Spherical harmonic identification using a priori information about an electrical device

Abstract

This paper deals with the use of spherical harmonic expansion to identiiy a magnetic multipolar equivalent model to a given electrical device. If the method presents many advantages, its use In an inverse problem approach reqdres to be cautious in the choice of the number of required magnetic sensors and their Icwation This article propws a method using a priori information like periodicities or symmetries in order to -B , , , = G -4 4 whwc: h c a is a 3K-dimension vector of induction componmta on smsors) A is a (N-2+2Nm~-dimension vector of the different s, coefficients G is s (3K, Nma+2Nm,) -dimomion matrix of spherical harmonic. sbOngy decrease the required number Of A didacticThe system (2) gives all the harmonic cefficients related to example of spherical harmonic identification illustrates how powerful the method is the source. If the quantity of information given by the magnetic sensors (3*K induction components) is smaller than I. INTRODUCTION The Spherical Harmonic Identification (SHI) is used for many applications to determine a model of a source [I]. Thanks to this model, the magnetic induction can be computed where sensors could not be set. However, the limit of this inverse problem is due to the high number of magnetic sensors required to do a precise spherical harmonic model [2].The main interest of the SHI is the strong link between the spherical harmonic identified coefficients and the geometry of the source. Therefore, if the geometry of the source is well known, these information can be used before using the SHI. It will strongly reduce the number of the characteristic harmonic coefficients and at the same time the number of required magnetic sensors.This paper focuses on a method that from the geometry determines the main harmonic coefficients of the source and saves sensors. A didactic example of a four pair-poles electrical motor was simulated using FEM method to illustrate the proposed method.

Error Analysis for Near-Field EMC Problems Based on Multipolar Expansion Approach

“…The Bayesian method could be applied to insert the results of the previous measurements to the new measurements as a prior information. The prior information could also be the knowledge of the geometry of the DUT or mechanic uncertainties in the measurements [10].…”