LAUSR

Abstract Response surface modeling is an essential technique for identifying the optimal input parameters in a process, especially when the physical knowledge about the process is limited. It explores the relationships between the process input variables and the response variables through a sequence of designed experiments. Conventional response surface models typically rely on a large number of experiments to achieve reliable modeling performance, which can be cost prohibitive and time-consuming. Furthermore, nonlinear input-output relationships in some processes may not be sufficiently accounted for by existing modeling methods. To address these challenges, this paper develops a new response surface modeling approach based on hybrid multi-task learning (H-MTL). This approach decomposes the variability in process responses into two components–a global trend and a residual term, which are estimated through self-learning and MTL of Gaussian process (GP), respectively. MTL leverages the similarities between multiple similar-but-not-identical GPs, thus achieving superior modeling performance without increasing experimental cost. The effectiveness of the proposed method is demonstrated by a case study using experimental data collected from real-world ultrasonic metal welding processes with different material combinations. In addition, the hyperparameter selection, the effects of the number of tasks, and the determination of the stopping criterion are discussed in detail.