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<p>Polynomial chaos expansions (PCEs) have been recognized as an effective metamodel due to their strong global regression fit. The present work introduces a novel active learning algorithm that combines PCEs with Monte Carlo simulation for reliability analysis. Sparse Bayesian learning (SBL) is employed to estimate the model parameters of PCEs, which not only yields a sparse solution to enhance the PCE generalization but also provides the distributions of output predictions at unknown points. To minimize the computational cost in constructing SBL-based PCE, an active learning strategy considering prediction dependence between different inputs is utilized to sequentially choose new informative samples. Once a new training sample is chosen, the PCE model is adaptively updated to incorporate the new information and refine predictions. This process is repeated until the designated stopping criterion is met. In this work, a stability-based criterion is adopted, which requires the iterative results to become sufficiently stable before the procedure is terminated. The effectiveness of the method is examined through several examples, and the results show that it achieves high accuracy and good computational efficiency. The good performance of the proposed algorithm suggests that it is a promising option for geotechnical reliability analysis, particularly for computationally expensive problems.</p>

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An efficient active learning-based method for reliability analysis of geotechnical structures using sparse polynomial chaos expansion

  • 期刊论文

  • 发表日期：

    2026年2月14日

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  • Zhengwei Li,
  • Wenping Gong,
  • Zilong Zhang,
  • Tianzheng Li

摘要

Polynomial chaos expansions (PCEs) have been recognized as an effective metamodel due to their strong global regression fit. The present work introduces a novel active learning algorithm that combines PCEs with Monte Carlo simulation for reliability analysis. Sparse Bayesian learning (SBL) is employed to estimate the model parameters of PCEs, which not only yields a sparse solution to enhance the PCE generalization but also provides the distributions of output predictions at unknown points. To minimize the computational cost in constructing SBL-based PCE, an active learning strategy considering prediction dependence between different inputs is utilized to sequentially choose new informative samples. Once a new training sample is chosen, the PCE model is adaptively updated to incorporate the new information and refine predictions. This process is repeated until the designated stopping criterion is met. In this work, a stability-based criterion is adopted, which requires the iterative results to become sufficiently stable before the procedure is terminated. The effectiveness of the method is examined through several examples, and the results show that it achieves high accuracy and good computational efficiency. The good performance of the proposed algorithm suggests that it is a promising option for geotechnical reliability analysis, particularly for computationally expensive problems.