The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Proceedings

APPLIED ELECTROMAGNETICS
AND MECHANICS

Edited by
Phuong Ho-Thanh, Ha Ta-Hong, Ngan Huynh-Kieu, Chi Dang-Kim

The 7th Asia Pacific Symposium on Applied Electromagnetics and Mechanics
July 25-27, 2012, Ho Chi Minh city, Vietnam

JAPAN SOCIETY OF APPLIED ELECTROMAGNETICS AND MECHANICS

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Enhance the Sensibility of the Eddy Current Testing
Hiroki KIKUCHIHARA1), Iliana MARINOVA2), Yoshifuru SAITO1),
Manabu OHUCH3), Hideo MOGI3) and Yoshiro OIKAWA3)
1)
Graduate School of Hosei University, Tokyo 184-8584, Japan
2)
Technical University of Sofia, Sofia 1756, Bulgaria
3)
Denshijiki Industry Co., Ltd, Tokyo 115-0051, Japan
Eddy current testing (ECT) is one of the most representative nondestructive testing methods for metallic
materials, parts, structures and so on. Operating principle of ECT is based on the two major properties of magnetic
field. One is that alternating magnetic field induces eddy current in all of the conducting materials. Thereby, an
input impedance of the magnetic field source, i.e., electric source, depends on the eddy current path. Second is thatthe magnetic field distribution depends only on the exciting but also the reactive magnetic fields caused by theeddy currents in targets. Former and latter are the impedance sensing and magnetic flux sensing types,
respectively.
This paper concerns with an improvement of sensibility of the impedance sensing method. Sensibility of the
ECT is improved by means of two steps. One is an optimum exciting frequency selection. We employ the naturalparallel resonant frequency of ECT coil. The other is to increase the sharpness of the resonance curve on
impedance versus frequency characteristic by changing the coil connection. Thus, we have succeeded indeveloping the ECT sensor having up to 4 times higher sensibility compared with those of conventional one.
Key words: Eddy current, Nondestructive testing, Resonant frequency

1

magnetic fields induces eddy current in all of the conducting

Introduction

materials. Thereby, the input impedance of the magnetic
Modernengineering

productssuchasair-plane,

automobile, smart building, high speed train and so on are
essentially composed of metallic materials for forming theshape of product, suspending the mechanical stress andconstructing the structural frames. In particular, the masstransportation vehicles, e.g. large air plane, hi-speed train,
express highway bus and so on, carrying a large number ofpeople are required ultimately high safety as well as
reliability.
To keep the safety of such vehicles, nondestructive testing
to the metallic materials is one of the most important
technologies because most of the structure materials arecomposed of the metallic materials.
Various nondestructive testing methods, such as eddy
current testing (ECT), electric potential method, ultrasonicimaging and x-ray tomography, are currently used. Amongthese methods, ECT does not require complex electronic
circuits and direct contact to target. Furthermore, target
whose major frame parts are composed of conductive
metallic materials can be selectively inspected by ECT[1,3].
Operating principle of ECT is very simple. The ECT isbased on the two major properties of magnetic field. One isthat exposing the conductive materials to the alternating

field source, i.e., electric source, can detect the change ofthe target impedance caused by defects blocking eddy
current flowing. The ECT based on this principle is called
impedance sensing type. The other type utilizes a separately
installed sensor coil to detect the leakage magnetic fluxchange. The magnetic field of ECT is composed of two
components: one is the exciting and the other is the reactive
magnetic fields. The reactive magnetic field is caused by theeddy currents in the target so that change of eddy current
paths changes the reactive magnetic fields. Thus, theindependently installed sensor detects this magnetic fieldchange. This type is called a separately sensing coil type.
This paper concerns with an improvement of sensibility of
the impedance sensing method. Improvement of thesensibility is carried out in the two major steps.
The first step is to select the optimum exciting frequency.
We select the natural parallel resonant frequency of the ECT
sensor coil when facing with a wholesome part of target. A
system comprising the ECT facing with the wholesome partof target takes the maximum pure resistive impedance.
When the ECT sensor coil meets with a defect of target, thisresonance condition is essentially not satisfied. This makes
it possible to maximize the deviation between the resonanceand not resonance impedances.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

The second step is to increase the resonant impedance aswell as to sharpen the peaky impedance versus frequency
characteristic by changing the coil connection [4]. Since thenatural parallel resonance impedance become larger, thenthe deviation between the resonance and not resonance
impedances is essentially larger. This essentially enhances
the sensibility of ECT sensor.
2

Enhancement of ECT Sensibility

2.1 Operating principle of ECT
Let an arbitrary finite length solenoid coil shown in Fig.
1(a) be an eddy current sensor coil. When we put on this(a) Impedance |Z| vs. Frequency f.

sensor coil on a copper plate as shown in Fig. 1(b) andapply an alternating current to the sensor coil, because of the
Faraday¶s law, eddy current is induced as a reaction of thealternating magnetic fields. Measure the input impedance ofthe sensor coil is able to diagnose a difference of the target
copper plate condition between no defects (Fig. 1(b)) and
2mm crack defect(Fig. 1(c)). This is similar to thesecondary impedance change detection from primary input
terminal in a conventional single phase transformer.

E 3KDVHĳYV)UHTXHQF\I.

Thus, it is obvious that a simple finite length solenoid coilcan detect the defects of the target conducting materials.
This is the operating principle of ECT.

Fig.2 Frequency characteristics of the impedance and phase.

2.3 Optimum operation frequency
Decision of ECT operation frequency is of paramount
1 mm(a)Coil(a)Coil(b)Copper plate with 1mm
thickness

importance, because sensibility and searching depth of ECT
are greatly depending on the operation frequency.
Theoretically, the operation frequency of ECT can bedecided by taking the target conductivity and its skin-depth
into account. However, final selection of operation

1 mm
2mm

(c)1mm(c)2mm Air-gap
AirgapFig.1 Tested coil and the measurement conditions.

frequency is determined by the past experiences and thepractical tests.
In the present paper, we select the natural parallel resonant
frequency of the ECT sensor coil when facing with a

2.2 Natural resonant phenomena of ECT coilwholesome part of target. The ECT facing with the

Any of the coils always exhibit an inductive property

wholesome part of target takes the maximum pure resistive

because of the magnetic fields around them by applying a

impedance. When the ECT sensor coil meets with a defectcurrent into the coil. However, any of the coils have theof target, the resonance condition is essentially not

capacitances among the coils. Even though a simple finite

established. Therefore, the input impedance from sensor coillength solenoid coil shown in Fig. 1(a), it is possible toinput terminals is also reduced to small in value compared

observe its natural resonance phenomena as shown in Fig. 2.

with those of the resonant one. Namely, a deviation between

Figs 2(a) and 2(b) are the frequency f versus impedance |Z|

the resonance and not resonance impedances becomes

and the frequency f versus phase ȯ characteristics,

maximum value.

respectively.

A sensibility İ of ECT is defined by

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

parallelH

reference  measured
u100 > %@ ,reference(1)

conductors

and

their

resonant

connection,

respectively. Denoting R, L, M as the resistance,
self-inductance and, mutual inductance, it is possible todraw an equivalent circuit of the resonant connected two

where the reference and measured in (1) refer to the input

conductors as shown in Figs. 3(c), 3(d). Fig.4 shows a

impedances from the ECT coil terminals when facing thedifference between the normal and resonant coil connection

ECT coil with the wholesome and defect parts of target,[4]. Practically, the resonant connection is carried out by

respectively.

twisting the two coils to uniform the facing side of both

2.4 Enhancement of quality factor Q

conductors as shown in Fig. 5 [5].

The sensibility of (1) is greatly depended on the quality
factor Q of the parallel resonance defined by

Q

where

f0 ,
'f

(2)

f 0 and 'f are the resonant frequency and the(a) Normal(b) Resonance typeFig.4 Comparison of the normal with resonant coil connections.

bandwidth, respectively.
The quality factor Q represents a sharpness of the resonant
curve on the impedance versus frequency coordinate. So

Fig. 5 Example of a pair of twisted coils

that high Q in (2) means high sensibility in (1).
To increase the quality factor Q, we employ the resonant

3 Experimentconnection shown in Fig. 3. Figs. 3(a) and 3(b) are the two

3.1 Tested target peace and trial ECT coils
Fig. 6 shows a target peace which is composed of the twodifferent types ofmaterials (SUS304 and SUS316). A

vertical line shape artificial crack having 10mm length,
0.2mm width and 0.5mm depth had been made to thesandwiched SUS by the electrical discharge machining. Fig.
(a) Two conductors.

(b) Connection of the two
conductors.

6 shows a 20mm by 20mm target area. The ECT sensors
measured at the 9 by 9 sampling points with 2.5mm regularspacing on this 20mm by 20mm square area.

(c) Equivalent electric circuit of the connected conductors.

(d) Modified equivalent electric circuit of the connected
conductors.
Fig.3 Principle of a resonance coil connection.

Fig. 6 Target test piece and measured points.
The test peace is composed of the two different types of SUS
materials. A line shape artificial crack having 10mm length,
0.2mm width and 0.5mm depth had been made to the sandwiched
SUS by the electrical discharge machining. A 20mm by 20mm
square area is measured at the 9 by 9 points with 2.5mm regularspacing sampling

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

We have worked out a lots of ECT coils for comparison.

3.2 Conventional ECT operating at 256kHz

Table 1 lists the representative 6 tested ECT coils. Everytested coil is wound around the Manganese-Zinc type ferrite
bar used as an axial core material. No.1 is a normal ECT,
No. 2 is a resonance type not employing twisting of coil,No.3 is a resonance type employing 100/m twisting, No.4 isa resonance type employing 150/m twisting, No.5 is aresonance type employing 200/m twisting, and No.6 is aresonance type employing 400/m twisting.

No.1

No.2

No.3

Table 1. Specification of the trial ECT coils.
NormalConductor length
50cm
Diameter of conductor
0.1mm
Axis core
Ferrite bar (MnZn)
Coil outer diameter
2.4mm
Coil inner diameter
2mm
Coil length
6mm
Number of twisted turns
0
Number of coil layers
2Resonant
Conductor length
50cm
Diameter of conductor
0.1mm
Axis
Ferrite bar (MnZn)
Coil outer diameter
2.4mm
Coil inner diameter
2mm
Coil length
6mm
Number of twisted turns
0
Number of coil layers
2
Twisting

No.4

Twisting

No.5

Twisting

No.6

Twisting

Conductor length
50cm
Diameter of conductor
0.1mm
Axis
Ferrite bar (MnZn)
Coil outer diameter
3mm
Coil inner diameter
2mm
Coil length
5mm
Number of twisted turns
100/m
Number of coil layers
3
Conductor length
50cm
Diameter of conductor
0.1mm
Axis
Ferrite bar (MnZn)
Coil outer diameter
3mm
Coil inner diameter
2mm
Coil length
5mm
Number of twisted turns
150/m
Number of coil layers
3
Conductor length
50cm
Diameter of conductor
0.1mm
Axis
Ferrite bar (MnZn)
Coil outer diameter
3mm
Coil inner diameter
2mm
Coil length
5mm
Number of twisted turns
200/m
Number of coil layers
3
Conductor length
50cm
Diameter of conductor
0.1mm
Axis
Ferrite bar (MnZn)
Coil outer diameter
3mm
Coil inner diameter
2mm
Coil length
5mm
Number of twisted turns
400/m
Number of coil layers
3(a) No.1 Normal(b) No.2 Resonant(c) No.3 Twisting(d) No.4 Twisting(e) No.5 Twisting(f) No.6 TwistingFig. 7 Defect searching results. Any sensor coils can detect
the two different kinds of base metallic materials.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

At first, we evaluated the line shape crack in Fig. 6 byconventional ECT employing 256kHz operating frequency.
Fig.7 shows the results of defect searching. Observe theresults in Fig. 7 suggests that any of the sensor coils arecapable of detecting the two different kinds of base metallic
materials. Further, it is difficult to decide which sensor is thehighest sensibility. In the other words, normal ECT defect(a) No.1 Normal

searching using a particular operating frequency neverreflects on the difference of the conductor connection andcoil twisting.
3.3 ECT operating at resonant frequency
Any types of ECT coils have their own natural resonant
frequency even if they are facing with the target without any
defect. No.1,2,3,4,5 and 6 ECT coils in Table 1 have the(b) No.2 Resonant

natural resonant frequencies, 4650, 4950, 3650, 3300, 3425
and 3475 kHz, respectively. Fig. 8 shows the typicalfrequency characteristics of the trial ECT coils.

(c) No.3 Twisting(a) No.1(d) No.4 Twisting(e) No.5 Twisting(b) No.2(f) No.6 Twisting(c) No.4
Fig. 8 Frequency f vs. impedance |Z| characteristics of the ECTFig. 9 The results of defect searching. Any sensor coils can detectcoils (a) No.1, (b) No.2 and (c) No.4, respectively.

two different kinds of base metallic materials.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Fig. 9 shows the defect searching result using each of the distinct

target, the resonance condition has not been established.

natural resonant frequencies. Comparison of the results in Fig. 7This has led that the impedance has reduced to small value

with that of Fig. 9 reveals that the resonant frequency operation iscompared with those at resonant condition. As a result, a

far superior sensibility in any ECT coils. In particular, No. 4 in Fig.

deviation between the resonant and9(d) exhibits nearly 10% deviation. This fact is verified that the

impedances has become the maximum. Thus, the sensibility

quality factor of No.4 in Fig. 9(b) is far excellent compared withof ECT sensor has been enhanced.

those of No.1 and of No.2.

Further, connection of the conductors to be applied a half

not resonantof the source voltage to adjacent conductors has made it
possible to enhance the capacitive effect among the
conductors. Practically, this connection has been carriedout by twisting the two coils to uniform the facing side ofboth conductors. Due to this enhancement of the capacitiveeffects, the resonant frequency has been reduced andsucceeded in increasing the sensibility.
(a) No. 1
References[1] I.Marinova, S.Hayano and Y.Saito, Ployphase eddy current
testing, Journal of Applied Physics, Vol. 75, No.10, pp.
5904-5906, 1994.
[2] N.Burais and A.Nicolas, Electromagnetic field analysis inremote field eddy current testing systems, IEEE Transactions on
Magnetics, Vol.25, No.4, pp.3010-3012, 1989.
(b) No.2[3] S.McFee and J.P.Webb, Automatic mesh generation for h-p
adaption, IEEE Transactions on Magnetics, Vol.29, No.2,
pp.1894-1897, 1993.
[4] Y.Midorikawa, S.Hayano and Y.Saito, A resonant phenomenon
between adjacent series connected coils and its application to aals, Advanced Computational and Design Techniques inApplied Electromagnetic Systems, Vol.6, pp. 633-639, 1995.
[5] S.Hayano, Y.Nakajima, H.Saotome and Y.Saito, A new typehigh frequency transformer, IEEE Transactions on Magnetics,(c) No.4
Fig. 10 Comparisons among the Quality Factor Q of the No.1,
No.2 and No,4 ECT coils.

4 Conclusion
New innovative idea to enhance the sensibility of ECT
sensor has been proposed in this work. Our idea needs not
any special tools but requires a consideration of natural
resonance phenomena-, i.e., utilization of the resonant
impedance, frequency and capacitive effect among the coils.
We have selected the natural parallel resonant frequency of
the ECT sensor coil when facing with a wholesome part oftarget. When the ECT sensor coil has met with a defect ofVol. 27, No.6, pp.5205-5207, 1991.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Fluctuation Frequency Analysis of the Barkhausen Signals
Jun KAWAZOE*1, Iliana Marinova*2 and Yoshifuru SAITO*1
Graduate School of Hosei University, Tokyo 184-8584, Japan*2
Technical University of Sofia, Sofia 1756, Bulgaria*1

Ferromagnetic materials are widely used for various artificial products such as cars, trains, ships and so on.
Because of its mechanical property, iron steel is most popular in use for the frame materials. Nondestructive
testing of iron steel is an extremely important way to maintain their mechanical reliability. As is well known factthat the Barkhausen signals are emitted from only the ferromagnetic materials having magnetic domain structures.
Also this signal varies depending upon their past mechanical as well as radioactive stress histories.
In the present paper, we have applied a generalized frequency fluctuation analysis to the Barkhausen signals
to detect the various mechanical stresses. Surprisingly, it has been succeeded in clarifying that application of ourfrequency fluctuation analysis to the Barkhausen signals makes it possible to detect the several kinds ofmechanical stress.
Key words: Barkhausen signal, Frequency fluctuation, Signal processing, Least squares

1. Introduction
Barkhausen signal is popularly observed in the
ferromagnetic materials composed of the magnetic domain
structures, e.g. iron, nickel, cobalt and garnet, when they aremagnetizing. Also, it is well known that the Barkhausen
signals are very sensitive to the physical external input, suchas mechanical stress and radioactive damage, to theferromagnetic materials.
The iron and its composite ferromagnetic materials arewidely used for main frame materials to support themechanical structures in many artificial products andconstructions. Because of their essential role, they arealways got mechanical stress and they keep their pastmechanical stress histories. Nondestructive detection of
their mechanical stress as well as residual stress is ofparamount importance for keeping the safety of themechanical structures, since it is possible to see ahead oftime what extent the mechanical structure will maintaintheir strength for further use.
According to the past researches concerning to a
relationship between the Barkhausen signal and appliedmechanical stress, it has been revealed that Barkhausen
signals are very sensitive to the mechanical stress andradioactive damage but any deterministic regularity has notbeen found [1,2].
Recently, only a macroscopic regularity has beenreported by means of a frequency fluctuation analysis
approach [3]. Principal purpose of this paper is thatconventional frequency fluctuation analysis employing only
1st order fluctuation is generalized to the frequency
fluctuation analysis employing the nth order fluctuations.
As a result, we succeed in extracting the distinct
difference between the stressed and not stressed Barkhausen
signals. Also, we succeed in visualizing in a most clear
manner on the four dimensional space, whose coordinates
are composed of the terms representing the higher orderfrequency fluctuation terms of Barkhausen signals.

One of the most famous frequency fluctuations is the 1/f
frequency fluctuation, which can be observed in most of thenatural phenomena such as natural wind, sea water waves,river flow sound and so on gives a healing effect to thementalities via human sensibilities[4].
Conventional 1/f frequency analysis is that applicationof the 1st order least squares to the both Fourier power
spectrum and frequency extracts the 1st order frequency
fluctuation, i.e., Log of Fourier power spectrum isapproximated by Log of a0 + a1f, yields a 1st orderfrequency fluctuation characteristic, where a0 and a1 are the0th and a 1st order frequency fluctuation terms, respectively.
If the frequency fluctuation term a1 takes a1=1, then we
have the 1/f frequency fluctuation.
On the other side, we generalize this conventional 1storder frequency fluctuation to the nth order frequency
fluctuation characteristics, i.e., Log of Fourier power
spectrum is approximated by a Log of a0 + a1f+a2f2+ ...+
anfn, where a0, a1, a2, ,..., an are the 0th, 1st 2nd, ... ,nth orderfrequency fluctuation terms, respectively. Careful
examination of the coefficients a0, a1, a2, ,..., an leads to theprecise frequency fluctuation characteristic of the
Barkhausen signal.
Second important key point of our approach is how tovisualize the dependency of the 0th, 1st, 2nd, ... ,nth orderfrequency fluctuation terms to the externally applied forces.
According to our experimental results on this research,most of the frequency fluctuation characteristics are
sufficiently represented up to the 4th order terms. So that let
the normalized 1st, 2nd, 3rd, 4th order frequency fluctuation
coefficients be respectively the coordinate values on the x-,y-, z-axes, and point color, then up to the 4th order frequency
fluctuation characteristics locate the three dimensional spacecoordinate position and point color. Thus, comparison
among the different specimens of this diagram visualizes aneach of the distinct characteristics depending on theirmechanical stress conditions.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

2. Frequency Fluctuation Analysis
2.1 Basic equations
Let us consider an arbitrary signal g(t) and its Fourier
power spectrum G(f), and take the logarithm of both Fourier
Spectrum G(f) and frequency f. Plot the log G(t) on the log fcoordinate represents a frequency characteristic of the signal
g(t) on the frequency domain, i.e., the frequency
characteristic of the original signal is represented on a x-y
plane coordinate system whose horizontal x- and verticaly-axes are corresponding to the logarithms of Fourier power
spectrum G(f) and of frequency f, respectively.
In order to represent a global frequency characteristic of
the original signal g(t) in frequency domain, apply afollowing power series function:a0  a1 f  a2 f  ...  an f ,
n

2

h f

(1)

in this x-y plane makes it possible to evaluate the higher
order frequency fluctuation analysis.
The coefficients a0, a1 a2, ,..., an in (1) are determinedby least squares asA1ª¬C T C º¼ CT Y ,(2)

Fig.1. Barkhausen signal measurement devices.
The tested specimens are the silicon steels with the
0.35mm thickness, 30mm width and 100mm length. The
tested specimen is put on the upper two head surfaces of U
shape ferrite core wound the 300 turns exciting coil. The
specimen in Fig.1 is excited by flowing a 1A sinusoidal
alternating current through this exciting coil.
Fig. 2 shows a typical frequency characteristic of a
Barkhausen signal under no stress.

where a superscript T denotes a matrix transpose; thevectors A, Y and matrix C are respectively given by

A

Y

> a0

a1 . an @ ,ª¬h f0 h f1
ª1 f 0 f 02«
2
«1 f1 f1
C «1 f 2 f 22
«
.
«. .
«1 f
f m2
m
¬
m ! n.

T(3)
T. h f m º¼ ,
.
.
.
.
.

f 0n º»f1n »f 2n » ,». »f mn »¼(4)(5)

In (3)-(5), a number of equations m, i.e. number of thesampled frequencies f0, f1 f2, ,..., fn, always greater than thoseof unknowns n, i.e., number of the coefficients a0, a1 a2, ,...,
an. In most case, this condition is satisfied because of thenumber of sampled frequency m is much greater than thoseof the order n of the function h(f) in (1).
2.2 Classical 1st order frequency fluctuation
Fig. 1 shows a Barkhausen signal measurement devices.

Fig. 2. An example of typical frequency characteristicof a Barkhausen signal under no stress.
The frequency characteristic in Fig. 2 is obviously
divided into two frequency regions. One is lower frequency
region whose frequency fluctuation can be approximated by
f-2.26 derived from 1st order approximation in (1), and theother higher one is a dispersing signal whose frequency
fluctuation can be approximated by f 0, i.e. white noise.
On the other side, Fig. 3 show a typical frequency
characteristic of Barkhausen signal under 3kg stressed.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Log Power
1
1.0

1.5

2.0

2.5

3.0

Log f

3.5

1
2
3
4
5
6

Fig. 3. An example of typical frequency characteristicof a Barkhausen signal under 3kg stressed.
The frequency characteristic in Fig. 3 is also divided
into the two frequency regions. One is lower frequency
region whose 1st order frequency fluctuation can beapproximated by f-1.69, and the other higher one is adispersing signal whose frequency fluctuation can beapproximated by f 0.
Consideration to the difference between the first orderfrequency fluctuations f-2.26 and f-1.69 suggests that an
application of the 3kg stress to the tested silicon steel
changes the steep 1st order gradient -2.26 to the smoothly
gradient -1.68. This result had been verified by the 1st orderfrequency fluctuation analysis to the 30 distinct sample
specimens [3].
Thus, it is possible to detect the stress on the
ferromagnetic materials by the classical 1st order frequency
fluctuation analysis [3].
However, several difficulties are still remaining: One is
how to decide the frequency range to be computed thefrequency fluctuation characteristic. Second is that the 1storder frequency fluctuation analysis is only effective to a
relatively large stress, even though it is required to detect themuch more smaller stresses.
2.3 Generalized frequency fluctuation
Fig. 4 shows a frequency fluctuation characteristic
under no stress along with a curve obtained by up to the 4thorder power series function in (1), where the frequency
sampling points have been taken in a logarithmic order.
To check the reproducibility of the coefficients
a1 , a2 , a3 , a4 , we have 10~12 times independently
measured and computed these coefficients a1 , a2 , a3 , a4in (1) to the same specimen.

Fig. 4. Example of typical frequency characteristic ofa Barkhausen signal under no stress along withan up to 4th order power series curve in (1).
After normalizing all of the coefficients a1 , a2 , a3 , a4
to be the values between 1 and 0, let the normalized
coefficients a1 ' , a2 ' , a3 ' , a4 ' be respectively corresponded
to the x-, y-, z-axes values and point color, then this makes it
possible to visualize a dispersion characteristic of thecoefficients a1 ' , a2 ' , a3 ' , a4 ' . Fig. 5 shows a dispersion
characteristic of these coefficients a1 ' , a2 ' , a3 ' , a4 ' .
Combination of Figs. 5(a) with 5(b) reveals that thedispersion is limited along the vicinity of a hatched surface
in Fig. 6.
1.0

z 3rd order 0.5
1

1.0
y 2nd order 0.5
0.0
0.0

0.5
x 1st order

1.00(a) x-y plane

1.0

y 2nd order 0.5
1

0.0 0.0
0.0
0.5
1.0
0.5
z 3rd order x 1st order
1.00(b) x-z plane
Fig.5. Dispersion of the frequency fluctuation coefficients.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Comparison of the dispersion characteristics in Fig. 5(a)with that of Fig. 9(a) demonstrates a distinct effect of theapplied stress. Also, comparison of the dispersion
characteristics a1 ' , a2 ' , a3 ' , a4 ' in Fig. 5(b) with that of Fig.
9(b) suggests the same as before.
Combination of Figs. 9(a) and 9(b) yields the results
shown in Figs. 10 and 11.
1.0

z 3rd order 0.5

Fig.6. The normalized frequency fluctuation coefficientsa1 ' , a2 ' , a3 ' , a4 ' dispersing area (hatched surface).
Consideration to the hatched region in Fig. 6 suggeststhat an individual difference among the sound silicon steel
without any stresses could be limited along the vicinity of
the hatched surface in Fig. 6.

1

1.0
y 2nd order 0.5
0.0
0.0

0.5
x 1st order

1.00(a) x-y plane

2.4 Stress visualization
We have carried out the random stresses visualization inmuch the same as described in Section 2.3. These stresses
were applied to the specimen by hanging the random
weights by a string as shown Fig. 7.

1.0

y 2nd order 0.5
1

0.0 0.0
0.0
0.5
1.0
0.5
z 3rd order x 1st order
1.0
0

Fig.7. The stresses are applied by hanging the weights.
Fig. 8 shows one of the frequency fluctuation
characteristics under stress along with a curve obtained by
the 4th order power series function in (1).

(b) x-z plane
Fig.9. Dispersion of the frequency fluctuation coefficients.

Log Power
1
1.0

1.5

2.0

2.5

3.0

3.5

Log f

1
2
3
4

1

5
6

Fig. 8. One of the frequency characteristic of the
Barkhausen signals under stress along withthe 4th order power series curve in (1).
Fig. 9 shows the dispersion characteristics ofcoefficients a1 ' , a2 ' , a3 ' , a4 ' .

0Fig. 10. The normalized frequency fluctuation coefficientsa1 ' , a2 ' , a3 ' , a4 ' difference between the stressed andno stressed groups on the x-y plane.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

Log Power
1
1.0

1.5

2.0

2.5

3.0

3.5

Log f

1
2
3
4
1

5
6

0

Fig. 11. The normalized frequency fluctuation coefficientsa1 ' , a2 ' , a3 ' , a4 ' difference between the stressed andno stressed groups on the x-z plane.
Observation of the dispersion characteristics of thestressed specimens suggests that the normalized coefficientsa1 ' , a2 ' , a3 ' , a4 ' in (1) do not disperse but focus on arelatively small area. On the contrary, the normalized
coefficients a1 ' , a2 ' , a3 ' , a4 ' in (1) of the stress freespecimens disperse the vicinity of hatched area in Fig. 6.
This means that the externally applied stress suppresses thedispersion and confines them into the small space in Fig. 6.
2.5 Bending effect visualization

Fig. 13. One of the frequency characteristics of the
Barkhausen signal after bending a specimen along withthe 4th order power series curve in (1).
1.0

z 3rd order 0.5
1

1.0
y 2nd order 0.5
0.0
0.0

0.5
x 1st order

We have carried out the bending effect visualization inmuch the same as described in Section 2.4.
As shown the bended examples in Fig. 12, the 4
specimens were bended 0, 5, 15, and 45 degree. After thatthese 4 specimens were recovered to the original straight
form.

1.0

0

(a) x-y plane

1.0

y 2nd order 0.5
1

0.0 0.0
0.0
0.5
1.0
0.5
z 3rd order x 1st orderFig. 12. No bended and 5 degree bended.
Fig. 13 shows one of the frequency fluctuation
characteristics after bending along with a curve obtained by
the 4th order power series function in (1).

1.00(b) x-z plane
Fig.14. Dispersion of the frequency fluctuation
coefficients.
Fig. 14 shows the normalized dispersion characteristics
of coefficients a1 ' , a2 ' , a3 ' , a4 ' .
Comparison of the dispersion characteristics in Fig. 5(a)with that of Fig. 14(a) demonstrates a distinct effect of thebending. Also, comparison of the dispersion characteristics
in Fig. 5(b) with that of Fig. 14(b) suggests the same as
before.

The 2012 Asia - Pacific Symposium on Applied Electromagnetics & Mechanics

1

frequency fluctuation characteristics could be visualized in athree dimensional space. This has clarified each of the
distinct differences among the specimen having the same
specifications, also clarified the measurement data
dispersions.
As the concrete examples, we have applied our method
to the stress visualization of the silicon steels, andsucceeded in extracting the characteristics of the stressed
specimens. Also, we have applied our method to the pastbended history detection. This has led to the similar results
obtained in the stress detection. Thereby, it has beenclarified that the distinct difference between the paststressed or bended histories is difficult.

0

Fig. 15. The normalized frequency fluctuation coefficientsa1 ' , a2 ' , a3 ' , a4 ' difference between the bending andnot bending groups on the x-y plane.

References
[1]
[2]

[3]

[4]
1

0

Fig. 16. The normalized frequency fluctuation coefficientsa1 ' , a2 ' , a3 ' , a4 ' difference between the bending andnot bending groups on the x-z plane.
Combination of Figs. 14(a) and 14(b) yields the results
shown in Figs. 15 and 16.
Observation of the dispersion characteristics of thebended specimens suggests that the normalized coefficientsa1 ' , a2 ' , a3 ' , a4 ' in (1) do not disperse but focus on arelatively small area. On the other side, the normalized
coefficients a1 ' , a2 ' , a3 ' , a4 ' in (1) of the bended freespecimens disperse the vicinity of the hatched surface in Fig.
6. Thereby, the externally applied bending stress suppresses
this dispersion and confines them into the small space in Fig.
6.
Thus, it is obvious that the distinction between the
stressed and bending effects is difficult from the Barkhausen
signal analysis.
3. conclusion
Previously, we have succeeded in detect the appliedstress on the silicon steel by means of the frequency
fluctuation method [3].
This paper has generalized this approach, i.e., 1st orderto the nth order frequency fluctuations. Further, the 4th order

R M. Bozorth: Ferromagnetism, p. 462 (IEEE PRESS)
M. Katsumata, S. Hayano and Y. Saito: A Study ofBarkhausen Phenomenon Visualization, The Visualization
Society of Japan, B203, July (2003).
S. Nojima and Y. Saito: Application of Frequency
Fluctuation to Barkhausen Signals and its Application, J.
Magn. Soc. Jpn., 35, 380-385 (2011).
M. Teranishi, K. Maruyama, S. Hayano, and Y. Saito:
Visualization of 1/f Frequency Component in Dynamic
Image of Natural Phenomena, The Visualization Society ofJapan, B108, July (2005).