AM-GMSIS: An Efficient Reliability Evaluation Method for Passive Nuclear Safety Systems Based on Ensemble Neural Network and Adaptive Multimodal Sampling

Traditional Monte Carlo simulation methods face challenges such as low computational efficiency and insufficient accuracy when analyzing the reliability of nuclear power plant passive systems with small failure probabilities. To address this, this paper proposes an adaptive metamodel-based Gaussian mixture subset simulation-importance sampling (AM-GMSIS) method for reliability assessment of problems involving nonlinear responses and potentially multimodal failure boundaries. The AM-GMSIS method combines subset simulation and importance sampling and utilizes an ensemble neural network (ENN) as the surrogate model. In the sampling stage, AM-GMSIS adaptively identifies and covers multiple failure domains using a Gaussian mixture model coupled with the Bayesian information criterion, providing an adaptive sampling density for the ENN-based active learning process. Simultaneously, the algorithm is driven by the prediction uncertainty provided by the ENN and the U-function to efficiently acquire active learning samples, with the aim of improving the surrogate accuracy in the vicinity of the failure boundary. Numerical examples indicate that AM-GMSIS provides accurate and stable estimates when dealing with strong nonlinearity and multi-failure domain problems. Finally, the algorithm is applied to the reliability analysis of a nuclear power plant's passive residual heat removal system, quantifying its failure probability under a station blackout accident as (Formula presented.). A sensitivity analysis was further conducted to identify the input parameters with the largest influence on the model response, illustrating the potential engineering usefulness of the proposed framework.