An active learning Kriging model with adaptive parameters for reliability analysis

The prevalence of highly nonlinear and implicit performance functions in structural reliability analysis has increased the computational effort significantly. To solve this problem, an efficiently active learning function, named parameter adaptive expected feasibility function (PAEFF) is proposed using the prediction variance and joint probability density. The PAEFF function first uses the harmonic mean of prediction variances of Kriging model to judge the iteration degree of the current surrogate model, to realize the scaling of the variance in the expected feasibility function. Second, to improve the prediction accuracy of the Kriging model, the joint probability densities are applied to ensure that the sample points to be updated have a higher probability of occurrence. Finally, a new failure probability-based stopping criterion with wider applicability is proposed. Theoretically, the stopping criterion proposed is applicable to all active learning functions. The effectiveness and accuracy of the proposed PAEFF are verified by two mathematical calculations and three engineering examples.