Sample-efficient robust Bayesian optimization with Gaussian mixture model for spindle vibration suppression design

Robustness represents a fundamental consideration in structural design, particularly in the context of high-speed spindle systems where computational efficiency is of critical importance. While the majority of gradient-free optimization strategies rely on currently observed maximum values, the robust optimum remains inherently unobservable. To address this challenge, a Bayesian optimization framework is introduced in which Gaussian mixture models are employed in place of conventional Gaussian distributions, thereby reducing approximation errors in the estimation of robust objective functions. Furthermore, an entropy approximation method based on Monte Carlo sampling is proposed to facilitate the computation of entropy within the Joint Entropy Search acquisition function for scenarios involving non-Gaussian distributions and unobservable robust optima. Experimental results indicate that the proposed approach achieves up to a 14% improvement in vibration suppression performance in high-speed spindle design compared to baseline configurations.