AGP-MCS+D: An active learning reliability analysis method combining dependent Gaussian process and Monte Carlo simulation

Evaluating structural reliability usually requires substantial calls of the expensive-to-calculate models, which significantly increases the computational cost. Active learning strategies have been widely studied in the field of reliability analysis because of their effectiveness in reducing calls. By combining Gaussian process and Monte Carlo simulation, a new learning strategy considering dependence is designed, based on which a novel adaptive surrogate model approach called AGP-MCS+D is proposed. Firstly, surrogate modeling based on dependent Gaussian process makes complete use of the output information of the model under efficiently optimized parameters. Secondly, the influence of the dependence between predictions and the joint probability density function of the input variables on the variance of failure probability are considered simultaneously, and the stopping condition based on the relative error is adopted to effectively ensure the computational accuracy. Thirdly, different failure levels are considered based on the different situations, and samples with more evaluation value are obtained by an adaptive clustering and selection strategy, which remarkably reduces the computational cost. Three classical examples and an engineering example of aero engine gear are analyzed, and the results demonstrate that the proposed method is effective in ensuring the accuracy and improving the efficiency of reliability analysis.