A Unified Framework for Integrated Optimization Under Uncertainty

Abstract

Reliability and robustness are two main attributes of design under uncertainty. Hence, it is necessary to combine reliability-based design and robust design at the design stage. In this paper, a unified framework for integrating reliability-based design and robust design is proposed. In the proposed framework, the probabilistic objective function is converted to a deterministic objective function by the Taylor series expansion or inverse reliability strategy with accounting for the probabilistic characteristic of the objective function. Therefore, with this unified framework, there is no need to deal with a multiobjective optimization problem to integrate reliability-based design and robust design any more. The probabilistic constraints are converted to deterministic constraints with inverse reliability strategy at the same time. In order to solve the unified framework, an improved sequential optimization and reliability assessment method is proposed. Three examples are given to illustrate the benefits of the proposed methods.