A novel step-wise AK-MCS method for efficient estimation of fuzzy failure probability under probability inputs and fuzzy state assumption

For efficiently estimating the fuzzy failure probability under the probability inputs and fuzzy state assumption (profust model) which generally includes three states, i.e., the absolute safety state, the full failure state and the fuzzy safety-failure transition state, a novel step-wise AK-MCS method is proposed. In the first step, the Kriging model is adaptively updated by U learning function to accurately recognize if the points in the sample pool are in the safety state or in the failure one, where the exact values of performance function at these points are not concerned in the process of updating the Kriging model. After the Kriging model converges so that all points of the sample pool in the absolute safety state and the fully failure state can be well distinguished, the retained points in the sample pool belong to the fuzzy safety-failure transition state and construct the reduced new sample pool. In the second step, the first converged Kriging model continues to be adaptively updated in the reduced new sample pool. The exact values of the performance function at these points locating in the fuzzy safety-failure transition state are concerned for accurately estimating the fuzzy failure probability. Thus, a global learning function based on the total prediction error is used to select training point in order to update the Kriging model. By using the step-wise strategy and collaborating Kriging surrogates through two-step updating processes with different learning functions, the fuzzy failure probability can be efficiently estimated as a post-processing without any extra calls of the performance function. An automobile front model, a simplified wing box structure model and an icing forecast model are used to illustrate the efficiency and accuracy of the proposed method.