A single-loop reliability sensitivity analysis strategy for time-dependent rare events with both random variables and stochastic processes

To deal with the time-dependent reliability sensitivity (TDRS) analysis of rare events with both random variables and stochastic processes, a single-loop sampling procedure combined with the cross entropy-based importance sampling strategy (CEIS), namely SCEIS, is derived to lighten the computational burden without loss of precision. Firstly, the TDRS indices are derived to make them implementable by a single-loop importance sampling (IS) procedure. Then, the quasi-optimal IS density is obtained through the extension of the cross-entropy method, which is an adaptive procedure that overcomes the challenges of determining the position and number of design points in traditional IS. Furthermore, the SCEIS can be easily implemented to estimate the TDRS indices for problems with small failure probability. Three examples involving numerical and engineering problems are analyzed to demonstrate the performance of the proposed method. The results obtained from comparing with other existing methods reveal that the proposed method provides satisfactory TDRS analysis for rare events while significantly reducing computational costs.