Noisy Kriging for robust shape optimization of mechanical systems with a nonlinear and gradient-free expensive black-box figure of merit

We expose a way to deal with robust shape optimization of mechanical structures under a nonlinear and gradient-free expensive figure of merit. Driving parameters impact the geometry of the considered structures, and are subject to uncertainties. Considering that observations of an expensive black box representation of the figure of merit can be transferred to a noisy Kriging metamodel, the balance between the starting set of observations and enrichment cost is the key point to an enhanced way to reach the robust Pareto front. We present in this paper an applicative example, consisting of a disc-pad device exhibiting squeal-noise behavior, which exposes the benefits and drawbacks of the proposed approach for such complex figures of merit, as the squeal noise level is nonlinear and gradient-free. Pairing the noisy Kriging model with a relevant enrichment process for a limited additional cost shows potential for the ultimate purpose of finding robust optimal solutions.