Data-driven sparse polynomial chaos expansion for models with dependent inputs  

作　　者：Zhanlin Liu Youngjun Choe 

机构地区：[1]Industrial&Systems Engineering,University of Washington,Seattle,WA,USA

出　　处：《Journal of Safety Science and Resilience》2023年第4期358-365,共8页安全科学与韧性（英文）

基　　金：This work was supported in part by the U.S.National Science Foundation(NSF grants CMMI-1824681,DMS-1952781,and BCS-2121616).

摘　　要：Polynomial chaos expansions(PCEs)have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs by decomposing the output in terms of polynomials of the inputs.PCEs for models with independent inputs have been extensively explored in the literature.Recently,different approaches have been proposed for models with dependent inputs to expand the use of PCEs to more real-world applications.Typical approaches include building PCEs based on the Gram–Schmidt algorithm or transforming the dependent inputs into independent inputs.However,the two approaches have their limitations regarding computational efficiency and additional assumptions about the input distributions,respectively.In this paper,we propose a data-driven approach to build sparse PCEs for models with dependent inputs without any distributional assumptions.The proposed algorithm recursively constructs orthonormal polynomials using a set of monomials based on their correlations with the output.The proposed algorithm on building sparse PCEs not only reduces the number of minimally required observations but also improves the numerical stability and computational efficiency.Four numerical examples are implemented to validate the proposed algorithm.The source code is made publicly available for reproducibility.

关 键 词：Uncertainty quantification Polynomial chaos expansion Sparse polynomial chaos expansion Gram-Schmidt orthogonalization 

分 类 号：TP31[自动化与计算机技术—计算机软件与理论]