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ARTMAP NETWORK AND WAVELET ANALYSIS FOR FLAWS
CHARACTERIZATION
M. C. Moisen1, 2, H. Benítez1, L. Medina*1, E. Moreno3, G. González4, and L. Leija4
1 DISCA-IIMAS-UNAM, México D. F.; México 2 UAG, Acapulco, México, 3 ICIMAF, La
Habana, Cuba, 4 CINVESTAV, México D. F:, México
Abstract: Ultrasonic pulse-echo technique has been successfully used in a non-destructive testing
of materials. This method aims to characterize the propagation path and/or to determine the
physical properties of reflectors in terms of their location, size, orientation, and porosity. To
perform ultrasonic non-destructive evaluation (NDE), an ultrasonic pulsed wave is transmitted
into the materials using a transmitting/receiving transducer. The spectral analysis of the
backscattered echoes has been widely used for flaws detection, frequency-shift estimation, and
dispersive echoes characterisation. An innovative methodology is presented in this paper, in order
to characterise flaws within the tested material
A pattern recognition technique based on ARTMAP network and wavelet transform is used as a
digital processing tool that allows the geometry of flaws being determined. This technique
consists of two non-supervised neural networks named ART2 (Adaptive Resonance Theory) and
the Mexican hat wavelet transform.
An aluminium block with three man-made defects of circular geometries was scanned, by moving
a single ultrasonic transducer along two perpendicular paths, producing two reflectivity maps
containing the flaws information. The signal processing method proposed here used the received
signals as follows: The total set of signals was split into two subsets, depending on the scanning
path. The 10% of each subset was used to train an ART2 network, via the spectral information
produced by the Mexican hat wavelet and the rest of them to validate the system. The ARTMAP
network build a map field, since flaws are present in both axes, map field reproduced the flaws
contour, based on the proper selection of vigilance and learning parameters.
Introduction: Ultrasonic flaw detection is an important technique to assure the quality of
materials non-destructively. The goal for ultrasonic inspection is the detection, location and
classification of internal flaws and defects. However, the detection capability is often limited by
the interference noise produced by scatterers randomly distributed throughout the material.
Spectral analysis is often adopted since the noise due to grain scattering exhibits variability in
time domain.
Neural networks are well suited to signal classification in instrumentation. They have the ability
to generalise and produce a result on the basis of incomplete data. For a neural network to reliably
classify defects the training database must contain sufficient of each type of defect for the training
operation to be effective. Where the type of defect is initially unknown it may also be possible to
use automatic pattern classification and a self-organising network to generate the appropriate
output states [1].
ARTMAP is a class of neural network architecture that perform incremental supervised learning
of recognition categories and multidimensional maps in response to input vectors presented in
arbitrary order [2].
ART stands for Adaptive Resonance Theory and was introduced by Grossberg in 1976. The main
feature of all ART systems is a pattern matching process that compares the current input with
selected learned category representation. ART is capable of developing stable clusters in response
to arbitrary sequences of input patterns by self-organisation. ARTMAP extends the ART design
to include both supervised and unsupervised learning. In ARTMAP, the chosen ART categories
learn to make predictions in the form of mappings to output classes. Minimax learning rule
enables the fuzzy ARTMAP system to conjointly minimise predictive error and maximise code
compression or predictive generalisation.
ARTMAP [2] network has as main characteristic to perform incremental learning of recognition
categories and multidimensional maps. This network is a supervised neural network associated to
vector categories in order to construct a map. Two kinds of vectors are used, first vector is related
to first ART network (ART2A) and it is identified as unknown vector. Second vector is related to
second ART network (ART2B) and it is identified as predicted vector. Both ART2 networks
perform a matching procedure in order to construct a map of those similarities between selected
vectors.
The structure of this neural network consists of two ART2 networks [3]. Each ART2 network is
independent in principle, although, first network modifies its vigilance parameter according to
certain behaviour from MAP field.
Both ART2 networks follow the approach presented by Frank et al. (1998) [4]. This scheme is
shown in Fig. 1.
Output Vector
1 2 3 4 n
Input Vector, Neurons
Array
W
W
W W
W
W
W
W
W
W
1 2 3 4 5
Figure 1. ART2 Network
The idea is to identify already classified patterns and categorize new patterns. This network is
divided into two stages: a) bottom up (input-output) competitive learning and b) top-down
(output-input) learning. The network stores patterns as sets of weights assigned to the paths
connecting the input units to each of the output units. Presentation of an input vector causes the
output units to be activated, the amount of activation depending on the similarity between the
input vector and the stored pattern. Finding the nearest neighbour is simply a matter of deciding
which output unit has been activated the most. The weights that connect each output unit to the
input units represent the typical pattern of the class to which the output unit belongs. The weights
that connect the input units to each output unit represent the same pattern, except that their values
are normalised. The networks also have a mechanism for adding new category units to the output
layer. This process is controlled by two parameters: the vigilance parameter and the learning
parameter. The vigilance parameter, ρ, specifies how similar de input pattern is to be classified as
belonging to the same category, and the learning parameter, η, controls the step size for weight
adjustments.
The current input of the network is stated as A. This is normalized using the Euclidian media
defined by
A
A
A
I
=
=
m
∑
i
1
=
a
2
i (1)
where am is the mth element of A. The new generated vector I is used to perform another vector
named as t based on
t
∑
j i
w
=
i
m
1
=
i
ij (2)
where is an element of weight matrix generated by previous pattern classification.
ij
w
t
From element, a new vector is performed, stated as T. This vector represents the interaction
between the already known weight matrix and the input vector. The maximum element from
current t becomes the winner for this input vector then the stage bottom-up is completed. The
maximum value of current t is compared against to vigilance parameter ρ in order to determine if
this current minimum value is closed to vigilance parameter. If this it so, the related winning
vector W
j
j is declared as representative pattern of the input A. Afterwards, Wj is modified by
new
J W
I
( ) old
+
()= 1 (3)
W η
η -
J
where η is defined as learning parameter.
Alternatively, if ρ
≤ tJ then a new pattern has been identified. Then a new vector Wj is
concatenated to weight matrix. This new vector is the current input vector I.
The selected network (ARTMAP Network) has the peculiarity of map field construction that
represents the main characteristics of any pattern combination. This algorithm consists of two
ART2A networks integrated to a map field as shown in Fig. 2.
MAP
Field A Field B
Match
Tracking
Input Vector Target Vector
ART2AA
ART2AB
Figure 2. Structural construction of ARTMAP Network
Since the algorithm performed by each ART2 network has been defined, it is important to define
how the map field is build. In this case both output vectors (from each ART2 network), named as
ya and yb respectively, are send to map field. In there, the index of the winner neuron from first
neural network is considered in order to select the respective vector from the related weight
matrix from map field. Once the weight vector is selected, it is compared against output vector
(yb) from ART2B network. There are four possible cases with relation to map field selection.
x
ab
-
=
∧
Jth
w
y
b
w
ab
J
y
b
0
ab
J
Jth
y
active
are
from
element
and
from
element
If
Jth
y
active
not
is
from
element
and
active
is
from
element
If
Jth
Jth
y
a
a
a
Jth
Jth
y
active
is
from
element
and
active
not
is
from
element
If
a
Jth
y
y
b
b
y
b
y
b
active
not
are
from
element
and
from
element
If
(4)
If
b
ab
ab y
x ρ
< (5)
then ρa is increased until it is slightly larger than
∧ I
w
I
1
-
a
J (6)
where Wab is defined dimensional correct with respect to vectors ya and yb. This matrix (Wab) is
initially declared by 1's and is modified according to xab results.
The ART2A networks had been trained with time-scale information from the received signals.
The time-scale process is based on wavelet analysis.
Wavelet analysis refers to a collection of methods that have found increasing use in signals
processing, image analysis, and data compression.
The wavelet transformation of a time varying signal x(t) consists of computing coefficients that
are inner products of x(t) against a family of "wavelets". These wavelets ψa,b(t) are labelled by
scale and time location parameters a and b. In continuous wavelet transform, the wavelet
corresponding the scale a and time location b is
1
()
t
b
ψa ψ
b
t
-
=
, (7)
a
a
where ψa,b(t) is the mother wavelet, which can be thought as a bandpass function. The continuous
wavelet transform (CWT) is given by [5]
( ) ( ) ( )
∫= dt
t
t
x
b
a
CWT b
a
x
*
,
, ψ (8)
where * stands for complex conjugation.
Wavelet series (WS) coefficients are sampled CWT coefficients. Time remains continuous but
time scale parameters are sampled on a "dyadic" grid in the time-scale plane (b,a). A usual
definition is
CWT
C j
j k
b
a
x
= =
Z
k
j
= ,
for
k
j ∈
, (9)
2
,
2
k
j
( ) ( )
t
-
j
=2 2
2
-
j
k
t
-
ψ, ψ (10)
the wavelets are, in this case,
and the original signal can be recovered though the following formula
() ( )
=∑∑
t
x ,
Z
j Z
k
∈∈
, ~
k
Cj t
ψ (11)
k
j
where ( )
t
~
ψ are also of the form of ψ j,k(t)
A simple example of wavelet with infinite support is the so-called Mexican hat, defined by the
second derivative of a Gaussian function as
k
j,
() () ()
t
2 2
exp
2
-
t
2
-
=
d
2
t 0
exp
1 ψ
ψ =
dt
2
() ( )
-
t
2
,
1
t
-
= (12)
This wavelet has excellent localisation in time and frequency domains and clearly satisfies the
admissibility condition. [6].
Results: All experiments were carried out with a Hydrophone scanning system (Specialty
Engineering Associates SEA, CA, USA), two Personal computers (Pentium II, 128 RAM), and a
digital oscilloscope (TDS-340 Tektronix, Oregon, USA). This system is able to control a motor to
move the ultrasonic transducer along the x-axis, y-axis and z-axis with a 10µm step. The system
can also store the waveforms, calculate the parameters and display a graphical representation of
the experimental data.
In a typical experiment, the ultrasonic transducer and the phantom are immersed in a water tank
(see Fig. 3), then the transducer is excited producing a pulse, the computer-controlled motor
moves the transducer point by point, and an oscilloscope records the corresponding signal from
each point and stores it. The transmission and triggering of the ultrasonic pulse of the transducer
were controlled via a pulse-eco card MATEC SR9000 (Matec Instrument Companies, MA,
USA).
The circular Krautkrammer (CR-RHP, GAMMA, 2.25X.50, BNC) ultrasonic transducer able to
transmit a pulse at 2.25 MHz has been used. The phantom is an aluminium block of 70x70x40
mm3, with three man-made circular flaws diagonally located.
POSITIONING
SYSTEM
(xyz)
COMPUTER
2
COMPUTER
1
ULTRASONIC
PULSER
x
y
PREAMPLIFIER
WATER TANK
DIGITAL
OSCILLOSCOPE
Figure 3. Experimental Setup
The proposed ARTMAP architecture was applied to simulated and real data. The simulation of
received signals and the ARTMAP algorithm had been developed on MATLAB platform. The
ARTMAP algorithm was tested when the ART2AA and ART2AB networks were trained with and
without wavelet information.
In order to test the ARTMAP network algorithm, simulated signals were used. Those signals with
additive white noise represent the scanned medium along x and y-axis, where three point-in-
homogeneities are diagonally located. The received signals were split into two different sets: the
first set is related to the x-axis scanning direction and the second to the y-direction, as shown in
Figure 4.
(a) (b)
Figure 4 Simulated received signals: a) along x-axis and b) along y-axis.
The ARTMAP algorithm was first applied to the normalised (see eq. 1) received signals in order
that ART2AA and ART2AB patterns were computed and the map image produced as shown in
Figure 5. The learning and vigilance parameters values are shown in Table 1
When the signals are wavelet transformed using the Mexican hat mother wavelet (eq. 12) and
normalised, the output patterns of ART2AA and ART2AB and the autoregressive map are shown
in Figure 6.
The main differences of ARTMAP outputs when the network is trained with and without wavelet
analysis are: a) the noisy patterns in Figures 5a and 5b are cleared when Mexican hat wavelet
transform is included in the digital process (see Figures 6a and 6b), and b) the vigilance
parameter of ART2AB is slightly diminished, reducing the number of patterns in the wavelet-
ARTMAP network (see Table 1).
The same digital process was applied to real data. Two perpendicular B-scans were made
acquiring two sets of received signals as shown in Figure 7. Each signal was wavelet transformed
and normalised to compute the input vector of each ART2A networks. Those vectors generate the
patterns that produce the map of similarity among them as shown in Figure 8.
Since the real data is quite noisy, due to reflections coming from in-homogeneities, bottom of
water tank, impurities, among others, the number of patterns in ART2AA and ART2AB is quite
large, compared to the patterns produced when simulated data is used in the digital process. Also
the vigilance and learning parameters are varied as shown in Table 1.
Figure 5. Patterns and images of ARTMAP process: a) ART2AA, b) ART2AB, c) contour, and d)
image of xab.
Figure 6. Patterns and images produced by ARTMAP-wavelet process: a) ART2AA, b) ART2AB,
c) contour, and d) image of xab.
Discussion: Present results show how this composite algorithm can overcome noise presence
inherent to those processed signals. In fact, there are several variables to be considered such as
the selection of the mother wavelet, the vigilance and learning parameters and the structure of the
network itself.
It has found, on simulation and experimental basis, that Mexican hat wavelet presents suitable
results respective to the noise inherent in the studied signals. Figure 5c and Figure 6c depicted
clearly the intersections of selected patterns from ART2A networks. It is important to highlight
that this intersections are defined as part of the construction of the map within the ARTMAP
network. This map does not produce those intersections because the spatial relationship of the
input signals, it is constructed based on similar locations of the patterns.
Figure 7. B-scan experimental data: (a) along x-axis and b) along y-axis
Figure 8. ARTMAP output for real data: a) ART2AA patterns, b) ART2AB patterns, c) contour
and d) image of the digital process result.
(a) (b)
Parameter
(a)
(b)
(c)
ρa
0.800
0.800
0.650
ηa
0.750
0.750
0.751
ρb
0.800
0.770
0.872
ηb
0.750
0.750
0.750
ρab
0.750
0.790
0.700
Table 1. ARTMAP parameters values when normalised input vectors are: a) raw signals and b)
normalised wavelet transformed signals.
Conclusions: This paper has presented a novel approach for non-destructive testing based on a
combined algorithm of wavelet transform and ARTMAP network. The autoregressive map is
built considering the following: a) the orthogonal characteristic of the two B-scan, and b) the
selected neural network that has the advantage of map construction by the intersection of
common patterns.
When simulated signals with additive white noise are used as input vector of the ART2A
networks the number of pattern due to noise is reduced when the signals are wavelet transformed,
however the resulting map is not clearly affected. However if real data is the input vector the
number of patterns produced by the ART2A networks is drastically diminished when Mexican
hat is applied to the received echoes. Even though that this number is larger than 2000 for the
ART2AA case. It can be reduced, therefore the time consuming process, if the echoes coming
from the faces and bottom of the phantom are neglected.
This technique has presented not only flaw location it has produced flaw characterisation as a
result of map construction. This may enhanced the idea of multidimensional pattern recognition.
Further studies are pursued in terms of a NDT autonomous procedure where the ARTMAP
network can separate several types of flaws as well as determine certain geometric characteristics
of them. Alternatively, further work is pursued in order to incorporate wavelet decomposition
characteristics into ARTMAP learning procedure as well as map construction.
References:
[1] Margrave F. W., Rigas K., Bradley D. A., Barrowcliffe P., "The Use of Neural Network in
Ultrasonic Flaw Detection", Measurement 25, pp. 143-154, 1999.
[2] Carpenter G. A., Grossberg S., Markuzon N., Reynolds J. H., Rosen D. B., "Fuzzy ARTMAP:
A Neural Network Architecture for Incremental Supervised Learning of Analog
Multidimensional Maps", IEEE Trans. Neural Network 3, pp. 698-713, 1992.
[3] Carpenter G. A., Grossberg S., "The ART of Adaptive Pattern Recognition by a Self-
Orginizing Neural Network", IEEE Computer 21, pp. 77-88, 1988.
[4] Frank T., Kraiss K. F., Kuhlen T., "Comparative Analysis of Fuzzy ART and ART-2A
Network Clustering Performance", IEEE Trans. Neural Network 9, pp. 544-559, 1998.
[5] Akay M., "Time Frequency and Wavelets in Biomedical Signal Processing", IEEE Inc., New
York, 1998
[6] Debnath L., Wavelet transforms & their applications", Birkhauser, Boston 2002.
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