Multi-stage online robust parameter design based on Bayesian GP model

Abstract

Online robust parameter design (RPD) for the complex production process has recently attracted increasing attention among researchers and practitioners. However, the existing online RPD methods usually ignore the model uncertainty of initial steps, which may lead to the overestimated optimal solutions in the early stage of online RPD. This paper proposes a multi-stage robust optimization approach based on the Bayesian Gaussian process (BGP) model to improve the robustness of the optimal solutions of the online RPD process. First, the Gibbs sampling method is used to estimate the hyperparameters of the BGP model. Second, the global optimization and clustering analysis techniques are combined to determine the optimal design region of input variables. Consequently, the Bayesian posterior probability analysis technique is used to obtain the optimal robust design region for performing the online parameter optimization. Finally, an online RPD model is constructed by integrating the global optimization algorithm, parameter update strategy, and quality loss function. The proposed approach is validated through a simulation example and a laser drilling case study. The comparison results show that the proposed approach obtains more robust optimal solutions than the existing ones.