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An expanded sparse Bayesian learning method for polynomial chaos expansion

机译：多项式混沌扩展的扩展稀疏贝叶斯学习方法

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Polynomial chaos expansion (PCE) has been proven to be a powerful tool for developing surrogate models in various engineering fields for uncertainty quantification. The computational cost of full PCE is unaffordable due to the "curse of dimensionality" of the expansion coefficients. In this paper, an expanded sparse Bayesian learning method for sparse PCE is proposed. Firstly, basis polynomials of the full PCE are partitioned into significant terms and complementary non-significant terms. The parameterized priors with distinct variance are assigned to the candidates for the significant terms. Then, the dimensionality of the parameter space is equivalent to the assumed sparsity level of the PCE. Secondly, an approximate Kashyap information criterion (KIC) rule which achieves a balance between model simplicity and goodness of fit is derived for model selection. Finally, an automatic search algorithm is proposed by minimizing the KIC objective function and using the variance contribution of each term to the model output to select significant terms. To assess the performance of the proposed method, a detailed comparison is completed with several well-established techniques. The results show that the proposed method is able to identify the most significant PC contributions with superior efficiency and accuracy. (C) 2019 Elsevier Ltd. All rights reserved.
机译：已被证明多项式混沌扩展（PCCE）是在各种工程领域开发代理模型的强大工具，以进行不确定量化。由于膨胀系数的“维度诅咒”，完整PCE的计算成本是不起动的。本文提出了一种稀疏PCE的扩展稀疏贝叶斯学习方法。首先，完整PCE的基础多项式被划分为重大术语和互补的非重大术语。具有不同方差的参数化前沿被分配给候选者以获得重要术语。然后，参数空间的维度等同于PCE的假定稀疏度水平。其次，为模型选择导出了实现模型简单性和拟合良好性之间平衡的近似克什映像信息标准（KIC）规则。最后，通过最小化KIC目标函数并使用每个术语的方差贡献来提出自动搜索算法，以选择重要术语。为了评估所提出的方法的性能，以几种良好的技术完成了详细的比较。结果表明，该方法能够以优异的效率和准确性识别最大的PC贡献。 （c）2019 Elsevier Ltd.保留所有权利。

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