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Modeling of Spatial Uncertainties in the Magnetic Reluctivity

Jankoski, Radoslav and Römer, Ulrich and Schöps, Sebastian :
Modeling of Spatial Uncertainties in the Magnetic Reluctivity.
[Online-Edition: https://doi.org/10.1108/COMPEL-10-2016-0438]
In: COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 36 (4) pp. 1151-1167. ISSN 0332-1649
[Article] , (2017)

Official URL: https://doi.org/10.1108/COMPEL-10-2016-0438

Abstract

Purpose In this paper a computationally efficient approach is suggested for the stochastic modeling of an inhomogeneous reluctivity of magnetic materials. These materials can be part of electrical machines, such as a single phase transformer (a benchmark example that is considered in this paper). The approach is based on the Karhunen-Loève expansion. The stochastic model is further used to study the statistics of the self inductance of the primary coil as a quantity of interest (QoI). Design/methodology/approach The computation of the Karhunen–Loève expansion requires solving a generalized eigenvalue problem with dense matrices. The eigenvalues and the eigenfunction are computed by using the Lanczos method that needs only matrix vector multiplications. The complexity of performing matrix vector multiplications with dense matrices is reduced by using hierarchical matrices. Findings The suggested approach is used to study the impact of the spatial variability in the magnetic reluctivity on the QoI. The statistics of this parameter are influenced by the correlation lengths of the random reluctivity. Both, the mean value and the standard deviation increase as the correlation length of the random reluctivity increases. Originality/value The Karhunen–Loève expansion, computed by using hierarchical matrices, is used for uncertainty quantification of low frequency electrical machines as a computationally efficient approach in terms of memory requirement as well as computation time.

Item Type: Article
Erschienen: 2017
Creators: Jankoski, Radoslav and Römer, Ulrich and Schöps, Sebastian
Title: Modeling of Spatial Uncertainties in the Magnetic Reluctivity
Language: English
Abstract:

Purpose In this paper a computationally efficient approach is suggested for the stochastic modeling of an inhomogeneous reluctivity of magnetic materials. These materials can be part of electrical machines, such as a single phase transformer (a benchmark example that is considered in this paper). The approach is based on the Karhunen-Loève expansion. The stochastic model is further used to study the statistics of the self inductance of the primary coil as a quantity of interest (QoI). Design/methodology/approach The computation of the Karhunen–Loève expansion requires solving a generalized eigenvalue problem with dense matrices. The eigenvalues and the eigenfunction are computed by using the Lanczos method that needs only matrix vector multiplications. The complexity of performing matrix vector multiplications with dense matrices is reduced by using hierarchical matrices. Findings The suggested approach is used to study the impact of the spatial variability in the magnetic reluctivity on the QoI. The statistics of this parameter are influenced by the correlation lengths of the random reluctivity. Both, the mean value and the standard deviation increase as the correlation length of the random reluctivity increases. Originality/value The Karhunen–Loève expansion, computed by using hierarchical matrices, is used for uncertainty quantification of low frequency electrical machines as a computationally efficient approach in terms of memory requirement as well as computation time.

Journal or Publication Title: COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
Volume: 36
Number: 4
Uncontrolled Keywords: uncertainty
Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute of Electromagnetic Field Theory
18 Department of Electrical Engineering and Information Technology > Institute of Electromagnetic Field Theory > Computational Engineering (2019 umbenannt in Computational Electromagnetics)
Exzellenzinitiative
Exzellenzinitiative > Graduate Schools
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
Date Deposited: 23 Sep 2017 17:02
Official URL: https://doi.org/10.1108/COMPEL-10-2016-0438
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