Robust parameter design based on Gaussian process with model uncertainty

In robust parameter design, it is common to use computer models to simulate the relationships between input variables and output responses. However, for the contaminated experimental data, the model uncertainty between computer models and actual physical systems will seriously impair the robustness of the optimal input settings. In this paper, we propose a new weighted robust design approach concerning the model uncertainty from outliers based on the robust Gaussian process model with a Student-t likelihood (StGP). Firstly, to reduce the impact of outliers on the output means and variances, the StGP modelling technique is adopted to estimate the relationship models for contaminated data. Secondly, the Gibbs sampling technique is employed to estimate model parameters for better mixing and convergence. Finally, an optimisation scheme integrating the quality loss function and confidence interval analysis approach is built to find the feasible optimisation solution. Meanwhile, the hypersphere decomposition method and data-driven method are applied to determine the relative weights of objective functions. Two examples are used to demonstrate the effectiveness of the proposed approach. The comparison results show that the proposed approach can achieve better performance than other approaches by considering the model uncertainty from outliers.