Generalized frequency fluctuation analysis of the geomagnetic fields
Mirai IIDA and Yoshifuru SAITOElectrical and Electronic Engineering, Hosei University

Iliana MARINOVATechnical University of Sofia 1756, Sofia, Bulgaria
Abstract
A big earthquake on March 11th 2011 occurred at the eastern side of Japan caused serious damages to the human life and themodern infrastructures. We try to evaluate a relationship between the earthquake and geomagnetic fields by means of thegeneralized frequency fluctuation analysis. The nth order fluctuation analysis methodology is one of the generalizations of the 1storder fluctuation analysis, i.e., the 1/f frequency fluctuation.
Keywords: Geomagnetic fields, Frequency fluctuation, Least squares.

1 INTRODUCTION
As is well known, most of the recent major disasters had beencaused by the natural earthquakes. In particular, a big natural
earthquake on March 11th 2011 occurred at the eastern side ofJapan caused serious damages to the human life and themodern infrastructures. Forecast of the big earthquake is ofparamount importance to protect not only our human life but
also modern infrastructures. Even though the intensive
investigations to forecast the time and location of the big
earthquake have been carried out and continued until now
mainly by the seismologists, it is still difficult to obtain thesatisfactory forecast accuracy in order to avoid the majordisasters [1].
In the present paper, we try to evaluate a relationship between
the earthquake and geomagnetic fields by means of the earthmagnetisms. More precisely, we try to evaluate therelationship between the earthquake and geomagnetic fields bymeans of the generalized frequency fluctuation analysis.
Well known frequency fluctuation is the 1/f fluctuations
observed in many natural phenomena such as the sound caused
by natural wind, illuminating strength by fireflies and so on [2].
Also, the other well known fact is that the 1/f fluctuations may
give the healing and relaxation effects to the human beings.
Previously, we have elucidated that application of the 1/f
fluctuation analysis to the Barkhausen signals accompanying
with the magnetization of ferromagnetic materials reveals thestress situations of the ferromagnetic materials [3-6].
One of the drawbacks of our developed frequency fluctuation

approach is to require human skill to decide the frequency
range to be analyzed [2]. The principal purpose of this paper isto remove this drawback from our generalized frequency
fluctuation method.
Our frequency fluctuation method is a generalization of thewell-known 1/f fluctuation analysis. Conventional 1/f
frequency fluctuation analysis employs a simple straight line
decided by the least squares in the both logarithmic frequency
and Fourier power spectrum space [2]. In addition, we havegeneralized the 1/f fluctuation analysis to a more sophisticatednth order fluctuation analysis methodology [3-6].
The nth order fluctuation analysis methodology is that the 1storder least squares approximation line is generalized to the nthorder least squares approximation curves to represent thefrequency characteristic in the both logarithmic frequency andFourier power spectrum space, i.e., a straight line
approximation is generalized to the nth order approximate
curves a0+a1f to a0+a1f+a2f2+
frequency and Fourier power spectrum space, where a0,a1,a2
and f are the 0th,1st,2nd order coefficients and frequency,
respectively.
2 FREQUENCY FLUCTUATION ANALYSIS
2.1 1/f frequency fluctuation
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 tide water waves,sound accompanying river flows and so on, giving a healing
effect to the mentalities via human sensibilities [2].
Conventional 1/f frequency analysis is that application of the
1st order least squares fit to the both Fourier power spectrum
and frequency extracts the 1st order frequency fluctuation, i.e.,
Fourier power spectrum is approximated by a0 + a1f, yields a
1st order frequency fluctuation characteristic in the both
logarithmic frequency and Fourier power spectrum space,
where a0 and a1 are the 0th 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.
When 1st order frequency fluctuation term takes zero, Fourier
power spectrum becomes a constant value regardlessfrequency as shown by a dotted line in Fig. 1. This type ofsignal is called the white noise, and gives uncomfortablefeeling to the human because of the too heavy randomness.
On the other side, regular signal, e.g., a1=-2 leading 1/f2 shownby a steep line in Fig.1, gives also uncomfortable feelingbecause of the too fixed regularity.

order vector A in (2) are determined by the least squares.
Further, if we are given the m+1 Fourier power spectra, i.e.,h(y0), h(y1), h(y2),, h(ym), then it is possible to compose thevector Y as (4), then a m+1 by n+1 rectangular matrix C (3)could be derived from the assumed higher order power series
function (1).
a0

a1

A

(2)

an

C

1

f0

f 02

f 0n

1
1

f1
f2

f12
f 22

f1n
f 2n

1

fm

f m2

f mn

(3)

h y0
h y1

Y

(4)

h ym

Since a condition m>>n is satisfied, then the least squares
could be applicable. Hence, the vector A whose elements are
the a0 , a1 , a2 , , an is evaluated by (5) [3-6].

CT C

A

1

CT Y

(5)
th

Figure 2 shows the typical signal and the 5 order curve which
are the thin lines and the thickBB2000lines,.CSV respectively.

Figure 1. 1st order frequency fluctuation

Log Power

Thus, a signal located at the midway between the complete
random and regular signals, i.e., a1=-1 in Fig. 1, is called the
1/f frequency fluctuation. This gives a comfortable feeling to
the human mentalities. Probably a reason why 1/f frequency
fluctuation signal gives the gentle and comfortable feeling to
the human sensibilities is that the 1/f frequency fluctuation
signal may be included in the most of the natural phenomena[2].
2.2 Generalization of the frequency fluctuation
Let us consider the both logarithmic frequency and Fourier
power spectrum space hereafter the dissections. When weapply the 1st order frequency fluctuation fit to the earthmagnetism signal, it is obviously difficult to extract theessential characteristics of the earth magnetism signal due toits intrinsic randomness. To overcome this difficulty, we
employ a higher order curve given by a power series of (1)instead of a simple line a0 + a1f.

h f

a0 a1 f

a2 f 2The coefficients a0 , a1 , a2 ,an f n(1), an which construct a n+1

1
0.5

1.0

1.5

2.0

2.5

3.0

3.5

Log f

1
2
3
4

Figure 2. Typical frequency characteristic of the signal drawn
by the thin lines and its 5th order least squares curve drawn by
the thick line.
2.3 Frequency fluctuation analysis of the geomagnetism
We apply the generalized frequency fluctuation analysis togeomagnetism data. The geomagnetic field data are defined ina vector field, and are represented by the three-dimensional
vector quantities [7]. The independent three elements H,D,I
are the geomagnetic fields in a certain observation point. The
other factors are evaluated from three elements by (6).

Figure 3. Geomagnetic field resolution elements

F
X2 Y2
H F cos(I )X H cos(D)Y H sin(D)Z F sin(I )

Z2

H2

Z2
(6)

Table 1. Various constants of geomagnetic field elements
FDI
Ha sunbeam being irradiated to the existing ionosphere between
the magnetosphere and the atmosphere of the earth. Therefore
the geomagnetic field has a change of 1 diurnal parallax
depending on the rotation of the earth. We call this "daily
fluctuations" of the geomagnetic field.
On the other hand, "geomagnetic secular variation" is thechanges in the geomagnetic field on time scales of about ayear or more. This geomagnetic secular variation, whose
period is from the several decades to the several hundred years,
is caused mainly by the interior of the earth.
For example, the declination D defined by the deviation
between the geomagnetic and geographical north directions inTable 1 is approximately 7 degrees in Tokyo metropolitan area,and has been 0.7 degree changed during recent 40 years. The
magnetic north component X almost is the same as those of
approximately 200 years ago so that the declination D is oneof the typical geomagnetic secular variations.
Since the geomagnetic secular variation is caused in theinterior of earth, then our generalized frequency fluctuation
analysis is applied to the declination D [7].
A thin line in Fig. 4 is an original frequency characteristic of adaily fluctuation for which the change of daily changes should
be one of the components of geomagnetic secular variation.
The frequency is divided into several frequency ranges 1-10,
10-100, 100-100 and so on while the logarithm base has beentaken to 10. Higher order approximates of (1) is applied toeach of the divided frequency ranges. Further, the normalized
coefficients a0 , a1 , a2 in (1) are respectively taken to the x,y,z
coordinate values of a three dimensional Cartesian coordinate
system, i.e., the frequency fluctuation characteristics arevisualized in the 3D space.

Z
X
Y
Independent three elements are the horizontal component H,
declination D, and a vertical component Z. Otherwise; a
combination of component X facing north, component Y
facing east, vertical component Z are used. But total intensity
F, inclination I, and declination D are used most. These arecalled three elements of the geomagnetic field. The dimensionof magnetic flux density F is a T (Tesla). The geomagnetism isvery small so that the dimension nT (nano Tesla) is commonly
used. Also, the dimension of inclination I and declination D is
minute unit.
The geomagnetic field is depending on time, and is caused by

Figure 4. Typical frequency characteristic of a daily
fluctuation whose frequency range is divided into the 1-10,
10-100, 100-1000 frequency ranges while the logarithm basehas been taken to 10.
On March 11th 2011, Japan islands were shaken by a big
earthquake whose magnitude is 9.0, and the epicenter is the
Miyagi east southeast offing. The focal region was theextensive from the Iwate to the Ibaraki offing.
Seismic intensity recorded at Esashi observatory station is alittle less than six. Also, seismic intensity recorded at
Kanoyama observatory station is less than five on theearthquake disaster day. The Kanoyama observatory station is
located at Kimitsushi in Chiba prefecture.

11 day , 4 order , low Region

a1 , a2 taking the values between the 0 to 1. Let us these
normalized coefficients a0 , a1 , a2 respectively be the x,y,z axis
values, then it is possible to visualize the results of generalized
frequency fluctuation analysis in a 3D space.

coefficient
40
20
1

20

2

3

4

Order

40
60

(a) 4th order
11 day, 5 order, low Region

coefficient
400
200
1

2

3

4

5

Order

200

Figure 6. Extraction of the singular point of a big earthquake
on March 11th 2011. A circle refers to the target frequency
range for the frequency fluctuation analysis.
Thus, we applied our approach to the declination D data on
March 11th 2011. Fig. 6 shows the frequency characteristic ofthe declination D data on March 11th 2011. A circle in Fig. 6
refers to a singular point of the frequency characteristic curve.

400(b) 5th order
11 day, 6 order , low Region

coefficient
1000
500
500

1

2

3

4

5

6

Order

1000
1500

(c) 6th orderFigure 5. The values of coefficients a0 , a1 , a2 , , an when
applying the curve of (1) to the first frequency 1-10 range in
Fig. 4, where the order n has been changed from the 4th to 6thin (1).
Our generalized frequency fluctuation analysis has employed
the declination D data recorded at the both Esashi andKanoyama observatory stations.
Fig. 5 shows the values of coefficients a0 , a1 , a2 , , an when(a) x-z surface view

applying the curve of (1) to the first frequency 1-10 range in
Fig. 4, where the order n has been changed from the 4th to 6thin (1). A target declination D data was recorded at the
Kanoyama observatory station on March 11th 2011.
Let us consider the first three coefficients a0, a1, a2 in Figs.
5(a)-5(c), then a second coefficient a1 takes a negative value
over the n=5th approximation curve while a1 takes always
positive value under the n=5th approximations.
Since the first three coefficients a0, a1, a2 take the similartendency as shown in the Figs. 5(b) and 5(c), then the n=5thorder curve may be considered as the maximum order torepresent the intrinsic frequency fluctuation characteristic of
the first low frequency range in Fig. 4.
The first three coefficients a0, a1, a2 are normalized to the a0 ,(b) x-y surface view
Figure 7. 3D visualization of the results when the generalized
frequency fluctuation analysis is applied to the declination D
data on March 11th 2011 recoded by Kanoyama observatory
station.

Our generalized frequency fluctuation approach is applied to
the low frequency range including the singular point in Fig. 6.
Figs. 7 and 8 show the results of this analysis, where the thicksolid dot denotes the point on March 11 th 2011. The anterior
and posterior days of this disaster day are denoted by theslightly thick solid dots in Figs. 7 and 8.
Thus, we have succeeded in extracting the big earthquake dayon March 11th 2011 among the one month 30 days declination
D data.

7 day , 5 order , low Region

coefficient
50

1

2

3

4

Order

5

50

(a) 5th order
7 day, 6 order , low Region

coefficient
4000
2000
1

2

3

4

5

6

Order

2000

(b) 6th order
7 day, 7 order, low Region

coefficient
40 000(a) x-z surface view

20 000
20 000

1

2

3

4

5

6

7

Order

40 000(c) 7th orderFigure 9. The values of coefficients a0 , a1 , a2 , , an when
applying the curve of (1) to the first frequency 1-10 range ofthe daily variation on April 7th 2011 recoded by Esashi
observatory station.

(b) x-y surface view
Figure 8. 3D visualization of the results when the generalized
frequency fluctuation analysis is applied to the declination D
data on March 11th 2011 recoded by Esashi observatory
station.

(a) x-z surface view

the day occurred the earthquake among the 1 month 30 days
daily variation data by means of the relevant signal processing
Methodology.
A serious problem is to find the relevant signal processing
methodology not depending on the expert skillfulness [3-6].
In the present paper, we have proposed one of the signal
processing methodologies not depending on the human skill.
REFERENCES(b) x-y surface view
Figure 10. 3D visualization of the results when the generalized
frequency fluctuation analysis is applied to the daily variation
data recoded by Esashi observatory station on April 7 th 2011.
To check the validity of our approach, we applied ourapproach to the daily variation on April 7th 2011 recoded by
Esashi observatory station when observed a magnitude 6.6
earthquake at the Fukushima Hama Street.
Fig. 9 shows the value of coefficients a0 , a1 , a2 , , an when
applying the curve of (1) to the first frequency 1-10 range ofthe declination D data on April 7th 2011, where the order n has
been changed from the 5th to 7th in (1).
Similar to the previous one shown in Figs.5, we have
employed the n=6th order approximation curve in (1) to extract
the characteristics of April 7th among the 30 daily variation
data on April in 2011.
Fig. 10 shows the results of our frequency fluctuation analysis,
where the thick solid dot denotes the point on April 7th 2011.
The x-z surface view in Fig. 10(a) succeeds to extract the April
7th, but the x-y surface view could not succeed to extract the
April 7th because of overlapping the results.
As shown above, a big earthquake whose magnitude 9 ispossible to extract the day occurred a big earthquake, and also
possible to extract the day occurred 6.6 magnitude earthquake
even though the anterior and posterior days could not
extracted.
3 CONCLUSIONS
The geomagnetic signals accompanying with the Great East
Japan Earthquake have been analyzed by the generalized
frequency fluctuation method. As a result, it has been clarified
that the geomagnetic signals accompanying with theearthquakes always inform the some kind of physical signals
concerning to the dynamics of earth.
A number of processed examples are too small to derive adeterministic conclusion.
A reliable result is that the geomagnetic field always includes
the earthquake information. Thereby, it is possible to extract[1] The Coordinating Committee for Earthquake Prediction,
Japan, http://cais.gsi.go.jp/YOCHIREN/index.e.html[2] T.Musha, S.Sato and Y.Yamamoto (Eds), "Noise in
Physical Systems and 1/f Fluctuation", Amsterdam IOP
Press, 1992.
[3] S. Nojima and Y. Saito, "Application of frequency
fluctuation to Barkhausen signals and its application", J.
Magn. Soc. Japan, 2011, vol. 35, pp. 380 385,
[4] Jun KAWAZOE, Iliana Marinova and Yoshifuru SAITO,"Fluctuation Frequency Analysis of the Barkhausen
Signals", Proceedings of The 2012 Asia - PacificSymposiumon
AppliedElectromagnetics&
Mechanics,pp.244-249.
[5] J.Kawazoe and Y.Saito, "Analysis of Frequency
Fluctuation Using Barkhausen Signal", J.Magn.Soc.Japan,
2013, vol.37, pp.320-326.
[6] Jun Kawazoe, Iliana Marinova, Yoshifuru Saito,"Fluctuation Frequency Analysis of the Barkhausen
Signals Under Static and Dynamic Stresses", IEEE Trans.
Magnetics, vol.49, No.5, pp.1997-1999, May, 2013.
[7] GSI Geomagnetic Survey,
https://geoinfo2.gsi.go.jp/contact/Inquiry2.aspx?pcode=10
02&bcode=100202&mcode=10020206
Contact E-mail Address: mirai.iida.27@gmail.com

Enhance the Sensibility of the Film Infinite Eddy Current Sensors
Takahiro HYUGA, Naoto ISHIKAWA, Yoshifuru SAITO

Iliana MARINOVATechnical University of Sofia
Sofia, 1756, Bulgaria
Manabu OHUCH, Takaharu KOJIMA
Denshijiki (Emic) Co. Ltd
Ukima 5-6-20, Kitaku, Tokyo 115-0051
Abstract
Previously, we have succeeded in exploiting a new high sensibility eddy current testing (ECT) sensor called the infinite coil.
Operating principle of this infinite coil is that two adjacent coils constructing the north and south poles alternatively set a zeromagnetic potential region and keep the same situation when eddy currents are flowing along the paths in parallel to the exciting
coils. If the eddy currents could not flow the paths in parallel to the exciting coil on the test specimen, then a zero magnetic
potential region between the two exciting coil moves toward the other position. This means that a sensing coil located at a mid
position of two exciting coil is possible to detect the disturbed magnetic fields, i.e., the defect in the test specimen could be caught
on the sensing coil signal.
In this paper, we have enhanced the sensibility of the infinite coil by increasing the no polarity zone between the north and south
exciting poles. Employment of the two semicircular exciting coils has made it possible to enlarge the no polarity zone (viz., zeromagnetic potential region). In addition, the results of the 3D finite element simulation and of the practical experiments haveverified that the our new developed semicircular infinite coil is higher sensibility than those of conventional one.
Keywords: nondestructive testing, ECT, design practice, enhancement of sensor

1 INTRODUCTION
Most of the industrial products and infrastructures arecomposed of the mechanical frames, and they support our
modern civilianized human life. Each of the machines iscomposed of the mechanical parts to support its mechanicalstrength as well as their shapes.
Major frame materials are the pure metallic or their compound,and are always stressed to maintain the highly civilized
modern human life. The stress is classified into the mechanical,
thermal and so on, which lead to the cause of fatigue anddefect.
To keep the highest safety and reliability, various maintenanceworks to the machines as well as infrastructures arecontinuously required as one of the most important tasks. To
evaluate the metal fatigue, one of the most fundamental andimportant methodologies is the nondestructive testing to themetallic materials [1].

The nondestructive testing makes it possible to evaluate thedefect size, shape and situations without any destroying anddecomposing the products. Further, we have several
nondestructive methods such as the eddy current testing (ECT),
electrical potential method, ultrasonic imaging, x-ray
tomography and so on [2,3].
Among various nondestructive methodologies, the ultra sonicmethod is capable of highly reliable and precise results, but it
is required the direct contact to the tested specimen. Also,
nondestructive inspection by the electrical potential method
requires direct contact to the target object. Radioactive method
is limited in its use from the safety handling viewpoint.
On the other side, the ECT is composed of the relatively
simple parts and needs not the direct contact to the tested
specimen. Furthermore it is possible to operate in a relatively
high speed, even though sometimes it is difficult to detect thedefects in the target metallic object depending on the eddy
current flowing paths. However, the ECT has versatilecapabilities as the nondestructive testing method.
The operating principle of the ECT is classified into two major
categories. One is the impedance sensing type whose operating
principle is that the ECT probe and target object are regarded
as the primal and secondary circuits of a transformer,
respectively. So that the change of secondary impedance
caused by the defects could be detected from the primal input
impedance change. One of the merits of the impedance sensing
type is that this ECT is composed of the simplest structures,i.e., only the ferrite bar for core material and conducting wires.
The other type is called the sensing coil type. The eddy
currents on a no defect metallic surface yield the opposing
magnetic fields to that of exciting currents. If there is a defectin the target metallic surface, then a part of the eddy currents
has to take a detour path at the defect position and a flux iscaused by this detour current. This flux is caught by anindependently set coil. So that this type is called "sensing coiltype".
Although a sensing coil type has higher sensibility than thoseof the impedance sensing type, the sensing coil type iscomposed of the somewhat complex structures, e.g.,
independent exciting and sensing coils are required.
Previously, we had exploited a highly sensitive sensing coiltype sens
the more high sensibility ECT sensor by considering the basic
operating principles along with the intensive three dimensional
finite element (3D FEM) simulations.
In our numerical simulations, we have assumed a line defectsearching problem. So that our design target of the sensor is
how to enhance the catching ability of the magnetic flux
caused by the detouring eddy currents due to this line defect.

2.1
When the alternating exciting currents flow through theexciting coils in an opposite direction, both two exciting coilconstruct the north and south magnetic poles, alternatively.
Thereby, as shown in Figure 1, an exciting magnetic flux
circulates through both of the two exciting coils.
Observe the exciting magnetic flux distributions shown in
Figure 2 reveals that there is the no polarity zone, i.e., zeromagnetic potential region between the two exciting coils.
When we put on the ferromagnetic materials into this zeromagnetic potential region, no magnetic field disturbance isoccurred because of the zero magnetic potential. Thereby, it ispossible to set the sensing coil wound around a ferrite bar in
the zero magnetic potential region as shown in Figure 2.
Even if the exciting magnetic flux passes through this zeromagnetic potential region, the surface of sensing coil isdirected in parallel to this magnetic flux. So that, any voltage
is not induced in the exciting coil.
the eddy currents flow as the image currents flowing in a
opposite direction to the exciting currents. When there is nodefect in a target object, the magnetic fields caused by theeddy currents never induce the voltage in the sensing coil. The
reason why no induced voltage in the sensing coil is that anyof the magnetic fields are directed in a parallel direction to thesensing coil surface.
However, if there is a defect in the target object, the detour
eddy currents essentially flow along with the defect. Thus, themagnetic flux caused by these detour eddy currents induces avoltage in the sensing coil, and this induced voltage reveals thedefect in the target object [5,6].

2

which is composed of the two planar exciting coils and one
sensing coil wound around the ferrite bar. According to theshape of the two exacting coils, we had named this sensor

2.2 Numerical Simulations
Figure 1.
thecircular coils on both side are the planar exciting coils.
The red rectangular box is the sensing coil woundaround a ferrite bar. The light blue arrows show themagnetic fluxes caused by the exciting currents.

3D FEM simulations. Table.1 lists various constants used forthe simulations.

located in parallel to the copper test plate whose dimension is
100×100×1mm3. A line defect is emulated by a 2×60mm2 slit,
and this slit shape defect is set to 0, 45, 90 degrees to thesensing coil axis, 0.2mm lift-off distance. In addition to theTable.1, the 256kHz sinusoidal exciting current having
300mA(rms) amplitude is flowing thorough the two exciting
coils.

Table 1. Various constants of the numerical simulations.
Exciting coil

Sensing coil

Outer diameter

24.0 [mm]Outer diameter

1.4 × 2.4 [mm]Inner diameter

8.0 [mm]

Inner diameter

1.4 × 2.0 [mm]Length0.4 [mm]

Length6 [mm]

Number of turns
Input
voltage(peak)
Frequency

20 turn

Number of turns

100 turn

1 [V]Axis core

256 [kHz](a) No defect

Mn-Zn/ferrite(Permeability: 3000)

Figure 3 shows the eddy current distributions on the target
copper plate and the magnetic flux density distributions in theferrite core.
Left of Fig. 3(a) shows the eddy current density distributions
when no defect in the target copper plate. Right of Fig. 3(a)shows a flux density distribution in the ferrite core. The flux
densities caused by the eddy currents are flowing along withthe sensor coil surface in parallel. This means no induced
voltage in the sensor coil when no defect in the target copper
plate.
Left of Fig. 3(b) shows the eddy current distribution when aline defect is located in parallel to the sensor coil axis. The
eddy currents flow along with this defect so that all of themagnetic flux caused by the eddy currents flow in a parallel
direction to the sensor coil surface. Right of Fig.3(b) shows theflux density distributions in the ferrite core of the sensor coil.
Left of Fig. 3(c) shows the eddy current distributions when aline defect is located 45 degree to the sensor coil axis. The
eddy currents flow along this line defect so that these eddy
currents yield the perpendicular magnetic flux component tothe sensor coil surface. Right of Fig. 3(c) shows the magnetic
flux densities in the ferrite core directed 45 degree to theferrite core axis. Thereby, the perpendicular magnetic flux
component to the sensor coil surface induces the output
voltage in the sensor coil.
Left of Fig. 3(d) shows the eddy current distributions flowing
the detour paths to the defect when the line defect is located ina perpendicular direction to the sensor coil axis. Because of
the flowing direction of the eddy currents, the magnetic flux
flows in a perpendicular direction to the sensor coil surface.
Although all of the magnetic flux caused by eddy currents are
directed to the perpendicular to the sensor coil surface, they
are cancelled each other. This means that it is difficult to(b) The line defect is located in parallel to the sensor
coil axis.

(c) The line defect is located 45 degree to the sensor
coil axis.

(d) The line defect is located in 90 degree to the sensor
coil axis.
Figure 3. Eddy current distributions in various defectconditions and the magnetic flux density distributions in
the ferrite core.

detect the line defect under this condition.
Figure 4 shows the induced voltage waveforms when the line
defect is directed 0, 45, 90 degrees to the sensor coil axis.
From the above results, it is found that the sensor coil could be
induced the voltage when the detoured eddy current causes theperpendicular component of the magnetic flux to the sensor
coil surface. The induced voltage in the sensor coil depends on
the perpendicular magnetic flux component to the sensor coilctional sensors.

Induced Voltage V

2

No Defect01

2. 10 6

4. 10 6

6. 10 6Time s8. 10 6poles. The two planar semicircular exciting coils construct thenorth and south poles alternatively by flowing the alternative
exciting currents. A region between the two adjacent straightline of the two exciting coils constructs the line shape nopolarity zone, i.e., zero magnetic potential region. The planar
exciting coils and the sensing coil wound around a ferrite core
as shown in Figure 5.
One of the big differences between the conventional and new
no polarity zone, i.e., the zero magnetic
potential region has been enlarged from the point in Figure 2
to the line in Figure 5.
As a result, it is possible to expect the higher sensibility of thecompared with those of
conventional planar circular shape

45
90

1

2

Figure 4 The induced voltages whose magnitude depends on
the angle between the sensor coil axis and the magnetic flux
flowing direction.
3

Figure 5
3.2 Numerical Simulations

3.1 Key points
As described in Chapter 2, the operating principle issummarized into the two key points.
The first is that there is no polarity zone, i.e., zero magnetic
potential region between the north and south poles when bothof the north and south poles are constructed by the exciting
coils.
When this zero magnetic potential region becomes a not zerosame to the on/off function of a switch.
The second is that the magnetic flux is passing through nopolarity zone, i.e., the zero magnetic potential region from thenorth to south poles. This magnetic flux is always directed inparallel to the sensor coil surface so that never induce thevoltage in the sensor coil.
If the direction of this magnetic flux flow to the ferrite coreaxis is changed within 90 degree, then the changed angle ismostly proportional to the induced voltage in the sensor coil.
In the other words, the directional change of the magnetic fluxchange within 90 degree is mostly proportional to the defectmagnitude.
In this paper, we propose the exciting coils having the planarand semicircular shape to enlarge no polarity zone, i.e., thezero magnetic potential region between the north and south

we employ the 3D FEM simulations. Table.2 lists various
constants of the exciting as well as the sensing coils.
Specification of the simulation model is as follows: The newplanar semicircular
test plate whose dimension is 100×100×1mm3. A line defect isemulated by a 2×60mm2 slit, and this slit shape defect is set to0, 45, 90 degrees to the sensing coil axis. 0.2mm lift-off
distance. In addition to Table. 2, The 256kHz sinusoidal
exciting current having 300mA(rms) is flowing thorough thetwo planar semicircular exciting coils.
Table. 2

Figure 6 shows the magnetic flux vector distribution and its
magnitude by the simulations.

Figure 7 shows an induced voltage waveform when the line
defect is directed 45 degree to the sensor coil axis. The newvoltage compared with those of conventional one.
ds a lower sensor
induced voltage compared with those of conventional one
when no detecting the defect.
The peak signal is the induced voltage at the 45 degree
between the line defect and the sensor coil axis. The noise isdefined the peak induced voltages at 0, 90, 180 degrees
between the line defect and the sensor coil axis. This leads tothe signal to noise, S/N, ratio definition. Comparison of thisS/N
icircular
thanthose of conventional one.

(a) Cross-sectional view of the magnetic flux density vector(a) Planar circular exciting(b) Planar semicircular exciting

coil

coil

(b) Plane view of the magnetic flux density vector
distributions of the new planar semicircular coil.
Figure 6. The magnetic flux density vector distributions andby the simulations.
Induced Voltage V

2

No Defect
10
2. 10 61

4. 10 6

6. 10 6Time s8. 10 645
90

2Figure 7. The induced voltages whose magnitude depend on
the angle between the sensor coil axis and the magnetic flux
flow direction in the sensing coil.

(c) Sensing coilFigure 8
middle and lower are the conventional coil, the new planar
semicircular coil and sensing coils wound around a ferritebar, respectively.
Figure 9 shows the experimentally obtained signal voltage
waveforms of the conventional as well as new planar
Table 3 summarizes the simulated and experimented results ofhigher sensor sensibility compared with those of conventionalone.

4 Conclusion

Induced Voltage V

0.05

No Defect0
2. 10 6

4. 10 6

6. 10 6Time s8. 10 6

45
90

0.05

(a)
Induced Voltage V

Acoil in the present paper. Employment of the two planar
semicircular exciting coils has made it possible to enlarge thezero magnetic potential region. Thereby, it has been possible
to enhance theIn addition, the results of the 3D FEM simulation and of thepractical experiments have verified that the newly developed
than that ofconventional one.
REFERENCES

0.15
0.10

No Defect

0.05

0
2. 10

6

4. 10

6

6. 10

6

Time s8. 10 6

0.05

45
90

0.10
0.15

(b)
Figure 9. Comparison among the experimentally obtained
sensor signal waveforms of the conventional as well as new

Because of the skillfulness to work out the practical coils, thelarge differences between the simulated and experimented
results in both of the conventional and new planar semicircularThe

differences

betweentheconventional

and

its

coil. This is because the geometrical shape is much more
serious parameter
semicircular coil.

[1] Narishige,S., Nishimizu,A., Koike,M. Abe, M., Narumi,
Y, Tsuge, T, (2010), Improved Detection Performanceusing a Multi-frequency Method of Eddy Current Testing
for Outside Circumferential Cracks near an Expansion of
Heat Exchanger Tubes, Non-Destructive Testing andCondition Monitoring, Vol. 52(6), June 2010, pp. 298-301.
[2] Hashizume, H., Yamada, Y., Miya, K., Toda, S., Morimoto,K., Araki, Y., Satake, K. and Shimizu, N., (1992),
Numerical and Experimental Analysis of Eddy Current
Testing for a Tube with Cracks, 1992, Vol.28, pp.1469 1472.
[3] Morozov, M., Rubinacci, G., Tamburrino, A. and Ventre,S., (2006), Numerical Models of Volumetric Insulating
Cracks in Eddy-Current Testing with Experimental
Validation, IEEE Trans. Magn. 2006, Vol.42, pp.1568 1576.
[4] Kikuchihara, H. and Saito,Y., (2013), Enhance theSensibility of the ECT Sensor, Journal of the Japan Societyof Applied Electromagnetics and Mechanics, Vol.21(3),2013.
[5] Maruyama,K., Marinova,I., and Saito,Y., (2014), Enhance
the Sensibility of the Resonance type ECT Sensor,
Materials Science Forum Vol. 792, 2014, pp 72 - 77.
[6] Maruyama,K., Marinova,I., and Saito,Y., (2015),
Developments of Flat
Coil for Defect Searching in theCurved Surfaces, E-Journal of Advanced Maintenance,(EJAM), Vol.7-1, 2015, pp. 59-65.
Contact
E-mailtakahiro.hyuga.8k@stu.hosei.ac.jp

Address:

Ingenious Resonance Circuit Connection for
Resonance Type Eddy Current Sensors
Kazuya OKUDA and Yoshifuru SAITO
Hosei University, Graduate School of Electrical and Electronic Engineering,
3-7-2 Kajino-cho, Koganei-shi, Tokyo 184-8684, Japan

Abstract
This paper describes the resonant connection for constructing a resonant circuit without any external capacitor. Resonance connection
is an ingenious circuit connection which makes it possible to utilize the line to line capacitor and inductance for resonance notrequiring any additional external capacitors.
In the present paper, the resonant frequency of ingeniously connected circuits could be controlled by changing the twist pitch of two
coils. Further, this resonant connection is applied to a resonant type eddy current sensor. As a result, it is revealed that our new
resonant type eddy current sensor has higher sensibility compared with those of conventional eddy current sensor.
Keyword: Ingenious resonant coils connection, Eddy current testing, Nondestructive testing

1 INTRODUCTION
Various non-destructive testing methods, such as eddy current
testing (ECT), ultrasonic testing (UT), radiographic testing (RT)and acoustic emission (AE) are currently used to the modern
airplane, high-speed train and express highway bus
maintenance. Among these methods, ECT does not require thecomplex electronic circuits, and does not need direct contact tothe tested specimens.
To overcome the various difficulties caused by theferromagnetic material properties as well as surface
deformation of the tested specimen, a multi-frequency drive
ECT probe had been proposed. As a result, several fruitfulresults had been reported for the tests of tube with cracks [1].
Also, numerical and experimental analysis of eddy current
testing for a tube with cracks had been carried with satisfactory
results. [2.3]
Operating principle of the ECT is classified into the two major
categories. One is that exposing the conductive materials to thealternating magnetic fields induces eddy current in all of the
conducting materials. Thereby, the input impedance of themagnetic field source, i.e., electric source, can detect the changeof the 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 flux change. The magnetic field of ECT iscomposed of two components: one is the exciting and the otheris the reactive component of magnetic fields. The reactive
component of magnetic field is caused by the eddy currents inthe target so that change of eddy current paths changes thereactive magnetic fields. Thus, the independently installed
sensor detects this magnetic field change. This type is called aseparately sensing coil type. In the other words, operating
principle of the separately installed sensing coil type ECT is asfollows: the sensing coil catches the magnetic field intensity
variation caused by the detour eddy currents flowing around adefect in the target metallic materials. [4-6].
The impedance sensing type is further classified into two types.
One is a simple impedance detecting type and the other is theresonant impedance detecting type. So that this latter type iscalled the resonance type ECT.
Previously, an ingenious coil connection exhibits a single
resonant frequency characteristics has been applied to work out
the noise filter for the power electronics circuits [4]. Further,
this ingenious coil connection has been applied to the resonancetype ECT [5]. Even though, the resonance type ECT utilizing
the ingenious coil connection exhibits higher sensibility
compared with those of a conventional ECT, the operating
frequency of the resonance type ECT is so high that it has been
forced to attach an external capacitor to reduce the resonancefrequency [6].
In the present paper, the resonant frequency of ingeniously
connected circuits could be controlled by changing the twist
pitch of two coils with the aid of ferromagnetic core materials.
As a result, it is revealed that our developed new resonant type
ECT has higher sensibility compared with those of conventional
impedance detecting type ECT sensor.

2 RESONANT TYPE ECT
2.1 Fundamentals
Let an arbitrary finite length solenoid coil shown in Fig. 1(a) bean eddy current sensor coil. When we put this sensor coil on acopper plate as shown in Fig. 1(b) and apply an alternating
current to the sensor coil, eddy current is induced as a reactionof the a
Measure the input impedance of the sensor coil is able todiagnose 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 the secondary impedance change detection
from primary input terminal in a conventional single phasetransformer. Thus, it is obvious that a simple finite length
solenoid coil can detect the defects of the target conducting
materials. This is the basic operating principle of the impedance
sensing type ECT.

Figure.1. Tested coil and the initial measurement
conditions.
2.2 Resonant Type ECT
Any of the coils always exhibit an inductive property becauseof the magnetic fields around them when applying a current into
the coil. Also, any of the coils have the capacitances among thecoils. Even though a simple finite length solenoid coil shown in
Fig. 1(a), it is possible to observe its natural resonancephenomena as shown in Fig. 3.

connection in Fig. 2(b) of the conducting wires are constructing
the normal and the ingeniously connected finite length solenoid
coils, respectively.

Figure. 3. Frequency characteristics of the impedances ofthe finite length coil shown in Fig. 1(a), on the copper
plate with 1mm thickness shown in Fig. 1(b) and on thetwo discrete copper plates shown in Fig. 1(c).
Decision of ECT operation frequency is of paramountimportance, because sensibility and searching depth of ECT are
greatly depending on the operation frequency. Theoretically,
the operation frequency of ECT can be decided by taking thetarget conductivity and its skin-depth into account. However,
final selection of operation frequency is determined by the pastexperiences and the practical tests.
In this paper, the operation frequency of ECT has been set to thenatural parallel resonant frequency of the ECT sensor coil whenfacing with a wholesome part of target. The ECT facing withthe wholesome part of target takes the maximum pure resistive
impedance. When the ECT sensor coil meets with a defect oftarget, the resonance condition is essentially not established.
Therefore, the input impedance of the input terminals is also
reduced to small in value compared with those of the resonant
one. Namely, a deviation between the resonance and notresonance impedances becomes the maximum value.
reference measured
reference(a) Normal.
(b) Ingeniously connection.
Figure. 2. Constructions of the finite lengths solenoid
coils. (a) Normal and (b) ingeniously connected
conducting wires.
Figure 3 shows that the normal in Fig. 2(a) and the ingeniously

100 %

(1)

where the reference and measured in (1) refer to the input
impedances from the ECT coil terminals when facing the ECT
coil with the wholesome and defect parts of target, respectively.

INGENIOUS COIL CONNECTIONS
3.1 Resonant frequency control(a) Two conductors(b)Connection of two conductors(c) Equivalent electric circuit of the connected conductors(d) Modified equivalent electric circuit of the connected
conductors
Figure. 4. Principle of an ingenious coil connection.
The most important key point to realize the ingenious
connection is to twist the coils as shown in Fig. 5. Twisting of
the coils makes it possible to control the resonant frequency due
to the stray capacitance between two coils.
Measuring the defect or no defect resonant impedances extracts
a shape of defect. Figure 6 shows an example of an extracted H
shape defect.

Figure. 5. Example of a pair of twisted coils

Figure.6. Extracted H shape defect by measuring theresonance impedances..
3 RESONANT TYPE ETC UTILIZING THE

Stray capacitance control makes it possible to govern the natural
resonance phenomena. The ingenious coil connection in Fig. 4
is one of the control methods of the stray capacitances among
the coils.
Twisting of the two coils in Fig. 5 is not only the facing between
the black and white coils into uniform but also it is possible tocontrol the resonant frequency.
We had worked out the 13 twisted coils by changing the twist
pitch as well as a number of layers. A coil diameter of the 13
twisted coils is 0.2mm.
Table 1 list the various constants of the 13 twist coils.
Table .1 Tested twist coils
Number of
Resonant
Twist pitchlayerfrequency[turn/m][layer][kHz]
1470.61309.0
1250.0
1
481.5
500.0
1
543.0
333.3
1
580.5
200.0
1
570.0
142.9
1
679.5
1470.6
2
233.5
500.0
2
173.0
333.3
2
181.5
200.0
2
180.0
142.9
2
252.5
1470.6
3
194.0
333.3
3
196.0
Figures 7 shows the frequency vs. impedance characteristics ofthe twist coils when changing the twist pitch as well as thenumber of layers.
Observe the impedance vs. frequency characteristics of thesingle layer coils in Fig. 7 reveals that increasing of the twist
pitch decreases the resonant frequency. However, it is foundthat increasing the number of layers decreases the effects oftwist pitch as shown in the Figs. 7(b)-(c).
To represent a relationship among the resonant frequency, twist
pitch and number of layers, we have derived an empiricalformula by a least squares.
Let us consider the x,y,z coordinate system, where thecoordinate values x,y,z are corresponding to the twist pitch,
number of layers and resonant frequency, respectively.
To represent a relationship among the twist pitch x, number oflayers y and resonant frequency z, let us consider an empiricalformula given byfc0

a1 x b1 y a 2 x 2
c11 xy a 3 x 3

b2 y 2

c12 xy 2c 21 x 2 y

(2)

x1

y1

x1n 1 y1

f2

1 x2

2

y2

2

x2 n 1 y21

f3

1 x32

y32

x3 n 1 y 3

f4

1 x4 2y4 2

x4 n 1 y 4

fm

1 xm 2ym 2

xm n 1 y m

f1

1

m

n,

c0
a1
b1 ,
cm1

y=C x,
x=(CTC)-1CTy,where C and CT are the system matrix and its
transpose, respectively
f 1367.94 0.33453x 0.0000283815x 2(a)Single layer(b) Double layers

874.771y 0.116112xy 156.323 y 2

(3)

(4)

Figure 8. Design curves for the ingenious connection resonant
circuit, where a resonant frequency is given as a function of
the twist pitch as well as number of layers.
Even though the coil diameter is limited to 0.2mm, a desiredresonance frequency decides the twist pitch and number oflayers from the design curves in Fig. 8.
Thus, our empirical formula approach makes it possible tocontrol the resonant frequency without any external capacitor.
3.2 Flaw detection(c) Triple layers
Figure. 7. The frequency vs. impedance characteristics of thetwist coils when changing the twit pitch as well as layers.

To demonstrate the usefulness of our resonance type ETC
utilizing the ingenious coil connections, we have carried out aflaw detection in a two-dimensional plane.
Figure 9 is the target test piece having an artificial defects ofwidth 2mm and depth 1mm.
Table.2 Prototype ECT sensor

We have m=13 equations and n=6 unknowns of (2) so that theleast squares of (3) gives 6 unknowns. Thus, we have theempirical formula (4).
As shown in Fig. 8, this empirical formula yields a set of design
curves for the ingenious resonant connection circuits, i.e., aresonant frequency is represented as the functions of the twist
pitch as well as number of layers.

Length of entire coil
2260mmCoil diameter
0.1mm
Number of turns
120turns
Length of solenoid coil
30mm
Number of layer
1Figure 9. Tested target metal sheet having the width 2mm
and depth 1mm artificial defect. Black dots denote themeasured points.
At first, we have designed our prototype of the resonant
connection type ECT coils by the empirical formula (4). Second,a ferromagnetic material whose diameter of 6 mm, length of 30
mm is employed to control the resonance frequency in a much
more precisely.
Table 2 lists various constants of an exploited resonanceconnection type ETC employing the ingenious coil connections
with a ferrite rod.
Figure 10(a) shows an impedance versus frequency of a normal
finite length solenoid coils without any ingenious connection.
Figure 10(b) shows an impedance versus frequency of theresonant connection type coils.

(a) Normal finite length solenoid coil(b) Resonant connection type coilFigure 10. The impedance versus frequency characteristicsof the coils.
A red square in Figure 9 shows a 20mm by 20mm target areafor ECT. The ECT sensors measured at the 9 by 9 sampling
points with 2.5mm regular spacing on this 20mm by 20mm
square area.
A driving frequency of both the normal finite length coil in
Figure 10(a) and the resonant connection type coils in Figure10(b) has been set to 256kHz.
Setting the reference point at a lower left corner in Figure 9
gives the sensibilities of (1).
Figure 11(a) shows a sensibility distribution of the normal finite
length solenoid coil.
Figure 11(b) shows a sensibility distribution of the resonanceconnection type coils.

(a) Normal finite length solenoid coil(b) Resonant connection type coilFigure. 11. Sensibility of (1) distributions of the normal
finite length solenoid coil and the resonant connection typecoil..
The sensibility distributions in Figure 11 reveals that theresonant type coil yields a far excellent sensibility comparedwith those of the normal finite length solenoid coil.
In the other words, nearer the exciting frequency is the resonant
frequency of the sensor coil, the more high sensibility the sensor
coil exhibits.
To confirm this, we have carried out an experiment a resonanceconnection type coil installed around a ferrite bar.
Figure 12 shows an impedance versus frequency of the resonant
connection type coils installed to the ferrite rod. Obviously, theresonant frequency of this coil is nearer to the exciting
frequency 256KHz.
Figure 13 shows a sensibility distribution of the resonanceconnection type coils installed to the ferrite rod..
Thus, we have succeeded in exploiting the new resonance type

Even though this new resonance type ECT sensor does not need
any external capacitor to maintain a stable resonance state andhas a very high sensitivity, consideration of the skin depth has
lead to employ a lower operating frequency.
To overcome this resonant frequency control, this paper
proposes an empirical formula based of the least squares. As aresult, we have succeeded in designing the resonance type ECT
without any external capacitor.
REFERENCES
Figure 12. A frequency versus impedance characteristics ofthe resonance connection type coil installed to a ferrite rod.

Figure 13. Sensibility distribution of the resonanceconnection type coil installed to a ferrite rod..
ECT sensor having high sensibility.
A most important key point is that nearer the exciting frequency
is the resonant frequency of the sensor coil, the more highsensibility the sensor coil exhibits.
4 CONCLUSION
This paper has been described to the improvement of theresonant type ECT.
Previously, we had proposed an eddy current sensor of newresonance type by an ingenious coil connection.

[1] S.Narishige, A.Nishimizu, M.Koike, Y.Abe, Y.Narumi,
T.Tsuge, Improved Detection Performance using a Multifrequency Method of Eddy Current Testing for Outside
Circumferential Cracks near an Expansion of Heat
Exchanger Tubes, Non-Destructive Testing and Condition
Monitoring, Volume 52, Number 6, pp.298-301, June 2010.
[2] H.Hashizume, Y.Yamada; K.Miya, S.Toda, K.Morimoto,Y.Araki,
K.Satake,
N.Shimizu,
Numerical
andExperimental Analysis of Eddy Current Testing for a Tube
with Cracks. IEEE Trans. Magn. 28, pp.1469-1472, 1992,.
[3] M.Morozov, G.Rubinacci, A.Tamburrino, S.Ventre,
Numerical Models of Volumetric Insulating Cracks in
Eddy-Current Testing with Experimental Validation, IEEE
Trans. Magn. 42, pp.1568-1576, 2006.
[4] Y.Midorikawa, S.Hayano and Y.Saito, A resonant
phenomenon between adjacent series connected coils and its
application to a noise filter, Advanced Computational and
Design Techniques in Applied Electromagnetic Systems,
Vol.6, pp. 633-639, 1995.
[5] H. Kikuchihara, I. Marinova and Y. Saito, Enhance theSensibility of the Eddy Current Testing, Journal of the Japan
Society of Applied Electromagnetics and Mechanics, Vol.
21, No. 5, pp.356-361, 2013.
[6] K. Maruyama, I. Marinova and Y. Saito, Enhance theSensibility of the Resonance Type Eddy Current Testing,Materials Science Forum Vol. 792, pp.72-77, 2014.
Contact E-mail Address: kazuya.okuda.2n@stu.hosei.ac.jp