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.

时变失效可能性（TDFP）可以在模糊不确定性下合理地测量时变结构的安全程度，但在性能和安全性的权衡下，由于时变失效的可能性，设计缺乏优化。因此，建立了模糊不确定性下基于时间的基于故障可能性的设计优化（T-PBDO），并提出了一种基于时间的基于性能的性能度量方法（T-PMA）。在提出的T-PMA中，TDFP约束等效地转换为与所需目标TDFP相对应的性能函数约束。最小性能目标点（MPTP）及其在性能函数约束中相对于目标TDFP的相应时刻是通过逆TDFP分析的单环优化方法确定的。通过对目标TDFP进行逆TDFP分析完成的策略可以避免在不必要的隶属度下对性能函数进行分析，从而提高了求解T-PBDO模型的数值稳定性和计算效率。数值算例和三个工程案例研究被引入以验证所提方法的有效性。结果表明，所提出的T-PMA是准确的，并且其效率高于直接优化方法。数值算例和三个工程案例研究被引入以验证所提方法的有效性。结果表明，所提出的T-PMA是准确的，并且其效率高于直接优化方法。数值算例和三个工程案例研究被引入以验证所提方法的有效性。结果表明，所提出的T-PMA是准确的，并且其效率高于直接优化方法。