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

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

A modified inverse scheme for magnetic material characterization of an electromagnetic device with minimal influence of multiple geometrical uncertainties

The properties of the magnetic core materials inside electromagnetic devices can be retrieved by solving an electromagnetic inverse problem. In such inverse problems, the unknown parameters are recovered by interpreting well-chosen measurements using a forward numerical model. However, the modeling errors originating from the uncertainties of the geometrical parameter values often degrade the accuracy of the recovered values of the material parameters. In this paper, we propose an efficient inverse scheme for reducing the effect of multiple geometrical uncertainties. This deterministic technique adapts the objective function to be minimized with the sensitivity of the forward numerical model to the uncertain parameters. The proposed methodology is validated for the identification of the magnetic material parameters of a few electromagnetic devices, where the forward model exhibits multiple geometrical uncertainties. The numerical results show a large reduction of the recovery errors within an acceptable computational time

Local magnetic measurements in magnetic circuits with highly nonuniform electromagnetic fields

In this paper, local magnetic measurements are carried out in magnetic circuits with highly non uniform electromagnetic field patterns, including excitation winding and/or air gaps, as in the case of rotating electrical machines. The effect of sensor choice, sensor noise sensitivity, electromagnetic field nonlinearity, and magnetic shielding are investigated. Moreover, the validity of the local magnetic measurements is confirmed by numerical models

A Rogowski-Chattock coil : sources of error

The local magnetic field is measured by means of magnetic sensors, such as a Rogowski-Chattock coil. The main advantage of the Rogowski coil is its capability to measure the field strength directly at the sample surface because both ends of the coil can be installed very close to the specimen surface. However, the measurements are affected by numerous errors, which are comprehensively discussed in this paper

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

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

A robust inverse approach for estimating the magnetic material properties of an electromagnetic device with minimum influence of the uncertainty in the geometrical parameters

The magnetic properties of the magnetic circuit of an electromagnetic device (EMD) can be identified by solving an inverse problem, where sets of measurements are properly interpreted using a forward numerical model of the device. However, the uncertainties of the geometrical parameter values in the forward model result in recovery errors in the reconstructed material parameter values. This paper proposes a novel inverse approach technique, in which the propagations of the uncertainties in the model are limited. The proposed methodology adapts the cost function that needs to be minimized with respect to the uncertain geometrical model parameters. We applied the methodology onto the identification of the magnetizing B-H curve of a switched reluctance motor (SRM) core material. The numerical results show a significant reduction of the recovery errors in the identified magnetic material parameter values

An efficient program for modeling, control and optimization of hybrid renewable-conventional energy systems

-In this paper, a generic and an efficient model for hybrid renewable-conventional electrical energy systems is presented. This simulation model is successfully validated by means of HOMER. Moreover, two control strategies for electrical power dispatch are described. Furthermore, an optimization problem is formulated and solved, using Genetic algorithm technique, for optimizing the size of system components where the overall cost of the system is minimized. Four case studies are investigated. The results show a dependence of the size of the system components on the meteorological characteristics of the area under consideration, which validate the proposed methodology

A priori error estimation of magnetic material characteristics using stochastic uncertainty analysis

By interpreting electromagnetic or mechanical measurements with a numerical model of the considered electromagnetic device, magnetic properties of the magnetic circuit of that device can be estimated by solving an inverse numerical electromagnetic problem. Due to measurement noise and uncertainties in the forward model, errors are made in the reconstruction of the material properties. This paper describes the formulation and implementation of the error estimation and the prediction of which measurements that need to be carried out for accurate magnetic material characterization. Stochastic uncertainty analysis, based on Cramér-Rao bound (CRB), is introduced and applied to the magnetic material haracterization of a Switched Reluctance Motor (SRM) starting from mechanical (torque) and local magnetic measurements. The traditional CRB method that estimates the error due to measurement noise is extended with the incorporation of stochastic uncertain geometrical model parameters

A modified migration model biogeography evolutionary approach for electromagnetic device multiobjective optimization

Inthispaper, we present anefficient androbust algorithm for multiobjective optimization of electromagnetic devices.Therecentlydeveloped biogeography-based optimization (BBO) is modified byadapting its migration model function so as to improve its convergence.The proposed Modified Migration Model biogeography-based optimization (MMMBBO) algorithm is applied into the optimal geometrical design of an electromagnetic actuator. This multiobjective optimization problem is solved by maximizing the output force as well as minimizing the total weight of the actuator. The comparison between the optimization results using BBO and MMMBBO shows the superiority of the proposed approach