A Selection Strategy for Kriging Based Design of Experiments by Spectral Clustering and Learning Function

Abstract

Reliability analysis evaluates the failure probability of structures considering random variables of a system. Existing methods such as first-order reliability method (FORM) and second-order reliability method (SORM) are difficult to predict the failure probability of implicit functions in mechanical structures. Monte Carlo simulation (MCS) can predict the failure probability with high accuracy, but it is time-consuming. Agent-based methods such as the Kriging model have the approved performance to predict the failure probability in both efficiency and accuracy. An active method is proposed in this paper to improve the efficiency of predicting the probability of failures by combining the Kriging model and MCS, using a new learning function and its stopping condition. A representative selection strategy is developed based on spectral clustering to decide sample points in the design of experiments (DoEs). The new learning function integrates uncertainty and similarity of predicted Kriging values to search the next best sample point for updating the initial DoE. The learning process is terminated based on the stopping condition for a given accuracy of predicted probability of failures. Four case studies are conducted to validate the proposed method. Results show that the proposed method can predict the probability of failures with improved accuracy and reduced time.