·Home ·Table of Contents ·Computer Processing and Simulation  Flaw Detection in Ultrasonics Using Wavelets Transform and Split Spectrum Processing
DRAI Redouane, KHELIL Mohamed & BENCHAALA Amar Centre de Recherche Scientifique et Technique en Soudage et Contrôle (CSC),
Laboratoire de Traitement du Signal et de l'Image,
Route de DelyIbrahim, BP 64, Chéraga, Alger, Algérie
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Abstract :
In ultrasonic techniques, information on defects characterization
possibilities have required more evolved techniques development than classical
methods. To obtain a high probability of defect detection, these methods use
signal processing algorithms in order to enhance signal to noise ratio. In
this paper, some signal processing algorithms like split spectrum processing
(SSP) and wavelets are developed and implemented on computer allowing their
utilization in processing of ultrasonics NDT results.
Key words :NDT, Ultrasonic, Split spectrum techniques,
continuous wavelets, digital wavelets.
Introduction :
The Non Destructive Testing has to allow to obtain the highest possible
probability detection, the most exact size and the exact orientation of
dangerous defects that the specimen to control can contain.
New methods in
ultrasonic NDT have been developed since some years. They are based on the
fact that the ultrasonic signal received from a defect contains a sum of
information forsaken by the classical techniques. These later consider that
the essential information to take into account is the maximal amplitude of the
ultrasonic echo collected and this whatever the nature of defects. The
possibility to acquire some information allowing to characterize defects in
nature, size and orientation has necessitated the development of techniques
more evolved than those that are regrouped under the general technical term of
ultrasonic imaging.
In ultrasonic flaw detection, it is often difficult to
distinguish the flaw signal from the background grain noise. This noise often
masks the flaw signal, creating a hindrance to detection. In this article, we
contribute by the development of some signal processing techniques in order to
enhance flaw visibility and to improve the probability of defects detection.
So, we plan to :
 Develop an algorithm called Split Spectrum Processing that consists in
dividing the echo defect spectrum in slices and apply the inverse Fourier
transform in order to improve signal noise ratio.
 Develop an algorithm based on wavelets transform in order to enhance
flaw visibility. This tool have generated much interest in various
applications such as speech coding, pitch detection, image compression,
multiresolution analysis and estimation of multiscale processes. The idea of
examining signals at various scales and analyzing them with various
resolutions has, in fact, emerged independently in many fields of
mathematics, physics and engineering. Wavelet decomposition introduces the
notion of scale as an alternative to frequency and maps a signal into a
timescale plane. Each scale in the timescale plane corresponds to a
certain range of frequencies in the timefrequency plane.
 Show the application of these techniques on very absorbing materials
containing defects.
Through this study, we can show that
application of signal processing techniques in ultrasonic can be an optimal
solution to the different problems encountered in NDT of materials.
1. Problem position
The detection method quality maybe estimated by the signal to noise ratio
in the receipt system output. All developed detection methods have as a goal
increasing this ratio in order to increase inspection sensitivity (1). Among
these methods, we can mention :
We achieve N acquisitions of the presumed
defect signal and we make a temporal mean.
Let r_{i}(t) the received signal in the i^{th}
acquisition
 (1)

with b_{i}(t) = noise uncertain section (no reproducible from one
experience to another) measure and amplification noise,w_{i}(t) = noise coherent section , owed to reflections parasites (noise of grains or geometry defects), part
reproducible from one experience to another,s_{i}(t) = defect signal.
We calculate
This average allows to reduce the uncertain part of the noise. The
coherent part of noise is not modified. The signal to noise ratio gain is in
general weak, the noise measurement represents a weak part of the observed
noise only.
For it, we developed algorithms based on techniques named
Split Spectrum Processing and wavelets transform improving this ratio.
2. Split Spectrum Processing (SSP)
This technique consists in working in wide band and to cut the signal spectrum up in slices (Split Spectrum Processing ).
2.1. ConstantBandwidth (2)
Let e(t) a wide band incident signal and r(t) the received signal, we have
:
 (2)

where g(t) is impulsionnal response of the target (a defect in
material)
 (3)

we calculate the Fourier transform (FT) of the
crosscorrelation C_{re}(t)
 (4)

The spectrum of crosscorrelation is cut up in
slices of adjacent frequency bands g_{i}(f)
 (5)

We can show that it is then
equivalent to transmit a large band signal e(t) for N narrow band signals as:
 (6)

The detection algorithm developed by Bilgutay and al. consists to
do the following operations
 Calculate the spectrum of C_{re}(t)
 Cut up this spectrum in N adjacent bands g_{i}(f)
 Calculate the inverse Fourier transform of C_{i}(t) of each band,
 Normalise the signals C_{i}(t), we obtain
Bilgutay (3) proposes some methods and we have choosen this one, we calculate
 (7)

We can even consider to achieve the linear combinations of C_{i}(t), coefficients
being chosen
in order to give back the maximum of output signal to noise
ratio.
2.2. ConstantQ Decomposition (4)
Since SSP employs constant bandwidth windows, the timefrequency
resolution is fixed over the entire timefrequency plane. This imposes a
limitation on the analysis of high frequency signals of short time duration as
resolution in time and frequency simultaneously cannot be made arbitrarily
small.
An alternate method of spectral decomposition which overcomes the
resolution limitation of constant bandwidth windows, may instead be utilized
to obtain the frequency diverse ensemble.
The constant relative bandwidth
decomposition employs wide band windows at high frequencies and narrow band
windows at low frequencies in contrast to the constant analysis window
( .2). We can see also it in timefrequency plane (fig.3).
Fig 2: SSP with Q constant

Fig 3: timefrequency plane 
Such a decomposition is termed "constantQ", where Q is the constant frequency to
bandwidth ratio denoted by:
 (8)

The individual narrow band spectra
X_{j}(f) may be written in terms of the received signal spectrum,
X(f), as:
 (9)

where fj is the center frequency of the j^{th}
individual gaussian filter, and bj, the filter bandwidth. The frequency
diverse ensemble is then expressed in the time domain as:
 (10)

In
order to reconstitute y(t) output signal, we have combined xj(t) signals by
two different methods:
 Minimization method (expression given in paragraph 2.1).
 Square root of xj(t)product method:
 (11)

3. Wavelets Transform (4).
The frequency diverse ensemble with constant relative bandwidth may also
be obtained through the continuous wavelet transform (CWT). As widely
documented, wavelet has generated much interest in various applications such
as speech coding, pitch detection, image compression, multiresolution analysis
and modeling and estimation of multiscale processes.
3.1. Continuous wavelet transform
The continuous wavelet transform decomposes signal x(t) in a sum of
elementary contributions called wavelets which well localized both in time and
frequency domain. These wavelets are obtained by dilations ( or compressions)
and translations from an original wavelet (analyzing wavelet) y (t):
 (12)

Where variables a and b are
simultaneously the dilatation and the translation parameters.
With
3.2. Discrete wavelet transform
Using discrete wavelet transform, we can apply the same algorithm given by
SSP in order to improve the detection probability of defects and enhance
signal to noise ratio. This transform defined by Debauchies in 1988 is given
by:
where y _{m,n}(t) constitute an
orthonormals functions family.
The discrete wavelet transform of analogue
temporal signal is given by :
 (13)

Where W_{m,n} are details
parameters.
The reconstruction of signal x(t) is expressed (inverse
transform) :
 (14)

Experiments and results
 In order to apply Split spectrum processing and wavelets methods, we
have chosen a very absorbing ultrasonic material sample. We can see in this
signal, an echo with coherent noise between 2 and 4 microseconds, the
results are displayed graphically and discussed.
 In figures 4 and 5, we have applied constant bandwidth algorithm in
order to enhance signal to noise ratio. With theirs methods (minimization
and square root of product), we can confirm that give a good signal to noise
ratio.
 In figures 6 and 7, we have applied Q constant algorithm on the same
signal and a simulated signal. We have obtained a better result.
 Continuous wavelets are applied also, figure 8 shows results given by
this tool. Image illustrated by figure 9, demonstrates energy concentration
at the same echo position.
 Finally, in figure 10 we have tried to apply discrete wavelet on the
same signal, we can say that we have obtained a good detection of defect
echo but we have to investigate in this field in order to enhance signal to
noise ratio.
Fig 1: Implementation of Split Spectrum Processing 
Fig 4: b constant SSP minimisation method.

Fig 5: b constant SSP by square root of product method. 
Fig 6: Simulated signal.Q constant SSP square root of product method .

Fig 7: Q constant SSP. 
Fig 8: Continuous wavelet Transform

Fig 9: Calculation and drawing of CW coefficients. 
Fig 10: Discret Wavelet Transform. 
References :
 Paradis, L. Development of methods and a device of signal processing
adapted to NDT by ultrasonic waves, Thesis of Doctor Engineer, INP
Grenoble, (1983).
 Drai, R. Khelil, M. & Benchaala, A.
"Elaboration of some signal
processing algorithms in ultrasonic techniques : Application to materials
Ndt.". Ultrasonics, Vol.38 (18)2000, pp.503507  Ed. elsevier.
 Bilgutay, N. M., Newhouse, V.L., and Furgason, E.S. "Flaw visibility
enhancement by split spectrum processing technique". Ultrasonics
symposium. (1981), 878883.
 Rashmi, M., Bilgutay N. M. and Kagan Kaya, O. "Detection of ultrasonic
anomaly signals using wavelet decomposition." Materials evaluation (Nov.
1997), 12741279.