Time-dependent sequential optimization and possibility assessment method for time-dependent failure possibility-based design optimization

Time-dependent failure possibility-based design optimization (T-PBDO) can provide the balance between the optimal performance and the safety requirements under the fuzzy uncertainty. However, there lacks efficient methods to solve the T-PBDO model. In this paper, a time-dependent sequential optimization and possibility assessment method (T-SOPA) is proposed to solve T-PBDO efficiently and accurately. By introducing an equivalent transformation of the constraint defined by the target time-dependent failure possibility (TDFP), the proposed T-SOPA method divides T-PBDO into some iteratively sequential cycles. Each cycle of the T-SOPA includes two steps: the equivalent deterministic optimization and the inverse TDFP assessment with respect to the target TDFP, and these two steps in T-SOPA are executed independently, i.e., the deterministic optimization and the inverse TDFP assessment are completely decoupled from each other in one cycle. The number of sequential cycles for achieving the convergent solutions of the design parameters is greatly reduced in the proposed T-SOPA due to the decoupling strategy, and the inverse TDFP assessment completed by the single-loop optimization can help improve the computational efficiency of the T-SOPA. A numerical example and three engineering examples are introduced to verify the effectiveness of the proposed T-SOPA. The results show that the proposed T-SOPA is accurate and efficient.