Time-dependent performance measure approach for time-dependent failure possibility-based design optimization

Time-dependent failure possibility (TDFP) can reasonably measure the safety degree of time-dependent structure under fuzzy uncertainty, but there lacks design optimization under the constraint of TDFP for the trade-off of the performance and the safety. Thus, a time-dependent failure possibility-based design optimization (T-PBDO) under fuzzy uncertainty is established, and a time-dependent performance measure approach (T-PMA) for solving T-PBDO is proposed in this paper. In the proposed T-PMA, the TDFP constraint is equivalently transformed into the performance function constraint corresponding to the required target TDFP. The minimum performance target point (MPTP) and its corresponding time instant in the performance function constraint with respect to the target TDFP are determined by the single-loop optimization method of inverse TDFP analysis. This strategy completed by the inverse TDFP analysis with respect to the target TDFP can avoid analysis of the performance function under the unnecessary membership level, and then lead to improve the numerical stability and computational efficiency of solving the T-PBDO model. A numerical and three engineering case studies are introduced to verify the effectiveness of the proposed method. The results show that the proposed T-PMA is accurate, and its efficiency is higher than that of the direct optimization method.