Instrumentation & Measurement Magazine 25-7 - 49

Authors in [8] propose an iterative inversion approach for
predicting 3-D defect geometry from MFL observations using
a multiresolution wavelet transform as well as a radial
basis function neural network (RBFN). Space mapping (SM)
methodology is used in the inversion procedure in [8]. A
wavelet transform domain finite impulse response (FIN) filtering
technique for eradicating seamless pipe noise (SPN)
in MFL data is presented in [9], [10]. Wavelet-based techniques
for de-noising and classification are presented by
authors in [11], [12]. FIR filter is used in [13] to offer an adaptive
solution for channel equalization in MFL inspection.
A model-based probability of detection evaluation method
for MFL inspection of natural gas transmission pipes is presented
in [14]. Authors of [15] provide a comparison of the
MFL approach with ultrasonic techniques. Other connected
subjects can be found in [16]. Based on measurements of one
tangential component of MF, [17] provides a rapid direct approach
for estimating crack characteristics in rectangular
surface-breaking cracks. In [18], for example, authors create
a calibration surface that plots MFL signal strength against
two crack depth as well as length parameters.
Magnetic Flux Leakage Detection in
Wire Rope
A magnetic field sensor measures the MLF, which transmits
data on inclusions or anomalies such as corrosions, abrasion,
broken wires and dimensions or positions of defects that are
realized by an appropriate digital data processor. Because of
the volume constraint, obtaining high defect resolution with a
coil sensor is quite challenging.
These capabilities include the adaptability to the testing of
pipelines with different diameters, wireless motor control and
wireless data transmission. It is composed of a set of powerful
permanent magnets, which are supported by cross-shaped
metallic blocks.
Faraday's Law of EMI with Z-filter in EM
Decomposition
Magnetic field B measured in Tesla units characterizes magnetic
fields generated by currents as well as estimated using
Ampere's Law or Biot-Savart Law. The relationship used to define
the magnetic field is:
HB //B M 00 0


where the relationship of B is expressed by:

B HM

(1)
The potential distribution that solves Laplace's equation
in two dimensions for a thin homogeneous and isotropic plate
without a break is (x′,y′), given by:
2 x ,y 0

with boundary conditions as ϕ( d/2′y ′ )=+Vo
ϕ(−d/2′y′)=−Vo
.
The current density distribution J (x′,y′), is predictable
to be uniform with a direction anti-parallel to the x′ -axis
and potential φ depend only on x′. Thus, the relationship reduces
to:
  xx  
22
/0
and potential is obtained as:
 x Kx L


(5)
(4)
and
(6)
The boundary condition given by (6) is applied to find constants
K and L to obtain:
 x Vx d
 2/o
 
The current density is given by:

 



 
J x ,y J0
x
xd
ii
2V0
(7)
(8)
Now, the MF B(r) at any point external to a volume v′ consists
of distribution of current J(r) given by:
 
B    '
 
r
0

4 ||3
v
( ') (r

rr

Faraday's Law of EMI
Faraday's Law of EMI (referred to as Faraday's law) is a fundamental
law of electromagnetics that explains how an MF
relates with an electric circuit to yield an EMF. Named for
Michael Faraday who researched coil and magnet, this law
explains motors, transformers, inductors and generators.
When flux passes through this coil EMF is produced during
experiment. When a conductor is exposed to a changing MF,
Faraday's law states that a current will be induced. Lenz's
law states that induced current opposes the produced magnetic
field. Fleming's right-hand rule determines current flow
direction.
(2)
Units for H and M will be identical in amperes/meter, and
magnetization of a substance is the quantity M in these
relationships.
The relationship between B and H can also be expressed
by: B=μm
H
 K mm 0
 
October 2022
(3)
Faraday's Experiment
Faraday used a magnet and a coil in this experiment and attached
a galvanometer across coil. The magnet was at rest
when galvanometer is started, hence there was no deflection,
i.e., the needle of galvanometer was at center or zero
point. When the magnet moved away from the coil, the needle
deflected in the opposite direction, and when the magnet
returned to its original location about the coil, the needle of the
galvanometer returned to zero. It is also worth noting that the
IEEE Instrumentation & Measurement Magazine
49
Jr r ')

dx dy dz
' ''
(9)
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