Efficient reliability analysis via a nonlinear autoregressive multi-fidelity surrogate model and active learning

For complex engineering problems, multi-fidelity modeling has been used to achieve efficient reliability analysis by leveraging multiple information sources. However, most methods require nested training samples to capture the correlation between different fidelity data, which may lead to a significant increase in low-fidelity samples. In addition, it is difficult to build accurate surrogate models because current methods do not fully consider the nonlinearity between different fidelity samples. To address these problems, a novel multi-fidelity modeling method with active learning is proposed in this paper. Firstly, a nonlinear autoregressive multi-fidelity Kriging (NAMK) model is used to build a surrogate model. To avoid introducing redundant samples in the process of NAMK model updating, a collective learning function is then developed by a combination of a U-learning function, the correlation between different fidelity samples, and the sampling cost. Furthermore, a residual model is constructed to automatically generate low-fidelity samples when high-fidelity samples are selected. The efficiency and accuracy of the proposed method are demonstrated using three numerical examples and an engineering case.