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In robust parameter design (RPD), estimating the response surface model from the noisy experimental data is critical for parameter optimization. The multivariate Gaussian process (MGP) model has become a popular tool for response surface modelling. However, most existing MGP models may not effectively evaluate the uncertainty of noisy data. This article proposes a stochastic MGP for efficient emulation and robust optimization by considering uncertainty. Firstly, the hierarchical modelling technique is adopted to estimate the relationship model with noisy data. Secondly, the hyperparameters are estimated by the Gibbs technique, and the Bayesian averaging method is used to measure the parameter uncertainty. Finally, a novel optimization model integrated with the Bayesian averaging and quality loss function is developed to find the optimal solution. Two case studies are used to illustrate the effectiveness of the proposed method. The results show that the proposed approach obtains smaller quality loss than the existing ones.

Robust optimization with uncertainty using a stochastic multivariate Gaussian process model