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<p>Efficiently estimating extremely small time-dependent failure probability (TDFP) is a challenge for highly reliable engineering structures. To address this challenge, this paper proposes an efficient clustering-based stratified importance sampling (CSIS) method. The proposed CSIS alternately constructs mixture importance sampling (IS) densities and stratifies the input space. It uses samples from mixture IS densities to enable time-dependent performance function to adaptively divide the input space into time-dependent failure stratifications with decreasing probabilities. Then, clustering analysis is conducted on failure samples within each stratification to construct mixture IS densities for subsequent stratifications. After failure stratifications approach the target failure domain, the current mixture IS densities are used to estimate extremely small TDFP. In the proposed CSIS, adaptive stratification reduces the exploration complexity of rare time-dependent failure domain. Meanwhile, the explicitly formulated mixture IS densities, which are constructed on clustering centroids of failure samples in each stratification, significantly reduces TDFP estimation variance by stepwise approaching critical regions contributing most to TDFP. And computational efficiency of CSIS is further enhanced by the adaptive Kriging model of time-dependent performance function. Examples demonstrate that the proposed method achieves significant computational efficiency improvements over existing advanced methods while maintaining accuracy of estimating extremely small TDFPs.</p>

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An efficient clustering-based stratified importance sampling method with double-loop Kriging model for extremely small time-dependent failure probabilities

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Hengchao Li,
  • Zhenzhou Lu,
  • Yuhua Yan,
  • Yixin Lu,
  • Jiangji Qu,
  • Xingcheng Wang

摘要

Efficiently estimating extremely small time-dependent failure probability (TDFP) is a challenge for highly reliable engineering structures. To address this challenge, this paper proposes an efficient clustering-based stratified importance sampling (CSIS) method. The proposed CSIS alternately constructs mixture importance sampling (IS) densities and stratifies the input space. It uses samples from mixture IS densities to enable time-dependent performance function to adaptively divide the input space into time-dependent failure stratifications with decreasing probabilities. Then, clustering analysis is conducted on failure samples within each stratification to construct mixture IS densities for subsequent stratifications. After failure stratifications approach the target failure domain, the current mixture IS densities are used to estimate extremely small TDFP. In the proposed CSIS, adaptive stratification reduces the exploration complexity of rare time-dependent failure domain. Meanwhile, the explicitly formulated mixture IS densities, which are constructed on clustering centroids of failure samples in each stratification, significantly reduces TDFP estimation variance by stepwise approaching critical regions contributing most to TDFP. And computational efficiency of CSIS is further enhanced by the adaptive Kriging model of time-dependent performance function. Examples demonstrate that the proposed method achieves significant computational efficiency improvements over existing advanced methods while maintaining accuracy of estimating extremely small TDFPs.