A blackbox yield estimation workflow with Gaussian process regression applied to the design of electromagnetic devices

Abstract

In this paper an efficient and reliable method for stochastic yield estimation is presented. Since one main challenge of uncertainty quantification is the computational feasibility, we propose a hybrid approach where most of the Monte Carlo sample points are evaluated with a surrogate model, and only a few sample points are reevaluated with the original high fidelity model. Gaussian process regression is a non-intrusive method which is used to build the surrogate model. Without many prerequisites, this gives us not only an approximation of the function value, but also an error indicator that we can use to decide whether a sample point should be reevaluated or not. For two benchmark problems, a dielectrical waveguide and a lowpass filter, the proposed methods outperform classic approaches.

Efficient yield optimization with limited gradient information

“…• V1dfo-ref: reference solution -problem solved with classic MC for estimation and the derivative free optimization (DFO) solver Py-BOBYQA [2] • V2mix-na: mixed strategy proposed in Section 3 with classic MC for estimation and non-adaptive Newton method for optimization • V3mix-a: mixed strategy proposed in Section 3 with classic MC for estimation and adaptive Newton-MC for optimization • V4mix-ha: mixed strategy proposed in Section 3 with Hybrid-GPR approach [4] for estimation and adaptive Newton-MC for optimization…”

“…For that reason, there is research on efficient yield estimation, using e.g. importance sampling [5], surrogate modeling [1,11,10] or hybrid approaches [8,3,4]. These hybrid approaches combine classic MC with surrogate methods, e.g.…”

“…Gaussian process regression (GPR), cf. [4]. Since this work focuses on the optimization process, we will not go into the details here.…”

Multi-Objective Yield Optimization for Electrical Machines using Machine Learning

“…For that reason, they introduced a hybrid approach, which evaluates most of the MC sample points on the surrogate model, and a small subset of so-called critical sample points on the high-fidelity model. In [8] a GPR-Hybrid approach has been recently introduced for problems in high-frequency engineering.…”

“…The average torque is the QoI and equipped with a lower bound it becomes a performance requirement. We apply the GPR-Hybrid approach from [8] to the modeled PMSM in order to achieve efficient and accurate yield estimates. In contrary to [8], the uncertain parameters are not the optimization variables.…”