Sequential Optimization and Mixed Uncertainty Analysis Method for Reliability-Based Optimization

Abstract

A reliability-based optimization method under both aleatory and epistemic uncertainties is studied. The mixed uncertainties are analyzed by combined probability and evidence theory. If the mixed uncertainty analysis is directly embedded in reliability-based optimization to quantify the uncertain features of each search point, it would be computationally prohibitive. To address this problem, a sequential optimization and mixed uncertainty analysis method is proposed to decompose the reliability-based optimization problem into separate deterministic optimization and mixed uncertainty analysis subproblems, which are solved sequentially and alternately until convergence is achieved. The research focus is how to transform the reliability-based optimization problem into its quasi-equivalent deterministic formulation according to the information obtained in the uncertainty analysis. It is proposed to first decompose the total reliability target into each focal element of the epistemic uncertainties, so as to simplify the complex mixed uncertainty problem into several mixed probability and single-interval subproblems. In each focal element, the algorithm to transform the uncertain objective and constraint into the quasi-equivalent deterministic formulations is developed by extending the existing probabilistic performance measure approach with probability and evidence theory. The effectiveness and efficiency of the sequential optimization and mixed uncertainty analysis method are testified with one numerical example and one practical satellite conceptual design problem.