Gilles Cauffet

Recent improvements for solving inverse magnetostatic problem applied to thin shells

In this paper, we propose a new approach to solve the magnetostatic inverse problem. The goal of the work is, from measurements of the magnetic field in the air, to rebuild a model for the magnetization of a ferromagnetic shell structure. Its then possible to calculate the field where sensors cannot be placed. This problem is usually ill posed or rank-deficient, its then necessary to use mathematical regularizations. These techniques are based upon the injection of knowledge about the mathematical behavior of the solution. We preferred to add physical information. This solution allows us to get a faithful solution and to reduce significantly the number of sensors. Moreover, our method has been tested on a mock-up with real measurements and led to very promising results.

How to well pose a magnetization identification problem

This paper presents an original approach for determining the unknown magnetization of a ferromagnetic shell. Magnetic measurements using sensors close from the device under test are used to rebuild distributions located on the shell. These distributions are representative of the magnetization and tangential moments or charges can be used. This identification problem is a particular case of an inverse problem and is generally ill posed. Instead of using classical mathematical tools to solve such a problem, we preferred to change it in a better posed one by adding our physical knowledge of the problem. All our results have been validated on a mockup with real measurements.

Magnetization identification problem: Illustration of an effective approach

This paper deals with the problem of magnetization identification. We consider a ferromagnetic body placed in an inductor field. The goal of this work is, from static magnetic field measurements taken around the device, to obtain an accurate model of its magnetization. This inverse problem is usually ill‐posed and its solution is non‐unique. It is then necessary to use mathematical regularization. However, we prefer to transform it to a better posed one by incorporating our physical knowledge of the problem. Our approach is tested on the magnetizations identification of a real ferromagnetic sheet.

Modeling of static magnetic anomaly created by iron plates

This paper deals with the modeling of thin steel shells placed in a static magnetic field. The variable used is the scalar reduced potential. In front of the diversity of the formulations encountered, it proposes a methodological approach of different methods and compares them, in term of speed and easiness of computation.

Scalar Potential Formulation and Inverse Problem Applied to Thin Magnetic Sheets

Our goal is to identify sheet steel magnetization with near field measurements. Indeed, direct calculation of the whole magnetization is impossible because the remanent part of the magnetization is nondeterminist. Consequently, our strategy is to obtain a magnetostatic formulation able to compute magnetic field as close as possible to the sheet and which is adapted to solve an inverse problem. In this paper, a scalar potential integral formulation is introduced and compared to a magnetization formulation. We are especially interested in the magnetic anomaly created by ferromagnetic ships.

Magneto-Mechanical Effects Under Low Fields and High Stresses— Application to a Ferromagnetic Cylinder Under Pressure in a Vertical Field

This study focuses on the effects that a ferromagnetic material undergoes when subjected to high stresses under low magnetic field. In order to predict the magnetic signature, we show that the Jiles magnetization law of approach can be applied to model induction measured by external sensors, and an analytical solution is derived in the case of our prototype, a cylinder subjected to an internal pressure up to 100 Bars in a vertical field. Comparison between model predictions and measurements shows an error lower than 5%.

Spatial harmonic current density basis for faults identification in fuel cell stack from external magnetic field measurements

An original approach used for the identification of faults in fuel cell stacks is presented. It is based on the 3D reconstruction of the current density from external magnetic field measurements which is an ill-posed magnetostatic linear inverse problem. Suitable current density and magnetic field basis are proposed in order to define both local and global faults on a fuel cell stack. In order to ensure the uniqueness of the solution, the inverse problem is regularized thanks to the truncated singular value decomposition (SVD).

Identification of ferromagnetic thin sheets magnetization: Use of gradient and potential measurements

Purpose – This paper aims to present the use of magnetic gradient, and magnetic potential measurements in the specific case of magnetization identification for a thin sheet. Usually, induction measurements are only used.Design/methodology/approach – After a brief description of the magnetic gradient and magnetic scalar potential notions, methods to calculate them are presented and validated. These two kinds of measurements are tested for a numerical identification case. Then, virtual measurements can be generated and used for inverse problem resolution. Advantages of using induction, magnetic gradient or magnetic potential measurements are then discussed.Findings – A previous method to solve inverse problem based on induction measurement has been increased by the capability of using other kind of measurements. A numerical approach has allowed to validate the use of magnetic gradient or magnetic scalar potential measurement as information sources.Originality/value – Usually, induction measurements are only...

Study of the inverse problem resolution quality: application to low‐field magnetostatic

Purpose – This paper presents a method to improve inverse problem resolution. This method focuses on the measurement set and particularly on sensor position. Based on experiment, it aims at finding sensor position criteria to insure the least bad inverse problem solving.Design/methodology/approach – The studied device is a magnetized steel sheet measured by four sensors. Three optimization techniques are compared: condition number, solid angle and signature optimization.Findings – An efficient criterion to compare the inverse problem resolution quality is presented. The comparison of optimization techniques shows that only signature optimization gives accurate results.Research limitations/implications – A relative simple case is studied in this paper: only four sensors are used to measure a steel sheet. Moreover magnetostatic low‐field case is supposed. Nevertheless techniques presented could be applied to more complex studies. Condition number and solid angle optimizations techniques should be tested wit...