Multi-response robust optimization using GP model with variance calibration

Abstract

Gaussian process (GP) modeling is a powerful surrogate modeling technique to deal with robust parameter design problems for complex products/processes. The predicted variance of GP models is a crucial criterion for measuring the output response variation. However, most existing robust optimization methods always ignore the variance uncertainty in the modeling process, which may weaken the effectiveness of the obtained optimal solution. This article proposes a novel robust optimization approach considering the variance uncertainty with calibration technique to address the foregoing challenges. Firstly, the multi-response Gaussian process (MGP) model with the sparse estimation technique is constructed to estimate the relationship between the input and output. Secondly, the predicted variance is calibrated using bootstrapped sampling and conditional simulation techniques. Then, the interval analysis technique is adopted to measure the response uncertainty. Finally, an optimization approach incorporating improved variance estimation is proposed to find the optimal robust parameter settings. A numerical simulation example and a real case study are used to illustrate the effectiveness of the proposed approach. The results show that the proposed method improves the robustness of the optimal solution compared to the existing ones.