A sparse surrogate model for structural reliability analysis based on the generalized polynomial chaos expansion. (June 2019)

• Record Type: Journal Article
• Authors: Liu, Qian; Zhang, Xufang; Huang, Xianzhen
• Is Part Of: Proceedings of the Institution of Mechanical Engineers. Volume 233:Number 3(2019:Jun.)
• Page Start: 487
• Page End: 502
• Publication Date: 2019-06
• Subjects: Sparse regression -- polynomial chaos expansion -- non-intrusive method -- structural reliability analysis; Reliability (Engineering) -- Mathematical models -- Periodiclals; Risk assessment -- Mathematical models -- Periodicals; Engineering design -- Mathematical models -- Periodicals; 620.00452
• DOI: 10.1177/1748006X18804047
• Languages: English
• ISSNs: 1748-006X

Abstract

The reliability analysis of a structural system is typically evaluated based on a multivariate model that describes the underlying mechanistic relationship between the system's input and output random variables. This is the need to develop an effective surrogate model to mimic the input–output relationship as the Monte Carlo simulation–based on the mechanistic model might be computationally intensive. In this regard, the article presents a sparse regression method for structural reliability analysis based on the generalized polynomial chaos expansion. However, results from the global sensitivity analysis have justified that it is unnecessary to contain all polynomial terms in the surrogate model, instead of comprising a rather small number of principle components only. One direct benefit of the sparse approximation allows utilizing a small number of training samples to calibrate the surrogate model, bearing in mind that the required sample size is positively proportional to the number of unknowns in regression analysis. Therefore, by utilizing the standard polynomial chaos basis functions to constitute an explanatory dictionary, an adaptive sparse regression approach characterized by introducing the most significant explanatory variable in each iteration is presented. A statistical approach for detecting and excluding spuriously explanatory polynomials is also introduced to maintain the high sparsity of the meta-modeling result. Combined with a variety of low-discrepancy schemes in generating training samples, structural reliability and global sensitivity analysis of originally true but computationally demanding models are alternatively realized based on the sparse surrogate method in conjunction with the brutal Monte Carlo simulation method. Numerical examples are carried out to demonstrate the applicability of the sparse regression approach to structural reliability problems. Results have shown that the proposed method is an effective, non-intrusive approach to deal with uncertainty analysis of various structural systems.