STRESS EVALUATION BY CHAOTIC CHARACTERISTIC OF
BARKHAUSEN NOISE
Y. Tsuchida and M. Enokizono
Department of Electrical and Electronic Engineering, Oita University,
700 Dannoharu, Oita 870-1192, JAPAN
ABSTRACT. This paper presents a tensile stress evaluation of mild steel plates by chaos of
Barkhausen noise. The stress of magnetic materials affects magnetic domains, so the amount of
the stress can be evaluated by Barkhausen noise. After the evaluations of Barkhausen noise by
the original signals, spectrums and auto-correlation functions are performed, the reconstructed
attractors which is one of the typical treatment of the chaos are examined to use them for the
stress evaluation of the mild steel.
INTRODUCTION
It is well known that the movement of the 180-degree magnetic domain walls inside
magnetic materials generates Barkhausen noise. The stress condition can be evaluated
by Barkhausen noise before a crack appears on the surface because the dislocation induced
by the stress affects the movement of the magnetic domain walls. However, it is difficult
to quantify the amount of the stress by Barkhausen noise because Barkhausen noise is a
very complicated nonlinear signal. So, the special evaluation method should be
established to use it for the stress evaluation effectively [1-3]. Conventionally, the power
of Barkhausen noise was calculated to find the difference depending on the stress
condition. We also have used this evaluation for a heat-fatigued stainless steel plate and
reported the possibility of the quantitative evaluation by the change of the power. We
made clear that the power of the heat-fatigued sample was varied slightly even though the
stainless steel used was told as non-magnetic material [1]. In this previous investigation,
we noticed that the calculation of the power from Barkhausen noise meant that we
calculated the summation of the complicated signal, and we eliminated some of the
effective information of the signal due to this summation. A more effective evaluation
method should be established to use a complicated non-linear signal for the stress
evaluation effectively. Therefore, we paid attention for the chaos of Barkhausen noise
because the chaos theory could treat a signal as a non-linear one [4-7]. First, we
examined if Barkhausen noise itself could be categorized as chaotic phenomena [2, 3].
We examined four points to the measured Barkhausen noise from silicon steel sheets to
check whether it is chaotic or not [2, 3]. These four points are; (1) the complexity of
Barkhausen noise itself in the time domain, (2) the existence of a specific discrete peak of
the spectrum after Fourier transform, (3) the distribution of the correlation function, and
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
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Material: Mild steel
Measured point
200
unit : mm
FIGURE 1. Dimension of mild steel plate for tensile stress test and measured point of Barkhausen noise.
Li ^®wm
wtm »t,§
_
(t|
:
:If
(|l)$flliOf
FIGURE 2. Measurement system and sensor for Barkhausen noise.
(4) the self-similarity of the constructed attractors from Barkhausen noises [2, 3, 5]. The
chaotic phenomena of Barkhausen noise have been made clear theoretically and under a
single grain of magnetic material [8, 9]. In this paper, the change of the attractor
constructed from measured Barkhausen noise after a tensile stress test is examined to use
it for the stress evaluation of the mild steel.
MEASUREMENT FOR TENSILE STRESS EVALUATION
Specimen and Tensile Stress
Figure 1 shows a specimen for a tensile stress test. The mild steel plate named as
SS400 (defined in Japanese Industrial Standard, C : 0.1 - 0.2 %, P : less than 0.050 %, S :
less than 0.050 %, Tensile strength : 400 - 510 MPa) was used for the measurement. The
size of the plate is 200 mm x 20 mm and the thickness of it is 1.5 mm. Barkhausen noise
is measured at one point on the surface as shown in Figure 1 before and after the tensile
stress test. The velocity of the strain of the tensile stress is 1mm per one minute. The
specimens used are as-rolled in this paper.
Sensor and Measurement System
Figure 2 (a) and (b) show the measurement system and the sensor for the tensile
stress evaluation, respectively. This sensor was selected after the examination of several
sensors [2, 3]. In the selected sensor, the edge of one side was sharpened to measure
Barkhausen noise in as small an area as possible. The core of this sensor is made of wide
band ferrite. First, the computer generates the signal to excite the specimen through the
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x
i+2r
time
FIGURE 3.
(a) Time series data
(b) Constructed artractor
Explanation of embedding method to construct artractor from time series data.
oscillator and the power amplifier. The Barkhausen noise is measured by the computer
from the pick-up sensor attached on the surface of the specimen through the low noise
wideband preamplifier and the wave memory (a data acquisition devise). The low noise
wideband preamplifier has a high pass analog filter, so this filter eliminates the frequency
components around the excitation signal from the measured signal. Barkhausen noise is
transferred to a PC after being digitized by the wave memory.
CHAOTIC ATTRACTOR
The space, which is made by the position and the velocity, is called as the phase
space, and the complicated non-linear phenomena can be examined by the phase space.
As for the time series data, the one group can be reconstructed by m-number data picked
up at each i sampling period. The times series data can be written as (1),
V
0>
V
1>
V
2>
«««
'
V
«'
I 1 I
\/
here the total number of the time series data is n. The three data is reconstructed as
(xQ9xT9 jc2r), O19 xl+T9 xl+2T)9 •••••, (xn_2T9 xn_T, xn)9 each data group shows a point in
three-dimension as shown in Figure 3 (b). This is called reconstructed attractor. In this
paper, two dimensional attractors are constructed as (2).
(xl9xl+T)9 (x2,x2+T)9 (x39x3+T)9 • • • , ( x n _ T , x n ) .
(2)
The procedure, which draws the attractor from the time series data as shown in Figure 3, is
called as the embedding method and this method is used for the examination of the chaos
of time series data.
RESULTS AND DISCUSSIONS
Figure 4 shows the stress-strain curve of the measured structural steel plates. As
shown in this figure, the tensile strength of the specimens is about 400 MPa. Barkhausen
noise is measured by the four stressed conditions, those are before stressed, applied 10 %
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450
400
•5T 35°
ij 300
250
200
150
100
50
10
20
40
30
Strain [%]
FIGURE 4. Stress-stain curve of measured structural steel plates.
0.5
Time [|o.s]
1
1.5
Time fris]
(a) Strain: 0%
(b) Strain: 10%
1
Timers]
Time [MS]
1.5
(d) Strain: 44%
(c) Strain: 20%
FIGURE 5. Measured Barkhausen noise from steel plates before and after tensile stress test.
strain, 20 % strain, and 44 % strain. We prepared four different samples for these four
stress conditions. Figure 5 (a) shows Barkhausen noise measured from the non-stressed
steel plate, and Figure 5(b), (c), and (d) show ones measured from 10 %, 20 %, and 44 %
strain steel plates, respectively. The exciting frequency 50 Hz and exciting current 300
mA were applied in the exciting coil. Barkhausen noise generates where the variation of
the exciting flux is large, so two parts of the large amplitude appear during one period of
the exciting frequency as shown in Figures 5. From these figures, it can be said that
some signal difference is recognized before and after the tensile test, however, it is
difficult to distinguish the stressed condition from these signals. Figures 6 show the
spectrums from the measured Barkhausen noises. In these figures, it is shown that the
Barkhausen noises mainly occur in the frequency range around 120 kHz. The amount of
the tensile stress could not be distinguished from these figures, too. Figures 7 show the
auto-correlation functions from Barkhausen noises. The auto-correlation functions of all
stress conditions drop sharply just after the parameter m=0. This is one of the factors
that the time series signal can be categorized into the chaotic phenomena. Figures 8
through Figures 12 show the constructed attractors with the time delay i = 8000, 9000,
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100
200
300
Frequency [kHz]
100
400
FIGURE 6.
400
(b) Strain: 10%
(a) Strain: 0%
200
300
Frequency [kHz]
200
300
Frequency [kHz]
400
100
200
300
Frequency [kHz]
400
(c) Strain: 20%
(d) Strain: 44%
Spectrum of Barkhausen noise from steel plates before and after tensile stress test.
§
'!
°
i-o.5
|-0.5
o
'S
< -1
a
< -i
4
6
Patameter m
4
6
Patameter m
(b) Strain: 10%
___p_p_
Autocorrelation function C(m)
P
P
(a) Strain: 0%
4
6
Patameter m
|
1
. . . . . . . . . . . .(. . . . . . . . . . . j. . . . . . . . . . . .
0
2
4
6
Patameter m
8
x 1 04
(c) Strain: 20%
(d) Strain: 44%
FIGURE 7. Auto-correlation function of Barkhausen noise from steel plates before and after tensile stress
test.
10000, 15000, 25000, 30000, 40000, 50000, 60000, 70000 and 80000 sampling points.
Now, the frequency of the excitation current is 50 Hz (equivalent as 200000 sampling
points) and the frequency of the Barkhausen noise is 120 kHz (equivalent as 83 sampling
points). Therefore, selected sampling points for the time delay has no relation to the
frequencies of the excitation and the Barkhausen noise itself. Figures 8 show the
attractors from the background noise. The small circles in all figures show the attractors
constructed from the background noise. Figures 9 show the attractors constructed from
measured Barkhausen noise before the tensile test. The attractors with the time delay i is
8000, 9000 and 10000 don't look like the specified shape, though the attractors with the
time delay T - 15000, 20000, 25000, 30000, 40000, 50000, 60000 and 70000 look like the
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1=8000 (SOOjis
>
% = 9000 (900us)
10
'0
T
•f,
2
•o
,„
__
'0
i = 20000 (2000u S)
-10
-5
1 =50000 (5000 us)
,„
0
5
>
5 —— _ _ !—— ——
-10
-5
0
5
10
-10
X. x 10'3
-5
0
5
10
T
T
1
!
-10
-10
-10
x. x 10-3
80000 (8 OOOu
10
'0
r
10
i
X x 10'3
70000 (7 000 p s
1 =60000 ( <
_
f
X x 10°
—— 1——
-10
X x 1C'3
—
-10
1 = 25000 (2500)1
5 •—
T
-10
X x 10-3
'o
T
\
„
•4--
__
h
10
5 —— —— 1—— ——
1
-10
X x 10'3
1 = 40000 (A 000 us)
,„
i=15000 ( 1500 )is)
— .__!___
5
-10
X x 10'3
30000 i2WOO us)
,„
m
•f*
i _,
-10
x x ID'3
1=10000 (lOOOus)
— .__!—|—
5
-V-
i
i
,„
__
5
——
-5
-10
0
5
10
-10
-10
X x 10'3
-5
0
5
10
-10
X x 10'3
-5
0
5
10
X x 10'3
FIGURE 8. Constructed Attractors from background noise by various time delay parameters for
embedding method with out samples.
9000 (900 us)
0
Q
-5
0
5
10
-1 = 30000 (3000)15)
-10
-5
0
5
10
x = 40000 (4000 us)
1()
T = 10000 (1000 us)
-10
-5
0
5
x= 15000 (1500ns)
-t = 20000 (2000 us)
10
1 = 50000 (5000 us)
lfl
lft
1Q
-c = 60000 (6000 us
<io- 3
X x 103
FIGURE 9. Constructed Attractors from Barkhausen noise by various time delay parameters for
embedding method (before tensile test).
-10
-5
0
5
10
-10 -5
0
5
10
-10 -5
-10
-5
0
5
10
-10 -5
0
5
10
-10 -5
0
0
5
5
10
-10 -5
10
-10 -5
0
0
5
5
10
-10 -5
10
-10 -5
0
5
0
10
5
10
-10 -5
0
5
10
-10 - 5 0 5
FIGURE 10. Constructed Attractors from Barkhausen noise by various time delay parameters for
embedding method (Strain 10%).
9000 (900 us)
= 30000 (3000 us)
,„
t = 40000 (4000 us)
.„
1= 10000 (1000 us)
,„
-c= 15000 (1500 us)
ln
1= 20000 (2000 us)
,„
t = 50000 (5000 us)
,„
x = 60000 (6000 us)
,„
t = 70000 (7000ns)
1 = 25000 (25QOus)
FIGURE 11. Constructed Attractors from Barkhausen noise by various time delay parameters for
embedding method (Strain 20%).
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FIGURE 12. Constructed Attractors from Barkhausen noise by various time delay parameters for
embedding method (Strain 44%).
cross shape. And the attractor with 80000 looks like the horizontal line. As mentioned
above, these time delays don't have the relation with frequency, so these shapes must
express something different but the characteristics of the signal. Figures 10, 11 and 12
show the attractors at the strain 10, 20 and 44 %, respectively. Some differences can be
found through Figures 9 to 12, however furthermore examination is necessary to use the
attractors for the stress evaluation.
CONCLUSIONS
Barkhausen noise is measured before and after the tensile stress test and examined
the possibility of the stress evaluation by the chaotic attractors of Barkhausen noise. As
a result, the following can be described,
(1) Some signal difference of Barkhausen noise is recognized before and after the tensile
test, however, it is difficult to distinguish the stressed condition from these signals.
(2) Some difference of the trajectory of the attractors is also observed depending on the
stress condition.
So far, we can say that there are some relationships between the attractors
constructed from the Barkhausen noise and the tensile stress. The chaos theory can treat
the signals as complicated nonlinear ones, therefore, it can be useful to adopt it if the
relationship is made clear in details.
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