Bayesian optimization based on Expected P-box Improvement and application in HEG Shock Tunnel Cylindrical Model Experiment

The design of acquisition functions is a key research focus in Bayesian optimization. Recent studies have highlighted the importance of accounting for the impact of candidate sample points on surrogate model uncertainty. To address this need, we introduce probability box (P-box) as a metric, which comprehensively captures surrogate model uncertainty. We propose a novel Gaussian process regression (GPR)-based P-box estimation method, overcoming the computational inefficiency of traditional double-loop sampling. Further, we develop two acquisition functions based on Expected P-box Improvement, tailored for distinct objectives: (1) Global Expected P-box Improvement (GEPBI), which maximizes global P-box changes to improve surrogate model accuracy, and (2) Boundary Expected P-box Improvement (BEPBI), which targets P-box boundary changes to efficiently locate the global optimum. To address computational inefficiency in high-dimensional problems, we use the multi-start stochastic gradient ascent algorithm to calculate GEPBI and BEPBI. The proposed acquisition functions are validated on three test functions and an engineering black-box problem: the HEG shock tunnel cylindrical model experiment. GEPBI outperforms Posterior Variance (PV) and Expected Integrated Error Reduction (EIER) in accuracy for a multimodal function. BEPBI surpasses Expected Improvement (EI), Lower Confidence Bound (LCB) and Knowledge Gradient (KG) in global optimum for a function with numerous local optima. Their advantages are more pronounced when initial samples are biased. Both methods demonstrate significant advantages in handling high-dimensional complex functions and engineering black-box problems. • GPR-based P-box model is proposed to quantify surrogate model uncertainty. • Two novel EPBI acquisition functions (GEPBI and BEPBI) are proposed. • EPBI considers the impact of candidate points on the posterior of the surrogate model. • GEPBI significantly improves surrogate model accuracy, while BEPBI excels in locating optimal values. • Multi-start stochastic gradient ascent enhances the computational efficiency of GEPBI and BEPBI.