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.

用于复杂生产过程的在线稳健参数设计 (RPD) 最近引起了研究人员和从业人员越来越多的关注。然而，现有的在线RPD方法通常忽略初始步骤的模型不确定性，这可能导致在线RPD早期的最优解被高估。本文提出了一种基于贝叶斯高斯过程（BGP）模型的多阶段鲁棒优化方法，以提高在线RPD过程最优解的鲁棒性。首先，使用 Gibbs 抽样方法来估计 BGP 模型的超参数。其次，结合全局优化和聚类分析技术，确定输入变量的最优设计区域。最后，贝叶斯后验概率分析技术用于获得最佳鲁棒设计区域，用于执行在线参数优化。最后结合全局优化算法、参数更新策略和质量损失函数构建在线RPD模型。通过仿真示例和激光钻孔案例研究验证了所提出的方法。比较结果表明，所提出的方法比现有方法获得了更稳健的最优解。