A Method to Optimize the Magnetic Susceptibility of
Ferromagnetic Objects
BIAN Qiang, LIU Da-ming, TONG Yu-de, ZHOU Guo-hua
College of Electrical and Information Engineering
Naval University of Engineering
Wuhan, China
tzbianqiang@163.com, tongyude@126.com
Abstract—With respect to the difficulty of getting the
magnetic susceptibility of ferromagnetic objects in engineering,
with the measured data of magnetic field, the multi dimensional
optimizing model for magnetic susceptibility is established based
on the element surface integral method in calculating induced
magnetic field of ferromagnetic objects and the Differential
Evolution algorithm with the advantage of global multi
dimensional optimizing is introduced to solve it. Then, the
induced magnetic field of ferromagnetic object can be fixed.
Finally, a magnetic-field measurement experiment for a hollow
cylinder is designed and the result shows that the multi
dimensional magnetic susceptibility and the induced magnetic
field of ferromagnetic objects can be calculated efficiently and
accurately.
Keywords—element surface integral; the magnetic
susceptibility; the Differential Evolution algorithm;induced
magnetic field calculation
I. INTRODUCTION
As the typical ferromagnetic object, the vessel would be
magnetized in the earth magnetic field, and the induced
magnetic field would be generated on its surround, which
makes the vessel easier to be attacked by the magnetic weapons
in water and to be detected by the antisubmarine aircrafts. To
promote the magnetic self-protection ability of the vessel, the
induced magnetic field of the vessel should be obtained
precisely to design the best vessel degaussing system.
Nowadays, the most conventional forecasting methods of the
vessels’ induced magnetic field include the finite-element
method (FEM) and the integral equation method. FEM could
be used to solve the Laplacian equation satisfy to the induced
magnetic field’s scalar potential. However, in this method,
boundary condition should be set and a sizable region should
be divided to the discrete elements whose number could be
reaching millions that makes the data storage and the
calculation very large[1],[2]. However, with the integral
equation method, only the vessel should be meshed that makes
the elements number decrease greatly and the calculation more
simple[3],[4],[5],[6]. The primary premise of calculating the
ferromagnetic object’s induced magnetic field is to obtain its
magnetic susceptibility precisely. According to the property
that the ferromagnetic object’s magnetic susceptibility keep
constant fundamentally in the low intensity magnetic
environment[7], based on the measured data of magnetic field
in the low intensity magnetic environment and the element
surface integral model, the multi dimensional optimizing model
for magnetic susceptibility in the low intensity magnetic
environment is established and the Differential Evolution
algorithm is introduced to solve it. Finally, the multi
dimensional of magnetic susceptibility was inverted
successfully. A magnetic-field measurement experiment for a
hollow cylinder with two capped terminals is designed and the
result shows that the multi dimensional magnetic susceptibility
and the induced magnetic field of ferromagnetic objects can be
calculated efficiently and accurately with the method proposed
in this paper.
II.
THE MAGNETIC FIELD MODEL WITH ELEMENT SURFACE
INTEGRAL
As is showed in Fig. 1,
V is the volume of ferromagnetic
object,
S is its surface, r is the point radius vector,
is the
intensity of magnetization。
Fig. 1. The magnetization model for ferromagnetic objects
Presuming that there is no free current in this region, the
scalar magnetic potential formula of the uniform magnetized
ferromagnetic object as follows[7],[8].
This work was supported by National Natural Science Foundation of
China(Grant Nos. 51107145,61203193).
BIAN Qiang is corresponding author(tzbianqiang@163.com).
978-1-4673-7189-6/15/$31.00©2015 IEEE