds, for input into the advisory system, two new techniques (Boxing and thinning techniques) have been developed. Reasonable agreement has been found between these two techniques and conventional techniques, such as Fourier transforms. ii A fuzzy expert system has been developed as a decision making process for the mon-itoring and advisory system. Rules forming the basis for the advisory system are pre-sented. An advantage of this modular structure is that new rules may be easily appended to the existing rule-base in view of further knowledge gained through interviewing ex-perts, experiments or theoretical developments. Finally, feasibility of this approach has been demonstrated through numerical simu-lations of various sea conditions on a range of ship forms. i i i Table of Contents Abstract ii Table of Contents iv List of Tables viii List of Figures ix Acknowledgement xiii Nomenclature xiv 1 Introduction 1 1.1 General remarks 1 1.2 Review of Fishing Vessel Casualties 2 1.3 Literature Review 9 1.4 Objective 11 2 An Overview of a Monitoring and Advisory System 13 2.1 Analysis of Capsizing Modes 13 2.2 General Layout of the Monitoring and Advisory System 17 3 Static Stability 24 3.1 Background 24 3.2 Static Stability Criteria 25 i v 3.3 Estimation of Metacentric Height 28 3.3.1 Estimating the Coefficient of GZ curve 28 3.3.2 Spectral Analysis 34 4 Measurements of Wave Propert ies 37 4.1 Introduction 37 4.2 Analysis of Radar Images 41 4.3 Data collection 42 4.3.1 Application of Fourier Analysis to Image Spectra 43 4.3.2 Boxing Technique 46 4.3.3 Thinning Technique 50 4.3.4 Comparison of Image Processing Techniques 57 4.3.5 Conclusion of Measurement of Wave Properties 59 5 Ship D y n a m i c s 61 5.1 Estimation of Wave Height 61 5.2 Roll Natural Frequency 69 5.2.1 Maximum Entropy Method 70 5.3 Estimation of Probabilities 79 5.3.1 Probability of Roll Angle passing a limit value in time T 79 6 Deve lopment of A Fuzzy Expert Sys tem 84 6.1 Introduction 84 6.2 Introduction to Fuzzy Logic 85 6.3 Fuzzy Expert System 87 6.3.1 Determination of Membership functions 88 6.3.2 Input Output Forms and Interpretation 90 v 6.3.3 Inference Method 91 6.3.4 Defuzzification 94 6.4 Explanation of the Rules Used by the Expert System 95 7 Numerica l Simulations 105 7.1 Low Cycle Resonance Simulations 107 7.2 Pure Loss of Stability Simulations 113 7.3 Resonant Excitation Simulations 119 7.4 Simulation of Soehae (Korean) Ferry Accident 131 8 Conclusions and Future work 135 8.1 Conclusions 135 8.2 Contributions of this research 137 8.3 Future Work 138 Bibliography 139 Appendices 145 A Encounter Frequency 146 B F F T Algor i thm 148 C M E M S p e c t r u m 151 D Sea S p e c t r u m s 157 D.l I .T.T.C. Sea Spectrum 157 D.2 Bretschneider Sea Spectrum 158 E Catalogue of Radar Image series 160 VI F Capsizing Times 162 G Rules 163 H Membership Functions 168 H.l Setting the values of membership functions 168 I Glossary 172 vii List of Tables 1.1 Statistics for Fishing Vessel Casualties in Canada 7 3.1 Comparison between original and estimated GM values 36 4.1 An comparison of the present methods with other conventional methods . 58 5.1 Estimated wave heights 69 5.2 Comparision of Maximum Entropy method and Fourier transforms . . . . 70 5.3 Results from MEM natural frequency estimator 77 5.4 Comparison of natural frequencies 79 5.5 Result of statistical analysis for time histories of capsizing 83 7.1 Hydrostatic particulars of UBC series 105 7.2 Inputs for following seas low cycle resonance simulations 107 7.3 Inputs for pure loss of stability simulations in following seas 114 7.4 Quartering seas simulation for UBC # 0 1 124 7.5 Quartering seas simulation for UBC # 0 3 125 7.6 Quartering seas simulation for UBC # 0 7 125 7.7 Quartering seas simulation for UBC # 0 9 126 7.8 Results From Static Stability Calculation of the Seohae 132 '7.9 Input Data for Dynamic Stability Simulations 133 F . l Capsizing times obtained from model tests in San Francisco Bay 162 vm List of Figures 1.1 Total number of casualties 8 2.1 Two critical conditions for a ship in following waves 14 2.2 Fluctuations in ship stability 14 2.3 GZ curve of American Challenger for two extreme wave positions . . . . 16 2.4 Wave directions with respect to the ship 17 2.5 General layout for monitoring and advisory system 20 2.6 An example for Transducer locations 21 2.7 General layout of Decision Module 23 3.1 Possible stability conditions 26 3.2 An example of GZ curve 28 3.3 9th order polynomial fit 29 3.4 Body plan of single chine vessel 30 3.5 Estimated GZ for single chine vessel 32 3.6 Final estimation of GZ curve 33 3.7 Roll decay curve for GM # 1 34 3.8 Roll decay curve for GM # 4 35 4.1 An example of radar screen 42 4.2 Radar image from 1130 November 23 44 4.3 Spectrum of Radar image from 1130 November 23 (FFT) 44 4.4 Contour plot of Radar image from 1130 November 23 (FFT) 45 IX 4.5 Steps for Boxing Technique 46 4.6 An example preprocessed image 47 4.7 Boxing Technique 48 4.8 Wave direction calculated using boxing technique 49 4.9 Steps for thinning technique 51 4.10 An example image after thresholding 52 4.11 An example image after thinning and segmentation 53 4.12 An example image after the cleaning process 54 4.13 An example wave segments with original image 55 4.14 A histogram of wave orientation 56 4.15 Finding wave direction 57 4.16 Difference in calculation of frequencies between FFT and Present method 59 5.1 An facsimile recorder output printed onboard Lash Italia 62 5.2 An example RAO for heave motion of UBC series model # 2 65 5.3 Comparison of experimental and estimated RAOs for UBC series . . . . 66 5.4 Typical recorded heave motion data for UBC # 2 67 5.5 Estimation of wave height 68 5.6 Convergence of MEM natural frequency estimator 75 5.7 Results of MEM natural frequency estimator for single degree of freedom system 76 5.8 Spectrum of roll motion 77 5.9 Roll motion data for American Challenger 78 5.10 Roll motion spectra for American Challenger 78 5.11 Sample functions crossing level x — a with positive slope 80 x 5.12 Favorable combinations of x and x which results in crossing of x = a during dt interval 80 5.13 Typical t ime histories of capsize sequence of American Challenger vessel recorded on San Francisco Bay 82 6.1 A general layout for Fuzzy Expert System 88 6.2 Membership functions 89 6.3 Degree of membership for a crisp data value 90 6.4 Degree of membership for a fuzzy data value 91 6.5 The max - min inference method 92 6.6 The max - dot inference method 94 6.7 The centroid defuzzification methods 95 6.8 Two extreme positions of the wave 96 6.9 Stability changes with a frequency twice the natural roll frequency . . . . 97 6.10 An experimental simulation for low cycle resonance 98 6.11 An example quartering seas motion data leading to capsizing 101 6.12 An example following seas motion data leading to capsizing due to loss of transverse stability 102 6.13 GZ curve of American Challenger for two different wave conditions . . . 103 6.14 An example motion data leading to capsizing due to broaching 104 7.1 Body plans of UBC series 106 7.2 Low cycle resonance simulation in regular waves for UBC # 0 1 109 7.3 Low cycle resonance simulation in regular waves for UBC # 0 3 110 7.4 Low cycle resonance simulation in regular waves for UBC # 0 7 I l l 7.5 Low cycle resonance simulation in regular waves for UBC # 0 9 112 7.6 Low cycle resonance simulation in irregular waves 113 xi 7.7 Pure loss of stability simulation for UBC # 1 115 7.8 Pure loss of stability simulation for UBC # 3 116 7.9 Pure loss of stability simulation for UBC # 7 117 7.10 Pure loss of stability simulation for UBC # 9 118 7.11 Quartering seas simulations for UBC # 0 1 120 7.12 Quartering seas simulations for UBC # 0 3 121 7.13 Quartering seas simulations for UBC # 0 7 . . 122 7.14 Quartering seas simulations for UBC # 0 9 123 7.15 Beam seas simulations for UBC # 0 1 127 7.16 Beam seas simulations for UBC # 0 3 128 7.17 Beam seas simulations for UBC # 0 7 129 7.18 Beam seas simulations for UBC # 0 9 130 7.19 The Seohae Ferry after it was brought to surface 131 7.20 Body Plan of the Seohae Ferry 132 7.21 Capsizing Simulations of the Seohae 133 7.22 Capsizing Simulations of the Seohae 134 xn Acknowledgement The author wishes first of all to express his sincere thanks to his supervisors, Dr. S. M. Cah§al and Dr. A. B. Dunwoody for the steadfast guidance and encouragement throughout this research, his supervisory committee, Dr. P. LeBlond, Dr. F. Sassani and Dr. R. G. Gosine for many valuable suggestions and comments. Special thanks to Dr. Mehmet Atlar, whose suggestions and guidance aided immeasurably in the development of my thesis. I would like to thank Karadeniz Technical University, Turkey for sponsoring this research. I would also like to express my sincere gratitude to the Dynamotive Corporation, especially Mr. Reinhold C. Roth (president &: CEO), for their interest, encouragement and financial support for this project. I am also grateful to my colleagues, Ayhan Akmtiirk, Alejandro Allievi, Erhan Budak, Yetvart Hosepyan, and Haw L. Wong for their thorough technical discussions or other social events. Naturally, the bulk of my gratitude goes to my family for their constant support and encouragement. xiii Nomenclature A ACT A44 B CB cu D g G GZ H I k k LBP Lx, Ly M St s(f) T (Ve Un : Projected lateral area : Critical wave amplitude : Added mass moment of inertia : Beam : Block coefficient : Upper deck area coefficient : Damping coefficient : Acceleration due to gravity : Center of gravity : Restoring moment arm : Effective depth of the ship superstructure : Mass moment of inertia : Wave numbers in x and y directions : Length between perpendiculars : Spatial length : Metacenter : Sea spectra : MEM spectral density function : Draft : Encounter frequency : Natural frequency (Jjw WeXp U 17(0 9 Pk <t> 4>c A ft : Wave frequency : Expected number of crossing at any level : Ship speed : Surface height : Roll angle : Autocorrelation function : Angle between ship and wave directions : Angle of deck immersion : Displacement : Nyquist limit X V Chapter 1 Introduction 1.1 General remarks Engineering problems can not be isolated from a question of safety since every human endeavour can not be free of hazards or risks. It is apparent that a need for safety measures will be influenced by an existence of such hazards or risks. In this respect fishing vessels are no exception. Every engineer engaged in marine activities should, to some extent, involve himself in the development of methods aimed at providing the utmost marine safety. Fishing is a difficult and hazardous occupation, a fact that no-one will deny today. This is an occupation that wears and tears hard on body and soul. In general, the term safety implies that no accident is acceptable but this is in contrast to the maritime field where the reality is that a substantial risk of accident is always present. Safety work is always difficult, as it is difficult to say what is safe and what is not? It is often a question of opinion. Statistics can help to prove a point, but then accidents can be claimed to happen to other people, e.g. those with the careless crew. Improved safety costs money, but on the other hand, it does save lives, reduces injuries and brings peace of mind. Prevention of accident in the marine industry may be considered in three stages 1. Design stage 2. Construction stage 1 Chapter 1. Introduction 2 3. Operation stage At the design stage, it is important to check whether any safety regulation is violated or not, and to determine what kind of recommendations are provided by the rules of the classification societies. It is also necessary to design an adequate protective system to withstand the effects of accidents. Thus, every possible means of eliminating hazards can be taken into proper consideration. The next stage is the construction stage. Its function is mostly related to the su-pervision of whether those safety features considered in the design stage were properly constructed and provided. The operation stage, " Navigare necesse est, vivere non necesse est ". To sail is compulsory, to live is not compulsory; this ancient saying reveals how the need for an operative merchant marine was evaluated in the past. Fortunately, since then, the eval-uation of human life has been considerably upgraded. Several rules of classification societies are based on the assumption that the ships receive "ordinary seaman-like treatment." This is not necessarily limited to handling in heavy weather and may include other factors, such as those resulting from stability, stowage of heavy cargo, shear forces and bending moments due to cargo and ballast loading and distribution, or collision and grounding avoidance. The captain is expected to exercise good seamanship yet the guidance given to him with regard to the behaviour of the ship in heavy weather and weather conditions is minimal and usually limited to his own experience in general or at best with the specific ship in particular. 1.2 R e v i e w of Fishing Vessel Casualties To understand the current state of marine safety and to make a positive move forward for the promotion of marine safety, a brief review of the historical and technical aspects Chapter 1. Introduction 3 of fishing vessel safety is made in this section. As a result of the trawler losses in 1968 a committee of Enquiry into Trawler safety was set up under the chairmanship of Admiral Sir Deric Holland-Martin in the UK. The final report of the enquiry was published in 1969 and made many recommendations to ensure the safety of fishing vessels. One of the main recommendations on design and construction was that the Board of Trade (currently the Marine Division, Department of Trade) should seek powers to lay down statutory requirements on the stability of newly built trawlers. The committee also considered that the International Maritime Organization's stability criteria would provide a suitable starting point for stability standards in the light of experience. The recommendations of the committee of Enquiry were adopted by the UK. govern-ment and legislation followed which resulted in the Fishing Vessels (Safety Provisions) act 1970 and ultimately the Fishing Vessels (Safety Provisions) Rules 1975. The rules cover most aspects of fishing vessel safety and include requirements for freeboard, sta-bility, fire protection and watertight integrity. Although the recommendations of the Holland-Martin Enquiry were directed primarily to vessels of 24.4 metres in length and above, the 1975 rules require mandatory survey of fishing vessels 12 metres in length and above. In 1977 at the Torremolinos Convention for vessels over 24m in length, guidelines for safety of fishing vessels less than 24m in length were drawn up by joint IMO/FAO working group in 1980. In September 1976, the Norwegian research vessel M/S Helland Hansen capsized and sank 18 miles north west of Svinoy lighthouse off the west coast of Norway. In 1977, the Norwegian Directorate decided to order model experiments for a further investigation of the accident. The reason was primarily that stability calculations had shown that the vessel fulfilled the requirements of the Torremolinos Conference 1977, as well as the almost corresponding Norwegian requirements [1]. Chapter 1. Introduction 4 After investigation, the following recommendations were made [2]: 1. Due to the relatively large energy content of moderate waves of 4-6m, small vessels should ideally be self righting. This can often be achieved by constructing the wheel house such that it is weathertight, which implies doors and windows of stronger construction. 2. The GZ curve requirements should in any case be strengthened by requiring positive GZ values up to angles of 80° - 90° . 3. Openings where water can enter the vessel during heeling to 80° — 90° must be closed weathertight, or restricted in size in relation to the size of space to which they lead. 4. Bulwarks, although providing protection in moderate weather, are dangerous in breaking waves. They increase the wave moment and trap water on deck. Rails, combined with low bulwarks, if necessary, should therefore replace high bulwark on small vessels. In February 1974 the Hull trawler Gaul disappeared in heavy seas off the north cape of Norway. The formal investigation into this disaster concluded that the Gaul capsized and foundered after being overwhelmed by heavy seas. The inquiry considered many possible causes for the disaster and expressed a hope that these would be further investigated by naval architects in the Department of Trade with a view to promoting greater safety. In due course the Department of Trade requested the National Maritime Institute to carry out model experiments on the fishing vessel Gaul to achieve this end [3]. The findings of this investigation are consistent with the view that the Gaul was not lost as a result of inadequate intact stability or poor seakeeping qualities. It would seem most probable that the cause of her loss was due to the severe waves, wind, and the Chapter 1. Introduction 5 possibility of encountering a large steep wave at that time in the area of the North Cape bank associated with some other unknown circumstances such as partial flooding from some cause. The most serious loss of stability considered in this investigation and one that could have been sufficient to cause the Gaul to list heavily and founder is that due to consider-able amounts of water present simultaneously on the trawler deck and factory deck, such condition might conceivably arise from the result of a combination of flooding from the salt water supply to the processing pump on the factory deck and water flooding through to an access door on the starboard side of the trawler deck. M.S.J. Reilly examined fishing vessel loss rates for the period 1961 - 80 and compared the trends of those rates for the period of the committee of inquiry into trawler safety (1971 - 80) with the years preceding the circumstances of that inquiry (1961 - 70). He provided a qualitative evaluation of mortality from occupational accidents sustained by deep sea and inshore fisherman between 1961 and 1980. In 1985, the Marine Directorate of the Department of Transport considered it appro-priate to commission an independent study of "Total Losses" and "Serious casualties" casualty records, after 10 years following the introduction of the fishing vessels (safety provision) rules 1975. This study was done by the Sea Fish Authority. The objective of the investigation was to determine the factors of prime importance in influencing the ca-sualty rate for fishing vessels. This was done by statistical analysis of data obtained from an examination of the Marine Directorate's casualty records. This study was extended in 1986. This analysis also deals with vessels actually fishing or on passage to and from the fishing grounds as a separate group. The adequacy of the International Maritime Organization (IMO) recommendation A168 for minimum intact stability criteria of fishing vessels has been widely debated since its introduction in 1968. The fact that losses still occur raises questions on the level Chapter 1. Introduction 6 of this stability standard and whether it is maintained in practice. This paper discusses the stability and seaworthiness of fishing vessels in the light of recent experience with UK vessels and makes some suggestions for improvement in safety of those vessels [33]. Morrall and MacNaught [4] emphasised that the IMO standards are absolute minima; from research and known casualty evidence, the indications are that when levels of sta-bility are reduced below IMO standards the probability of capsize becomes progressively greater as these criteria are degraded. Even when IMO stability standards are complied with, safety from capsizing can not be guaranteed. This is because, the required parameter values of the still water statical stability curve are based on a small number of vessels with variability of ship loading and sea conditions at the time of loss. The parameter values selected for this type of stability criteria are independent of vessel size, type, operational and weather conditions and the margin of safety must therefore vary for each vessel and must be unknown. Ship designers and approving authorities need to have guidance on what are accept-able safe minimum values of the stability properties for the many different types and sizes of ships. The International Maritime Organization (IMO) has been working towards the devel-opment of "physical" criteria which would manifestly enable safety assessment relative to external forces and thus provide indications of safety margins. H. Bird and A. Morrall [5] introduced the safeship project. The aim of this project was to advance existing knowledge of large amplitude rolling motion and ship capsize mechanisms so as to develop better design criteria and stability regulations. At the end of this study, the following comment was made on static stability criteria: "Simple statical righting lever curves will always serve a useful purpose. Because of their relation to the hull form geometry and obvious physical meaning. They are helpful both to naval architects and to ships officers. In the future, they could be more effectively Chapter 1. Introduction 7 derived from dynamic criteria." Y.S. Yang [6] suggested that because so many of the factors influencing the capsizing of ships are essentially probabilistic in nature, it follows that stability assessment must ultimately be based on some form of risk analysis. Yang explained that the assessment of the risk that a given ship, with a given set of characteristics, will capsize (or reach some other unacceptable condition of stability) during its expected life, must in the end attempt to take account, in a rational and logical way, of the many varying parameters which influence that risk. He devised a practical scheme for the formal assessment of risk of capsize for a given ship. This might initially provide a basis for comparative assessment of ship safety against capsizing and also for exploring the influence of ship design parameters on survivability. Considering only the loss of lives and money as a result of marine accidents, it is easy to realize the importance of the preventing of capsizing of small boats. The following table shows a summary of marine accidents [7]. As seen from figure 1.1, the most important cause for casualties is operational mistakes. Year 1988 1989 Collision 35(3)! 45(5) Grounding 190(16) 161(14) Striking 11(2) 48(14) Sinking 29(21) 5(2) Foundering 14(8) 38(28) Capsizing 14(8) 12(4) Total 293(58) 309(67) Table 1.1: Statistics for Fishing Vessel Casualties in Canada Accidents at sea are rarely the result of a single event; and it is likely that safety assessment must eventually be based on techniques, such as fault tree analysis, which can model the possible sequences of events or malfunctions leading to an accident [8]. 1 Figures in parentheses indicate the total number of vessel lost Chapter 1. Introduction Environmental '50% Operational Mistakes 66.10% Unkown 11.60% Others 3.10% Equipment and structural failure 8.10% Vessel condition 3.60% Figure 1.1: Total number of casualties Kose [8] investigated the accidents of fishing vessels by using the Fault Tree analysis method. The Fault tree analysis is a logical and diagrammatic method used to evaluate the probability of an accident resulting from sequences and combinations of faults and failure events. A fault tree describes an accident - model which interprets the relation between the malfunction of components and observed symptoms. Thus the fault tree is useful for understanding logically the mode of occurrence of an accident. Further-more, given the failure probabilities of system components, the probability of a top event occurring can be calculated. More explanation of this method can be found in [8]. In this study, the following ranking was found: • Human Error • Shift of Cargo and Fish on deck • Taking Catch and Towing • Faulty design Chapter 1. Introduction 9 • Equipment error This ranking shows that human error is the most important cause of the loss of vessels. Major human errors are described as [8] : • Improper lookout • Misjudged effects (wind, current, speed) • Failure to ascertain position • Carelessness / inattention • Improper corrective procedures • Failure to determine wave properties • Crew asleep (present but asleep from fatigue) • Absorbed in secondary task • Watch keeper distracted by non-routine event 1.3 Literature R e v i e w The above findings are not very suprisings for a marine researcher. To solve this prob-lem, researchers are working on two different areas ; improvement of vessels seakeeping characteristics and heavy weather damage avoidance systems. The first one is mostly done by doing towing tank experiments or theoretical calculations. The second one is to install a system on board. In this study, we are interested in the development of an onboard system. Chapter 1. Introduction 10 In 1975, Lindemann and Nordenstr0m [9] developed a system for ship handling in rough weather. In this system, they measure the accelerations of the ship in six degrees of freedom and stresses at a cross section in the aft quarter length. The main concern of this project was the weather damage on a ship hull and equipment on board. In 1976, Hoffman [10] analysed the impact of seakeeping on ship operation and dis-cussed considering shipboard guidance as well as shore-based systems. He suggested using charts and ship - shore communications for routing in heavy weather. In 1979, a catalog for a heavy weather guidance system [11] was developed for FF-1052 class ships. The catalog provides the ship operator with hard copy, quantitative predictions as to how the ship responds in a seaway and some guidance for avoiding excessive ship motions or related events, such as slamming and deck wetness that may cause damage to the ship during heavy weather. This catalog relies on the operator to specify the height, period and directionality characteristics of the seaway. Hoffman [12, 13] published his results on the integration of shipboard and shore-based system for operation in heavy weather. In this research, they installed the system on board the LASH ITALIA. The system was used by officers on the bridge during heavy weather to evaluate trends of accelerations and bending stresses as well as to provide comparative levels of response evaluation for establishing a performance index for the vessel. A similar system designed specifically for Great Lake bulk carriers [14] was installed on a 1000 foot ship. Emphasis in this system was on the hull girder response including separation of the signal due to wave-induced and springing components and provision of separate guidance data for each of these responses. Details of the system are given in [14] In parallel with the above described works, two similar projects were underway in Norway [15, 16] and in Holland in a joint venture with Lloyds [17]. The experience Chapter 1. Introduction 11 gathered from these two projects are used to cover the extremely important areas of training and indoctrination of the on-board user to derive maximum benefits out of such a system. A different type of heavy weather vessel response control system for use in offshore construction was introduced in the early part of 1977 in the North Sea [18]. The system monitors roll, boom tip, absolute and relative motion. The predictive mode of the system provides the operator with the ability to simulate any condition that the vessel is likely to encounter during the operation without having to expose the ship to such hazards as losing the boom due to excessive angular displacement etc. The above-mentioned studies are mainly for big ships and their structural and equip-ment safety. None of them dealt specifically with stability of the ships. In 1982, a microcomputer based capsize alarm system was developed by Koyama [19]. In this system a pendulum was used to measure ship motions; mean period and root mean square of rolling were used to assess the safety of the vessel. As a result of an inadequate pendulum system, the results were not very reliable at high speeds. 1.4 Object ive There is probably no better source of assessment of the seriousness of the situation than the experienced captain on the bridge. However, just as the human "sensor" cannot detect the levels of all responses experienced by the ship, he cannot always know which maneuver to select to alleviate that situation. The monitoring, recording and predictions of response level provide more definite criteria as to when to act. The question of how to act is just as important as when to act. Since in most cases the ship is not provided with any data on its seakeeping characteristics and capabilities, the captain's actions follow his own logic, based ideally on experience with the particular type of ship, loading Chapter 1. Introduction 12 condition and weather condition. The options open to the captain are not always as clean cut as may be implied from the foregoing scenario. If , for example, the excessive roll is a result of quartering seas approaching the ship from the port side, the decision whether to seek a change by decreasing the angle, that is to more beam seas, or increasing the angle to somewhere close to following seas, is not so obvious since it depends to a large extent on the size of the ship, its speed of advance and wave properties. In such a case some guidance in the decision-making process could be useful. The aim of this study is to develop a reliable monitoring of vessels and environmental parameters playing an important role in the capsizing of vessels and establishment of corrective action to increase the reliability of the vessel or to avoid capsizing. There are two main considerations ; • The system should measure a minimum amount of data. In order to make this system practical and least costly, the equipment that already exists on board such as radar should be used. • The system should not interfere with the operation of the ship. This is specially important for fishing vessels. Since the vessel is their working environment, it is feared that anything interfering with fishing operation would be removed. It should also be noted that the system developed in this research is a monitoring and advisory system, not a control system. The aim of the system is to help the captain to decide on an appropriate course of action based on information derived from basic ship-based sensors. The suggested action also includes feedback regarding the conditions that makes the vessel unsafe. Chapter 2 A n Overview of a Monitoring and Advisory S y s t e m 2.1 Analysis of Capsizing M o d e s As a basis for deciding on the appropriate parameters and general layout of the monitoring and advisory system, capsizing modes and statistics are examined. Experimental and theoretical calculations show that capsizing modes can be divided into 6 categories [20, 21] 1. Low cycle resonance 2. Pure loss of stability 3. Resonant excitation 4. Broaching 5. Loss of transverse stability in beam to quartering seas 6. Impact excitation due to a steep wave Low cycle resonance can be recognized by the frequency of the roll motion. The essential prerequisite for this to occur is an encounter frequency (see Appendix B) nearly equal to the twice the roll natural frequency. Figure 2.2 shows this phenomenon in terms of roll angle and changes in stability (restoring moment) of the ship. The phenomenon appears to occur approximately in the following sequence [22]. As an initial condition, assume that the ship has an initial roll angle 6Q to port side (Figure 2.2), when the wave 13 Chapter 2. An Overview of a Monitoring and Advisory System 14 Wave Direction (b) Figure 2.1: Two critical conditions for a ship in following waves Port e, Roll Angle 0 Restoring Moment ~~ e, time Starboard 0i Figure 2.2: Fluctuations in ship stability e3 Chapter 2. An Overview of a Monitoring and Advisory System 15 trough is at midship (Figure 2.1 a.). While the ship is rolling to the starboard side, the crest of a wave moves to amidships (Figure 2.1 b.) , reducing the stability of the ship (Figure 2.3) and it takes a large roll (0a in Figure 2.2). This wave moves past the ship and a trough comes into the midship position (Figure 2.1 a.) while the ship is rolled over to port side, resulting in increased restoring moment (Figure 2.3). This causes the ship to roll back upright, acquiring a high roll angular velocity by the time it reaches the upright position. Another wave crest, meanwhile, moves into the amidship position, resulting in diminished stability once again as the ship starts rolling past upright and to the starboard side (62 in Figure 2.2). The ship then rolls over to the starboard against a diminished restoring moment (#3 and Restoring moment Figure 2.2). This process continues until either the ship capsizes or it moves out the wave group and the roll motion dies down. Pure loss of stabil i ty occurs when the righting arm (GZ) decreases to the point that there is not sufficient restoring energy in the vessel to upright itself. The essential prerequisite for this to occur is a ship speed nearly equal to the wave phase velocity so that the ship remains almost stationary relative to wave crest for a sufficient length of t ime to capsize (Figure 2.1 b. and Figure 2.3). This usually occurs in a following sea at high speed. The ship simply loses all stability when the crest of a high, steep wave moves into the amidship position. Broaching implies the loss of directional control. A vessel may broach in two ways. 1. When the vessel speed is close to the phase speed of the wave, it is forced to move along with the wave so that it becomes directionally very unstable and broaching may occur in a relatively short time span (eg. 50 to 150 seconds). 2. When the vessel is hit from astern by sufficiently steep waves in a successive manner, it can be yawed to such an extent that rudder action cannot rectify the situation before the next wave yaws the vessel even further. Chapter 2. An Overview of a Monitoring and Advisory System 16 E o S en I 2S CO o -25 -50 0 10 20 30 40 50 60 70 Roll Angle Figure 2.3: GZ curve of American Challenger for two extreme wave positions Resonant exc i tat ion refers to the condition where the vessel is excited at its natural roll frequency by beam to stern quartering seas (Figure 2.4), very large roll angles may result, if the wave amplitude is sufficiently large. Loss of transverse stabil ity in beam seas to quartering seas (Figure 2.4) refers to the same phenomenon as pure loss of stability. There is however a significant speed dependence for pure loss of stability, while loss of transverse stability may occur at any speed [21]. Impact exci tat ion due to steep, possibly breaking waves from a beam causing the vessel to heel to a large angle [21]. In addition to the above, two different modes can occur in a combined fashion, for example, broaching may be followed by pure loss of transverse stability, or resonant excitation may be followed by loss of transverse stability. As seen from the above capsizing modes, there are three critical conditions for inducing ship instabilities: Chapter 2. An Overview of a Monitoring and Advisory System 17 • wave speed equals ship speed in following seas • encounter frequency equal to twice the roll natural frequency • encounter frequency equals roll natural frequency. Equation 2.1 shows that encounter frequency is a function of wave frequencies, ship speed and the angle between ship and wave directions. Figure 2.4: Wave directions with respect to the ship 2.2 General Layout of the Monitoring and Advisory Sys tem The following parameters need to be measured to identify the capsizing modes explained above. Chapter 2. An Overview of a Monitoring and Advisory System 18 1. Wave properties : Encounter frequency is shown to be very important factor in ship capsizing. Encounter frequency is given by : w. U oje = cuw -— cos(^) (2-1) 9 where we : Encounter Frequency u>w: Wave frequency U : Ship speed <f> : Angle between wave direction and ship direction g : Acceleration due to gravity As seen from equation 2.1, encounter frequency is a function of wave frequency and direction. Therefore, these wave properties are needed to decide the reliability of a vessel. 2. Vessel speed : It is shown that capsizing modes 1, 2, 3, 4 have a strong dependency on ship speed, that is why, this information is necessary for the advisory system to make a decision. 3. Responses of vessel (heave, roll) The above mentioned capsizing modes are for heavy weather conditions. Unfortu-nately, this is not the case always, there are some examples in the statistics [7] that vessels were lost when the weather was relatively calm. Investigations [23] on these ac-cidents show that these accidents occured because of free surface effects, overloading or going from sea to river (density change). Therefore, the monitoring system should also Chapter 2. An Overview of a Monitoring and Advisory System 19 monitor static stability characteristics of the vessel. The following parameters need to be measured to monitor static stability. 1. Draft and tr im : These are used in static stability calculations to find the displace-ment of the ship. Since the body plan of the vessel is assumed to be known from the design stage, displacement of the ship can be calculated by integrating up to the draft at each station. 2. Levels of water and fuel tanks : This information is used to make free surface corrections. This correction is detailed in chapter 3. A general layout of the monitoring and advisory system is given in Figure 2.5. As seen from Figure 2.5, this system consists of three subsystems: • Measurement sub-system • Calculation sub-system • Advisory sub-system Measurement sub-sys tem is divided into 4 sub-systems: 1. Radar - Frame grabber : This sub-system provides the necessary information to the advisory sub-system for wave parameter calculations. This system uses the ship radar as an environment monitoring system and obtains radar images, then information about waves is extracted from these images. A detailed explanation of this procedure is contained in chapter 4. 2. Loran-C and ship's log: Provides position of the vessel with respect to ground so, speed of the vessel. Chapter 2. An Overview of a Monitoring and Advisory System 20 Measurement i Sub-system Calculation Sub-system Advisory Sub-system Decision Module Screen Display of Recommended Corrective Action Figure 2.5: General layout for monitoring and advisory system 3. Pressure transducers : Provide necessary information such as draft tr im and levels of each tank for static stability calculation. Pressure transducers can be used to measure draft and trim. An example of trans-ducers locations are shown in Figure 2.6. Chapter 2. An Overview of a Monitoring and Advisory System 21 • © m® \± • Pressure Transducers Figure 2.6: An example for Transducer locations Pressures need to be measured at least at four different locations. Three of those say on starboard side of the ship (as shown in Figure 2.6). The fourth one is port side of the amidship. Sensors 1,2 and 3 can be used to calculate static draft and trim. Sensors 2 and 4 may be used to find heeling angle. 4. Accelerometers :Accelerometers can be used to measure vessel responses for dy-namic stability of the vessel. Calculation sub-sys tem consists of 6 categories (see Figure 2.5). 1. Wave field estimator : The wave properties such as frequency and direction are found from radar images by using image processing techniques. A detailed expla-nation of this can be found in Chapter 4. 2. Ship speed estimator : Position of the ship at any time can be obtained from Loran-c and this can be used to estimate ship speed. Chapter 2. An Overview of a Monitoring and Advisory System 22 3. Hydrostatic particulars : These are physical parameters of the ship such as length beam, draft, curves of form which are known after construction. 4. Metacentric height : The position of the center of gravity is also necessary for static stability calculations. Estimation of metacentric height is explained in detail in section 3.3. 5. Restoring arm (GZ) curve : In order to decide initial stability of the vessel, this curve is needed. International Maritime Organization (IMO) and most countries have some rules regarding area under this curve to be met. This concept will be explained in Chapter 3. 6. Roll dynamics estimator: There are three different calculations in this section : • To calculate the probability of the roll angle exceeding a limit value in a certain time • Expected maximum roll angle • Natural roll frequencies. Detailed explanations of these three method is given in chapter 5. 7. Heave motion : This can be used to estimate wave height. Explanation for this methodology can be found in chapter 5. Advisory S y s t e m (also known as Decision Module) uses the data from calculations and applies rule of thumb in order to identify corrective action that should be taken by the captain of the vessel. A general layout of Decision Module is given in Figure 2.7 Chapter 2. An Overview of a Monitoring and Advisory System. 23 Figure 2.7: General layout of Decision Module Suggestions : Display the suggested action by a fuzzy expert system on a monitor or alarm from a speaker. Chapter 3 Static Stability 3.1 Background Although, stability criteria for a vessel in relatively calm waters (rolling angle less then 15°) are well established, still accidents occur in these conditions. For example, an accident happened in British Columbia in July 1992. The skipper of the fishing vessel said that I feel disappointed it happened in my own back yard. I have been fishing these waters 43 years and I have never seen anything like it. . . . We were just coming through the narrows and the catch shifted. She rolled on us really slowly. . . . . The Province newspaper July 1992. Investigation on this accident by Marine Casualty Investigation Division shows that the vessel did not have enough stability to upright herself even under small external forces. This was caused by the free surface effects of the fuel tanks and liquid in the holds. Even though captain knew the effects of free surface on ships stability, he had no way of measuring or monitoring water levels in the tanks. If he had had this information, this accident may have been prevented. Another interesting example was told by Ian Bayly of Transport Canada. This was during one of the training courses for captains of fishing vessels. An Instructor was teaching the static stability of the vessels, and explaining the 24 Chapter 3. Static Stability 25 importance of GM (metacentric height), after 10 minutes, a captain stood up and said that you are talking about GM, but I have a Caterpillar engine in my vessel, what am I doing here ? Unfortunately, there are more examples like this in the statistics.(see [7]). That is why, it is decided to include the static stability monitoring part in this system. In order to calculate the static stability, the draft, trim and body plan of the vessel have to be known. 3.2 Stat ic Stabil i ty Criteria Consider a ship floating upright on the surface of a motionless water. In order to be at rest or in equilibrium, there must be no unbalanced forces or moments acting on it. There are two forces that maintain this equilibrium: the force of gravity and force of buoyancy. When a ship is at rest, these two forces are acting in the same vertical line, and in order for the ship to float in equilibrium, they must be exactly equal numerically as well as opposite in direction. When the ship is heeled by an external inclining force, the center of buoyancy is moved from the centerline plane of the ship. There will usually be a separation between the lines of action of the force of gravity and the force of buoyancy. This separation of lines of action of the equal forces, which act in opposite directions, forms a couple whose magnitude is equal to the product of one of these forces ( displacement) and distance separating them (GZ). In Figure 3.1 (a), where this moment tends to restore the ship to the upright position, the moment is called a positive righting moment and the perpendicular distance between the two lines of action is the righting arm (GZ). Suppose that the center of gravity is moved upward to such a position that when the ship is heeled slightly, the buoyancy force acts in a line through the center of gravity. In Chapter 3. Static Stability 26 the new position, there are no unbalanced forces, or in other words, the ship has a zero moment arm and a zero moment. In figure 3.1 (b), the ship is in neutral equilibrium, with both righting moment and the righting arm equal to zero. If one moves the center of gravity even higher, as in Figure 3.1 (c), the separation between the lines of action of the two forces as the ship inclines slightly, is in the opposite direction from that in Figure 3.1 (a). In this case, the moment does not act in the direction that will restore the ship to the upright, but rather will cause it to incline further (negative stability). Stable M : Metacenter G : Center of gravity B : Center of bouyancy Unstable Figure 3.1: Possible stability conditions Chapter 3. Static Stability 27 The most satisfactory means of presenting a complete picture of stability is a plot of righting arm with its angle of inclination which is called a static stability curve. Such a curve may be used to determine several important characteristics which are: • The righting arm at any inclination • Metacentric height (GM) (see Appendix I) • The angle of maximum righting moment • The range of stability • Dynamic stability (related to the area under the GZ curve). The righting arm moment equals the righting lever times displacement. An example GZ curve is given in Figure 3.2 where (/)c is the angle of deck edge immersion. The area under the curve represents the ability of the ship to absorb energy imparted to it by wind or any other external force. The recommendations of the International Maritime organization (IMO) with regard to intact stability standards are: • Area under GZ curve up to 30° should not be less than 0.05 rad-m • Area under GZ curve between 30° and 40° should not be less then 0.030 rad-m • Area under GZ curve up to 40° should not be less then 0.09 rad-m • Minimum initial GM should not be less then 0.35 m • The maximum righting lever should occur at an angle of heel equal to or greater than 30°. Chapter 3. Static Stability 28 * (rad) Figure 3.2: An example of GZ curve In order to calculate the GZ curve, the position of center of gravity, body plan of the vessel and displacement need to be known. It is assumed that body plan of the vessel is given. The displacement can be found from draft and trim measurements and the body plan of the vessel. The only unknown to estimate the GZ curve is the location of the center of gravity. 3.3 Est imat ion of Metacentr ic Height Metacentric height (GM) is estimated by using two different methods; 3.3.1 Es t imat ing the Coefficient of GZ curve In order to identify the stability conditions of the vessel defined by the GZ curve, the location of the center of gravity must be determined. The ship's rudder can be used to create free rolling by turning it to one side and back [24, 25]. The equation of the motion for a ship freely rolling may be written as : Chapter 3. Static Stability 29 where / : DJ> (I + A44)(p + D4> + R<f> = 0 Mass moment of inertia Added mass moment of inertia : Damping moment (3.1) R(j> : Restoring moment rearranging equation 3.1, one obtains Rcf) = _ ( / + AAi)'<j> - Dj> (3.2) In order to decide the general form of the GZ curve, polynomial of different orders are fitted to some known GZ curves. The 9th order polynomial is found to be the best fit to different GZ curves (Figure 3.3). tsi o 0.0 0.2 0.4 0.6 Roll Angle (Rad) 0.8 1.0 Figure 3.3: 9th order polynomial fit then, the general form for the GZ curve is assumed as: R(j) = a0<f> + a-L<p2 + a2(f>3 + a3<f)4 + a 4 ^ 5 + aS(f)6 + a6(f>7 + a7(pa + a%<f>9 (3.3) Chapter 3. Static Stability 30 Since the equation of motion must be satisfied at any point on the rolling curve, there are more equations than unknowns. These equations can be solved by using a least square method. The above explained method is applied to a fishing boat studied at UBC. For this calculation, a single chine model was used. Hydrostatic particulars and body plan of the model are given below. Figure 3.4: Body plan of single chine vessel Length (LBP) 1.805 m Displacement 115.4 kg Beam 0.539 m Block Coeff. (CB) 0.531 Depth 0.352 KM 0.3 m Draft 0.246 GM 0.05 m The damping coefficient was estimated by using Himeno's method [26]. In this Chapter 3. Static Stability- Si method, total roll damping is estimated as the sum of equivalent linear damping co-efficients. That is : where BR : Bp : BE : BL: Bw '• BBK BR = Bp + BE + BL + Bw + BBK Equivalent linear roll damping Frictional damping Eddy damping Lift damping Wave damping Bilge keel damping (3.4) a more detailed explanation of this method can be found in [26]. The following GZ curve was found using this method. As seen from Figure 3.5, for small angles, the fit is good, but it is not good for large angles as there is very limited information at large angles. Therefore, this estimated curve is used to calculate GM only. Since GZ = GM sin(< )^ (for small angles), GM can be found from this curve. By combining this GM information and the informations given (body plan, draft, trim), a better estimation of the GZ curve is found [24, 27] (see Figure 3.6). Chapter 3. Static Stability 32 0.50 0.38 a 0.25 -0 . 1 3 -o.oo ----GfU #4 j /' / , i /' i i ! \ i j EstMnatedj '. \ \ , i . i . i .\ i \ -0 .2 O.O 0 .2 0 .4 0 .6 0 .8 1.0 1.2 1.4 Rol l A n g l e Figure 3.5: Estimated GZ for single chine vessel Chapter 3. Static Stability 33 IVl CD 0 .12 0.11 0 . 0 9 0 . 0 8 0 . 0 7 0 . 0 5 0 . 0 4 0 . 0 3 0.01 O.OO | G M #1 I 0?^~~^~>|_ ! l . . y £ L l X J. 1 - %r r i - - \ - - T - - - -• V ^ • !~ Jr.sTirr>ateri \ I_ o.o 0 . 2 0 .4 0 . 6 0 . 8 1.0 a 0.5 0.4 0.3 0.2 0.1 O.O -O.I i 1 i I I I t j | G M #41 J-^5**—"j***-^^ i i ^s^ \ \ ! ~ 1 " Es t ima ted • • i i i i i i i : . i . i , i , i , i , i . i . O.O 0.1 0 .3 0.4 0.6 0.8 0.9 1.1 1.2 Roll Angle Figure 3.6: Final estimation of GZ curve Then, by using Canadian Coast Guard rules (or International Maritime Organiza-tion's rules), a decisions about the stability (safety) of the vessel can be made. Chapter 3. Static Stability 34 3.3.2 Spectral Analysis It is assumed that the mean period of roll decay curve is very close to the natural frequency. Then, if the mean period of roll is known, the location of the center of gravity can be obtained by using the following equation. GM = (74 + AAi)ul P9& (3.5) where (I4 + A44) : Virtual mass moment of inertia u}n : Natural frequency A : Displacement Thus, the accuracy to which GM can be determined is dependent upon the knowledge of (74 + ^44) and A as well a s u n . 2 0 •5 10 15 0 -10 25 50 GM#1 75 10O 125 time (sec) Figure 3.7: Roll decay curve for GM # 1 Chapter 3. Static Stability 35 20 £15 < O10 5 0 -5 -10 -15 0 ' » . . " t / V V v s l . . . . i 25 GM#4 i 50 > i . . . . i 75 100 time (sec) Figure 3.8: Roll decay curve for GM # 4 This method is used to estimate the GM of the single chine vessel mentioned above. Free roll decay data is used to find the natural frequencies of the vessel. Figures 3.7 and 3.8 show roll decay curves of the vessel for two different loading conditions [28]. The following equation is used to estimate (I4 + A44) [29, 30]. He Hi, i-^r = f[CbCu + 1.10c(l - c6)(-f - 2.0) + - | ] B2 where f = 0.177 - 0.2 for fishing vessels CB '• Block coefficients Cu : Upper deck area coefficient Cu = Area / (Length x Beam) He : Effective depth of the ship structures He = D + (A / LBP) (3.6) Chapter 3. Static Stability D : Molded depth A : Projected lateral area of superstructures LBP : Length between perpendicular (see Appendix I) T : Draft (see Appendix I) B : Beam From the above equation, the value of kxx for the heavy condition is found as; kxx = 0.36685 (3.7) The Table 3.3.2 shows the results found from this method. Original Estimated (in) (in) GM # 1 0.256 0.286 GM # 4 1.969 1.78 Table 3.1: Comparison between original and estimated GM values An error analysis is done to check dependence of the estimation of GM on kxx, A and U)n. In the first step, kxx is increased 10%, this affected estimation of GM « 10%, which corresponds 0.0078m (GM # 1 ) and 0.065 (GM # 4 ) . Then, un is decreased 10%, this corresponds 10% correction to the estimation of GM. By assuming that the above errors all act in the same direction, the overall error in the estimation of GM will be less than 20%. This estimate is on the conservative side, since at times errors may act in opposite directions, thus in practice the prediction errors will be between 5 and 20%. This result can be improved by using a better method to estimate kxx such as experiments and keeping a log of weight added to the vessel. Chapter 4 Measurements of Wave Propert ies 4.1 Introduct ion Measuring wave properties has been a challenge for researchers for some times. There have been some at tempts to solve this problem. Most of these studies focused on three different areas: 1. Shipboard Observation 2. Floating buoy 3. Remote sensing Tucker[1956] developed an instrument that measures waves from a ship. In principle, the instrument measures the height of the water surface relative to a point on the ship's hull and adds this to the height of the point relative to an imaginary reference surface, thus giving the height of the water surface independent of the position of the ship. While in such an instrument there is a frequency attenuation effect for the shorter wavelengths, the spectrum can be partially corrected for the error introduced. Certain of the British weather ships have been fitted with Tucker meters, and wave height records have been collected on a routine basis while on station, although these strip chart records have not been routinely used to calculate the point spectra. Deleonibus and et al. [31] observed wave height spectra from the USNS Kane with a semiportable bow-mounted wave system. Distance from the sea surface to a transducer 37 Chapter 4. Measurements of Wave Properties 38 at the bow of the Kane was measured with an infrared height sensor. Displacement of the bow associated with surface wave motion was obtained with a static pressure measuring device. Wave height spectra were estimated by cross-spectrum analysis of signals from these two devices. Voronovich and at al. [32] investigated the possibility of using a wire wave-gauge to measure wave parameters from a ship at drift. Waves were measured by a resistance string wave recorder whose sensor was hung out at the bow or stern of the ship. The effect of rolling was taken into account by synchronous recording for an accelerometer that records the vertical acceleration of the suspension point for the wave gauge. An alternative approach has been to fit a buoy with an inertial measurement system. The quantities recorded are wave slope in two perpendicular, known compass directions and surface displacement (by double integration of the measured vertical acceleration). From records of these quantities against time, it is possible to estimate the distribution of variance with respect to direction in any frequency band [Longuet-Higgins, Cartwright and Smith 1963]. If assumptions are made as to the nature of the spreading function, it is possible to generate a simplified directional spectrum estimate from these data. This technique has been used primarily for special situations such as full scale trials and no large collections are available for more general application. The use of HF radar to measure various parameters characterizing sea state was suggested by Crombie [33] over four decades ago. He correctly deduced from measured echo spectra that the dominant (first order) return was explained by the simple Bragg or diffraction-grating mechanism. Since then, considerable interest has been shown in the application of remote sensing techniques to the measurement of ocean waves and currents. These studies have largely dealt with the use of three forms of radar systems: SAR (synthetic aperture radar), SLAR (side-looking aperture radar), and HF (high frequency Chapter 4. Measurements of Wave Properties 39 radar). Because of the size of the antennas required, HF radar has only been deployed as a land-based system. SAR and SLAR systems, however have been successfully used in aircraft and orbiting satellites, thus allowing large areas of the oceans to be scanned. In addition to these widely reported remote sensing techniques, some limited interest has also been shown in the use of conventional marine radar imaging for the collection of the ocean data. Ijima and at al. [34] and Wright [35] were among the first to report the use of such radar for imaging ocean waves. Oudshoorn [36], Willis and Beaumont [37], Evmenov et al. [38] and Mattie and Harris [39] have also reported wave images obtained by radar. These researchers visually inspected the radar images to obtain estimates of the mean wave direction, wave length and period. Recently, it has been proposed that digitized pictures of ship radar images of ocean waves be processed in order to obtain the spectral characteristics of the surface wave field. The corresponding scheme (backscattered microwave power —• light intensity of the radar screen —» gray level density on a film —* numerical gray level —> two-dimensional Fourier transform) is considered by Hoogeboom and Rosenthal [40]. The imaging takes place owing to the modulation of the backscattered microwave power by the long ocean waves through short wavelength Bragg-scattering waves as well as effects of shadowing by the wave crests (important at low grazing angles). The preliminary studies [41] show by calculating two-dimensional power spectra that the spectral properties of such images are similar to those obtained from the conventional pitch- and-roll buoy measurements. The spectral value of each wave number seems to be a well defined function of the corresponding value of the directional surface wave spectrum, depending smoothly on the environmental and radar parameters. Chapter 4. Measurements of Wave Properties 40 Hence two-dimensional power spectra obtained by processing ship radar images con-tain useful information about the wave directionality. But, uncertainty of 180° (am-biguity) remains in the determination of the wave propagation direction. It is hardly possible to remove this ambiguity simply by looking at the image of an irregular wave field. This disadvantage is usually overcome by assuming that waves travel inshore [42] or downwind which require additional information and leaves aside the possible detec-tion of upwind traveling [43], wave reflection from obstacles [44], or backscatter caused by bottom irregularities [45]. In the last two cases the power spectra of the main and reflected wave trains usually occupy the same region of the wave number plane and hence remain indistinguishable. A major problem exists in the interpretation of two dimensional wave number spectra, whether they are obtained from ship radar or any other imaging system, since 180° directional ambiguity exists in the resulting spectra. For relatively simple wave spectra, this ambiguity can be removed by assuming that the mean wave direction will be closely related to the wind direction. For more complex sea conditions, where there may be waves propagating at large angles to the wind, or if the wind direction is unknown, such a method is no longer applicable. Atanosov and et al. [46] suggested a possible solution of the ambiguity problem for spatial power spectra of arbitrary wave fields by processing two images in the spectral do-main, the second obtained shortly after the first one, making use of the known dispersion relation. This ambiguity appears if the "frozen" surface at one specific time is used for the derivation of the power spectrum. By using two successive images it is possible to gen-erate unique two dimensional power spectra, which may be useful in many situations to determine the actual direction of wave propagation. Chapter 4. Measurements of Wave Properties 41 Young et al. [47] developed an analysis technique for a full time series of radar images; each taken at successive revolution of the radar antenna. They concluded that the introduction of the third time dimension in the analysis has the advantages of providing information on the wave phase speed and hence the magnitude and direction of the near surface currents, removing the directional ambiguity inherent in the two dimensional analysis and providing an extremely high signal to noise ratio. Ziemer and Rosental [48] looked at the transfer function from the wave field to the PPI-image. They investigated behavior of the image transfer function by measurement and computer simulations. 4.2 Analysis of Radar Images The fact that marine radars give returns from ocean waves has been known for many years. Indeed, such returns (sea clutter) can pose serious problem in marine navigation [49], as they can obscure echoes from small objects such as buoys. In fact, special sea clutter controls are fitted to most commercial radar systems to facilitate the suppression of the returns from waves. Figure 4.1 shows a photograph of the radar screen (plan position indicator or PPI) in which wave images are clearly visible. Interpretation of coherent radar signals often involves the calculation of a power spectrum or a periodogram that describes the frequency content of the data. The con-ventional Fourier approach, based on the work of Wiener and of Blackman and Tukey [50], relates the autocorrelation function of a signal and its power spectrum through the Fourier transform. Cooley and Tukey popularized the Fourier approach with the com-putationally efficient fast Fourier transform (FFT) which has dominated the analysis of radar data. Chapter 4. Measurements of Wave Properties 42 4.3 Data collection Image data used in this study was collected by M. Allingham [51] and J. Buckley [52], throughout the Grand Banks ERS-1 SAR Wave Spectrum Validation Experiment cruise [53]. Figure 4.1: An example of radar screen Sea surface radar backscatter data was collected by an Integrad RSC-20 radar digitizer and scan converter connected to a Racal-Decca BT362 standard ship's radar. The radar unit transmitted either 0.05/xs or 0.25/is long pulses at a peak power of 25 kW and a frequency of 9.80 GHz. The antenna rotation was approximately 25 rotations per minute at a pulse repetition frequency of 1200 [52]. Chapter 4. Measurements of Wave Properties 43 4.3.1 Applicat ion of Fourier Analysis to Image Spectra Young et al.[1983] present a concise explanation of how a time series of two dimensional maps of sea surface height (or radar backscatter) can be transformed into a directionally unambiguous wave spectrum (or radar images spectrum). M. Allingham and J. Buckley [51, 52] extracted twenty-four sub-arrays of data at 15° intervals around the ship Hudson. Each 'data cube' had dimensions of 64 by 64 pixel by 16 images, corresponding to a physical dimension of 1327 by 1327 m. The center of each sub-array lay at a distance of 64 pixels (1327 m) from the center of the main array ( the ship Hudson). This distance of 64 pixels corresponds to a depression angle of about 0.7°. Then, each array was passed to a three dimensional fast Fourier transform (FFT) routine. The output array from the F F T was then formed into a periodogram estimate of the radar determined wave spectrum by adding the squares of the real and complex transform coefficients and then summing over the positive frequency ranges (following Equation B . l l ) . More detailed explanation of this method can be found in [51]. In Figures 4.2,4.3,4.4, an example image , its spectrum and contour plot found from 3-D F F T developed by M. Allingham [51] and J. Buckley [52] are shown. In the figures, peaks show the dominant wave frequencies and wave direction is from small peak to big peak in Figure 4.2. Chapter 4. Measurements of Wave Properties 44 Figure 4.2: Radar image from 1130 November 23 Figure 4.3: Spectrum of Radar image from 1130 November 23 (FFT) Chapter 4. Measurements of Wave Properties 45 -0.10 -0.08 -0.07 -0.05 -0.03 -0.02 0.00 0.02 0.03 0.05 0.07 0.08 0.10 0.10 0.08 0.07 0.05 0.03 0.02 0.00 -o.o: -o.o: -o.o: -o.o: -O.Of -O.K -0.10 -0.08 -0.07 -0.05 -0.03 -0.02 0.00 0.02 0.03 0.05 0.07 0.08 0.10 Figure 4.4: Contour plot of Radar image from 1130 November 23 (FFT) In Figures 4.2 and 4.4, an example image , its spectrum calculated by a 3 - D. F F T technique based on Young et al [47] developed by Allingham and Buckley [51, 52] is shown. In the figures, peaks show the dominant wave frequencies and wave direction is from small peak to big peak. Calculation of this spectrum required approximately 12 minutes on an HP 720 work-station and is therefore computationally too intensive to be operationally useful for a vessel at sea (see Appendix F) . In view of the need for the wave parameters in 30 to 60 seconds, for input into the intelligent advisory system, two alternative techniques have been developed. The boxing technique is based on fitting a rectangle to the wave pattern on the image, while the thinning technique derives the wave properties from a skeleton image of the radar. Chapter 4. Measurements of Wave Properties 46 4.3.2 Boxing Technique The stages in the boxing technique include those shown in Figure 4.5, Preprocessing find a white point Fit a rectangle Count number of white points Figure 4.5: Steps for Boxing Technique 1. Preprocess ing : Original images used in this analysis are in gray scale. In order to facilitate segmentation of the wave crests, a gray scale tophat process is applied to the original image in order to enhance the contrast between the crest and the trough and to merge the wave segments along the wave axis. The Tophat process consists of two different steps : Dilation and Erosion. Dilation is an operation which adds pixels to the boundary. It increases the size of the object. Erosion removes pixels from boundary. In Chapter 4. Measurements of Wave Properties 47 general, erosion and dilation are not inverses of one another. Therefore, using erosion after dilation smoothes away imperfections in wave crest boundaries. The crests are segmented by threshold, based on a statistical analysis of the gray-level histogram of the preprocessed radar (figure 4.6). The histogram is bi-modal with modes corresponding to the crests and troughs of the wave, and the threshold is selected to minimize the within-mode/between-mode variance ratio. Figure 4.6: An example preprocessed image Chapter 4. Measurements of Wave Properties 48 2. Wave Crest Orientation : In order to find the wave orientation a white point at the border of a wave crest (binary configuration) is selected. Next, the width of the configuration is checked, and a horizontal rectangular box (11 x 50 pixels) is established around the pattern, and the number of white points in this rectangle are counted. This process is repeated as the box is rotated by 5 degree increments through an angle of 180°. The fullness of the box is used to assess the goodness of the fit between the box and the wave, and the box orientation corresponding to the best-fit between the box and the wave is selected as the wave orientation. The boxing technique is carried out at four locations in each image and the average orientation is selected. Figure 4.7: Boxing Technique 3. Wave mot ion : The wave propagation direction is found by estimating the shift between a known wave in two consecutive images. In this method, a wave pattern ( a l l x 50 window) from the first image is convolved with the second image along a line normal to the wave orientation. In this process, fit between actual image points are considered rather than comparing the fit of the chosen rectangle. An error function calculated in least squares sense is given as, n Error Function = £] (x i - Xj)2 (4.1) l Chapter 4. Measurements of Wave Properties where X{ and Xj are pixel values in the first image and second image, respectively. The shift in window position between successive images that corresponds to the imum error gives the wave motion direction. \ I Wave Direction V •» \ \ * . ^ \ ^ « * ^ k * *<< * \ f^ V •J s 1 1 I < ; v " ^ <i ' " 3y "/ > • X \ • * * • : : * Figure 4.8: Wave direction calculated using boxing technique. Chapter 4. Measurements of Wave Properties 50 4. Wave Frequency : The unprocessed gray-level radar image is used to calculate the frequency of the dominant wave. Wave frequencies are found based on the selected wave orientation, the image points along a line that is orthogonal to the wave orientation are extracted from the image for spectral analysis. The FFT technique is used to calculate the wave numbers . Then frequencies are found by using dispersion relation. a; = y/gktanh(kd) (4.2) where k is wave number and d is water depth. The success of the boxing technique depends on the initial placement of the rectangu-lar box. The radar images tend to have limited regions in which the wave directions are obvious since there is considerable noise in the images and much of the wave information is obscured. The boxing technique works well if the box is placed in the vicinity of an obvious wave, although reliable automatic placement of the box remains as a problem. To improve the above procedure, a more global thinning technique has been developed. 4 .3 .3 Thinning Technique The stages involved in the thinning technique include (Figure 4.9), 1. Preprocess ing : This process is as described for the boxing technique. 2. Wave Crest Orientation : The binary radar image is transformed by the thin-ning process. In this process, boundary pixels are removed from the wave patterns whilst retaining connectivity. Thinning stops when no further pixels can be removed without causing loss of continuity. Consequently, the thinning algorithm needs to traverse the en-tire object boundary, marking pixels which are candidates for removal and remembering how many times each has been visited. Those candidates which have been visited only once are then removed. This process continues until only the skeleton or spine of each Chapter 4. Measurements of Wave Properties 51 object remains. Preprocessing f Convolve J J f Tophat V ^ ' (Threshold^) 'r ( Thinning ) V f segment j " ( Cleanup J (Coordinates) " r Line fit J 1 (orientation) Dilate Erode Figure 4.9: Steps for thinning technique The thinned image for the radar image of Figure 4.8 is illustrated in Figure 4.11. The skeletons run along the length of the objects corresponding to waves. Since there is considerable cross-linkage between waves in the binary image because of noise, shorter skeleton segments are evident in a direction normal to the wave. The skeleton of the entire radar image is then decomposed into distinct unconnected segments by removing all branch-points on the skeleton and all the small segments (less than 20 pixels) are removed. These individual segments are assessed in order to determine the Chapter 4. Measurements of Wave Properties 52 dominant wave orientation. The complexity of each segment is considered by measuring the curvature of the individual segments. Each segment that is sufficiently linear is fit with a a straight-line using the points on the segment. The following images (Figures 4.10, 4.11, 4.12) show the intermediate steps for the same radar image for the thinning technique . Figure 4.10: An example image after thresholding Chapter 4. Measurements of Wave Properties 53 Figure 4.11: An example image after thinning and segmentation Chapter 4. Measurements of Wave Properties 54 Figure 4.12: An example image after the cleaning process Chapter 4. Measurements of Wave Properties 55 Figure 4.13: An example wave segments with original image As seen from Figure 4.13, the lines selected correspond to the wave troughs not wave crests. In order to find wave crest, we needed to get rid of the center white blob caused by the ship, this increased the processing time. But finding wave troughs solved this problem completely. Chapter 4. Measurements of Wave Properties 56 7 6 -5 -2 4 o U Wi—iBi* iBiBi II™I—I" I M I " I " I " I I™I—I"I"I"I i—i—wi I" I" I w w i w w i — i I O I O O I O Q l Q Q « ) Q i n Q I O O l O O ! f l O t f ) g i i ) O I O O l O O l O Q « ) Q l O O , O O l O ^ ^ w r v i ( O P i ^ ^ f u 5 i f l ? < 5 i N r s « ) ( x ) ( > o - 0 0 « - T - ^ ( N i P 3 t o ^ ? i i o i i 5 ^ 5 f l r s N Orientation Angle (deg) Figure 4.14: A histogram of wave orientation As seen from Figure 4.14, a histogram of wave orientations is maintained, and the goodness-of-fit and the length of each segment are used to bias the histogram entries. The wave orientation corresponding to the peak in the histogram is selected as the dominant wave direction. 3 .Wave M o t i o n : Once the dominant wave orientation for a set of successive images has been deter-mined, a small region of an image in the vicinity of the dominant waves is compared with neighboring regions in successive image. This process is illustrated in Figure 4.15. Since the wave orientation is known from stage 2, comparisons between the initial image region and regions in successive images are restricted to shifts along the line normal to the wave orientation. The least-squares error between the regions is used as the basis for selecting the wave direction. Chapter 4. Measurements of Wave Properties 57 Area selected (10x50) First Image Convolution area (10 x 90) Second Image Figure 4.15: Finding wave direction 4.Finding the Wave Frequency : This step is as described for the boxing technique. 4.3.4 Comparison of Image Process ing Techniques It is important to clarify what each type of spectrum represents. A two dimensional ocean surface elevation spectrum (wave spectrum) contains information regarding the frequency / wave number distribution of the ocean wave potential energy and its direction of propagation. The analysis of pitch/roll/heave buoy measurements give such a two dimensional wave spectrum. On the other hand, a radar image spectrum found from F F T , boxing or thinning techniques is a two dimensional spectrum of the radar image of the sea surface, not a spectrum of the actual sea surface energy. Radar image spectra represent the square of the backscattered radar energy. Chapter 4. Measurements of Wave Properties 58 Thirty radar image sequences are used to compare these techniques. The list of these images can be found in appendix E. As seen from Table 4.3.4, the frequencies and direction found from the thinning tech-nique are very close to those found from conventional methods such as Fourier Transform (FFT) , wave buoy (Wavec) and satellite (ERS-1). Table 4.3.4 also shows the required computation time. Fourier transforms are computationally expensive methods. For ex-ample, analysing an image data (usually 512 x 512 X 16 ) can take about an hour, the F F T based method developed by AUingham and Buckley takes about 12 min to find wave direction and frequencies. But these methods are not fast enough to use in a monitoring system that is developed in this study. The two techniques developed take about 30 - 60 seconds. Time 1112 Nov. 12 1128 Nov. 20 1130 Nov. 23 Computation Time Wavec 1 Freq. (Hz) 0.084 0.110 0.168 0.094 0.139 0.120 -Dir. (Deg.) 201 159 80 215 160 71 -ERS-1 Freq. (Hz) -0.12 0.084 0.107 0.108 -Dir. (Deg.) -86 244 122 76 -FFT Freq. (Hz) 0.067 0.106 0.124 0.083 0.110 0.107 12 min2 Dir. (Deg.) 180 157 71 225 139 43 Thinning Freq. (Hz) 0.070 0.108 0.110 0.811 0.120 0.110 30- 60 Dir. (Deg.) 175 160 70 215 120 35 sec Table 4.1: An comparison of the present methods with other conventional methods 1 Wavec , ERS-1 and FFT values are taken from [51] 2This time is for the FFT method explained in [51], [52], other methods would take about an hour Chapter 4. Measurements of Wave Properties 59 0.14 0.12 0.09 I 0.07 0.05 0.02 0.00 10% 0.00 0.02 0.05 0.07 0.09 0.12 0.14 FFT Figure 4.16: Difference in calculation of frequencies between F F T and Present method 4.3.5 Conclusion of Measurement of Wave Propert ies In this chapter, as a part of the monitoring system, two new techniques (boxing and thinning techniques were developed to find wave direction and frequencies from ship radar. Although the boxing technique is easy to implement, it has limitation of being Chapter 4. Measurements of Wave Properties 60 local. That is, the accuracy of the method depends on the selected position of the box. The thinning technique is more global and captures more of the overall variations in the wave patterns. The histogram found from the thinning technique is suitable for the Fuzzy Expert System used in this study. The peaks of the histogram found from the thinning technique are used as membership functions of wave parameters The primary advantages the boxing and thinning techniques have over 3-D F F T is the reduced computational time of operation. Finding wave parameters with the 3-D FFT method can take about 12 min3 on an HP 720 work station. But the techniques developed take about 30-60 seconds on a 486-50 based PC. 3If the FFT method developed by Allingham and Buckley is used, otherwise it would take about an hour Chapter 5 Ship Dynamics 5.1 Est imat ion of Wave Height This section discusses wave height calculations for usage in the monitoring and Advisory system. There are three common ways of estimating wave height from a ship. 1. Visual observation 2. Ship-shore communication 3. Onboard system 1. Visual observation : The most basic and ancient source of data on waves is the visual observations made on board ships. The accuracy of these observations may vary from officer to officer depending on his relative experience. Observers tend to underestimate the heights of following seas and overestimate head seas because of the difference in ship behavior, and the periods reported are often influenced by the ship's natural pitch period [13]. Although this method of observation is subjective and crude, when data are col-lected over a wide area by radio and redistributed to all participating ships, the data do have a limited usefulness in establishing seastate conditions and in short range storm avoidance. 61 Chapter 5. Ship Dynamics 62 2. Ship-shore communications : The transmission of weather conditions and gale warning bulletins, using conven-tional communication channels available on board have, for many years, been major means of advising the captain of the expected weather conditions ahead. A typical example of a facsimile recorder output, giving wave height contours over the Atlantic, is shown in Figure 5.1. Though the picture is of a rather general nature, it does indicate expected wave heights of a storm advance. Such information is, in most cases, better than none; however it can also lead to wrong interpretations since the chart is limited to the wave height and does not provide any information with regard to the period of the wave, which is a major factor affecting the response of the ship. In spite of the explained disadvantages, this informations can be useful for routing or avoiding storm. Figure 5.1: An facsimile recorder output printed onboard Lash Italia Chapter 5. Ship Dynamics 63 3. Onboard systems The use of the ship itself, as a means of measuring the encountered wave system, is not necessarily new and the Ship Board Wave Recorder (SBWR), otherwise known as Tucker wave meter [54], has been in use for the past 30 years. The data obtained from these ships, after some additional processing, constitutes the backbone of design wave data available today [13]. A similar approach for using the ship responses as a means of determining the encoun-tered wave system is by way of utilizing the response spectra obtained from measurements on board and the response amplitude operator (RAO) of that specific response to obtain the wave spectra. The method is refered to as a "reverse procedure". The response of a ship at 0 speed to a given sea spectrum and heading is: RES2 = T I RA02(u;,x)S((uJ,Xi)dxcLj (5.1) Jo J% where RAO (w, x) is the response amplitude operator as a function of frequency (a;) and heading (%) to the component wave, and S^(uJ,Xi) is the spectral ordinate as a function of frequency and component direction. At a specific frequency, equation 5.1 reduces to : RES2 = / RA02(u;, X ) ^ ( u ; , * > f r (5.2) where RES is the response of the vessel. The short-crested spectrum may be repre-sented as the product of a point spectrum and a spreading function SF(%i): St(uj,Xi) = Si(u,)SF(xi) (5.3) If the above representation of a short-crested spectra is assumed, equation 5.2 can be written as: Chapter 5. Ship Dynamics 64 R E S 2 H = / RA02(u;, x)St(v)SF(xi)dX (5.4) Jx Since the point spectrum is independent of %, the expression becomes RES2(u,) = S((u) f RA02(a,, X)SF(Xi)dX (5.5) Jx Solving for the spectral ordinate : S i M ~ SxRAO\u,x)SF(Xi)dx ^ The derivation for the forward speed case is similar, with equation 5.6, becoming : S ( ( a , ) " 1JxRAO\.,X)SF(x,)dX ( 5 7 ) where J = (l-Wcos(X)u)e/g)' (5.8) LU2V cos(x) UJ. = UJ where V is forward speed. This equation offers the principle of a method for estimating the sea spectrum from a ship's response to waves. Since finding motion spectra requires a long time, the RAO is used to estimate wave height from the estimated heave amplitude (Zi/3). The RAO (response amplitude operator) of a ship for each wave direction and speed can be obtained from either experiments or ship motion programs. In this study shipmo.for [55] was used to obtain RAO. An example RAO is given in Figure 5.1. Chapter 5. Ship Dynamics 65 Encounter Frequency (w (\_/gj2) Figure 5.2: An example RAO for heave motion of UBC series model # 2 Figure 5.1 shows a general comparison of estimated and experimentally found RAOs for 12 UBC series. As seen from this figure, estimated results are within %10 of experimen-tally found results. Therefore, for such a ship, theoretical RAO's can be used to estimate wave height. As seen from Figure 5.1, this operator gives relative ship motion with respect to non-dimensional encounter frequency. Since encounter frequency can be found from radar image processing ( see in Chapter 4), the only unknown in this equation 5.7 to find wave height is heave amplitude. Heave motion data (Figure 5.4) is used to find estimated heave amplitude (Zi/3). To Chapter 5. Ship Dynamics 66 find (Zi/3), heave amplitudes are put in descending order. The average of 1/3 of the maximum heave amplitudes is used as the estimated significant heave amplitude. Figure 5.3: Comparison of experimental and estimated RAOs for UBC series Chapter 5. Ship Dynamics 67 -S • I - H £< s < a» £ 0.06 0.04 0.02 0.00 jg -0.02 -0.04 -0.06 0 50 100 150 200 250 300 Time (sec) Figure 5.4: Typical recorded heave motion data for UBC # 2 Chapter 5. Ship Dynamics 68 Estimated wave heights by using the above explained technique are given in Figure 5.5 and Table 5.1. It can be seen from Figure 5.5, that the error in estimation of wave height is less then %10. 8.0 ^ 7.0 •a £ 6.0 > M g to W 5.0 4.0 3.0 t-2.0 ; : : ! s ^ * ^ ^ ^ : I^T X^ : , / • ;^-^ 10% 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Wave Height Figure 5.5: Estimation of wave height Chapter 5. Ship Dynamics 69 Sig. Wave Height (m) 2 2 2 3 3 4 4 4.5 4.5 4.5 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 Wave Period 7 9 11 8 11 8 11 8 11 15 7 9 11 13 15 7 9 11 13 15 7 9 11 13 15 Estimated wave height (m) 1.842 1.940 2.085 3.128 3.128 3.907 4.171 4.396 4.692 4.779 4.607 4.851 5.214 5.288 5.310 5.527 5.822 6.256 6.346 6.372 6.448 6.792 7.299 7.403 7.434 error (%) 7.9 3.0 4.3 4.2 4.2 4.3 2.3 2.3 4.2 6.2 7.8 2.9 4.27 4.27 6.21 7.876 2.97 4.27 6.21 6.21 7.87 2.97 4.27 5.76 6.21 Table 5.1: Estimated wave heights 5.2 Rol l N a t u r a l F r e q u e n c y It is assumed that the vessel rolls at its natural frequency when excited by random waves. Therefore, the peak in the spectrum of roll motion corresponds to the roll natural frequency. The two most popular ways of finding spectrum of a time series are Fourier Transforms and Maximum Entropy method. Comparison of these two methods is given in Table 5.2. Chapter 5. Ship Dynamics 70 Feature Spectral window effets Linearity of spectrum Accuracy of frequency estimation Resolution of closely spaced frequencies Fourier Transfoms Convolution of window spectrum with true signal spectrum reduces resolution and allows leakage through window sidelobes Spectral estimation is linear To within ±l/2NAt Propotional to 1/JV Maximum Entropy method No window effect since autocorrelation function is estimated for all lags Estimation is nonlinear Not easily defined, but can be estimated very closely Data dependent, but resolution approximately proportional to 1/N2 Table 5.2: Comparision of Maximum Entropy method and Fourier transforms As seen from the above table, the Maximum entropy method (MEM) can estimate natural frequencies accurately and distinguish closely spaced frequencies. Therefore, this method is used to find the natural roll frequency of a ship. 5.2.1 M a x i m u m Entropy M e t h o d Choosing the best spectral-domain representation of a truncated discrete time series, for which only an imperfectly determined autocorrelation function can be calculated, is a major problem in signal analysis. Among the countless spectra that may be consistent with a given autocorrelation function, only one spectrum can be optimal. A set of rules governing that choice must be established. Jaynes [56] introduced a method of statistical inference called the " maximum entropy estimate". He showed that information theory (Shannon and Weaver, 1949) provides a criterion for selecting the best statistical description of a process when only a partial knowledge of that process is available. The optimal choice is the only one which is maximally non-committal with regard to any missing data, and which is simultaneously constrained to be consistent with all available data. The result is the best estimate that Chapter 5. Ship Dynamics 71 could have been made on the basis of the data at hand. The application of maximum entropy spectral analysis has met with considerable suc-cess in geophysics. Burg [57, 58] presented the formulation resulting from the application of entropy consideration to spectral determinations and also a method of computing the required prediction error coefficients. The maximum entropy method (MEM) using the Burg algorithm was applied by Ulrych [59], who showed the resolution properties of this approach. Theoretical considerations concerning the development of MEM have been presented by Barnard [60], Edward and Fitelson [61], Smylie et al. [62]. The maximum entropy MEM spectrum of a stationary, random, uniformly sampled process is found as the spectrum that results from maximizing the entropy of that process. In applying the concept of maximum entropy to spectral analysis we begin with the relationship between the entropy (strictly speaking, the entropy rate for an infinite process) and the spectral density S(f) of a stationary Gaussian process. H = TT r l°9S(f)df (5.9) 4/jV J - /AT where /jy is the Nyquist frequency. The derivation of equation (5.9) is shown in detail in [62] . Rewriting (5.9) in terms of the autocorelation <j)(k) of the process gives H = TT f^ M £ (Kk)exp(-i2*fkAt)]df (5.10) 4/iV J-fN _oo where At is the uniform sampling rate. Maximizing equation (5.10) with respect to the unknown 4>{k) with the constraint that S(f) must also be consistent with the known autocorrelation 4>{k),..., <j>(M — 1) results in the MEM spectral estimate. This estimate expresses maximum uncertainty with respect to the unknown but is consistent with the known information. Chapter 5. Ship Dynamics 72 The variational procedure leads to the well known expression for the MEM spectral density [62] and [61], which for a linear process Xt is S(f) = — — T (5.11) 1 - Ek=i Akexp(-i2irkf0A) In (5.11), PM is a constant and the a, are prediction error coefficients that are deter-mined from data. Estimations of the Ak and M are given in Appendix C. Assuming for the moment that parameters Ak and a2 are known, it is found that equation 5.11 is actually a closed-form analytic equation for the response spectrum. Consequently, the search for relative maxima of the spectrum can be accomplished with the aid of a classical result from calculus which states that the derivative of a function is zero at an extremum. Since the spectrum is available in function form, one can locate any relative extrema of the power spectrum (i.e. relative maxima or minima) by solving T-° (5-i2) All frequencies which form the solution set of equation 5.12 must corresponds to extrema of the spectrum. Thus, this set of frequencies, which will be known as the set of critical frequencies, contains the natural frequency estimates. Before substituting the equation for MEM spectrum into equation 5.12, it is conve-nient to recast equation 5.11 in to a form more easily manipulated. |1 - £ Ake~^k^\2 = p0 + 2Y/Pk cos(27rA;/A) (5.13) k=o Jfe=l where : A0 = 1 (5.14) Chapter 5. Ship Dynamics 73 p—k Pk = Yl AiAi+k t = 0 The accuracy of this identity can be demonstrated by a straight forward manipulation involving an interchange of summation order. Alternatively, if the coefficients Ak are viewed as a time series, the pk can be interpreted as an autocorrelation function of the Ak's. Thus equation 5.13 is simply a restatement of the well known relationship between the Fourier Transform of a time series (ie.Ao, A\,..., Ap) and the Fourier Transform of its autocorrelation function (ie. pk)- Utilizing the identity of equation 5.13, the pth order MEM spectrum can be written as: S{f) = P + 2EPk=1pkcoS(2nkfA) ( 5 , 1 5 ) After substituting equation 5.15 into equation 5.12 and evaluating the derivative, the following result is obtained ZPk=1kpkSm(2irkfA) =Q \po + 2ZPk=1pkcoS(2TrkfA)\2 One set of solutions for equation 5.16 is obtained by finding all frequencies that cause the denominator to become infinite. However, comparing the denominators of equation 5.16 and 5.11, it is found that any solution, f0, obtained from the denominator of equation 5.16 becoming infinite, corresponds to a zero in the spectrum (ie. S(f) =0) . Since this condition is of no value in estimating peaks of the spectrum, the numerator of equation 5.16 must include all solutions which corresponds to maxima of the spectrum. Thus any frequency which corresponds to a relative maximum of the spectrum must also be a solution of equation 5.17. Chapter 5. Ship Dynamics 74 J2 kPk sin(2pkfA) = 0 (5.17) Conversely, any frequency which is a solution of equation 5.17 must corresponds to an extremum of the spectrum. While the solution set of equation 5.17 includes both maxima and minima (excluding zeros of the spectrum) it is a relatively simple task to determine which type of extrema a given solution corresponds to. One way of checking the solution type is to simply plot the spectrum and verify the extrema graphically. Since, this method is not suitable for this study, another method which uses second derivatives employed for determining the solution types. This method identifies maxima and minima of a function with positive and negative second derivatives of the function respectively. Accordingly, the second derivative of the pth order MEM spectrum evaluated at f0, a solution of equation 5.17, is given by <PS(f). Aira2pA3 E L i k2Pk cos(2irkf0A) (5.18) df2 lf-f° [p0 + 2Y;pk=1pkcos(2irkfoA)]2 Since the denominator of equation 5.18 is always positive, the sign of the second derivative is decided by the numerator. Consequently, the second derivative test can be written as J2 k2pk COS(27T/0A) < < 0 —y relative maxima at /o = 0 —» indetermined with this test (5.19) > 0 —> relative minima at /o This test has proved very useful in the estimation of natural frequencies in that solutions of equation 5.17 can be quickly and easily verified as a maxima without the use of graphics or interaction with the analyst. Chapter 5. Ship Dynamics 75 This above procedure is used in the estimation of roll natural frequency. In order to check the convergence and to find the optimum number of data points needed, the above explained methodology is applied to the single degree of fredom roll motion. It is assumed that the roll motion of a ship, when subject to a pure rolling moment, M(t) , may be modelled by second order differential equation of the form : l]> + B<j) + C<t> = M(t) (5.20) where, I is the roll mass moment of inertia of the ship (including added mass moment of inertia), (f> is the roll angle, Bcj) and C(j) damping and restoring moments respectively. In these simulations, the roll moment was chosen as M{t) = Arand() + Bsin(toi) where, rand() is a random number generator, A and B are constants. (5.21) CD 0 . 6 0 0 . 5 5 0 . 5 0 0 . 4 5 0 . 4 0 0 . 3 5 0 . 3 0 0 . 2 5 0 . 2 0 ' \ W BWtart«d \ l v _ _ - - ^ \ - \ \ \ i , I , I , I ~~, r-7---r--r-T~~-, 5 0 1 OO 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 Number of data points Figure 5.6: Convergence of MEM natural frequency estimator As seen from, Figure 5.6, estimations yield to the correct answer after 150 mea-surement points. Figure 5.7 shows the accuracy of the estimations for different natural Chapter 5. Ship Dynamics 76 frequencies. "is CO 0 Original ISJatural Frequency Figure 5.7: Results of MEM natural frequency estimator for single degree of freedom system As the next step, the above method is applied to the single chine vessel (see Chapter 2.). Firstly, an experimentally obtained roll decay curve [28] (Figure 3.7) is used to estimate the roll natural frequency. In this step, it is assumed that the ship rolls at its natural frequency, when its freely rolling. Secondly, a ship motion program (RolLdyn.C) [63] was run to obtain roll motion data in following seas. In this run, a Bretschneider spectrum (see Appendix D) is used to simulate incoming waves. Results of this simulation for different significant wave heights are shown in Table 5.3 and Figure 5.8. Chapter 5. Ship Dynamics 77 S < Sig. Wave Height (m) 0.8 0.9 1.2 1.5 Original (rad/s) 0.408 0.408 0.408 0.408 Estimated (rad/s) 0.382 0.38 0.383 0.385 Table 5.3: Results from MEM natural frequency estimator 2.0 1.5 CD % 1-° 0.5 0.0 0.00 0.04 0.08 0.12 0.16 0.20 Frequency (Hz) Figure 5.8: Spectrum of roll motion The same methodology is also applied to find the natural frequency of the American Challenger vessel. For this analysis, experimental results from reference [64] are used. Chapter 5. Ship Dynamics Figure 5.9 shows a time series of roll motion of American Challanger. Results of MEM analysis of this data is shown in Figure 5.10. As seen from 5 Table 5.4, the results are very close. Figure 5.9: Roll motion data for American Challenger x 3 f o.o 0.1 0 . 2 0 . 3 0 . 4 0 . 5 F r e q u e n c y (Hz . ) Figure 5.10: Roll motion spectra for American Challenger Chapter 5. Ship Dynamics 79 Actual (given) 0.7 Estimated by MEM 0.69 Table 5.4: Comparison of natural frequencies 5.3 Est imat ion of Probabil i t ies It is well known that vessels are not designed to withstand all weather conditions. Vessels are supposed to seek a shelter under some conditions. These conditions are usually different than explained in previous chapters. For example, assume that wave height is increasing gradually, but frequencies are not in the resonance range and wave direction is beam seas. This condition does not satisfy any capsizing modes mentioned earlier. In order to identify these sort of conditions, the following two probabilistic approaches are used. 5.3.1 Probabil i ty of Roll Angle passing a limit value in t ime T Let x(t) be the roll response of a vessel. Assume that x(t) is a stationary, random process, and uJexp is the expected frequency of crossing the limit level x = a with positive slope [65]. Figure 5.11 considers the geometry involved in a function crossing the level x = a during particular time interval dt. All functions cross the line t = t (Figure 5.11, but only a small fraction of these cross the line x — a with positive slope x > 0 during the interval dt. Two such samples are indicated in Figure 5.11. Suppose that dt is so small that the samples can be treated as straight lines in the interval. If a function crosses the line at t = t with an x value less then a, it will also cross x = a, if its slope x at t = t has any value from infinity down to the limiting value (a - x) / dt [65]. Using this statement, any Chapter 5. Ship Dynamics 80 function can be examined to determine whether or not its combination of x and x values will yield a crossing of x = a (Figure 5.12). x A Figure 5.11: Sample functions crossing level x = a with positive slope x - a - x dt x x - a . Figure 5.12: Favorable combinations of x and x which results in crossing of x = a during dt interval An analytical method of examining combinations of x and x values is provided by the Chapter 5. Ship Dynamics 81 joint probability distribution of x and x for stationary processes [65]. The probability of a sample having x between x and x + dx and having x between x and dx is p (x , i )dxd i . In the (x , i ) plane the favorable combinations of x and x values are shown in the shaded area of Figure 5.12 between the line x = a and line where x equals the limiting value (a - x) I dt. Now the expected number of crossing of x — a during the dt is just the same as the fraction of favorable combinations out of all possible combinations, since favorable combinations will yield exactly one crossing while unfavorable combinations gives no crossing. Finally the expected number of such crossing per unit t ime can be written as [65]: J roo pa Vexp = T7 / dx p(x, x)dx (5.22) dt JO Ja-idt where the integration limits have been chosen to cover the shaded area in Figure 5.12. For small values of dt, the x variable is substantially equal to a in the x integration so that , one obtains, by letting dt —> 0 [66] vexp = / xp(a, x)dx (5.23) Jo This result for the expected number of crossing of the level x = a, with positive slope, per unit time, applies to any stationary process not neccesarily normal [65]. In order to evaluate Equation 5.23, the following assumptions are made. Roll motion (x(t)) is an ergodic, stationary Gaussian (normal) random process with zero mean. This requires that the joint density takes the following form. P(x,x) = o exP ZTTO'xO'x X + X (5.24) Chapter 5. Ship Dynamics 82 Note that Equation 5.24 implies that x and x are uncorrected. Substituting in Equation 5.23 and evaluating the integral, one finds _ 1 cr± Wexp = 7, exP 2-K crx 2ol (5.25) This equation gives the probability of crossing at any level of a in a unit time. On the other hand, if one wants to find in time T, Wexp — T ^ (-a2 -exp 2nax~ f \ 2ax J Similarly, expected maximum roll angle can be found as [67]: (5.26) f°° (—T <Jx E[Xmax] = 1 - expl -exp JO \ Z7T ax —x dx (5.27) In the evaluation of the above method, use can be made of results from the San Fran-cisco Bay experiments, reported by Haddara et al. [64, 21] to calculate the probabilities of capsizing. A typical motion time series of a model run that ended with capsize is shown in Figure 5.13 [64, 21]. CO a> CD CD top £ o 4 2 8 3 1 2 5 1 6 7 2 0 8 2 5 0 T i m e ( s e c ) Figure 5.13: Typical t ime histories of capsize sequence of American Challenger vessel recorded on San Francisco Bay Chapter 5. Ship Dynamics 83 The following results were found by using statistical analysis : Variance Standard deviation Absolute deviation Standard error 124.946670 11.1779547 8.42763428 0.790400753 Table 5.5: Result of statistical analysis for time histories of capsizing Substituting these results into Equation 5.26, and using a time limit as 30 minutes gives Expected Frequency of Roll angle crossing 60° in 30 minutes is 4.3 times In this study, the limit for expected frequency is set as 1, that is, if the expected frequency is bigger than 1, a warning will be issued. In this case warning is return t o port . The limit for roll angle is set at either 60° or the angle of deck immersion whichever is less. Similarly, the expected maximum roll angle in 30 minutes was found as 100°. The limit is 60°. Chapter 6 Deve lopment of A Fuzzy Expert Sys tem 6.1 Introduct ion In recent years, expert systems have received increased attention as practical applications of artificial intelligence to solve real problems. In traditional rule - based approaches, knowledge is encoded in the form of antecedent - consequent structures; when new data is encountered, it is matched to the antecedent clauses of each rule, and those rules where antecedents match the data exactly are fired, establishing the consequent clauses. This process continues until a desired conclusion is reached, or no new rules can be fired. This forward propagation scheme for logical inference assumes that all facts are known precisely, a constraint which is rarely satisfied in the marine field. There is almost always uncertainty present; uncertainty in the facts, and uncertainty in the rules describing ca-sual relationships among facts. Results of radar image processing techniques can be used as an example of uncertainties in measurements. As seen from Figure 4.14, wave direc-tion is not clear. Therefore, in order to handle this uncertainty, a triangular membership function between 15° and 40° is used as a wave direction. The following rule shows the uncertainties in the rules. " If the wave direction is following seas (Figure 2.4), and the encounter frequency is close to twice the natural roll frequency, then the ship is in danger ". In this rule, there are two elements of fuzzyness: • Definition of wave direction : Following seas can be considered as fuzzy input, because the boundaries of following seas could be ±20° of wave direction exactly 84 Chapter 6. Development of A Fuzzy Expert System 85 from behind. • Relationship between frequencies : The relation between encounter and natural roll frequency is given as "close or equal". This description is a fuzzy description. To consider these uncertainties, a fuzzy expert system is used in the decision making step. A general introduction to fuzzy logic is necessary to explain the methodology which is used by a fuzzy expert system. 6.2 Introduct ion t o Fuzzy Logic Fuzzy logic is a superset of conventional (Boolean) logic, that has been extended to handle the concept of partial truth, t ruth values between "completely true" and "completely false". It was introduced by Lotfi Zadeh [68] in the 1960's as a means of modelling the uncertainty of natural language. Fuzzy Subsets There is a strong relation between Boolean logic and the concept of a subset, there is also a similar relationship between fuzzy logic and fuzzy subset theory. In classical set theory, a subset U of a set S can be defined as a mapping from the elements of S to the elements of the set {0,1}, U:S-* {0,1} This mapping may be represented as a set of ordered pairs, with exactly one ordered pair present for each element of S, and the second element is an element of the set { 0,1}. The value zero is used to represent non-membership and the value one is used to represent membership. The t ruth or falsity of the statement: Chapter 6. Development of A Fuzzy Expert System 86 X is in U is determined by finding the ordered pair whose first element is X. The statement is true if the second element of the ordered pair is one, and the statement is false if it is zero. Similarly, a fuzzy subset F of a set S can be defined as a set of ordered pairs, each with the first element from S, and second element from the interval [0,1], with exactly one ordered pair present for each element of S. This defines a mapping between elements of the set S and values in the interval [0,1]. The value zero is used to represent complete non-membership, the value one used to represent complete membership, and values in between are used to represent intermediate degrees of membership. The set S is referred to as the universe of discourse for the fuzzy subset F. Frequently, the mapping is described as a function, the membership function of F. The degree to which the statement X is in F is true is determined by finding the ordered pair whose first element is X. The degree of the t ruth of the statement is the second element of pair. Logic Operat ion The standard definitions in fuzzy logic are : t ru th (not x) = 1.0 - t ruth (x) t ruth (x and y) = minimum(truth(x) , truth(y)) t ru th (x or y) = maximum(truth(x) , truth(y)) It should be noted that if just the value zero and one were used in these definitions, the t ru th table obtained would be same as the one expected from conventional Boolean logic. This is known as the extension principle, which states that classical results of Boolean logic are recovered from fuzzy logic operations when all fuzzy membership grades are restricted to the traditional set 0,1. This effectively establishes fuzzy set and logic as a true generalization of classical set theory and logic. In fact, by this reasoning all crisp Chapter 6. Development of A Fuzzy Expert System 87 (traditional) subsets are fuzzy subsets of this very special type. 6.3 Fuzzy Expert S y s t e m Fuzzy expert systems deal with uncertainty in their knowledge base and the information supplied, in a rational and understandable way, based on the use of fuzzy logic. They use a collection of fuzzy membership functions and rules, instead of Boolean logic, to reason about data. The rules in a fuzzy expert system are usually of a form similar to general If - Then rules. As an example we can study the following rule which says that if waves are coming from behind (following seas) and the difference between wave speed and ship speed is small and the speed of the ship is high then reduce speed. IF wave-direction IS follow AND (DW_speed_SSpeed) IS Zero AND Ship_speed IS high THEN DShip_speed IS moderate-negative where wave_direction, (DW_speed_SSpeed), and Ship_speed are input variables, and DShip_speed is an output variable, moderate-negative is a membership function (fuzzy subset) defined on wave_direction, Zero is a membership function defined on (DW_speed_SSpeed) and so on. The antecedent (the rule's premise) describes to what degree the rule applies, while the conclusion (the rule's consequent) assigns a membership function to each of one or more output variables. Figure 6.1 shows a general layout for the fuzzy expert system. Left hand sides are the input variables, available to the fuzzy rules and the right hand sides are the possible outputs desired from fuzzy rules. Chapter 6. Development of A Fuzzy Expert System 88 Change_Direction Change_Speed Return Port Ballast / Deballast Figure 6.1: A general layout for Fuzzy Expert System 6.3.1 Determination of Membership functions A fundamental tenet of fuzzy set theory is that observations can partially belong to predefined sets. This is in sharp contrast to the traditional Boolean logic, in which membership in a set is an all or nothing proposition. Suppose that we have measured Chapter 6. Development of A Fuzzy Expert System 89 ship's speed and have sets called slow, medium, and high. Boolean logic would dictate that memberships are determined by means of fixed cut off points, say at 5 and 10 m/ s . Speed which is at least equal to 10 would be a member of the high set, while all others would be in either the medium or slow set. This is illustrated in the upper part of Figure 6.2. On the other hand, fuzzy definitions of this set allow for partial membership. A ship speed slightly higher than 4 m/ s would be almost a full member of the slow set and only trivially a member of the medium set. 5m/s would be a half-member of each set. Slow Medium High 5 10 Boolean logic demands crisp membership Slow V / Medium V / High 4 5 10 Fuzzy logic allows partial membership Figure 6.2: Membership functions Limits of each member of membership functions of input variables used in this study are obtained from experimental and theoretical calculations. Chapter 6. Development of A Fuzzy Expert System 90 6.3.2 Input Output Forms and Interpretation Expert systems used are capable of dealing with incoming and computed information in two different forms: crisp or fuzzy. Crisp data consist of single values. Most real world devices, such as accelerometers generate crisp data. Fuzzy data consists of an array of believability values each between zero and one such as wave directions found from radar images. The degree to which a data value belongs to a fuzzy subset (its membership in the fuzzy subset) is computed somewhat differently depending on whether the data value is crisp or fuzzy. When data is crisp, the degree of membership is the value of the fuzzy subset's membership function at that data value, as shown in Figure 6.3. Fuzzy subset (membership functional Crisp Value /— Degree of Membership Figure 6.3: Degree of membership for a crisp data value Chapter 6. Development of A Fuzzy Expert System 91 When the data value is fuzzy, the degree of membership is determined as the maximum degree of membership value for the intersection of the membership functions for the fuzzy data value and fuzzy set as shown in Figure 6.4 Fuzzy subset (Membership function) Fuzzy value £ _ Degree of Membership y<?M>, Figure 6.4: Degree of membership for a fuzzy data value 6.3.3 Inference M e t h o d The process of applying the degree of membership computed for a production rule premise to the rule's conclusion to determine the actions to be performed is called performing an inference, one is inferring the actions to be performed from the premise. There are several methods for performing fuzzy logic inferences. Two of the most common methods are the max-min and max-dot (also known as the max - product) method. In either inference method, the basic concept is that a value (set) to be assigned to the output is scaled by or clipped to the degree of membership for the premise, and that Chapter 6. Development of A Fuzzy Expert System 92 all of the scaled or clipped sets for all of the rules that set this output unionized together to form the final membership function. In reality, in most cases the two methods give similar results. T h e M a x - Min Inference M e t h o d In the max - min inference method, the final output membership function for each output is the union of the fuzzy sets assigned to that output in a conclusion after clipping their degree of membership values at the degree of membership for the corresponding premise, as shown in Figure 6.5. In Figure 6.5, PM and PS are positive medium and positive small respectively. Rules A B — • C Low If A is Low OR B is Low Then C is PM If A is Low And B is Medium Then C is PS Final Value of C (Suggested) Figure 6.5: The max - min inference method Centroid Chapter 6. Development of A Fuzzy Expert System 93 As seen from the first rule in Figure 6.5, the conclusion is assigned after the following steps: • Find the corresponding belief values for inputs A and B • Find the maximum of these corresponding values, since relationship is given by "OR". • Clip the membership function of C from the maximum value found at step 2. The resulting membership function (PM) from the above steps is the result of rule 1. The results for rule 2. is found by similar steps. Then, these two resulting membership functions are used to find the final value (suggestion) by a defuzzyfication method (see section 6.3.4). T h e M a x - D o t Inference M e t h o d In the max - dot or max - product inference method, the final membership function for each output is the union of the fuzzy sets assigned to that output in a conclusion after scaling their degree of membership values to the peak at the degree of membership for the corresponding premise, as shown in Figure 6.6. The conclusion is assigned by using similar steps as explained in "max - min inference method". The only difference here is that the maximum point is used as the t ip of triangular membership function. The max - min inference method is used in this study to find the final decision. Chapter 6. Development of A Fuzzy Expert System 94 Rules A B — • C If A is Low OR B is Low Then C is PM If A is Low And B is Medium Then C is PS Final Value of C — • (Suggested) Centroid Figure 6.6: The max - dot inference method 6.3.4 Defuzzification All fuzzy logic inference methods result in fuzzy values for all output information. In order to generate a single crisp value, a method is needed to pick a value that represents the membership function in the best possible way. These methods are called defuzzifications. There are several methods of performing this defuzzification. Two of the most commonly used ones are the height and the centroid method. The height defuzzification method picks an average of the output values corresponding to the centroid of the scaled or clipped output membership functions as the crisp value for an output, weighted by the heights of the clipped or scaled output membership function. Low / A is Low Min( A is Low, B is Medium ) Chapter 6. Development of A Fuzzy Expert System 95 This method could give misleading results, when it is used in those cases where the membership function graphs are not symmetrical [68]. Therefore, the centroid method is used in this study for defuzzification, as seen from Figure 6.7 Final Value V Centroid Figure 6.7: The centroid defuzzification methods 6.4 Explanation of the Rules Used by the Expert System This section explains the general rules used by the fuzzy expert system. In the rule base developed, there are different rules for different situations. For example, for the same rule, there are different solutions for say different ship speeds, such as when it is high reduce speed, or when it is medium change direction. In this section, instead of giving all these combinations of the rules, a general explanation of a rule is given and how Chapter 6. Development of A Fuzzy Expert System 96 and where it is obtained is explained. The expert system has 36 rules to cover possible combinations of the rules explained in this section. Rule 1 : This rule is extracted from theoretical and experimental studies. If wave length is equal to ship length and encounter frequency is twice the natural roll frequency and wave direction is following to quartering seas then a) Reduce speed until wave speed is more than 20% of the ship speed. b) Change Direction. Two extreme positions of the wave, namely, with a crest at the ends and with a crest amidship are shown in Figure 6.8. Wave Direction (b) Figure 6.8: Two extreme positions of the wave For a normal ship form with flared sections at the ends and wall sided sections amidships, it can be seen that the inertia of the waterplane is different in each case. It is greater Chapter 6. Development of A Fuzzy Expert System 97 than the still water value with wave crest at the ends, and less than the still water value with the wave crest amidship. If the ship is now given an initial roll due to a small disturbance, it will roll at its natural period until the energy provided by the disturbing force is dissipated in damping. However, if the period of stability fluctuation and the natural rolling period of the ship have the right ratio, it is possible that the initial rolling angle will not only be sustained, but will build up. A qualitative explanation of this is as follows: Suppose that the stability changes with a frequency twice the natural rolling frequency of the ship, and that the phase of the rolling and the stability changes are as shown in Figure 6.9. Roll Angle time Starboard e3 Figure 6.9: Stability changes with a frequency twice the natural roll frequency Starting with the initial angle 0o, during the swing back to an upright position the stability is higher than average, and the stability moment is in the direction of the motion. After crossing zero, the stability is now opposing the motion, but its value is now low. Therefore, &\ is greater than 60. Rolling back to zero again, the stability is now adding to the motion and its value is high. Thus the rolling motion builds up continuously. This Chapter 6. Development of A Fuzzy Expert System 98 is known as low cycle resonance. An example simulation for low cycle resonance is shown in Figure 6.10. In this simulation, the roll period is approximately equal to the natural roll period and the encounter period is half the period of roll. The wave length is approximately equal to the ship length. = 0.975 60 ^_^ co CU CD J-i 60 o> T3 s « / CD 60 < 1—1 o 04 40 20 0 -20 -40 -60 -80 -100 50 100 150 200 Time (sec) Figure 6.10: An experimental simulation for low cycle resonance Chapter 6. Development of A Fuzzy Expert System 99 Rule 2 : If Roll natural frequency is equal to g/8U and Wave height is high T h e n a) increase speed (if there is enough power) b) Change speed. From the previous works on the roll of a ship in astern regular waves [63, 69], it was found that the worst roll conditions exist when the roll natural frequency of the ship was one half the encounter frequency of the waves. On that basis, it is anticipated that a ship travelling in astern random sea would experience its greatest problem when the roll natural frequency is equal to one half the singular frequency in the metacenter height spectrum [63, 69]. u;n = g/SU This condition could occur, for instance, if a ship with a 20 second roll periods were travelling at a speed of approximately 5 m/ s (10 knots). If a ship found itself in such a situation, it would be beneficial to increase speed until the singular frequency in the spectrum was at least 20 percent below the roll natural frequency. If sufficient speed reserve exists for the ship to be able to increase speed by this amount, then the roll problem should dissipate. Otherwise, a decrease in speed may be necessary [63, 69]. Rule 3 : If wave direction is beam seas and wave height - ships beam is zero or negative then change direction Chapter 6. Development of A Fuzzy Expert System 100 This rule is found as a rule of thumb from statistical work called "Fishing vessels limits study" by SNAME [70]. In this research, surveys were sent to 12000 fishermen. The primary interest of this project was to identify wind and sea limits for fishing vessel. Statistical data and analysis can be found in [70]. Rule 4 : If wave direction is beam or quartering seas and wave height is high and natural roll frequency is equal to encounter frequency t h e n change direction This condition is called resonant excitation. It has been shown by experimental and numerical simulations [21, 71, 72] that if the vessel is excited at its natural roll frequency, it may result in very large roll angles if the wave amplitude is sufficiently large. An example for this capsizing due to resonant excitation is shown in Figure 6.11 for the quartering sea condition [21]. It is seen that the vessel rolls at the encounter period, which is approximately equal to the natural roll period. The roll motion is 180° out of phase with the wave motion and has a negative mean; the roll angles are negative in the crests and positive in the troughs. There is no tendency for capsizing during the passage of the first wave group, while in the second wave group the roll amplitude is seen to increase after t=200 s until the vessel capsizes on the crest of a wave at t=265 s. Chapter 6. Development of A Fuzzy Expert System 101 3= -30 - L , - — ^ r—-^ ; , 1 i • , , i F~ - r - • • | . • i , ; — r—, - I 0 20 40 SO 80 LOO [20 140 160 160 200 220 240 2E0 100 • 3 0 J . . . , . . . , . . . , . . . i . . . , . . . , . i i | i i i | i i i , i i | . i i j . i i j i p i , I 0 20 40 60 80 100 120 140 ISO 180 200 220 240 260 Figure 6.11: An example quartering seas motion data leading to capsizing Rule 5 : If wave direction is following seas and wave height is high and wave speed is approximately equal to the ship speed then a) change direction b) change speed This capsizing mode is known as loss of transverse stability in following seas. An Chapter 6. Development of A Fuzzy Expert System 102 CO 0» 0) o> T3 's*~~s o> W) 3 ^^ o « 40 20 0 -20 -40 -60 -80 0 50 100 150 Time (sec) Figure 6.12: An example following seas motion data leading to capsizing due to loss of transverse stability example motion record for this sort of capsizing is shown in Figure 6.12. This capsize mode is characterized by the vessel being heeled over to one side for a prolonged period of time due to lack of sufficient restoring energy in the system and where roll period is not equal to the natural roll period. Typical conditions of this mode are steep, large amplitude waves, and a large enough ship speed so that the vessel stays in the wave crest for a relatively long period, during which static stability is reduced. An example GZ curve for this condition is shown in Figure 6.13. As seen from this figure, when a wave crest is at the midship, the vessel does not have enough restoring Chapter 6. Development of A Fuzzy Expert System 103 moment to upright herself. A small external force could capsize the vessel. c 50 o E o 5 O) § 25 % CD 0 -25 -50 C • • >^ 1—*= -y ^ N^ Wave trough at midship / ^ - --^Calm Water \ ==^r____vvave crest at midship \ \ \^V . . . . 1 . . . . I . . . . I . . . . I . . . . I . . . \ 1 . . ) 10 20 30 40 50 60 70 Roll Angle Figure 6.13: GZ curve of American Challenger for two different wave conditions Rule 6 : If wave direction is quartering seas and wave height is high and wave length is equal to 70% - 80% of the ship length then a) change direction b) change speed The following example represents the mode of capsizing preceded by broaching [21]. In reference [21], capsizing is predicted to occur in steep, quartering seas and a wave Chapter 6. Development of A Fuzzy Expert System 104 > O 0) o -J t-J o cc L 0) 3 3 O D OJ U -J DU -6 0 -\ /*" *_ J \. — T 1 1 1 1 1 r — 1 r \ y * \ ' - X « 1 1 I 1 ^. — < ^—-. ,— 20 40 60 80 100 120 MO-J 120 30 — T 1 1 1 ; — 40 60 80 100 -30-• 1 1 1 1 1 r 0 20 120 Figure 6.14: An example motion data leading to capsizing due to broaching length of about 80 percent of the ship length. The motion records in Figure 6.14 show that up to about t=75 s, a steady yaw angle of <j) = —12° is reached. Subsequently, during the passage of four wave crest, the yaw angle monotonically in-creases to —35° (despite the rudder being hard over), thereby putting the vessel in a position broadside to the waves, at an angle of 15° off the wave crest parallels. This part constitutes the broach. During the initial stage of the broach, the roll angle was quite large (40°), and once the vessel reached the broad side position to the waves, the angle of roll increased rapidly, and vessel capsized on the crest of a wave. Chapter 7 Numerical Simulations The capsizing modes mentioned above were simulated by using three different programs. These are SHIPM04 [55], MOTION.FOR [28] and ROLL_DYN.C [63, 69]. Shipmo4 developed by DREA is a frequency domain ship motion program, while Motion.for and RolLdyn.c developed at U.B.C. are time domain programs for regular and irregular fol-lowing seas respectively. All simulations were performed for 4 different types of vessels. Hydrostatic particular and body plan of those vessels are given in Table 7.1 and Figure 7.1. Length (ft) Beam (ft) Draft (ft) Volume (tonnes) cb Natural frq. U B C # 1 70.00 22.86 9.25 271 0.566 0.448 U B C # 3 91.00 22.86 9.25 308 0.5666 0.448 U B C # 7 70.00 22.64 9.17 196 0.471 0.453 U B C # 9 70.00 22.64 9.17 160 0.465 0.414 Table 7.1: Hydrostatic particulars of UBC series These simulations were performed in three different stages: 1. Low Cycle Resonance 2. Pure Loss of Stability 3. Resonant Excitation 105 Chapter 7. Numerical Simulations 106 20 15 r io B. 5 •10 UBC Series* 01 •S 0 / / / V// ' I 5 10 Figure 7.1: Body plans of UBC series Chapter 7. Numerical Simulations 107 Encounter frequency1 Wave length (ft) Wave direction Wave height (ft) Ship speed (knots) U B C # 1 0.93 65 following 9.0 10 U B C # 3 0.90 85 following 9.1 11.2 U B C # 7 0.93 65 following 9.0 11.0 U B C # 9 0.88 65 following 9.0 11.0 Table 7.2: Inputs for following seas low cycle resonance simulations 7.1 Low Cycle Resonance Simulations These simulations were performed in regular and irregular waves. Inputs used in these simulations are given in the following table. As seen from Figures 7.2, 7.3, 7.4, 7.5 a., the vessel capsized within 180 seconds, if no corrective action was taken. It should also be noted from this figure that capsizing occured in a very short time after the ship started rolling. This is in agreement with some reports [23] of accidents that happened in similar situations. The same parameters were then used as inputs to the fuzzy expert system (advisory system) and the following two rules were fired in generating a suggested action : IF wave-direction IS follow AND WaveJieight IS MEDIUM AND WL_SL IS ZERO AND WE_2WN IS ZERO AND ship_speed IS HIGH THEN change_speed IS NS Chapter 7. Numerical Simulations 108 IF wave_direction IS follow AND WaveJieight IS HIGH AND WL.SL IS ZERO AND WE_2WN IS ZERO AND ship_speed IS HIGH THEN change-speed IS NM The suggested action given by the fuzzy expert system was to reduce speed by 3 knots. Based on this change, the simulation program was again run to observe the effects of this change on the ship motion. In this run, all parameters were kept at the initial conditions, except the ship speed, which was reduced by 3 knots. Since the monitoring and advisory system takes about 1 minute to determine an action and 30 seconds were given for the ship to start to response, this run was initiated using the conditions at t ime 90 in the initial run that lead to capsizing. As seen from Figures 7.2, 7.3, 7.4, 7.5 b., the vessel did not capsize under the new conditions and the largest angle was between 5° and 15°. Figure 7.2 shows low cycle resonance simulation runs for UBC series model # 0 1 . As seen from Figure 7.2 a., the vessel rolls about 20° approximately at 60 seconds, then the roll decays rapidly. But at about time = 160 seconds, the ship starts rolling and capsizes at t=195 seconds. These results are in good agreement with the accidents reported under similar conditions [23, 64]. Figures 7.2, 7.3, 7.4, 7.5 also show similar patterns before capsizing. As seen from these figures, there is no clear indication of capsizing for a captain to recognize the danger, since the vessel rolls once or twice before actually capsizing. Chapter 7. Numerical Simulations 70 109 ! * o CO CD T3 <D < — o DC 70 59 48 36 25 14 3 -9 -20 50 100 150 Time (sec) 200 0 50 100 150 200 Time (sec) 250 Figure 7.2: Low cycle resonance simulation in regular waves for UBC # 01 Chapter 7. Numerical Simulations 110 „ „ CO CD CD o> CD - a CD O J 75 cc 4 0 2 0 0 - 2 0 - 4 0 - 6 0 CO CD CD O S CD _CD C D O -80 5 0 1 0 0 - 8 0 150 200 Time (sec) o 50 100 150 200 250 300 350 Time (sec) Figure 7.3: Low cycle resonance simulation in regular waves for UBC # 03 Chapter 7. Numerical Simulations 111 6 0 ^_^^ CO <D CD <D • o CD OJ £Z < "o oc 4 0 2 0 0 -20 -40 CO CD CD i _ O ) CD 3, J!2 < "o DC -60 41 82 123 164 Time (sec) 20£ 50 100 150 200 250 300 350 400 Time (sec) Figure 7.4: Low cycle resonance simulation in regular waves for UBC # 07 Chapter 7. Numerical Simulations 112 CO CD CD O l CD X J , 03 O DC CO CD CD OJ CD TO, _CD O J c < o 40 80 120 160 Time (sec) 50 100 150 200 250 300 350 Time (sec) Figure 7.5: Low cycle resonance simulation in regular waves for UBC # 09 Figure 7.6 shows similar results for irregular following seas. A detailed explanation of these simulation techniques can be found in [28, 63, 69] Chapter 7. Numerical Simulations 113 CD CD CD CD 2 . .92 CD O DC CO CD <D o> (D O 0.3 -0.2 0 50 100 1 5 0 Time (sec) 9 0 133 177 220 263 307 350 Time (sec) Figure 7.6: Low cycle resonance simulation in irregular waves 7.2 Pure Loss of Stabil ity Simulations This capsizing mode is characterized by the vessel being heeled over to one side for a prolonged period of time due to insufficient restoring energy in the system. Typical conditions for this mode are steep, large amplitude waves, and a large enough ship speed Chapter 7. Numerical Simulations 114 so that the vessel stays in the wave crest for a relatively long period, during which static stability is reduced. The motion records for pure loss of stability in following seas are shown in Figure 7.7, 7.8, 7.9, 7.10. In this simulation the following inputs were used. Wave direction Wave length (ft) Wave height (ft) Ship speed (knots) U B C # 1 180° 100 feet 8.5 ft 12 UBC # 3 180° 110 8.7 12 UBC # 7 180° 100 8.7 12.2 UBC # 9 180° 100 8.6 12.5 Table 7.3: Inputs for pure loss of stability simulations in following seas The following rule was selected by the advisory system to identify pure loss of stability. IF wave_direction IS follow AND WS_SS IS ZERO AND Wave_height IS HIGH AND ship_speed IS HIGH THEN change-speed IS NM Suggested action was to reduce speed by 3 knots. Following this suggestion, the simulation program was run again to observe the change in ship motion. Results after taking the suggested action are given in Figure 7.7, 7.8, 7.9, 7.10. As seen from Figure 7.7, 7.8, 7.9, 7.10, while the ship capsizes under those conditions, after the recommended action, the ship roll decays rapidly, and ship became stable. 7. Numerical Simulations 115 0 50 100 150 200 250 Time (sec) o 50 100 150 200 Time (sec) 250 Figure 7.7: Pure loss of stability simulation for UBC # 1 7. Numerical Simulations 116 50 100 150 200 250 Time (sec) 50 100 150 200 250 300 350 Time (sec) Figure 7.8: Pure loss of stability simulation for UBC # 3 7. Numerical Simulations 117 40 -20 --40 -60 _80 t • 1 • 1 • 1 ' 1 • 0 50 100 150 200 250 _S0 l i I i I i I i I i I i L 0 50 100 150 200 250 300 350 Time (sec) Figure 7.9: Pure loss of stability simulation for UBC # 7 Chapter 7. Numerical Simulations 118 CO CD CD i _ CO CD "O CD CD < — O cc "v> CD CD CD CD • o N» • *, ,* ' CD C D cr < o 10 0 -10 -20 -30 -40 -50 -60 -70 25 11 -2 -16 -29 -43 -56 -70 50 100 150 Time (sec) 200 0 50 100 150 200 250 300 Time (sec) 350 Figure 7.10: Pure loss of stability simulation for UBC # 9 As seen from Figure 7.7, 7.8, 7.9, 7.10, the vessel capsizes in a relatively short t ime after it starts rolling (when captain may realise the danger), if the wave height is big enough. For this mode of capsizing, there is a certain critical amplitude, say A^. if A < Acr, it was found that the roll motion (for a given initial roll angle) will decay to zero with increasing time, while for the case where A > Acr, the vessel will lean over to either Chapter 7. Numerical Simulations 119 side for a significant amount of t ime before capsizing. Although, numerical simulations show that Acr is approximately equal to the draft of the ship, more simulations with different types of vessels are needed to confirm this. 7.3 Resonant Exci tat ion Simulations Resonant excitation simulations were done in two different seas : Quartering and beam seas. In these two different wave directions, a Bretschneider spectrum (see Appendix D ) was used to simulate incoming waves. RMS roll motion values were used to compare results before and after the suggestion. The RMS roll angle cr0is given by : E * = j°° S{oje)duje (7.1) JO where S(uje) is the roll motion spectrum and u>e is encounter frequency. Figure 7.11 shows the resonant excitation simulation for UBC # 0 1 . In this simu-lation, the wave direction was 40° and ship speed was 9 knots. Using these inputs, the shipmo4.for program was run to obtain the RMS roll angle data. Then, the same con-ditions were used as inputs to the advisory system. The suggested action by the fuzzy expert system was to change direction by 30° towards following seas. These simulations were run for 6 different significant wave heights. The results of these two sets of runs are shown in Figure 7.11. Similarly, these runs were repeated for the other vessels. As seen from Figure 7.11, 7.12, 7.13, 7.14, reductions in RMS roll motion are about 50 - 60 %. Chapter 7. Numerical Simulations 45 40 35 < 30 25 20 15 10 • Before suggested action 1=1 After suggested action 5.5 6.0 6.5 7.0 7.5 8.0 Significant Wave_height Figure 7.11: Quartering seas simulations for UBC # 01 Numerical Simulations 121 *+u 35 30 25 20 15 i n -. a 1 • D « • « • Before suggested action D After suggested action c D a • D 1 , 1 , 1 , 5.5 6.0 6.5 7.0 7.5 8.0 Significant Wave_height Figure 7.12: Quartering seas simulations for UBC # 03 Chapter 7. Numerical Simulations 122 35 30 .2 25 too < 13 20 15 10 • Before suggested action n After suggested action 5.5 6.0 6.5 7.0 7.5 8.0 Significant Wave_height Figure 7.13: Quartering seas simulations for UBC # 07 7. Numerical Simulations m Before suggested action ° After suggested action 5.5 6.0 6.5 7.0 7.5 8.0 Significant Wave height Figure 7.14: Quartering seas simulations for UBC # 09 Chapter 7. Numerical Simulations 124 Figures 7.11, 7.12, 7.13, 7.14 show the results for quartering seas resonant excitations. In this simulation, the wave direction is 40° and the suggested action by the fuzzy expert system is to change direction by 30° toward following seas. During the decision making, the expert system checks conditions after the estimated action before giving the advise to the captain. The reason for this is to make sure that the vessel would not face a low cycle resonance or a pure loss of stability after the suggested action. As seen from Figure 7.11, 7.12, 7.13, 7.14, reductions in RMS roll motion are about 40 - 70 %. In these simulations, the feasibility of changing speed only is also investigated. These simulations were done for 7 different sea states. In order to investigate the effects of speed and direction , the simulation program was run by changing speed only, changing direction only and both. Tables 7.3, 7.3, 7.3, 7.3 show the results of these simulations. As seen from these tables, changing speed is not very effective for reducing roll motion under these conditions. From these results, it was decided to use only changing direction as a suggestion from the advisory system. Sig. wave height 5.94 6.25 6.55 6.80 7.04 7.55 7.99 Sea State 6 7 7 7 7 7 7 UBC # 01 before 33.49 35.18 36.88 38.23 39.58 42.45 44.80 change direction 11.55 12.15 12.74 13.20 13.67 14.67 15.49 change speed 30.95 32.57 34.10 35.35 36.60 39.26 41.45 both 9.66 10.16 10.65 11.05 11.44 12.28 12.97 Table 7.4: Quartering seas simulation for UBC # 01 Chapter 7. Numerical Simulations 125 Sig. wave height 5.94 6.25 6.55 6.80 7.04 7.55 7.99 Sea State 6 7 7 7 7 7 7 UBC # 03 before 30.35 31.89 33.43 34.65 35.89 38.49 40.63 change direction 12.50 13.40 13.80 14.40 14.80 15.90 16.78 change speed 28.80 30.26 31.72 32.89 34.05 36.53 38.56 both 11.75 12.35 12.95 13.44 13.92 14.94 15.78 Table 7.5: Quartering seas simulation for UBC # 03 Sig. wave height 5.94 6.25 6.55 6.80 7.04 7.55 7.99 Sea State 6 7 7 7 7 7 7 UBC # 07 before 26.46 27.44 28.77 29.83 30.89 33.14 34.99 change direction 8.42 8.84 9.27 9.62 9.96 10.69 11.29 change speed 25.04 26.31 27.59 28.61 29.62 31.78 33.56 both 8.15 8.57 9.27 9.62 9.64 10.35 10.94 Table 7.6: Quartering seas simulation for UBC # 07 Chapter 7. Numerical Simulations 126 Sig. wave height 5.94 6.25 6.55 6.80 7.04 7.55 7.99 Sea State 6 7 7 7 7 7 7 UBC # 09 before 37.51 42.99 45.07 46.73 48.39 51.92 54.83 change direction 19.72 22.44 23.53 24.40 25.27 27.13 28.65 change speed 33.86 40.16 42.11 43.67 45.22 48.52 51.24 both 16.84 22.45 23.59 24.60 25.34 27.19 28.54 Table 7.7: Quartering seas simulation for UBC # 09 Similar results are found for resonant excitation at beam seas (see Figure 7.15, 7.16, 7.17, 7.18). In this case, wave direction is 80° . This was considered as mostly beam seas and partially quartering seas by the advisory system. The suggested action given is to change direction by 30° towards head seas. Reduction in RMS roll motion was about 40 - 60 %. Numerical Simulations • • --• --------• Before suggested action • After suggested action . • • • • • D a D a o 1 , 1 , 1 , 1 , • a 1 .• 0° , 1 < • D 1 , 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Significant Wave height Figure 7.15: Beam seas simulations for UBC # 01 7. Numerical Simulations • • -• a i 1 • Before suggested action D After suggested action * * • • * a D . « ° a , 1 , 1 , 1 , 1 . • ao , I , D 1 i 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Significant wave height Figure 7.16: Beam seas simulations for UBC # 03 apter 7. Numerical Simulations 30 25 20 15 10 I-----" -• o I • Before suggested action • After suggested action • • • • * a a D D a D , I , I , I , I • • P D > I > • a I i 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Significant wave height Figure 7.17: Beam seas simulations for UBC # 07 7. Numerical Simulations -~ --" -------D 1 • Before suggested action • After suggested action • • * • • D D D D , 1 , 1 , 1 , 1 •* D D , 1 , * a 1 i 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Significant wave height Figure 7.18: Beam seas simulations for UBC # 09 Chapter 7. Numerical Simulations 131 7.4 Simulation of Soehae (Korean) Ferry Accident A tragic accident struck the Korean people on the 10th of October 1993, when the Soehae Ferry capsized and sank. This accident claimed 270 lives. Figure 7.19 shows the Soehae ferry, when it was brought to the surface to retrieve more bodies trapped inside the vessel (The Korean Herald Newspaper). Figure 7.19: The Seohae Ferry after it was brought to surface According to eyewitnesses, the accident occurred very quickly. After turning to star-board, the vessel rolled two or three times and capsized. In this section, possible use of the monitoring and advisory system for this kind of accidents is discussed. The first step is to analyse the static stability of the vessel and check if it meets the rules, such as IMO or Coast Guard rules. These analyses were done just after the accident by Prof. K. P. Rhee of Seoul National University. A body plan of the vessel Chapter 7. Numerical Simulations 132 and the results from these analyses are given in Figure 7.20 and Table 7.4. 2.4 1.8 1.2 0.6 o.o -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 Figure 7.20: Body Plan of the Seohae Ferry Overall Length (m) LBP (m) Breadth (m) Depth mid. (m) Displacement (Ton) Draft (m) MTC (t-m) KG(m) GM(m) LCB (Aft -) (m) LCG (Aft -) (m) Loading Conditions Light ship 37.40 33.0 6.20 2.70 188.0 1.628 3.035 2.576 0.605 -0.926 -2.054 Light load departure ----205.2 1.715 3.352 2.518 0.623 -0.972 -2.516 light load arrival ----199.9 1.686 3.267 2.558 0.594 -0.957 -2.470 Full load departure ----231.7 1.886 3.754 2.508 0.592 -1.044 - 1.858 Table 7.8: Results From Static Stability Calculation of the Seohae Chapter 7. Numerical Simulations 133 According to the International Maritime Organization (IMO) stability rules, the min-imum GM should be bigger than 0.15 m. As seen from Table 7.4, the Seohae met this criteria under all conditions. The second step is to analyse the dynamic conditions. When the accident occurred, the ship was navigating at about 10 knots, estimated wave height was about 2.0 m, and the wave direction was following seas. There is no information available about wave frequencies or length. The following data is used to simulate the accident conditions. Ship Speed 10 Knots LBP 33.0 m Draft 1.90 Wave Height 2.0 m Wave Length 32.0 m Table 7.9: Input Data for Dynamic Stability Simulations S 0 S < o DC -25 -50 --5 10 15 20 Time (sac) 25 Figure 7.21: Capsizing Simulations of the Seohae As seen from Figure 7.21, the vessel was capsized within 28 seconds, after 3 rolls. Chapter 7. Numerical Simulations 134 This result is in agreement with the eyewitness reports. After the above simulation, the same conditions were input to the monitoring and ad-visory system. The recommended action was to reduce speed 3 knots. In this simulation, it is assumed that the captain had an option to analyse the situation before turning. That is, the captain input new heading and speed. Since the other information such as wave direction, frequencies and estimated height are available from the monitoring system, the advisory system only needs these two pieces of information to analyse the new condition. Figure 7.22 shows roll motion data of the vessel after suggested action. 2.5 < 0.0 • -2.5 -_ I M _ ^ M - H h . 50 100 _. . , 150 Time (sec) Figure 7.22: Capsizing Simulations of the Seohae These simulations show the possible use of a monitoring and advisory system. Because these simulations do not take some factors, such as shift of cargo, sloshing etc. into account, these results should only be considered as preliminary. But it is clear that a captain would have a better understanding of the vessel and environment conditions and more help to make a reliable decision. Chapter 8 Conclusions and Future work 8.1 Conclusions In this research, the architecture of an intelligent monitoring and advisory system has been developed. This system uses environmental information obtained from a number of sensors and proposes corrective action based on a rule-base derived from human exper-tise, experiments and theoretical research. This system has two primary advantages for practical application : • The system uses the available on-board equipment such as Loran-c, radar and computer, (most ships have nowadays) making the system less costly. • The system does not interfere with the operation of the vessel. Contrary to the previous work on this area, this system also monitors the static stabil-ity of the vessel. The importance of this can easily be seen from statistics on accidents. In this part, two different methods (dynamic inclining experiments) are developed for estimating metacentric height (GM) of the vessel. These are Estimating the coefficients of GZ curve and Spectral analysis. Reasonable agreements were found between predicted and experimental values. Monitoring the dynamic stability of the system is divided into two steps : 1. monitoring environment parameters 2. measurement and analysis of ship motions 135 Chapter 8. Conclusions and Future work 136 As a part of the monitoring system, processing of radar images is used as a method for extracting wave properties. Three-dimensional spectral analysis of a series of radar images has been previously demonstrated as a method for determining the orientation and direction of ocean waves. Unfortunately, this technique is very costly in terms of processing time which is in the order of 12 minutes on a dedicated HP Workstation [51, 52]. In view of the need for the wave parameters at a much faster rate (see Appendix F), in the order of 30-60 seconds, for input into the intelligent advisory system, alternative techniques based on image processing methods have been developed. Two techniques, the boxing technique and the thinning technique, have been developed to provide the required wave parameter data at an acceptable rate. The boxing technique finds the wave orientation by fitting thin rectangular boxes to wave regions in a binary radar image. The success of the boxing technique depends on the initial placement of the rectangular box. The radar images tend to have limited regions in which the wave directions are obvious. There is considerable noise in the images and much of the wave information is obscured. The boxing technique works well if the box is placed in the vicinity of an obvious wave, reliable automatic placement of the box still remains as a problem. In order to overcome the local nature of the boxing technique, a more global thinning technique has been developed. The thinning technique transforms a binary radar image by eroding all objects until only the skeleton or spine of each object remains. A histogram of wave orientations is maintained, and the goodness-of-fit and the length of each segment are used to bias the histogram entries. The wave orientation corresponding to the peak in the histogram is selected as the dominant wave direction. Since the wave orientation is known, compar-isons between the initial image region and regions in successive images is restricted to Chapter 8. Conclusions and Future work 137 shifts along the line normal to the wave orientation. The least-squares error between the regions is used as the basis for selecting the wave direction. Finally, the maximum entropy method is used to determine the wave frequency in a direction normal to the wave orientation. This technique has been tested on typical radar images and the re-sulting parameters are in agreement with both the 3-D spectral analysis technique and the simpler boxing technique. The primary advantage of the thinning technique over the boxing technique is the global nature of the orientation phase. A fuzzy expert system has been developed as a decision making process for the mon-itoring and advisory system. Rules forming the basis for the advisory system are pre-sented. An advantage of this structure is that new rules may be easily appended to the existing rule base in view of further knowledge gained through interview with experts, experiments or theoretical developments. Finally, the feasibility of the approach has been demonstrated through simulations of various sea conditions on a range of ship forms. Simulations show that the vessel considered capsizes very quickly, in the order of 2 - 2.5 minutes and usually after only a few rolls. As seen from Figures 7.2, 7.3, 7.4, 7.5, 7.7, 7.8, 7.9, 7.10, the maximum roll angle before capsizing is about 20°. Therefore, it is difficult for a captain can realise the danger under these conditions, since the captain cannot estimate the wave frequency and wave length. But having a system described in this thesis would help the captain to see the danger very quickly and take preventive action in time. This would prevent accidents and loss of lives. 8.2 Contributions of this research The main contribution of this research is to show the feasibility of obtaining environmetal data in a short time and the development of a suitable monitoring and advisory system Chapter 8. Conclusions and Future work 138 for safety of vessels. Using a fuzzy expert system based monitoring and advisory system to help to combine the knowledge already available from experts and experience with the knowledge gained from theoretical and experimental analysis to enhance the reliability of the system is another contribution. This research provides image processing techniques to find wave parameters from radar images in 30 - 60 second. This technique is also suitable for automated processing which is needed for this work. Other contributions include: Showing the need for monitoring static stability and providing a methodology for it. Using the ship as a sensor to estimate the wave height. 8.3 Future Work Further developments on this area may be suggested as : In stat ic stabil i ty : More experiments with different kinds of ships to test the estimation methods for GM is needed. 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Statistical approach in computer control of cement totary kilns. Journal of Automatica, 8:35 - 43, 1972. [83] H Akaike. Statistical predictor identification. In Ann. Inst. Statist. Math., vol-ume 22, pages 203 - 217, 1970. [84] H Akaike. A new look at the statistical model identification. In IEEE Trans. Automatic control AC-18, volume 19, pages 716 - 723, 1974. [85] R. H. Janes. Identification and autoregressive spectrum estimation. In IEEE Trans. Automatic control AC-19, volume 19, pages 894 - 898, 1975. [86] G. Klir and T. Folger. Fuzzy Sets, Uncertainty and Information. Prentice Hall, Englewood Cliffs:USA, 1988. [87] Togai Infralogic Inc. Irvine:USA. Fuzzy-C Development System: User's Manual. Bibliography 145 [88] E. Dougherty and C. R., Giardina. Image Processing - Continuous to Discrete, volume 1. Prentice-Hall, 1987. [89] J. Serra. Image Analysis and Mathematical Morphology. Academic Press, 1988. [90] E. Dougherty. Mathematical Morphology in Image Processing. Marcel Dekker Inc., 1991. [91] V. Atanasov, W. Rosenthal, and Ziemer F. Removal of ambiguity of two-dimensional power spectra obtained by processing ship radar images of ocean waves. Journal of Geophysical Research, 90 Cl:1061 - 1067, 1985. [92] Barrick E. D. Extraction of wave parameters from measured hf radar sea-echo doppler spectra. Radio Science, 12:415 - 424, 1977. [93] Belinda L. Derivation of directional ocean wave spectra by integral inversion of second order radar echoes. Radio Science, 12:425 - 434, 1977. [94] E. Kose, R. Gosine, and S. M. Calisal. Toward a real -time system for monitoring the safety of fishing vessel. In Marsim'93, St. John's Newfoundland, Canada, 1993. [95] A. C. Lindley. Practical Image Processing In C John Wiley & Sons, Inc, 1991. [96] D. Hoffman and W.H. Jr. Grazke. Heavy weather monitoring and guidance system on the s.s. lash italia (second phase of test and evaluation). Technical report, National Maritime Research Center NMRC-KP-197, 1980. [97] A. Nafarieh. A fuzzy logic rule-based automatic target recognizer. Intelligient system, 6:295 - 3 1 2 , 1991. [98] D. W. Bass, Haddara M. R., and B. Zou. A comparison of the roll damping characteristics of five small fishing vessels at zero speed. Proceedings of The Marine Dynamics Conference St. John's Newfoundland, pages 1 - 8 , 1991. [99] Haddara M. R. and D. W. Bass. On the form of roll damping moment for small fishing vessels. Ocean Engineering, 17:525 - 539, 1990. [100] Haddara M. R. and P. Bennett. A study of the angle dependence of roll damping moment. Ocean Engineering, 16:411 - 427, 1989. [101] R. C. Gonzalez and P. Wintz. Digital Image Processing. Addison Wesley Publishing Company, 1987. [102] B. K. P. Horn. Robot Vision. McGraw-Hill Book Company, 1986. Append ix A Encounter Frequency The t ime history of waves encountered by a moving point (a ship under way, for example) is significantly modified by the Doppler shift in the component frequencies of the wave system. Suppose an x0, y0 coordinate system, fixed in relation to the earth, and a regular progressive wave of amplitude ( and wave number k, propagating in a direction fi relative to the XQ axis. In the fixed coordinate system the free surface of the wave field is described by A.l [24] : C(x0,y0, t) = ( cos[k(x0 cos \i + y0 sin fj,) — ut + e] (A. l ) Now suppose further that a ship proceeds in the direction of the XQ axis at constant velocity UQ, and we wish to describe the wave field as would be observed from the moving ship. We assume a moving, x — y coordinate system with origin in the ship and whose x axis is aligned with the fixed x axis. Since the location of the ship at any instant t ime t, is Uot, the relation between the two coordinate sytems is : x0 = x + U0t (A.2) yo = y (A.3) (A.4) Substituting in Equation A.l the expression for the wave field as seen from the moving ship becomes: 146 Appendix A. Encounter Frequency 147 C(xo, yo, t) = C cos[kx cos fi + ky sin fi — (u> — kUo cos ^ i)< + e] (A.5) The coefficient of t in equation A.5 defines a frequency of encounter, a»e, and noting that k = tv2/g for deep water : u)2U oje — u>w — cos(< )^ (A.6) 9 where (jje : Encounter Frequency uiw Wave frequency U : Ship speed <f> : Angle between wave direction and ship direction Appendix B F F T Algorithm Young et al.[1983] present a concise explanation of how a time series of two dimensional maps of sea surface height (or radar backscatter) can be transformed into a directionally unambiguous wave spectrum (or radar images spectrum). Starting with sea surface height rj(£) where £ is a three dimensional vector (x,y,t), the three dimensional Fourier series can be written as i=i where Q£ = kxx + kyy — ut . Now since T}(£) is real valued, the complex conjugate of Equation B. l is n " ) = I>(Oi«p(-*nO (B.2) 3=1 It is clear from B.l and B.2 that F(Q) = F*(-n) (B.3) The variance spectrum is defined as m) = jj^\nm2 (B.4) where Lx and Ly are the spatial length of the data vector and T is the temporal length. The factor h \ T is chosen to normalize the variance so that 148 Appendix B. FFT Algorithm 149 E(Q)dn = a2 (B.5) •nN where fijv is the Nyquist limit and a2 is the variance of the data set. From Equation B.3 and B.4 it follows that E(Q) = E(-Q) (B.6) Equation B.6 shows that the variance spectrum is reflection symmetric about the point fi = 0 in wave number frequency space. Now in the case of a single sea surface height field (77 = rj(x,y), the two dimensional case). Equation B.6 simplifies to E(kx,ky) = E(-kx,-ky) (B.7) Thus any wave spectrum calculated from a single 'image' will be ambiguous as to the propagation direction. In the three dimensional data case, Equation B.6 can be rewritten as E(kx,ky,uj) = E(-kx,-ky,-io) (B.8) Each point in wave number frequency space corresponds to a plane wave in physical space, the phase speed of which is given by the time development of a fixed phase plane ft£ = (kxx + kyy — u;t) — constant (B-9) So it can be seen that two points in wave number frequency space mirrored about fi = 0 will have phase speed of opposite sign, and will represent counter propagating waves. To obtain the two dimensional spectrum E(Q) can be integrated with respect to LO Appendix B. FFT Algorithm 150 E{kx,ky)= / E(n)dcu (B.10) JwN However using this procedure the phase speed direction information is lost. Now if instead the integration is limited to only one-half of the ui space, say u) > 0 E(kx,ky)= j E(n)dcu (B.ll) Ju>0 then E will be asymmetrical. The phase speed direction for a given wave will then be that of its wavenumber k = [kx, ky). Conversely, if the integration is limited to the negative u) space the wave propagation direction will be (—kx,ky). Thus a series of sea surface height images can be processed into a directionally unambiguous wave spectrum. A p p e n d i x C M E M Spectrum Est imat ion of A R coefficients In order to compute the MEM power spectrum using 5.21, we must determine first of all the length of the required prediction filter M (or equivalently the order of the AR process) and second, the coefficients themselves. Since the method of determining M assumes knowledge of the coefficients, estimation of these parameters will be discussed first. Burg Est imates Burg[1967,1968] suggested a method of estimating the AR parameters (or equiva-lently the prediction error filter coefficients) that does not require prior estimate of the autocovariance function. The YW equations can be written as p(0) p(l) ••• p(M-l) p(l) p(0) ••• p{M-2) p(M-l) p(M-2) . . . p(l) where CLMJ is the j t h coefficient of the Mth order AR process. A recursive solution may be obtained by using the Levinson [73] and Durbin [74] procedure. The recursion obtains the estimates otsj, j = 1,2,3 from the estimates &2j, 151 &MI &M2 &MM — Pi h PM (C. l ) Appendix C. MEM Spectrum 152 j = 1,2 [75]. By using the first two equation of (C.l) with M=3 the estimates &31 and «32 may be expressed in terms of 6:33 in the form <23i a-32 (7(1) The above equation can be written as PV) PV) P(°) « 3 3 P(2) « 3 1 QI32 = (7(1) - 1 PO) m cci)-1^ PV) However, since substituting M = 2 in (C. l) gives 0.21 Q.22 C'(l)-1 PV) m it follows that (C.2) (C.3) (C.4) (C.5) &31 a32 — « 2 1 a 2 2 - a 3 3 « 2 2 a2i (C.6) It is convenient at this stage to obtain an alternate form of the YW formulation expressed by C.l . This alternate form, which is suggested by (C.6), will allow us to express the recursion for the Burg [57, 58, 76] estimates of AR coefficients in a very elegant form. In deriving (C.7) E(xt-ka — t) = 0 for k > 0. When k=0, however, E(xt-kat) = E{xtat) = E(al) = a\. Hence when k=0 p(0) = alP(l) + a2p(2) + ••• + aMp(M) + a\ (C.7) Appendix C. MEM Spectrum 153 C.7 allows us to write P(0) P(l) P(0) , (M) p(M - 1) rfo) 1 -<*i -<*M = ' °l 0 0 = PM+I 0 0 (C.8) p{M) p(M-l) •• The correspondence between the AR process and the prediction of xt from a knowledge of its past values identifies the constant PM+I a s the prediction error power resulting from convolution of xt with the M + l point prediction error filter 7 t . Burg [76] expressed the recursion in (C.6) using the formulation in (C.8) in the fol-lowing manner (7(3) = 1 - « 3 1 ~ « 3 2 - « 3 3 = (7(3) 1 -OL2l < -OL22 0 v J ' - a33 < 0 -CL22 > -a2\ 1 (C.9) Clearly, since (C.6) is independent of p(k), it can be used to relate a 3 i and d32 to ct2i and OL22, therefore the recursion of these coefficients is contained in (C.9). The p{k) in this equation represents some as yet undetermined estimates of the autocovariance function. To determine p(k), we can minimize Y,al (following the principle of least squares) with respect to 6:33. This procedure is equivalent to minimizing the prediction error power with respect to 0:33. Thus 0:33 may be obtained dff(Q=33) da33 (CIO) Appendix C. MEM Spectrum 154 where 5(033) is the residual sum of squares for the third order AR process and is given by N S(a33) = J2(xt ~ &3ixt-i - a32xt_2 - a.3Zxt-3f (C.ll) t = 4 Actually, the solution of (CIO) for a3 3 using estimates of 0:3! and a.32 obtained from the recursion given by (C.6) in fact corresponds to an approximate maximum likelihood estimation of these coefficients [75]. An important extension to (C . l l ) was proposed by Burg[1968] on the basis of the predictive interpretation of the AR process. Thus Burg suggested that the prediction error power be calculated by running the prediction error filter over the data in a forward and backward direction. The expression for the error power for the third order AR process is 1 N Pi = oTTJ qT X ^ 1 ' ~~ <*3lXt-i - a32Xt-2 - &33Xt-3)2 + (xt-3 - a31xt-2 ~ a 3 2 z t - i - oc33xt)2} (C.12) and OC33 is determined from dPi/da.33 = 0. The important point to notice about (C.12) is that P 4 is determined by running the filter over the data, not off the data. In the other words, no assumptions are made concerning the extension of the data outside the parameter space, and estimation of the AR coefficients is consistent with the principle of maximum entropy. If the estimate of ^(0) is computed in the usual manner: •'v t = i then the remaining autocovariance estimates may be determined recursively. It easily shown from (C.9) that Appendix C. MEM Spectrum 155 p(r) = Ep(r-k)aTk r = l,2,---,M (C.14) k=i Determinat ion of the order of the A R process An issue which must be dealt with in the course of computing MEM spectral estimates is the selection of the order which best matches the MEM spectrum to the true spectrum. The estimation of the order of the AR model from a realization of the process has been treated by a number of author [Anderson, 1963; Jones, 1964; Jenkins and Watts, 1969; Galbraith, 1971], but all these techniques lack to some extent the objective basis that is required . Akaike [77, 78, 79] proposed an estimating procedure which gives excellent results, and its application to MEM spectral analysis removes the chief shortcoming of these techniques. The Akaike criterion, which is called the final prediction error FPE, has been investigated by Gersch and Sharpe [80] with respect to the estimation of power spectra of finite order AR models and by Fryer et al. [81], who investigated the application of the F P E to multichannel t ime series [77, 78, 79, 82]. The Akaike [83] criterion minimizes the prediction error when the error is considered as the sum of the innovation and the error in estimating the AR parameters. For an Mth order fit: (FPF\ N + (M+1) 2 {FPE)M~ N-(M + I)SM ( C-1 5 ) where S\j is the residual sum of squares. Akaike [84] has extended this criterion through the application of the principle of maximum likelihood. The new criterion is called an information theoretic criterion (AIC) and allows the specification of the probability density function for the observation: Appendix C. MEM Spectrum 156 (AIC)k = —2log(maximized likelihood function) + 2k (C.16) where k is the number of independent parameters estimated. When the process is AR of order M with Gaussian errors the above expression reduces to: (AIC)M = NlogSls + 2(M + 1) (C.17) Since the 1 in eq. (C.17) is only an additive constant which reflects subtraction of the mean eq. (C.17) is usually written as: (AIC)M = NlogS2M + 2M (C.18) Gercsh and Sharpe [80], Akaike [84] and Jones [56, 85] have used the AIC successfully in a number of different applications. Generally, it has been found that the AR order given by the FPE and AIC criteria is the same. A p p e n d i x D Sea S p e c t r u m s D . l I . T . T . C . Sea S p e c t r u m Recommended by the 16th I.T.T.C. Sea Keeping Committee to be used as a standard for open ocean conditions, the spectrum is available as either a one parameter (Sig. Wv. Ht. (Hs)) or two parameter (Sig. Wv. Ht. (Hs) and Av. Period (Tl ) ) formulation. The general form for the spectral formulation is S(w) = (A/w5)e(-B/wl) m2 - sec (D.l) where w = wave frequency (rad/sec) and A and B are constants dependent upon whether one or two parameter formulation is required. The one parameter form relates to the case of fully developed sea conditions and is derived from data collected in the North Atlantic Ocean. The formulation is a modification of the Pierson-Moskowitz Spectrum using the relationship between Sig. Wv. Ht. and Wind speed at 19.5m above sea level for fully developed seas (i.e. that have an unlimited fetch). Therefore to define a number of spectra using this formulation, for each spectra required, a value for Hs is input usually in the range 1.0 to 10.0 m. The constants A and B are defined in this formulation as A = 0.0081<72 B = ljT (D - 2 ) a The two parameter spectrum is to be used for open ocean conditions and is again derived from wave data collected in the North Atlantic Ocean. The formulation requires values to be input for both Hs and T l . Therefore this formulation is to be used when a relationship 157 Appendix D. Sea Spectrums 158 between Hs and T l is known for the sea area in question or the Hs and T l combinations that can occur (e.g. scatter diagrams) are available. Usual values for Hs are in the range 1.0 to 10.0 m. Scatter diagram data may be for observed sea conditions so the relationship between these and the parameters used in the spectrum formulation must be determined. The constants A and B are denned as follows A = 1 7 3 ^ B = | £ (D.3) D . 2 Bretschneider Sea Spectrum This spectrum is for a fully developed sea with the formulation being derived on the premise that the wave period follows a Rayleigh distribution, as does the wave height. The spectrum is available as a two parameter formulation (Sig. Wv. Ht. (Hs) and Av. Period (T l ) ) and is of the following form, A -B S(w) = - — e ^ m2 — sec (D.4) w5 ' where Hs2 A = 2 6 3 — (D.5) B - ^ ( D , ) (D.7) This spectrum is to be used for open ocean conditions and is derived from wave data collected in the North Atlantic Ocean. To define a number of spectra using this formulation requires values for both Hs and T l for each required sea spectra Therefore this formulation is to be used in the case either when a relationship between Hs and T l Appendix D. Sea Spectrums 159 is known for the sea area in question or the Hs and Tl combinations that can occur (eg from scatter diagrams) are available. Usual values for Hs are in the range 1.0 to 10.0 m. Append ix E Catalogue of Radar Image series The following information is reproduced from [51] for convenience. RRMC X-Band Radar ERS-1 Cal/Val Cruise November 1991 The wave directions are described using numbered octans relative to ship's heading. Octan 1 is directly forward, 3 is starboard, 5 is aft, and 7 is to port. Wave direction is ambiguous. Times are UT. Ship speed is in knots. D a t e T i m e Wave Image Descript ion Swell 8-4. Wind waves 2-6 Rain showers Clear image 7-3 swell and 2-6 wind wave Good wave signal Rain reduce signal/noise but waves still visible Strong wave signal but considerable radar interference 7-3 wind wave. 8-4 swell Wind wave 6-2. Swell 8-4 Possible additional swell Heading Speed 12 12 14 14 14 09:38 14:46 11:42 11:57 12:12 14 20 20 12:42 11:30 13:00 119 119 87 94 99 1.2 11.6 1.4 0.5 2.1 160 Appendix E. Catalogue of Radar Image series D a t e T i m e Wave Image Description 20 13:30 Wind wave 6-2. Swell 8-4 Possible additional swell 20 14:00 Swell 8-4 becoming clearer 20 14:14 Crossed wind and wave swell 20 15:30 Crossed wind and wave swell 20 16:00 Crossed wind and wave swell 20 16:30 Crossed wind and wave swell 20 23:30 Crossed wind and wave swell Wind wave 8-4. 21 18:51 Wind wave 7-3. Wind 40 kt 21 19:42 Wind wave 8-4. Fairly monochromatic 21 20:35 Wind wave 8-4 Building sea 21 21:32 Wind wave 8-4 Building sea High speed 21 22:00 Wind wave and swell 8-4 21 22:30 Wind wave and swell 8-4 21 23:00 Wind wave and swell 8-4 21 23:30 Wind wave and swell 2-6 21 24:00 Wind wave and swell 2-6 Possible upwind / downwind test series 22 00:32 Wind wave and swell 2-6 Possible upwind / downwind test series 23 15:30 Swell 6-2. Wind wave 7-3 Possible swell 1-5 23 19:02 Wind wave and swell 8-4, Swell 1-5 23 19:40 Swell 8-4 and 7-3 23 20:08 Swell 1-5 23 20:33 Swell 7-3 and 6-2 23 23:30 Swell 1-5 and 2-6 23 24:00 Swell 1-5 and 2-6 24 01:30 Swell 1-5. Very much reduced signal strength Heading 270 280 272 297 285 276 273 267 272 91 276 271 282 11 255 Spee 1.3 1.3 1.5 3.0 1.8 2.0 1.5 3.4 1.6 13.1 2.8 1.9 0.9 4.0 1.6 272 336 1.8 1.7 356 84 180 259 313 293 304 0.6 2.3 0.3 1.5 2.5 2.1 0.4 Appendix F Capsizing Times The following Table is reproduced from [64] to show capsizing times. These experiments were done in San Fransisco Bay. Date 9-2-1971 9-13-1971 9-16-1971 n n » n » » » » JJ » 11 11 ii 11 n 9-21-1971 ii » » ii n » » ii ii ii ii ii ii ii ii 9-28-1971 Heading following quartering quartering following following following following quartering quartering quartering quartering quartering quartering following following Duration (sec.) 75 164 375 147 100 360 213 351 228 235 280 365 52 254 121 Capsize port port starbord port port starboard port starboard starboard starboard starboard starboard starboard port port Table F.l: Capsizing times obtained from model tests in San Francisco Bay 162 Appendix G 1. IF Wave_Height IS MED AND Wave_Direction IS MED AND WL_SL IS Z AND WE.2WN IS Z AND ShiP_Speed IS HIGH THEN Change_Speed = NB 3. IF Wave_Height IS MED AND Wave_Direction IS MED AND WL_SL IS Z AND WE_2WN IS Z AND Ship_Speed IS MED THEN Change_Direction = PS 5. IF WaveJHeight IS MED AND Wave_Direction IS MED AND GM_Singular IS Z AND Ship_Speed IS HIGH THEN Change_Speed = NB Rules 2. IF Wave_Height IS HIGH AND Wave_Direction IS MED AND WL_SL IS Z AND WE_2WN IS Z AND Ship_Speed IS HIGH THEN Change_Speed = NB 4. IF Wave_Height IS HIGH AND WaveJDirection IS MED AND WL_SL IS Z AND WE_2WN IS Z AND Ship_Speed IS MED THEN Change_Direction = PS 6. IF WaveJIeight IS HIGH AND WaveJDirection IS HIGH AND GM_Singular IS Z AND Ship_Speed IS HIGH THEN Change-Speed = NB 163 Appendix G. Rules 7. IF Wave_Height IS MED AND Wave_Direction IS MED AND GM_Singular IS Z AND Ship_Speed IS MED THEN Change_Direction = PB 9. IF WaveJDirection IS VL AND WH_Beam IS Z THEN Change_Direction = PB Return-Port = HIGH 11. IF WaveJDirection IS VL AND WH_Beam IS NB THEN Change_Direction = PB Return_Port = HIGH 13. IF WaveJDirection IS VH AND WH_Beam IS NS THEN ChangeJDirection = NB Return_Port = HIGH 8. IF Wave Jieight IS MED AND WaveJDirection IS HIGH AND GM_Singular IS Z AND Ship_Speed IS MED THEN ChangeJDirection = NB 10. AND WaveJDirection IS VL AND WHJ3eam IS Z THEN Change-Direction = PB Return-Port = HIGH 12. AND WaveJDirection IS VH AND WH JSeam IS Z THEN ChangeJDirection = NB Return J>ort = HIGH 14. AND WaveJDirection IS VH AND WH J3eam IS NB THEN ChangeJDirection = NB ReturnJ>ort = HIGH Appendix G. Rules 15. IF Wave-Direction IS VH AND WH_Beam IS NB THEN ChangeJDirection = NB ReturnJPort = HIGH 17. IF Wave-Height IS MED AND WaveJDirection IS MED AND WE_WN IS Z THEN ChangeJDirection = PB 19. IF Wave_Height IS HIGH AND WaveJDirection IS HIGH AND WE_WN IS Z AND WH_Beam IS Z THEN Change_Direction = PS 21. IF WaveJieight IS HIGH AND Wave_Direction IS HIGH AND WE_WN IS Z AND WHJBeam IS NB THEN Change_Direction = PS 16. AND Wave_Direction IS MED AND WH_Beam IS MED WE_WN IS Z THEN Change .Direction = PB 18. IF Wave-Height IS MED AND Wave-Direction IS HIGH AND WE_WN IS Z THEN Change-Direction = PS 20. IF WaveJieight IS HIGH AND WaveJDirection IS HIGH AND WE_WN IS Z AND WH-Beam IS NS THEN ChangeJDirection = PS 22. IF WaveJieight IS MED AND WaveJDirection IS LOW AND WE_WN IS Z AND WH JSeam IS Z THEN Change-Direction = NS Appendix G. Rules 25. IF Wave_Height IS MED AND Wave_Direction IS MED AND WE.WN IS Z AND WH_Beam IS NS THEN Change_Direction = NS 27. IF WaveJfleight IS HIGH AND Wave-Direction IS LOW AND WE_WN IS Z AND WH_Beam IS Z THEN Change_Direction = NS 29. IF Wave_Height IS HIGH AND WaveJDirection IS MED AND WS_SS IS Z AND Ship_SPeed IS HIGH THEN Change_Speed = NB 26. IF Wave_Height IS MED AND Wave-Direction IS LOW AND WE.WN IS Z AND WH_Beam IS Z THEN Change_Direction = NS 28. IF Wave_Height IS MED AND Wave-Direction IS HIGH AND WE_WN IS Z AND WH_Beam IS HIGH THEN Change_Direction = NB 30. IF Wave_Height IS HIGH AND Wave-Direction IS MED AND WS_SS IS Z AND Ship_Speed IS MED THEN Change_Direction = PB Change_Speed = PS Appendix G. Rules 31. IF Wave_Height IS HIGH AND Wave_Direction IS LOW AND WL_SL IS Z AND Ship_Speed IS HIGH THEN Change_Direction = PS Change_Speed = NS 33. IF WaveJHeight IS HIGH AND WaveJDirection IS LOW AND WL_SL IS Z AND Ship_Speed IS MED THEN Change-Direction = PS 35. IF Wave-Height IS HIGH AND Wave-Direction IS LOW AND WL_SL IS Z AND Ship-Speed IS MED THEN Change-Direction = NS 32. IF Wave-Height IS HIGH AND Wave-Direction IS LOW AND WL_SL IS Z AND Ship-Speed IS HIGH THEN Change-Direction = PS Change_Speed = NS 34. IF WaveJieight IS HIGH AND WaveJDirection IS HIGH AND WL_SL IS Z AND Ship-Speed IS HIGH THEN Change-Direction = NS Change_Speed = NS 36. IF WaveJieight IS HIGH AND WaveJDirection IS HIGH AND WL_SL IS Z AND Ship_Speed IS LOW THEN Change-Speed = PB Append ix H Membersh ip Functions H . l Se t t ing t h e values of membership functions Two methods are used to obtain the values of each member : 1. By definition : The values for wave direction with respect to ship is set by using the definition shown in Figure 2.4. 2. Theoretical calculations. Values of the some membership functions such as WL_SL, WE_2WN and ship speed are found by using simulation programs. These programs were run for different combina-tions of the membership functions to see their effect on ship behaviour. Then, member-ship values were obtained from these results to give suggestions if the vessel is in danger. For example, say when WL_SL is 1 m, the vessel capsizes, but when WL_SL is 2 m, vessel does not capsize, then this membership value is set to say 1.5 to accommodate the gray area in between values. Although, the values try to cover most ships, this is impossible for some variables such as ship speed and wave direction. For example, membership values for ship speed depend on maximum ship speed and available power on the ship. Therefore membership values for some variables such as ship speed and wave height have to be changed for series of ship e.g. series 60, UBC series. 168 Appendix H. Membership Functions Membership Meaning HIGH LOW MED NB NS PB PS VH VL VVH VVL Z High Low Medium Negative big Negative small Positive big Positive small Very high Very low Very very high Very very low Zero Appendix H. Membership Functions 170 Membership functions for wave Direction : 40 70 90 120 140 170 180 220 240 280 300 340 Membership function for wave height Membership function for Wave speed - Ship speed (WS SS) - 6 - 3 0 3 6 Appendix H. Membership Functions 171 Membership functions for Wave length - Ship length (WL SL) -3.5 -1.5 0 1.5 3.5 Membership function for Encounter frequency - twice roll natural frequency (WE-2WN) -2.5 -1.5 0 1.5 2.5 Membership function for Ship speed : 7.5 10 12.5 Appendix I Glossary Some ship related terminologies : Baseline Suppose a ship's basic hull shape is placed in an imaginary rectangular box whose bottom and sides just touch the ship's surface. The bottom of the this box may be used as a reference base and is called the baseline. Block coefficient (Cj,) The ratio of the volume of displacement to the volume of rect-angular block having a length appropriate to the type of ship and a beam and draft equal to that of the maximum section area. C° ' 1ST <U> Center of Buoyancy The center of bouyancy is the line of action of the resultant of all bouyant forces on the immersed portion of the ship's hull. It passes through the geometric center of the underwater form, at which point, it is called center of bouyancy. The height of the center of bouyancy above the keel is designated KB and determined by KB = ^- j Awzdz (1.2) where Aw is the area of waterplane at height z above the keel. 172 Appendix I. Glossary 173 Des igned Waterl ine ( D W L ) : Specially designated waterline is the designed water-line (DWL), where the ship is designed to float at a predetermined load (see Figure I Displacement The weight of the water that the ship displaces when floating freely is called displacement. The symbol A is used for displacement. Drafts The forward and after draft are those vertical distances from the baseline to the waterline of reference measured at the forward and after perpendicular. Length B e t w e e n Perpendicular (LBP) ; The length between perpendicular is cus-tomarily coincident with the designed waterline (DWL). For the merhant ship prac-tice, the location of the after perpendicular most frequently is coincident with the vertical rudder post (Figure I). In all cases, the forward perpendicular is coincident with the forward extremity of the DWL (Figure I). List, Hee l and Roll Ships are designed to and normally do, float upright. However, because of unsymmetrical loading conditions or other unbalanced forces, they may incline transversely with respect to their normal upright positions. Such transverse inclinations are described as list, heel or roll depending on the nature of the situa-tion. List describes a definite atti tude of transverse inclination of a static nature. Heel describes a temporary inclination, generally involving motion, whereas roll involves recurrent inclination from side to side. T h e Metacenter (M) The intersection of the vertical through the center of bouyancy of an inclined body or ship with the upright vertical when the angle of inclination approaches zero as a limit. Appendix I. Glossary 174 Metacentr ic Height ( G M ) The metacentric height is the vertical distance measured on the vertical centerline between the metacenter and the center of gravity. Metacentr ic Radius ( B M ) The metacentric radius is the distance between the center of bouyancy B and the metacenter M. heave sway ££ : Midship f / T: Draft ' t : Trim DWL surge AP (After Perpendicular) (Forward Perpendicular) M: Metacenter G : Center of gravity B : Center of bouyancy Appendix I. Glossary 175 Image processing related terminology: Bi -modal histogram A characteristic histogram pattern showing that image is pixels partition into two distinct classes. Convolution : Filtering a data series by integration or summation of data series with a kernel. Dilat ion A morphological operation during which an object is incresed in size by the addition of pixels from around its boundary. Erosion A morphological operation during which an object is decreased in size by the removal of pixels from around its boundary. Segmentat ion The division of an image into regions corresponding to objects or parts of objects. Thinning One technique for retrieving the medial axis of an object based on removing pixels from the object boundary whilst retaining connectivity. Threshold A pixel value at which a decision is made about the value assigned to the output. 

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