Multi-objective Robust Optimization using a Post-optimality Sensitivity Analysis Technique: Application to a Wind Turbine Design

摘要

Toward a multi-objective optimization robust problem, the variations indesign variables and design environment pa-rameters include the smallvariations and the large varia-tions. The former have small effect on theperformance func-tions and/or the constraints, and the latter refer to the onesthat have large effect on the performance functions and/or the constraints. Therobustness of performance functions is discussed in this paper. Apost-optimality sensitivity analysis technique for multi-objective robustoptimization problems is discussed and two robustness indices are introduced.The first one considers the robustness of the performance func-tions to smallvariations in the design variables and the de-sign environment parameters. Thesecond robustness index characterizes the robustness of the performancefunctions to large variations in the design environment parameters. It is basedon the ability of a solution to maintain a good Pareto ranking for differentdesign environment parameters due to large variations. The robustness of thesolutions is treated as vectors in the robustness function space, which isdefined by the two proposed robustness indices. As a result, the designer cancompare the robustness of all Pareto optimal solutions and make a decision.Finally, two illustrative examples are given to highlight the contributions ofthis paper. The first example is about a numerical problem, whereas the secondproblem deals with the multi-objective robust optimization design of a floatingwind turbine.