Adaptive surrogate model with active refinement combining Kriging and a trust region method

In the present paper an adaptive Kriging surrogate model with active refinement is proposed to solve component reliability analysis problems (i.e. with a single design point) with a reasonable limit for the dimensionality of the basic random variables space. The model uses an adaptive Kriging-based trust region method to search for the design point and predict the failure probability based on the first-order reliability method. This prediction is then verified or improved using Monte Carlo simulation with importance sampling based on a Kriging surrogate model built up iteratively around the design point using an active refinement algorithm. The usefulness of the proposed surrogate model in terms of accuracy and efficiency for practical engineering applications is shown with a numerical example involving an advanced nonlinear FEA structural model.