Abstract
Active-learning surrogate model–based reliability analysis is widely employed in engineering structural reliability analysis to alleviate the computational burden of the Monte Carlo method. To date, most of these methods are built based on the single-fidelity surrogate model, such as the Kriging model. However, the computational burden of constructing a fine Kriging model may be still expensive if the high-fidelity (HF) simulation is extremely time-consuming. To solve this problem, an active-learning method based on the multi-fidelity (MF) Kriging model for structural reliability analysis (abbreviated as AMK-MCS+AEFF), which is an online data-driven method fusing information from different fidelities, is proposed in this paper. First, an augmented expected feasibility function (AEFF) is defined by considering the cross-correlation, the sampling density, and the cost query between HF and low-fidelity (LF) models. During the active-learning process of AMK-MCS+AEFF, both the location and fidelity level of the updated sample can be determined objectively and adaptively by maximizing the AEFF. Second, a new stopping criterion that associates with the estimated relative error is proposed to ensure that the iterative process terminates in a proper iteration. The proposed method is compared with several state-of-the-art methods through three numerical examples and an engineering case. Results show that the proposed method can provide an accurate failure probability estimation with a less computational cost.
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Funding
This work has been financially supported by the National Natural Science Foundation of China (NSFC) under Grant No. 51805179, the National Defense Innovation Program under Grant No. 18-163-00-TS-004-033-01, and the Research Funds of the Maritime Defense Technologies Innovation No. YT19201701.
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Yi, J., Wu, F., Zhou, Q. et al. An active-learning method based on multi-fidelity Kriging model for structural reliability analysis. Struct Multidisc Optim 63, 173–195 (2021). https://doi.org/10.1007/s00158-020-02678-1
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DOI: https://doi.org/10.1007/s00158-020-02678-1