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UBC Theses and Dissertations

Conceptual design using probabilistic interval constraint satisfaction Loewen, Nathan


Dealing with uncertainty is one of the primary challenges engineers face in the conceptual design phase of a project. Engineers must make decisions with regards to uncertain design parameters that influence performance and cost. It is well recognized that decisions made in the concept phase of a project have far greater performance and economic impacts than decisions made during the detailed phase, yet most engineering analysis tools have limited capabilities to carry out risk analysis, sensitivity analysis, optimization, and design space mapping. This thesis proposes a methodology for coupling probabilistic techniques with recent advances in semi-quantitative analysis, specifically the application of interval analysis to numerical constraint satisfaction problems. The result is a method of analysis referred to as Probabilistic Constraint Satisfaction that can be used to analyze problems with probabilistic input and generate a probabilistic design space as an output. The methodology involves subdivision of the design space to a requested resolution and then testing the consistency of the constraint satisfaction problem at each subdivided location. This approach is very robust and is capable of solving a wide range of problems regardless of linearity or the availability of an explicit solution. Probabilistic data is integrated through the use of a solver which determines the valid interval for each of the probabilistic variables at a given point in the design space. The valid intervals are subsequently used to determine the probability of a feasible solution occurring at that point in the design space. The characteristics and capabilities of this methodology are illustrated through several engineering examples and a case study that involves the conceptual design of a novel radio antenna concept. The selected case study has several features that are common to conceptual design problems for novel and complex projects including design parameters with continuous domains, trade-offs between performance targets and cost, uncertain costing data, and limited existing experience to base the design on.

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