Limit state Kriging modeling for reliability-based design optimization through classification uncertainty quantification

Abstract

Reliability-based design optimization (RBDO) plays a vital role in considering the effect of uncertainties in the optimal design variables on the production reliability. Kriging-assisted RBDO methods can reduce the computational cost of conventional RBDO methods by replacing the time-consuming performance functions with Kriging models. Existing Kriging-assisted RBDO methods, however, are easy to fall into the low modeling efficiency issue or unsatisfied modeling accuracy issue because of the low utilization rate of sample resources. In this paper, an adaptive Kriging sampling strategy based on the Classification Uncertainty Quantification (KCUQ) was proposed. In KCUQ, the classification uncertainty of the Kriging model is sufficiently considered by (1) determining the new sample point based on the quantified misclassification probability and (2) checking the modeling accuracy based on the quantified number of misclassified random points. Moreover, KCUQ only updates the performance function with the largest classification error in each iteration such that all performance functions can be adaptively modeled based on their unique features. Two numerical case studies, vehicle side impact crashworthiness problem and the axle bridge turning parameters optimization application are used to demonstrate the performance of the proposed KCUQ method.