Structural Reliability Analysis Method Based on Kriging and Spherical Cap Area Integral

Abstract

In the structural reliability analysis, the first-order reliability method(FORM) often yields significant errors when addressing nonlinear problems. Although the second-order reliability method(SORM) can provide higher accuracy, the additional computation of the Hessian matrix leads to lower computational efficiency. Additionally, when the dimensionality of the random variables is high, the approximation formula of SORM can result in larger errors. To address these issues, a structural reliability analysis method based on Kriging and spherical cap area integral is proposed. Firstly, this method integrates FORM with the quasi-Newton algorithm Broyden-Fletcher-Goldfarb-Shanno(BFGS), trains the Kriging model by using sample points from the algorithm's iteration process, and combines the Kriging model with gradient information to approximate the Hessian matrix. Then, the failure surface is approximated as a rotating paraboloid, utilizing the spherical cap to replace the complex surface. For the n-dimensional case, the hyperspherical cap area expression is combined with the integral method to calculate the failure probability. Finally, the method is validated through three examples, demonstrating improved computational accuracy and efficiency compared to traditional methods.

Keywords

structural reliability analysis / quasi-Newton algorithm / Kriging model / spherical cap area integral

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Funding

National Natural Science Foundation of China(52375236)

Fundamental Research Funds for the Central Universities, China(23D110316)