Structural Reliability Analysis Based on Differential Evolution Algorithm and Hypersphere Integration

Abstract

In reliability analyses, the absence of a priori information on the most probable point of failure(MPP) may result in overlooking critical points, thereby leading to biased assessment outcomes. Moreover, second-order reliability methods exhibit limited accuracy in highly nonlinear scenarios. To overcome these challenges, a novel reliability analysis strategy based on a multimodal differential evolution algorithm and a hypersphere integration method is proposed. Initially, the penalty function method is employed to reformulate the MPP search problem as a conditionally constrained optimization task. Subsequently, a differential evolution algorithm incorporating a population delineation strategy is utilized to identify all MPPs. Finally, a paraboloid equation is constructed based on the curvature of the limit-state function at the MPPs, and the failure probability of the structure is calculated by using the hypersphere integration method. The localization effectiveness of the MPPs is compared through multiple numerical cases and two engineering examples, with accuracy comparisons of failure probabilities against the first-order reliability method(FORM) and the second-order reliability method(SORM). The results indicate that the method effectively identifies existing MPPs and achieves higher solution precision.

Keywords

reliability analysis / design point positioning / differential evolution algorithm / hypersphere integration

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Funding

National Natural Science Foundation of China(52375236)

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