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

Abstract

Abstract. Magnetic material properties of an electromagnetic device can be recovered by solving an inverse problem where measurements are adequately interpreted by a mathematical forward model. The accuracy of the material properties recovered by the inverse problem is highly dependent on the accuracy of these forward models. In order to ensure the highest possible accuracy of the inverse problem solution, all physics of the electromagnetic device need to be perfectly modeled using for example a complex numerical model. However, the more accurate 'fine' models demand a high computational time and memory storage. Alternatively, less accurate 'coarse' models can be used with a demerit of the high expected recovery errors. Therefore, the Bayesian approximation error approach has been used for reducing the modeling error originating from using a coarse model instead of a fine model in the inverse problem procedure. However, the Bayesian approximation error approach may fail to compensate the modeling error completely when the used model in the inverse problem is too coarse. Therefore, there is a definitely need to use a quite accurate coarse model. In this paper, the electromagnetic device is simulated using an adaptive Kriging based model. The accuracy of this 'coarse' model is a priori assessed using the cross-validation technique. Moreover, the Bayesian approximation error approach is utilized for improving the inverse problem results by compensating the modeling errors. The proposed methodology is validated on both purely numerical and real experimental results. The results show a significant reduction in the recovery error within an acceptable computational time.Keywords: Bayesian approach, inverse problem, Kriging models, modeling error. INTRODUCTIONRecently, the magnetic parameters of the magnetic core material inside an electromagnetic device (EMD), such as rotating electrical machines, have been retrieved using a coupled experimental-numerical electromagnetic inverse problem [1]. In these inverse problems, the measurements are interpreted using a forward model where the difference between the numerical model responses and the measurement quantities is iteratively minimized using a minimization algorithm. In practice, two major aspects can reduce the accuracy of the recovered solution of the inverse problem, specifically: measurement noise and inaccurate modeling. Measurement noise can be reduced to some extent by accurately performing the measurements. On the other hand, modeling errors basically originate from two main sources: the uncertain 'geometrical' model parameters and the way of modeling the physical phenomena of the EMD. The effect of the uncertain geometrical model parameters on the solution of the inverse problem has been extensively investigated by the authors, see [1]. In this reference, the EMD models are assumed to be perfect, i.e. all physical phenomena are modeled, or in other words, the EMD models exactly simulate the reality. To this end, the EMD needs to be modeled using a very complex ...