Abstract
Structural reliability analysis is usually realized based on a multivariate performance function that depicts failure mechanisms of a structural system. The intensively computational cost of the brutal-force Monte-Carlo simulation motivates proposing a Gegenbauer polynomial-based surrogate model for effective structural reliability analysis in this paper. By utilizing the orthogonal matching pursuit algorithm to detect significant explanatory variables at first, a small number of samples are used to determine a reliable approximation result of the structural performance function. Several numerical examples in the literature are presented to demonstrate potential applications of the Gegenbauer polynomial-based sparse surrogate model. Accurate results have justified the effectiveness of the proposed approach in dealing with various structural reliability problems.
Highlights
Structural reliability analysis needs to recursively run a performance function g(X) for an accurate estimation result of the structural failure probability
Analytical derivation for stochastic characteristics of the multivariate performance function is only feasible in rare cases. e Monte Carlo simulation (MCS) and its variants allow one to alleviate the difficulty to some extent [4,5,6]
Structural reliability analysis is typically evaluated based on a multivariate performance function that defines small failure probabilities
Summary
Structural reliability analysis needs to recursively run a performance function g(X) for an accurate estimation result of the structural failure probability. Is paper primarily focuses on the utility of the Gegenbauer polynomials for a sparse surrogate model to mimic the true but computationally demanding performance function in structural reliability analysis. Once the multivariate basis set based on the Gegenbauer chaos polynomials is constituted, the method of the orthogonal matching pursuit is further introduced to select primary functions to maintain the high sparsity of the surrogate model. E paper introduces the Gegenbauer polynomials to constitute the basis functions, and a variety of stopping criteria are further investigated for a robust OMP-based sparse regression model in structural reliability analysis. Combined with a variety of stopping criteria to realize the sparse regression, an effective surrogate model that mimics the true but computationally demanding performance function is determined for the structural reliability analysis.
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