Transcript Transilvania University of Braşov - ROMANIA Higher order statistics in magnetoacoustic NDT Nicolae Cretu*, Gelu M Nita**, Attila Boer*, Mihail Pop* *Physics Department, Transilvania University, Eroilor nr.

Transilvania University of Braşov - ROMANIA
Higher order
statistics in
magnetoacoustic
NDT
Nicolae Cretu*, Gelu M Nita**, Attila Boer*,
Mihail Pop*
*Physics Department, Transilvania
University, Eroilor nr. 29, Brasov, 500036,
Romania
**New Jersey Institute of Technology,
Center for Solar Terrestrial Research
Corresponding author: [email protected]
CNDT 2009 Prague
Introduction
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The present work contains a study for the application of some methods
from statistics in nondestructive evaluation and nondestructuve testing
The application of higher order statistics assumes that the most
evaluation methods involve the computer and his great facility to
compute large bloks of experimental data
Higher order statistics means statistics which implies higher order
central moments and cumulants
By definition for a discrete set of data the central moment of order m
is:
1 n
 ( xi   x ) m  ( x   x ) m 
n i 1
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The work analyses especially the aplication of the statistical magnitude
named Kurtosis to the magnetoacoustic phenomenon.
What´s the Kurtosis?
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By definition
K
4
( 2 ) 2
 4  ( x  x )4 
Central moment of order 4
   ( x  x )2 
2
Standard deviation
the Variance
•Is also used Excess of Kurtosis (EK) given by:
EK=K-3
Kurtosis of a signal with uniform
distribution in time
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K=1.8
EK=-1.2
Harmonic signal
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K=1.5
EK=-1.5
Gaussian signal K=3, EK=0
Spectral Kurtosis (SK)
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Operates in the frequency domain
Is a Kurtosis of the amplitudes of the
spectral components or of the power
spectral components
Can be used to detect transient signals
which appear during the evolution of
the phenomenon
Dynamic SK
Dynamic SK
The data aquisition has a special formalism:
-N spectra in time, each spectrum has a number m=1024 samples at the
aquisition frequency f.
-the m=1024 samples in time are used by FFT to produce a spectrum of
m=1024 frequencies between the limits –f/2, +f/2
-the Power Spectral Density (PSD) will contain m/2=512 components in the
frequency domain 0-f/2
-for a number M=300…500 of subspectra we compute S1 and S2:
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M
S1 
 Pk , m ;
m 1
M
S2 
 Pk2, m ;
k  frequencychannel
m 1
-for M subspectra we obtain an SK estimator given by:

M 
S
 M  2  1 ,
M  1
S1 
SK  1 for a signal with Gaussian distribution
SK 
SK for detection of the transient
signals
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SK
detection of
three
transient
stationary
signals
Magnetoacoustic emission
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The magnetoacoustic effect is specific for elastic magnetic materials , precisely for
ferromagnetic materials, and refeers to the generation of elastic waves in such materials
being magnetized in an alternating magnetic field. This effect is an indubitable proof of the
existence of the magnetic domains and magnetic domain walls, which explain the
magnetization processes in ferromagnets.
It is knew that during the magnetization process , following the magnetization curve of the
ferromagnetic materials with the increasing of the external field, first occurs the growing of
the magnetic domains, reversible rotation of the magnetization and at high levels of the
field irreversible rotation of the magnetization.
At high magnetic fields, only irreversible rotation of the magnetization exists and in this
case all domains in an ferromagnet must be oriented parallel with the external magnetic
field. But, the existence of the anisotropy or of structural imperfections like defects, gives
rise to destroy the local magnetic order and fix the domains in other orientation comparing
with the orientation of the external field. So, by applying magnetic fields higher than the
magnetic field corresponding to the saturation level, abrupt and discontinuous displacement
of magnetic domain walls pinned by inclusions,voids, dislocations, grain boundaries etc,
appear.
There are two important phenomena which appear :
-Barkhausen noise (BN)-detected in the form of voltage pulses which are induced in a
coil placed near the surface of the material.
-Magnetoacoustic Emission (MAE)- detected regularly by piezoelectric transducers
placed on the surface of the sample.
Magnetoacoustic signal
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acts like a nongaussian transient signal when the wall between the
magnetic domains are pinned around the crystall imperfections or
defects
Experimental setup
Sample placement
TDK and SK for a carbon steel sample
TDK and SK for Annealed Carbon Steel
TDK and SK for Ni
TDK and SK for a sample of Ni with
artificial created defect
Noise during the mesurements
Conclusions
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Estimation of some magnitudes from statistics
can give information about the nature of the
physical process in materials.
The estimation of dynamic K or SK can be
used as an active method of control in NDT
For estimation of dynamic K or SK during the
time, is better to use new generation of FPGA
aquisition boards.
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Thank you for attention!