Direct probability integral method-based system reliability sensitivity analysis and design optimization

Abstract

System reliability-based design optimization (SRBDO) can take an optimal trade-off between economy and safety in structural design with multiple failure modes, in which the evaluation of system reliability and its sensitivity is a challenging problem. Due to the complexity introduced by multiple failure modes, a unified and efficient method is required. In this study, the direct probability integral method (DPIM) is proposed to evaluate system reliability and its sensitivity efficiently, and a decoupled approach is established to attack time-invariant and time-variant SRBDO problems. Firstly, the decoupled framework based on first-order and second-order sensitivity is established for SRBDO problems. Furthermore, the first-order and second-order system reliability sensitivity with respect to distribution parameters of random variables are derived from the probability density integral equation, which significantly improves the computational efficiency. Finally, numerical example verifies the high accuracy and efficiency of DPIM for system reliability and its sensitivity analysis. It is shown that the proposed decoupled approach can address the intractable SRBDO problems efficiently.