Estimation method of current density between laminated thin sheets by inverse analysis of magnetic field (Application to short circuit localization)

Abstract

Analyses of magnetic field help find out internal states noninvasively and there are many applications of the analyses for nondestructive inspections. In the field of power sources, there has been a great discussion about behaviors of an internal short circuit in a lithium-ion battery. Since lithium-ion batteries supply or preserve high energy, the visualization of the current flow in the batteries is an important issue to prevent serious incidents by such short circuits. The basic structure of lithium-ion batteries is a type of laminated constructions of thin sheets. This study has developed a novel estimation method of the current density between laminated thin sheets by the inverse analysis of the magnetic field, and investigated its applicability to the short circuit localization. In the proposed method, the boundary element method (BEM) for thin plate, the Tikhonov regularization and the Kullback-Leibler divergence are applied. The BEM calculates the observation equation relating the current density to the magnetic flux density in high accuracy and high speed. The Tikhonov regularization reduces the influence of the measurement error on the estimated value. By using the Kullback-Leibler divergence as the criterion to determine the Tikhonov regularization parameter, it makes the standard deviation of the magnetic flux density useful to the evaluation of the estimated current density. In order to verify the proposed method, numerical simulations and actual measurements were performed. From the results of the numerical simulations and the actual measurements, it is concluded that the proposed method provides the location of the short circuit between the thin sheets through the estimation of the current density. Moreover, the limitation of the proposed method was observed in terms of the standard deviation of the magnetic flux density.

Keywords

• inverse problem
• laminated construction
• shell structure
• short circuit
• electromagnetic measurement
• nondestructive inspection
• boundary element method