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 ResearchCorresponding author: cretu.c@unitbv.ro

Transilvania University of Braşov - ROMANIA

CNDT 2009 Prague

Introduction

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:

The work analyses especially the aplication of the statistical magnitude named Kurtosis to the magnetoacoustic phenomenon.

mn

i

mi xxxx

n)()(

1

1

What´s the Kurtosis?

By definition

4)(4 xx

2)( xx

22 )(

4

K

Central moment of order 4

Standard deviation

•Is also used Excess of Kurtosis (EK) given by: EK=K-3

2 the Variance

Kurtosis of a signal with uniform distribution in time

K=1.8 EK=-1.2

Harmonic signal

K=1.5 EK=-

1.5

Gaussian signal K=3, EK=0

Spectral Kurtosis (SK)

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:

-for M subspectra we obtain an SK estimator given by:

M

m

kM

mmkPSmkPS

1

channelfrequency ;

1

2,2 ;,1

ondistributiGaussianwithsignalaforSK

S

SM

M

MSK

1

,11 1

2

SK for detection of the transient signals

SK detection of three transient stationary signals

Magnetoacoustic emission 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

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

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.

Thank you for attention!