<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In electromagnetic problems, the problem geometry may not always be exactly known. One example of such a case is a rotating machine with random-wound windings. While spectral stochastic finite element methods have been used to solve statistical electromagnetic problems such as this, their use has been mainly limited to problems with uncertainties in material parameters only. This paper presents a simple method to solve both static and time-harmonic magnetic field problems with source currents in random positions. By using an indicator function, the geometric uncertainties are effectively reduced to material uncertainties, and the problem can be solved using the established spectral stochastic procedures. The proposed method is used to solve a demonstrative single-conductor problem, and the results are compared to the Monte Carlo method. Based on these simulations, the method appears to yield accurate mean values and variances both for the vector potential and current, converging close to the results obtained by time-consuming Monte Carlo analysis. However, further study may be needed to use the method for more complicated multi-conductor problems and to reduce the sensitivity of the method on the mesh used.</p></abstract>

In electromagnetic problems, the problem geometry may not always be exactly known. One example of such a case is a rotating machine with random-wound windings. While spectral stochastic finite element methods have been used to solve statistical electromagnetic problems such as this, their use has been mainly limited to problems with uncertainties in material parameters only. This paper presents a simple method to solve both static and time-harmonic magnetic field problems with source currents in random positions. By using an indicator function, the geometric uncertainties are effectively reduced to material uncertainties, and the problem can be solved using the established spectral stochastic procedures. The proposed method is used to solve a demonstrative single-conductor problem, and the results are compared to the Monte Carlo method. Based on these simulations, the method appears to yield accurate mean values and variances both for the vector potential and current, converging close to the results obtained by time-consuming Monte Carlo analysis. However, further study may be needed to use the method for more complicated multi-conductor problems and to reduce the sensitivity of the method on the mesh used.

Spectral Stochastic Finite Element Method for Electromagnetic Problems with Random Geometry

Electrical, Control and Communication Engineering

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In electromagnetic problems, the problem geometry may not always be exactly known. One example of such a case is a rotating machine with random-wound windings....

Spectral Stochastic Finite Element Method for Electromagnetic Problems with Random Geometry

Published Online: Oct 23, 2014

Page range: 5 - 12

DOI: https://doi.org/10.2478/ecce-2014-0011

Keywords
Eddy currents, Finite element analysis, Stochastic systems, Random variables

© 2014 Riga Technical University

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Spectral Stochastic Finite Element Method for Electromagnetic Problems with Random Geometry

Published Online: Oct 23, 2014

Page range: 5 - 12

DOI: https://doi.org/10.2478/ecce-2014-0011

KeywordsEddy currents, Finite element analysis, Stochastic systems, Random variables

© 2014 Riga Technical University

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Eddy currents, Finite element analysis, Stochastic systems, Random variables