Abstract
Safe Bayesian Optimization (Safe BO) has demonstrated significant promise in enhancing data-driven optimization strategies in safety-critical settings, where model discrepancies, noisy measurements, and unknown safety constraints are prevalent. Despite these advancements, there still remains a limited understanding on the effectiveness and applicability of these Safe BO methods, particularly within process system engineering. Specifically, this study adapts and examines Safe Exploration for Optimization with Gaussian Processes (SafeOpt), Goal-oriented Safe Exploration (GoOSE), Gaussian Processes with Trust Region (GPs-TR) and Adversarially Robust Gaussian Processes (StableOpt). Methods such as SafeOpt and GoOSE face challenges in managing continuous systems due to their reliance on system discretization and together with StableOpt, lack the capability to manage multiple safety constraints. Thus, this work presents a comprehensive evaluation of state-of-the-art safe BO methods, with our own addition and enhancements, focusing on their performance in process system engineering. The performances of methods are assessed using a case study on the William Otto Reactor, focusing on convergence speed, unknown constraints mitigations, practicality, and robustness against adversarial perturbations. Overall, this study underscores the unique strengths and limitations of safe BO methods in process system engineering, advancing the field on data-driven approaches in safety-critical processes while also identifies areas where further improvements are necessary.