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A data-driven B-spline-enhanced Kriging method for uncertainty quantification based on Bayesian compressive sensing
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DOI：10.1016/j.ymssp.2023.111005.png)
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摘要
En 中文
Kriging is a powerful surrogate method for fitting smooth functions, and has been widely used in uncertainty quantification. However, for non-smooth functions, the performance of Kriging may be unsatisfactory. To overcome this drawback, we combine the advantages of spline functions and the Kriging model, and propose a data-driven B-spline-enhanced Kriging method (DDBSEK). Firstly, we establish the data-consistent orthogonal B-spline basis functions with the aid of the sample data of the input variables and replace the trend terms of the traditional Kriging model with these orthogonal B-spline bases. Then, by leveraging the fast marginal likelihood maximization algorithm and the Bayesian compressive sensing technique, an improved analytical Bayesian LASSO (least absolute shrinkage and selection operator) algorithm is developed to retain the active orthogonal B-spline bases. The proposed DDBSEK is validated using two types of numerical examples and one implicit engineering example. Results show that the proposed method is superior to the B-spline function model or the Kriging model alone.
Keyword:
Uncertainty quantification
Data -driven method
B -spline function
Kriging
Non -smooth function
Bayesian compressive sensing
期刊
IF:
8.9
论文数:
1.3W
被引数:
6.6W
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