Reliability Analysis Considering Model Uncertainty Based on Adaptive Expectation Maximization-Enhanced Stochastic Polynomial Chaos Expansion

Abstract Model uncertainty exists in stochastic simulators, which provides different responses when evaluated repeatedly, even with fixed input values. It is prevalent in multiple engineering fields, but research regarding reliability analysis (RA) under model uncertainty is relatively sparse. Although traditional surrogate models are widely applied in RA, they often ignore the model uncertainty. Stochastic polynomial chaos expansion (SPCE) is a recently developed stochastic surrogate model designated to emulate model uncertainty, yet its training requires time-consuming cross-validation and it lacks a specialized sampling strategy for RA under model uncertainty. Therefore, this work proposes an adaptive expectation-maximization-enhanced SPCE (A-EM-SPCE) for RA under model uncertainty. First, a novel SPCE training framework using expectation-maximization is proposed, where model coefficients and noise standard deviation are optimized simultaneously, and the Akaike information criterion is used for efficiently selecting the optimal truncation scheme and latent variable distribution. Second, an adaptive sampling strategy with hybrid probability density-driven learning function is proposed for failure boundary identification and prioritizing high-risk regions under model uncertainty. A decreasing strategy is also designed to balance exploration and exploitation during adaptive sampling. Numerical validations, along with a practical wind turbine case study, demonstrate the superior efficiency and accuracy of A-EM-SPCE in both surrogate model training and RA under model uncertainty.