Assessing the failure probability of complex aeronautical structure is a difficult task in presence of uncertainties. In this paper, active learning polynomial chaos expansion (PCE) is developed for reliability analysis. The proposed method firstly assigns a Gaussian Process (GP) prior to the model response, and the covariance function of this GP is defined by the inner product of PCE basis function. Then, we show that a PCE model can be derived by the posterior mean of the GP, and the posterior variance is obtained to measure the local prediction error as Kriging model. Also, the expectation of the prediction variance is derived to measure the overall accuracy of the obtained PCE model. Then, a learning function, named expected indicator function prediction error (EIFPE), is proposed to update the design of experiment of PCE model for reliability analysis. This learning function is developed under the framework of the variance‐bias decomposition. It selects new points sequentially by maximizing the EIFPE that considers both the variance and bias information, and it provides a dynamic balance between global exploration and local exploitation. Finally, several test functions and engineering applications are investigated, and the results are compared with the widely used Kriging model combined with U and expected feasibility function learning function. Results show that the proposed method is efficient and accurate for complex engineering applications.

中文翻译：

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通过最大化预期指标函数预测误差来进行可靠度分析的主动学习多项式混沌扩展

在存在不确定性的情况下，评估复杂航空结构的失效概率是一项艰巨的任务。本文开发了主动学习多项式混沌扩展（PCE）进行可靠性分析。所提出的方法首先在模型响应之前分配高斯过程（GP），该GP的协方差函数由PCE基函数的内积定义。然后，我们证明了可以通过GP的后均值推导PCE模型，并获得后验方差作为Kriging模型来测量局部预测误差。同样，推导了预测方差的期望值，以测量获得的PCE模型的整体准确性。然后，一个名为预期指标函数预测误差（EIFPE）的学习函数，提出了更新PCE模型实验设计以进行可靠性分析的建议。该学习功能是在方差偏向分解框架下开发的。它通过最大化同时考虑方差和偏差信息的EIFPE来依次选择新点，并在全球勘探和本地开采之间提供动态平衡。最后，研究了几种测试功能和工程应用，并将结果与​​广泛使用的结合了U和预期可行性函数学习功能的Kriging模型进行了比较。结果表明，该方法对于复杂的工程应用是有效且准确的。它通过最大化同时考虑方差和偏差信息的EIFPE来依次选择新点，并在全球勘探和本地开采之间提供动态平衡。最后，研究了几种测试功能和工程应用，并将结果与​​广泛使用的结合了U和预期可行性函数学习功能的Kriging模型进行了比较。结果表明，该方法对于复杂的工程应用是有效且准确的。它通过最大化同时考虑方差和偏差信息的EIFPE来依次选择新点，并在全球勘探和本地开采之间提供动态平衡。最后，研究了几种测试功能和工程应用，并将结果与​​广泛使用的结合了U和预期可行性函数学习功能的Kriging模型进行了比较。结果表明，该方法对于复杂的工程应用是有效且准确的。