Mechanical Engineering
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Item Sensitivity Analysis Based Approaches for Mitigating the Effects of Reducible Interval Input Uncertainty on Single- and Multi-Disciplinary Systems using Multi-Objective Optimization(2010) Hamel, Joshua Matthew; Azarm, Shapour; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Uncertainty is an unavoidable aspect of engineering systems and will often degrade system performance or perhaps even lead to system failure. As a result, uncertainty must be considered as a part of the design process for all real-world engineering systems. The presence of reducible uncertainty further complicates matters as designers must not only account for the degrading effects of uncertainty but must also determine what levels of uncertainty can be considered as acceptable. For these reasons, methods for determining and effectively mitigating the effects of uncertainty are necessary for solving engineering design problems. This dissertation presents several new methods for use in the design of engineering systems under interval input uncertainty. These new approaches were developed over the course of four interrelated research thrusts and focused on the overall goal of extending the current research in the area of sensitivity analysis based design under reducible interval uncertainty. The first research thrust focused on developing an approach for determining optimal uncertainty reductions given multi-disciplinary engineering systems with multiple output functions at both the system and sub-system levels. The second research thrust extended the approach developed during the first thrust to use uncertainty reduction as a means for both reducing output variations and simultaneously ensuring engineering feasibility. The third research thrust looked at systems where uncertainty reduction alone is insufficient for ensuring feasibility and thus developed a sensitivity analysis approach that combined uncertainty reductions with small design adjustments in an effort to again reduce output variations and ensure feasibility. The fourth and final research thrust looked to relax many of the assumptions required by the first three research thrusts and developed a general sensitivity analysis inspired approach for determining optimal upper and lower bounds for reducible sources of input uncertainty. Multi-objective optimization techniques were used throughout this research to evaluate the tradeoffs between the benefits to be gained by mitigating uncertainty with the costs of making the design changes and/or uncertainty reductions required to reduce or eliminate the degrading effects of system uncertainty most effectively. The validity of the approaches developed were demonstrated using numerical and engineering example problems of varying complexity.Item Robust Optimization and Sensitivity Analysis with Multi-Objective Genetic Algorithms: Single- and Multi-Disciplinary Applications(2007-11-21) Li, Mian; Azarm, Shapour; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Uncertainty is inevitable in engineering design optimization and can significantly degrade the performance of an optimized design solution and/or even change feasibility by making a feasible solution infeasible. The problem with uncertainty can be exacerbated in multi-disciplinary optimization whereby the models for several disciplines are coupled and the propagation of uncertainty has to be accounted for within and across disciplines. It is important to determine which ranges of parameter uncertainty are most important or how to best allocate investments to partially or fully reduce uncertainty under a limited budget. To address these issues, this dissertation concentrates on a new robust optimization approach and a new sensitivity analysis approach for multi-objective and multi-disciplinary design optimization problems that have parameters with interval uncertainty. The dissertation presents models and approaches under four research thrusts. In the first thrust, an approach is presented to obtain robustly optimal solutions which are as best as possible, in a multi-objective sense, and at the same time their sensitivity of objective and/or constraint functions is within an acceptable range. In the second thrust, the robust optimization approach in the first thrust is extended to design optimization problems which are decomposed into multiple subproblems, each with multiple objectives and constraints. In the third thrust, a new approach for multi-objective sensitivity analysis and uncertainty reduction is presented. And in the final research thrust, a metamodel embedded Multi-Objective Genetic Algorithm (MOGA) for solution of design optimization problems is presented. Numerous numerical and engineering examples are used to explore and demonstrate the applicability and performance of the robust optimization, sensitivity analysis and MOGA techniques developed in this dissertation. It is shown that the obtained robust optimal solutions for the test examples are conservative compared to their corresponding optimal solutions in the deterministic case. For the sensitivity analysis, it is demonstrated that the proposed method identifies parameters whose uncertainty reduction or elimination produces the largest payoffs for any given investment. Finally, it is shown that the new MOGA requires a significantly fewer number of simulation calls, when used to solve multi-objective design optimization problems, compared to previously developed MOGA methods while obtaining comparable solutions.