Robust optimisation of computationally expensive models using adaptive multi-fidelity emulation

Abstract

Computationally expensive models are increasingly employed in the design process of engineering products and systems. Robust design in particular aims to obtain designs that exhibit near-optimal performance and low variability under uncertainty. Surrogate models are often employed to imitate the behaviour of expensive computational models. Surrogates are trained from a reduced number of samples of the expensive model. A crucial component of the performance of a surrogate is the quality of the training set. Problems occur when sampling fails to obtain points located in an area of interest and/or where the computational budget only allows for a very limited number of runs of the expensive model. This paper employs a Gaussian process emulation approach to perform efficient single-loop robust optimisation of expensive models. The emulator is enhanced to propagate input uncertainty to the emulator output, allowing single-loop robust optimisation. Further, the emulator is trained with multi-fidelity data obtained via adaptive sampling to maximise the quality of the training set for the given computational budget. An illustrative example is presented to highlight how the method works, before it is applied to two industrial case studies.