An adaptive polynomial dimensional decomposition method and its application in reliability analysis
ISSN: 0264-4401
Article publication date: 11 May 2022
Issue publication date: 5 July 2022
Abstract
Purpose
The polynomial dimensional decomposition (PDD) method is a popular tool to establish a surrogate model in several scientific areas and engineering disciplines. The selection of appropriate truncated polynomials is the main topic in the PDD. In this paper, an easy-to-implement adaptive PDD method with a better balance between precision and efficiency is proposed.
Design/methodology/approach
First, the original random variables are transformed into corresponding independent reference variables according to the statistical information of variables. Second, the performance function is decomposed as a summation of component functions that can be approximated through a series of orthogonal polynomials. Third, the truncated maximum order of the orthogonal polynomial functions is determined through the nonlinear judgment method. The corresponding expansion coefficients are calculated through the point estimation method. Subsequently, the performance function is reconstructed through appropriate orthogonal polynomials and known expansion coefficients.
Findings
Several examples are investigated to illustrate the accuracy and efficiency of the proposed method compared with the other methods in reliability analysis.
Originality/value
The number of unknown coefficients is significantly reduced, and the computational burden for reliability analysis is eased accordingly. The coefficient evaluation for the multivariate component function is decoupled with the order judgment of the variable. The proposed method achieves a good trade-off of efficiency and accuracy for reliability analysis.
Keywords
Acknowledgements
The research presented in this paper was conducted with the support of the National Key R&D Program of China (Project No. 2019YFD1101003), the National Natural Science Foundation of China (Grant No. 51678092, 52178455) and the Fundamental Research Funds for the Central Universities (Project No. 2019CDXYTM0032). These supports are gratefully acknowledged.
Citation
Sheng, X., Fan, W., Zhang, Q. and Li, Z. (2022), "An adaptive polynomial dimensional decomposition method and its application in reliability analysis", Engineering Computations, Vol. 39 No. 7, pp. 2755-2780. https://doi.org/10.1108/EC-10-2021-0563
Publisher
:Emerald Publishing Limited
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