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A sequential stratified importance sampling method for extremely small time-dependent failure probability with high-dimensional input vector
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DOI：10.1016/j.probengmech.2025.103861.png)
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Abstract
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To address the challenge of estimating extremely small time-dependent failure probability (TDFP) high-dimensional input vector, we propose a sequential stratified importance sampling method (SSIS) with an ensemble stochastic configuration network (eSCN) embedded within SSIS (eSCN-SSIS) to improve efficiency. Initially, stratified cluster analysis is employed, enabling SSIS to construct a series of explicit importance sampling densities to explore the time-dependent failure domain layer by layer, thereby mitigating exploration of rare time-dependent failure domains and reducing variance in estimating extremely small TDFP. Subsequently, owing to the robust predictive capability of eSCN for high-dimensional input vector, eSCN is adaptively embedded into SSIS to replace the time-dependent performance function model; consequently, the required model evaluations are substantially reduced. Notably, even when applied to an explicit model, eSCN-SSIS is superior to Monte Carlo simulation (MCS), requiring considerably fewer model evaluations and shorter computational time. In contrast, although importance sampling based on the Kriging model surpassed MCS in term of model evaluations, it remained inferior in computational time. Owing to its hierarchical construction of explicit importance sampling densities and adaptive embedding of the eSCN, the proposed eSCN-SSIS applies to engineering problems characterized by extremely small TDFP and high-dimensional input vector, as verified by the presented examples.
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