A hybrid polynomial dimensional decomposition for uncertainty quantification of high-dimensional complex systems

Yadav, Vaibhav; Rahman, Sharif

doi:10.1016/j.probengmech.2014.08.004

Cited by 9 publications

(2 citation statements)

References 21 publications

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“…, 2018; Xu et al. , 2017; Wang and Matthies, 2018), polynomial dimensional decomposition (PDD) (Rahman, 2008, 2009, 2011, 2015; Yadav and Rahman, 2013; Ren et al. , 2016; Tang et al ., 2016, 2019; Lu, 2018), etc.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, its applicability is limited in situations involving sparse and noisy training data (Vohra et al, 2020). The parametric method mainly include the high-order response surface method (HRSM) (Gavin and Yau, 2008), polynomial chaos expansion (PCE) (Ghanem and Spanos, 1992;Xiu and Karniadakis, 2002;Zhang and Xu, 2021;SalehiA et al, 2018;Xu et al, 2017;Wang and Matthies, 2018), polynomial dimensional decomposition (PDD) (Rahman, 2008(Rahman, , 2009(Rahman, , 2011(Rahman, , 2015Yadav and Rahman, 2013;Ren et al, 2016;Tang et al, 2016Tang et al, , 2019Lu, 2018), etc. In the HRSM, the Chebyshev polynomials are used to determine the polynomial degree of each variable, and the constitution of the response surface is obtained based on an assumed criterion, and then the coefficients in the response surface is evaluated by uniformly distributed random sample points.…”

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confidence: 99%

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An adaptive polynomial dimensional decomposition method and its application in reliability analysis

Sheng

Fan

Zhang

et al. 2022

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PurposeThe 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/approachFirst, 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.FindingsSeveral examples are investigated to illustrate the accuracy and efficiency of the proposed method compared with the other methods in reliability analysis.Originality/valueThe 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.

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