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ULTRASONIC NDT FOR FLAWS CHARACTERIZATION USING ARTMAP NETWORK AND WAVELET ANALYSIS Abstract An innovative pattern recognition technique based on ARTMAP network and wavelet transform for flaws characterization is presented. This technique consists of two non-supervised neural networks named ART2 (Adaptive Resonance Theory) trained with the time-scale information given by the Mexican hat wavelet. The tested material with well-known defects was ultrasonically scanned along two perpendicular axes, producing two maps of reflectivity. The perpendicular information given by this scanning process was then used to get the time-scale information and network training. The ARTMAP network builds a map field, using the perpendicular information of the scanning processes producing a flaw contour, based on the proper selection of vigilance and learning parameters. Simulated and experimental results are presented. Keywords. Ultrasonic Non Destructive Testing, ARTMAP, Flaws Characterization 1. 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, which are randomly distributed throughout the material. Spectral analysis is usually adopted due to noise produced by grain scattering exhibits variability in the time domain. Neural networks are well suited to signal classification within instrumentation. They have the ability to generalize and produce a result on the basis of incomplete data. For a neural network to reliably classify defects, the training database must contain enough information of each type of defect. If the type of defect is unknown it might also be possible to use automatic pattern classification and a self-organizing network to generate the appropriate output states [1]. The main objective of this paper is to present an innovative algorithm for flaws characterization. The composite algorithm uses ARTMAP network trained with time-scale information of the ultrasonically received signals. The ultrasonic signals were taken by scanning the tested material along two perpendicular axes. 2. Theory ARTMAP is a type of neural network architecture that performs 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 [3, 4]. The main feature of all ART systems is a matching pattern 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-organization. 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. The ARTMAP [2] network has as its 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, the first vector is related to the first ART network (ARTA) and it is identified as the unknown vector. The second vector is related to a second ART network (ARTB) and it is identified as the predicted vector. Both ART networks perform a matching procedure in order to construct a map of those similarities between the selected vectors. The structure of this neural network consists of two ART networks [5]. Each ART network is independent in principle although the first network modifies its vigilance parameter according to certain behavior from MapField. 2.1 ART Neural Network The ART network’s general algorithm is sketched in Fig. 1. This network is based on the Frank [6] approach, and it considers three main stages: a) pre-processing, b) search and, c) adaptation. a) The pre-processing stage is the creation of an input pattern
r I , the initial prototypes or
categories W, and the values of vigilance (ρ) , learning (β), and choice (α) parameters. The input vector
r I contains information of the phenomenon to be studied
r A , related by
r I =
r A r A
(1)
The prototypes W can be initialized with random or constant values in the range of [0, 1]. The vigilance parameter ρ is the minimum degree of similitude between the input vector
r I , and any defined category
r W j that belongs to W.
The learning rate β affects how quickly the algorithm makes changes, it is chosen to prevent categories
r W j from moving too fast and therefore destabilizing the learning
process. The choice parameter α∈[0,∞], defines the maximum depth of search for a fitting cluster by providing a floating point overflow. b) Search Stage, is an iterative stage that can be split into two different processes: i) the choice and ii) the matching. i) Choice: once the input vector is computed, it must compare to the already defined prototypes. This process is in charge of finding the optimum category, defined as the category similar to
r I respect to the fuzzy conjunction
ˆ I ∧
r W j = min Ii,Wij{ } (2)
where Ii and Wij are i-element of r I and
r W j .
The maximum value of the fuzzy conjunction corresponds to the high net activity TJ, where J is the position of the winning vector within W. ii) Matching process: if the degree of similarity between the input and any category is equal or larger than ρ, then the prototype J, is chosen to represent the cluster containing the input, and its says that the network attains resonance. If the degree of similarity is less than ρ, then another category must be selected and compare to
r I . If any prototype
or category does not reached the degree of similarity, then a r I must be added to W as
new prototype. The adaptation is the last stage in the algorithm, where the winning prototype has to be updated respect to the input pattern, by
r W J
new = βr I ∧
r W J
old( )+ 1− β( )r
W Jold (3)
2.2 ARTMAP: Classical Approach 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 adaptive resonance theory modules, ARTA and ARTB, both networks are linked via an inter-ART module, called MapField (see Fig. 2). The ARTA contains input vectors and ARTB input patterns, where the input patterns in ARTB are the correct prediction given the input in ARTA. In this case both output vectors (from each ART network), named as
r Y A and
r Y B of
binary values represent the presence or absence of each possible feature (winning categories). The index (J) of the winner neuron from ARTA is considered in order to select the respective vector from the related weight matrix WAB from MapField. Once the weight vector is selected, it is compared against output vector (
r Y B ) from ARTB
network. There are four possible cases with relation to MapField selection.
r X AB =
r Y B ∧
r W J
AB If r Y A =
r Y B =1
r W J
AB If r Y A =1 and
r Y B = 0
r Y B If
r Y A = 0 and
r Y B =1
r 0 otherwise
⎧
⎨
⎪ ⎪
⎩
⎪ ⎪
(4)
This process is called activation, where a pattern r X AB is generated. Once
r X AB is
generated it must be compared with the already defined categories in ARTB. At this stage two possibilities may arise: i) The degree of similitude between
r X AB and
r Y B is
less than ρAB, then the MapField must be updated with the new information carried by r X AB , and, ii) if the degree of similitude is larger than the allowed value, then the vigilance parameter ρA must be slightly varied in order to generate a new winning vector that may be similar to any category in ARTB. This process is known as the match tracking stage. This algorithm is shown in Fig. 3. 2.3 Wavelet Transform In the ultrasonic non-destructive characterization of materials case, the reflections from discontinuities appear in the A-scan as abrupt time localized changes resulting in time varying spectral characteristics. As the ultrasonic signal is modulated to the transducer central frequency, the transient signal is commonly limited in time and in frequency. Indeed, the defect echo contains information dealing with the material, the discontinuity and often, the microstructures that generate echoes randomly distributed in time. The performance of an ultrasonic flaw detection method is evaluated by the success of distinguishing the flaw echoes from those scattered by microstructures. The analysis and filtering process of a signal is often performed in the frequency domain, and the impulse response is usually decomposed in a sum of sinusoids, with varying frequencies, amplitudes and phases. The Fourier transform [7] has been widely used for this purpose, however the loss of time information is one of its drawbacks. The wavelet transform [8] (WT) has many characteristics that make it a suitable tool for ultrasonic signals analysis. Among these features are good time and scale (frequency) localization, high signals similarity (one can tailor the wavelet structure to the signal being analyzed), constant relative bandwidth (this allows an estimation of frequency
components with high resolution), and some cases orthogonality (critical for matching a unique basis element to a portion of the signal). A set of different wavelet kernels including Coiflets, Daubechies, and Symmlets [9] has been used in the analysis and synthesis of ultrasonic signals. The selection of the optimum mother wavelet has been made by an experimental study of several mother wavelets defined in MATLAB and the wavelet that produces a maximal concentration of energy in the time-scale plane has been selected to train the ART2 networks. 3. Methodology. The classical algorithm of ARTMAP has been explained in Section 2. The present approach varies from the classical method in the definition of the ARTB [10]. The classical algorithm constructs the map-field based on a known database included in the ARTB, while the present approach considers that the input vectors of the ART’s are unknown, the only information is that the input vector in ARTA has perpendicular information respect to the input vector in ARTB. Therefore the classical algorithms is varied in the evaluation of eq. (4) as follows:
r X AB =
r W AB =
r W J
A +r
W JB[ ]T
If r Y A =
r Y B =1
r W AB otherwise
⎧ ⎨ ⎪
⎩ ⎪ (5)
where T indicates the transpose of a vector. Only two possible cases are evaluated in the proposed algorithm. This new WAB matrix is composed by the intersection of both weight vectors (the Jth-vector of WA and WB). If no similitude between ARTA and ARTB activated patterns is given, then WAB is not modified. Then the match tracking process, that varies ρA to get a new winning vector, is carried out. The methodology used for flaws location and characterization is sketched in Fig. 4. Simulated and experimental signals with well-localized defects were used to train and to validate the networks as follows: i) Two sets of perpendicular B-scan signals were simulated and acquired, named as Face A and Face B. ii) A signal containing defect information was chosen in order to experimentally found the optimum wavelet transform. Several mother wavelets defined in MATLAB were applied to the signals, the selected mother wavelet is chosen based on the minimum energy spread in the time-scale plane. The number of levels is considered when the minimum power of the transformations is reached. iii) For each A-scan signal, wavelet transform was applied to compute the time-scale information, and the scaled-vector that contains the higher power is selected. iv) The selected scaled-vector is then Hilbert transformed and normalized (eq. (1)), producing input vector
r I .
v) The initial values of WA, WB, and WAB are 0.3 for all entries. The learning and vigilance parameters are summarized in Table 1. vi) Once
r I A ,
r I B , WA, WB, and WAB are defined, the algorithms (Fig. 1 and Fig. 3) are
computed and the MapField produced. 4. Experimental Setup 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. 5), then the transducer is excited producing a pulse, the computer controls the motor that 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 3.5 MHz has been used. The phantom is an aluminium block of 70x70x40 mm3, with three man-made circular flaws diagonally located. Experimental parameters are summarized in Table 1. 5. Results The proposed ARTMAP architecture was applied to simulated and experimental data. Where both, the simulation process and the ARTMAP algorithm had been developed on a MATLAB platform. The signals were simulated considering three point sources diagonally located, and they are “seen” by the “virtual transducer” along two perpendicular axes (x and y axis), as shown in Fig. 6. The parameters used to develop the simulation data are in Table 1. It is worth mentioning, that no attenuation effect has been considered. Once the received signals are produced, the mother wavelet must be determined. For that matter several defined wavelets were applied to a signal that contains an echo revealing the presence of a flaw. Fig. 7 shows some of the time-scale images of different mother wavelets, being the Mexican Hat wavelet output (Fig. 7d) the one that produces the minimum energy spread. Fig. 8 sketches the graphical process to construct the MapField, when the noisy signal is considered as the input vector
r A , with no defect information. When the ARTMAP
algorithm is applied to a signal that contains flaws information, the MapField is constructed based on the intersection of the ARTA and ARTB winning vectors as shown in Fig. 9. If only two vectors
r A are considered, a noisy vector (see Fig. 8a) and a signal
with an in-homogeneity (see Fig. 9a), the generated MapField is built with the noisy patterns and the patterns containing the defect position (see Fig. 10). When all the received signals are wavelet transformed and used as input information to the ARTMAP algorithm, considering the parameters values given in Table 2, the reconstructed image shows three regions of maximal energy, that coincide with the point targets locations (see Fig. 11). If no wavelet transform is applied to the simulated signal, the number of noisy pattern in ART networks is increased (see Figs. 12a and 12b), therefore the number of computational operations. The proposed algorithm of ARTMAP-wavelet has been validated by applying it to experimental data. The phantom was scanned along the x and y-axis, storing the acquired signals in two matrices; their images are shown in Fig. 13 (upper). Since the composite algorithm builts the map based on the intersection of these two matrices, the metric of both matrices has to be homologated considering the following: the scanning process done along any axes, has to take into account two measured distances: i) the motor step (∆d=0.22 mm), which is the distance between any two adjacent transducer position, and ii) the minimum distance acquired by the system, that
means the distance between any two adjacent samples (ds=0.03mm). When the scanning process is done along the x-axis, the above distances are ∆d in x-direction and ds in y-direction, while in the scanning process along y-axis the distance ∆d is in y-direction and ds in x-direction. Therefore, a sub-sampling process is needed so that the x and y-distances are equal, as shown in Fig. 13 (lower). The following step is to determine the mother wavelet. For that, a signal that contains defect information is used and several continuous mother wavelets were applied to it. Fig. 14 shows images of four different mother wavelets, where the Mexican Hat being the chosen one. Then all signals are wavelet transformed and normalized (eq. (1)), to produce the input vectors used by ARTA and ARTB. The ART and ARTMAP algorithms are applied to the time-scale signals, using the parameters given in Table 2. The patterns (see Figs. 15a and 15b) and their intersections are shown in Fig. 15. 6. Discussion and Conclusions A composite algorithm of wavelet transform and ARTMAP network for flaws characterization was presented. One of the main contributions of this work relies on the proposed ARTMAP algorithm. The classical algorithm builts the map based on known classifications, and compared the new information with the known one. The MapField, in the proposed algorithm, is built with the intersection between two perpendicular patterns, where non of them are known a priori. The ultrasonic signals has inherent noise information, coming from the grain of the material and echoes from the material walls, this could lead the ART networks to create several noisy patterns, for that matter the wavelet pre-processing stage is proposed. The wavelet transform allows the spectral information of the ultrasonic signals in time and frequency (scale) at the same time. The main advantages of this representation are: a) the pattern produced by noise inherent in the ultrasonic signals does not notoriously vary from one signal to other, and b) the information of energy at a specific time allowing the flaws position be determined. To test the composite algorithm, simulated signals with additive white noise and no attenuation were developed. The Mexican Hat wavelet transform of 10 levels was applied to the simulated signals, and the input vectors to the networks are the time-scale vectors of maximum energy. The noise in this kind of representations seems attenuated in respect to the energy concentrated at the flaws location. These attenuated noisy signals do not generate different patterns in the ART networks. Therefore, the computational time is reduced. This was proved when the simulated signals were not wavelet transformed, and the number of noisy patterns increased in the ART networks. The validation of the algorithm was done with experimental data. The MapField was built with the intersection of the generated patterns of the two perpendicular B-Scans. The ARTMAP output not only gives number, geometry and position of the defects, also this technique is able to diminish the echoes coming from corners, the might give the false information as shown Face B in Fig. 13. Acknowledgements The authors would like to thank the National Council of Science and Technology (CONACYT-31959A) and Autonomous National University of Mexico (PAPIIT-
IN105303, IN1072207), for their financial support. Also the authors are very grateful to Dr L. Leija and Dr. G. González of the Research Center of Advance Studies (CINVESTAV) for their technical support. 7. 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] Grossberg S., “Adaptive Pattern Classification and Universal Recording II. Feedback, Expectation, Olfaction and Illusions. Biological Cyberneticus 23, pp. 187-202, 1976. [4] Grossberg S., “ How does a Brain build a Cognitive Code?”, Psychological Review 87, pp. 1-51, 1980. [5] Carpenter G. A., Grossberg S., “The ART of Adaptive Pattern Recognition by a Self-Organizing Neural Network”, IEEE Computer 21, pp. 77-88, 1988. [6] 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. [7] Proakis J. G., Manolakis D. G., “Digital Signal Processing : Principles, Algorithms, and Applications”, MacMillan, New York, 1992. [8] Debnath L., Wavelet transforms & their applications”, Birkhauser, Boston 2002. [9] Meyer Y, “Wavelets Algorithms and Applications”, SIAM, 1993. [10] Moisen M. C., Benítez H., Medina L., Moreno E., González G., Leija L., “ARTMAP Network and Wavelet Analysis for Flaws Characterization”, 16th World Conference on Nondestructive Testing, Montreal, Canada, 2004.
Figures and Table Captions
T J( )= max T j( ): j =1,K,N{ }
r I ∧
r W Jr I
≥ ρ
r W J
new = βr I ∧
r W J
old( )+ 1− β( )r
W Jold
W = W,
r I [ ] Y J( )= 0
j = j +1 n
Preprocessing r I , W, α, ρ, β
j = N
r Y =
1 j = J0 j ≠ J
⎧ ⎨ ⎩
Choice
Match
Adaptation
y
n
y
T j( )=
r I ∧
r W j
α +r
W j
T J( )= max T j( ): j =1,K,N{ } T J( )= max T j( ): j =1,K,N{ }
r I ∧
r W Jr I
≥ ρ
r W J
new = βr I ∧
r W J
old( )+ 1− β( )r
W Jold
r W J
new = βr I ∧
r W J
old( )+ 1− β( )r
W Jold
W = W,
r I [ ]
W = W,r I [ ] Y J( )= 0Y J( )= 0
j = j +1 n
Preprocessing r I , W, α, ρ, β
j = N
r Y =
1 j = J0 j ≠ J
⎧ ⎨ ⎩
r Y =
1 j = J0 j ≠ J
⎧ ⎨ ⎩
Choice
Match
Adaptation
y
n
y
T j( )=
r I ∧
r W j
α +r
W j
T j( )=
r I ∧
r W j
α +r
W j
Figure 1. ART Algorithm
ARTB
MAPFIELD Field B
ARTA
Field A
Match
Tracking
Known PatternInput vector
ARTBARTB
MAPFIELD Field B
ARTAARTA
Field A
Match
Tracking
Known PatternInput vector
Figure 2. Classical ARTMAP Architecture
ARTA ARTB
Eq. (4)
r Y A
r Y B
ρA =
r I A ∧
r W J
A
r I A
r
W JAB =
r X J
AB
WAB, ρAB
r X J
AB
r Y B
< ρAB
y
n
Input
Activation
Match Tracking
MapField
Learning
Pattern Generation
ARTA ARTB
Eq. (4)
r Y A
r Y B
ρA =
r I A ∧
r W J
A
r I A
r
W JAB =
r X J
AB
WAB, ρAB
r X J
AB
r Y B
< ρAB
y
n
Input
Activation
Match Tracking
MapField
Learning
Pattern Generation
Figure 3. ARTMAP Algorithm
ARTA
MapField
ARTB
Input data
Wavelets Transform
Face A
j
. . .
M
123
Face B
1 2 j N...... 1 2 j N......
j
. . .
M
123
MatchTracking
r I B
r I A
r Y B
r Y A
ARTA
MapField
ARTB
Input data
Wavelets Transform
Face A
j
. . .
M
123j
. . .
M
123
Face B
1 2 j N......1 2 j N...... 1 2 j N......
1 2 j N......
j
. . .
M
123j
. . .
M
123
MatchTracking
r I B
r I A
r Y B
r Y A
Figure 4. Composite algorithm ARTMAP-wavelet
Ultrasonic Transducer 3.5 MHz
Ultrasonic Pulser
Osciloscope 100 MHZ
Ultrasonic Transducer 3.5 MHz
Ultrasonic Pulser
Osciloscope 100 MHZ
Ultrasonic Transducer 3.5 MHz
Ultrasonic Pulser
Osciloscope 100 MHZ
Figure 5. Experimental Setup
Figure 6. Simulated B-scan Signals: a) along x-axis and b) y-axis
Figure 7. Wavelet outputs from simulated signals
(a)
(b)
(c)
(d)
Face A Face B
(e)
(a)
(b)
(c)
(d)
Face A Face B
(e)
Figure 8. Proposed methodology applied to flawless simulated data. a) noisy signals, b) its wavelet transform, c) the input vector
r I , d) ARTs’ patterns, and e) MapField.
(a)
(b)
(c)
Face A Face B
(d)
(e)
(a)
(b)
(c)
Face A Face B
(d)
(e)
Figure 9. Proposed methodology applied to simulated data. a) noisy signals with a flaw, b) its wavelet transform, c) the input vector
r I , d) ARTs’ patterns, and e) MapField
(a)
Face A Face B
(c)
(a)
Face A Face B
(c)
Figure 10. Network output when flawless signal and signal with a flaw are the input vector to the net: a) ARTA output patterns, b) ARTB output, and c) MapField.
Figure 11. Composite algorithm output when all simulated signal are considered.
(a) (b)
(c)
(a) (b)
(c)
Figure 12. ARTMAP output when all signal are used, but the ARTs’ are not trained with time-scale information.
Subsampling
Face A Face B
Subsampling
Face A Face B
Figure 13. Experimental data (upper) and its sub-sampled version (lower)
Figure 14. Wavelet transform of the experimental data that contains an in-homogeneity
Figure 15. Flaws image reconstruction. Table 1. Parameters used in the simulated and experimental processes. Table 2. ARTMAP parameters values when normalized input vectors are: a) time-scale simulated signals, b) simulated raw signals and b) normalized wavelet transformed of experimental signals.
Parameters Simulation Process Experimental Process Carrier Frequency f 1.25 MHz 3.5 MHz Sampling Frequency fs 4.5 MHz 100 MHz Wavelength λ 1.2 mm 1.71 mm Velocity of Propagation c 1500 m/s 6000 m/s Motor Step ∆x 0.6 mm 0.22 mm Total Number of Samples N 80 1495 Wavelet Levels L 10 10 Table 1.
Parameter (a) (b) (c) ρA 0.800 0.800 0.650 βA 0.750 0.750 0.751 ρB 0.800 0.770 0.872 βB 0.750 0.750 0.750 ρAB 0.750 0.790 0.700
Table 2