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By constructing an extended density that is independent of distribution parameters and covers their interested region, the coupling of statistical moment functions (SMFs) and the realization of distribution parameters can be removed. Then SMFs, estimated by sharing a set of sparse integral characteristic nodes of extended density, can be used to approximate the failure probability function (FPF). To enhance the efficiency of estimating SMFs and the FPF, an improved decoupling method is proposed by combining Bayesian sparse polynomial chaos expansion (B-PCE), where the required performance function predictions at all sparse integral characteristic nodes by estimating SMFs are completed by adaptively updating B-PCE model of the performance function. The main contribution of the improved decoupling method for estimating SMFs and the FPF is replacing the performance function by B-PCE model, and the proposed adaptive update strategy guarantees the accuracy of B-PCE model in predicting performance function, SMFs and the FPF. Examples demonstrate the superior computational efficiency of the proposed method over the existing method.

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An Improved Decoupling Method Combined with Bayesian Sparse Polynomial Chaos Expansion for Failure Probability Function Analysis Based on Statistical Moment Functions

  • 会议论文

  • 发表日期：

    2026年

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  • Hengchao Li,
  • Zhenzhou Lu

摘要

By constructing an extended density that is independent of distribution parameters and covers their interested region, the coupling of statistical moment functions (SMFs) and the realization of distribution parameters can be removed. Then SMFs, estimated by sharing a set of sparse integral characteristic nodes of extended density, can be used to approximate the failure probability function (FPF). To enhance the efficiency of estimating SMFs and the FPF, an improved decoupling method is proposed by combining Bayesian sparse polynomial chaos expansion (B-PCE), where the required performance function predictions at all sparse integral characteristic nodes by estimating SMFs are completed by adaptively updating B-PCE model of the performance function. The main contribution of the improved decoupling method for estimating SMFs and the FPF is replacing the performance function by B-PCE model, and the proposed adaptive update strategy guarantees the accuracy of B-PCE model in predicting performance function, SMFs and the FPF. Examples demonstrate the superior computational efficiency of the proposed method over the existing method.