Bayesian probability density evolution method for reliability analysis with stepwise uncertainty reduction
提出一种贝叶斯概率密度演化方法，通过逐步最小化失效概率的后验方差来提升结构可靠性分析的精度和效率，适用于需要主动学习策略的工程场景。
Although probability density evolution method (PDEM) empowered by active learning has shown promise for structural reliability analysis, improved uncertainty control and enhanced computational efficiency remain desirable. This paper enhances PDEM by minimizing the posterior variance of the failure probability in a stepwise manner. The major contributions of this study are threefold. (i) Posterior variance quantification . Instead of using a conservative upper bound, the exact posterior variance of failure probability estimated by PDEM is derived from a Bayesian inference perspective, providing a natural measure of epistemic uncertainty about failure probability. (ii) Learning function . An active learning strategy is proposed to reduce the posterior variance of failure probability to the greatest degree, where a multi-point look-ahead learning function called expected variance reduction (EVR) is analytically derived and then numerically evaluated by a tailored discrete importance sampling strategy. (iii) Multi-point enrichment . Stepwise maximization of EVR is implemented to perform the multi-point enrichment step, eliminating the need for additional heuristic batch selection procedures. The proposed approach is tested on four examples and compared against several existing reliability methods. Results indicate that the proposed method exerts better sample-selection behavior and provides a fair convergence criterion for active learning workflow, thereby achieving good computational accuracy and efficiency.