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Structural reliability analysis based on polynomial chaos, Voronoi cells and dimension reduction technique

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  • Xu, Jun
  • Wang, Ding

Abstract

Polynomial chaos expansions (PCEs) has been widely used to construct meta-models for structural reliability analysis. The computational effort of classical PCEs is unaffordable as the required number of deterministic model analyses grows exponentially with the dimension. Alternatively, the sparse PCEs are always built to alleviate this problem. This paper proposes an efficient method, which combines the sparse PCE with a novel unequal-weighted sampling strategy, i.e. Voronoi cells and the dimension reduction technique for structural reliability analysis. The unequal-weighted sampling strategy could converge fast to the ultimate goal of sequentially building a sparse PCE. Besides, when the dimension is high, the sliced inverse regression technique is employed to convert the original high-dimensional problem to a low-dimensional one. Then, a stepwise weighted regression method is involved to automatically determine the significant terms of the PCE and discard the insignificant ones for the reduced model. In this regard, the sparsity of the basis, the dimension reduction technique and the fast convergence of unequal-weighted sampling strategy lead to a considerably reduced computational cost. Four numerical examples with a large number of random variables are presented to validate the proposed method. The computational results show that the proposed method can establish fairly accurate meta-models for structural reliability assessment with low computational effort.

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  • Xu, Jun & Wang, Ding, 2019. "Structural reliability analysis based on polynomial chaos, Voronoi cells and dimension reduction technique," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 329-340.
    • Handle: RePEc:eee:reensy:v:185:y:2019:i:c:p:329-340
    DOI: 10.1016/j.ress.2019.01.001
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    Cited by:

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    7. Zuniga, M. Munoz & Murangira, A. & Perdrizet, T., 2021. "Structural reliability assessment through surrogate based importance sampling with dimension reduction," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
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    9. Xiao, Sinan & Oladyshkin, Sergey & Nowak, Wolfgang, 2020. "Reliability analysis with stratified importance sampling based on adaptive Kriging," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    10. Zhao, Tengyuan & Wang, Yu, 2020. "Non-parametric simulation of non-stationary non-gaussian 3D random field samples directly from sparse measurements using signal decomposition and Markov Chain Monte Carlo (MCMC) simulation," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    11. Saraygord Afshari, Sajad & Enayatollahi, Fatemeh & Xu, Xiangyang & Liang, Xihui, 2022. "Machine learning-based methods in structural reliability analysis: A review," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
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