Sequential multiple importance sampling for robust and efficient (possibly high-dimensional) reliability estimation

doi:10.1016/j.ymssp.2026.114798

Sequential multiple importance sampling for robust and efficient (possibly high-dimensional) reliability estimation

2026-08-01

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DOI：10.1016/j.ymssp.2026.114798

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This study proposes a sequential multiple importance sampling (SeMIS) method for the robust and efficient estimation of small failure probabilities. Unlike conventional sequential methods that force the final importance sampling density (ISD) to approximate the optimal ISD, SeMIS constructs a sequence of intermediate ISDs - comprising an expanded initial distribution followed by adaptively determined truncated distributions - to maximize overall sampling effectiveness. This cooperative strategy utilizes variance inflation to enhance the exploration of complex failure domains and hybrid truncation to minimize computational expenditure. Furthermore, the uncertainty of the SeMIS estimator is quantified through an innovative uncertainty propagation-based method, which enables the coefficient of variation to be predicted from a single simulation run. The performance of the algorithm is demonstrated through a series of low- and high-dimensional benchmark problems and two synthetic engineering applications. The results indicate that SeMIS provides more accurate and stable failure probability estimates than conventional sequential methods, characterized by reduced bias, lower deviation, and improved computational efficiency.

Keywords:

Failure probability estimation

Rare event simulation

Multiple importance sampling

Surrogate model

Uncertainty quantification

Sequential multiple importance sampling for robust and efficient (possibly high-dimensional) reliability estimation

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