Stochastic modeling error reduction using Bayesian approach coupled with an adaptive Kriging-based model

Abstract

Purpose

Magnetic material properties of an electromagnetic device (EMD) can be recovered by solving a coupled experimental numerical inverse problem. In order to ensure the highest possible accuracy of the inverse problem solution, all physics of the EMD need to be perfectly modeled using a complex numerical model. However, these fine models demand a high computational time. Alternatively, less accurate coarse models can be used with a demerit of the high expected recovery errors. The purpose of this paper is to present an efficient methodology to reduce the effect of stochastic modeling errors in the inverse problem solution.

Design/methodology/approach

The recovery error in the electromagnetic inverse problem solution is reduced using the Bayesian approximation error approach coupled with an adaptive Kriging-based model. The accuracy of the forward model is assessed and adapted a priori using the cross-validation technique.

Findings

The adaptive Kriging-based model seems to be an efficient technique for modeling EMDs used in inverse problems. Moreover, using the proposed methodology, the recovery error in the electromagnetic inverse problem solution is largely reduced in a relatively small computational time and memory storage.

Originality/value

The proposed methodology is capable of not only improving the accuracy of the inverse problem solution, but also reducing the computational time as well as the memory storage. Furthermore, to the best of the authors knowledge, it is the first time to combine the adaptive Kriging-based model with the Bayesian approximation error approach for the stochastic modeling error reduction.

Citation

Abou-Elyazied Abdallh, A. and Dupré, L. (2014), "Stochastic modeling error reduction using Bayesian approach coupled with an adaptive Kriging-based model", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 33 No. 3, pp. 856-867. https://doi.org/10.1108/COMPEL-10-2012-0230