A Decoupled Method for Credibility-Based Design Optimization with Fuzzy Variables

Fuzzy uncertainty (FU) exists widely in engineering applications, but there lack design optimization methods under FU, thus a credibility-based design optimization (CBDO) is focused to obtain the safety design under FU in this paper. Firstly, the concepts of credibility index and most credible point (MCP) are presented to measure the safety degree under FU, where the credibility index and the MCP, respectively, show similar properties as the reliability index and the most probable point under random uncertainty. Secondly, the inverse MCP (IMCP) is defined with respect to the required credibility, and the detailed method is established for searching IMCP, on which the performance measure approach (PMA) can be combined to solve the CBDO. Since the PMA combined with the IMCP includes a time-consuming double-loop strategy, the sequential optimization and credibility assessment (SOCA) is proposed to decouple the double-loop strategy thirdly. In the SOCA, a shifting vector constructed by the IMCP is used to transform the credibility constraint into an equivalent deterministic one, on which the double-loop strategy can be avoided to reduce the computational cost for solving the CBDO. One numerical example and two engineering examples fully illustrate the efficiency and accuracy of the SOCA.