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An active learning method for structural reliability combining response surface model with Gaussian process of residual fitting and reliability-based sequential sampling design

Wei Jianbao, Liu Zhijie, Sun Yuhang, Wang Xiaobang

Eksploatacja i Niezawodność

2025

Vol. 27, no. 1

art. no. 193443

It is quite challenging to attain an accurate reliability estimation on complex structures with low computational burden. Therefore, an active learning method combining the response surface model with the Gaussian process (GP) of residual fitting and reliability-based sequential sampling design is proposed for structural reliability analysis. This method first utilizes a random quadrilateral grid to perturb the uniform design sampling and generates a small set of initial design of experiments (DoE) to establish a high-precision initial response surface model efficiently. Then, a GP model for residual prediction is constructed by using the residuals of the initial response surface model, which allows the response surface function to be closer to the limit state function (LSF). Further, a reliability-based expected improvement (REI) learning function, which inherits the property of the EI function and considers the probability of feasibility of the samples, is developed for the selection of the most feasible points to update the response surface model and the GP model. The importance sampling (IS) combined with the proposed method is employed to assess the rare failure probability of structures. Ultimately, five numerical examples are used to validate the accuracy and efficiency of the proposed method.