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<p>Assessing small failure probabilities in structural reliability analysis is difficult, especially in high dimensions. Traditional reliability analysis methods often face challenges with the exponential growth in computational costs as the dimensionality of the problem increases. Although radial basis function (RBF) surrogate models are commonly used owing to their flexibility and efficiency in uncertainty quantification, the existing RBF-based methods are limited in handling small failure probabilities effectively. To overcome these limitations, we propose a new method, AMRBF-SS, which integrates multiple RBF kernel functions with subset simulation (SS). This approach enhances the capability of addressing small failure probability problems by incorporating local uncertainty estimates into an active learning function. We validated the accuracy and efficiency of AMRBF-SS through various numerical and practical examples. The AMRBF-SS method demonstrated significant improvements in solving high-dimensional small-probability problems. It achieves comparable accuracy to existing methods, while reducing the number of evaluations required. This advancement not only addresses a critical gap in current RBF-based reliability methods, but also provides a more efficient technique for tackling complex reliability analysis challenges.</p>

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AMRBF-SS: subset simulation with active learning and multiple kernels radial basis function for small failure probability prediction

  • 期刊论文

  • 发表日期：

    2025年2月20日

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  • Changle Peng,
  • Cheng Chen,
  • Tong Guo,
  • Weijie Xu

摘要

Assessing small failure probabilities in structural reliability analysis is difficult, especially in high dimensions. Traditional reliability analysis methods often face challenges with the exponential growth in computational costs as the dimensionality of the problem increases. Although radial basis function (RBF) surrogate models are commonly used owing to their flexibility and efficiency in uncertainty quantification, the existing RBF-based methods are limited in handling small failure probabilities effectively. To overcome these limitations, we propose a new method, AMRBF-SS, which integrates multiple RBF kernel functions with subset simulation (SS). This approach enhances the capability of addressing small failure probability problems by incorporating local uncertainty estimates into an active learning function. We validated the accuracy and efficiency of AMRBF-SS through various numerical and practical examples. The AMRBF-SS method demonstrated significant improvements in solving high-dimensional small-probability problems. It achieves comparable accuracy to existing methods, while reducing the number of evaluations required. This advancement not only addresses a critical gap in current RBF-based reliability methods, but also provides a more efficient technique for tackling complex reliability analysis challenges.