Efficient Bayesian optimisation of bounded general loss function for robust parameter design

Robust parameter design (RPD) has been generally employed to minimise the system quality loss caused by noise perturbation via setting control factors in engineering design. Bayesian optimisation algorithms have received increasing attention for RPD, which includes establishing the Kriging model and developing acquisition functions (AFs). In RPD, the quality loss function method is a common method to calculate the response deviation from a target value. The existing literature mainly focuses on setting the loss function as a quadratic function for easier calculation, while it is not always reasonable due to its unboundedness. In this paper, we propose three efficient Bayesian algorithms for bounded general loss functions for finding the optimal design of control factors based on a Kriging model. We develop a Monte Carlo sampling method to approximate the proposed AFs. Three numerical examples and a rocket injector case are used to demonstrate the effectiveness of the proposed algorithms.