Accurate computation of failure probability considering uncertain input parameters is very challenging within limited computational cost. An efficient surrogate model, referred to here as sparse variational Bayesian inference based polynomial chaos expansion (SVB-PCE), is formulated in this paper for reliability analysis. The sparsity in the polynomial basis terms is introduced by the automatic relevance determination (ARD) algorithm and the coefficients corresponding to the sparse polynomial bases are computed using the VB framework. The reliability analysis is performed on four typical numerical problems using the SVB-PCE model. The failure probability and the reliability index for all the examples are assessed accurately by the SVB-PCE model using fewer number of model evaluations as compared to the state-of-art methods. Further, the ARD enables to capture the most important terms in the polynomial bases which also reduces the computational cost in assessing the failure probability.

在不确定的计算成本范围内，考虑不确定的输入参数进行故障概率的准确计算非常具有挑战性。本文建立了一种有效的替代模型，在此称为稀疏变分贝叶斯推理基于多项式混沌扩展（SVB-PCE），用于可靠性分析。通过自动相关性确定（ARD）算法引入多项式基础项中的稀疏性，并使用VB框架计算与稀疏多项式基础相对应的系数。使用SVB-PCE模型对四个典型的数值问题进行了可靠性分析。与现有技术方法相比，所有示例的故障概率和可靠性指标均可以通过SVB-PCE模型使用较少数量的模型评估来准确评估。进一步，