A gradient-assisted learning strategy of Kriging model for robust design optimization

Robust design optimization (RDO) is a remarkable technique for improving product quality in an uncertain environment. The double-loop structure of RDO involves uncertainty quantification which leads to a prohibitive computational issue. Kriging is used to approximate response statistics to decouple the double-loop structure of RDO. Multimodal and highly nonlinear characteristics of response statistics impede the Kriging assisted RDO from obtaining an accurate optimal solution. This paper presents a gradient-assisted (GA) learning function composed of gradient, uncertainty, and distance terms to cope with such issues. The gradient term serves as the key basis for the proposed learning function to reflect the global trend and local optimum. The uncertainty term represents the prediction credibility of candidate samples and the distance term is used to avoid the cluster of training samples. These three terms collaborate in the proposed learning function to identify the updating samples to train the Kriging model of objective function. In order to terminate the training process efficiently, a new stopping criterion based on the gradient direction is proposed. Based on the trained Kriging model, genetic algorithm is utilized to search the robust optimal solution. Three examples were used to demonstrate the advantages of the proposed method.