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

Jun Xu and Ding Wang

Reliability Engineering and System Safety, 2019, vol. 185, issue C, 329-340

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.

Keywords: Structural reliability; Large dimension; Sparse polynomial chaos expansion; Voronoi cells; Sliced inverse regression (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:185:y:2019:i:c:p:329-340

DOI: 10.1016/j.ress.2019.01.001

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