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Flaw echo Location based on the Wavelet transform and Artificial Neural Network LIU Zhenqing Institute of Acoustics, Tongji University Shanghai 200092, P.R.China Contact

Abstract

This paper presents our research of locating an ultrasonic NDT flaw echo (determining the depth of flaw) of fiber reinforced composites using wavelet transforms and an artificial neural network. The depth information is extracted from a complex envelope of wavelet coefficients and two neural network methods - segmental mapping and continuous mapping are applied to locate the flaw echo. Wavelet transforms can provide joint time - frequency distribution with the multiresolution structure. In this paper, the orthonormal bases of compactly supported wavelets are constructed and the algorithm of fully sampling discrete wavelet transform, which is capable of extraction more information than conventional diadic sampling discrete wavelet transform, are established. Our ultrasonic NDT signals of fiber reinforced composites are processed by the fully sampling discrete wavelet transform. The results show that though the original flaw echo is not always significant in amplitude, the wavelet transform of flaw echo usually has larger wave amplitude - at least in one scale. So we use complex amplitude method to extract the position(depth) information of flaw echo. As the flaw echo complements are most significant in scale 4 and 5, we join the complex amplitude of the two scales into one dimensional signal to input the artificial neural network.
As to the artificial neural network, we employ the model of multilayer perception and use the back propagation(BP) algorithm to train it. We propose two methods to locate the flaw echo - segmental mapping and continuous mapping. In the segmental mapping, 3 neural nodes are set in the output layer to map the position of flaw echo to 8 segments and the correction rate reach 85.5%. While in the continuous mapping, only one neural node is set in the output layer to map the position of flaw echo to the corresponding continuous output value and the average prediction error is 5.1%.

1. Introduction

Fiber reinforced composites are finding an increasing use in the aerospace industry and ultrasonic nondestructive testing(NDT) of them has become necessary. Yet the conventional ultrasonic NDT methods do not work well because of some special characteristics of fiber reinforced composites such as high acoustic attenuation and high structure noise resulted from inhomogeneity. So it is necessary to employ signal processing approaches to process the detected signal. The fast Fourier transform(FFT) is the most commonly used signal processing technique. But it can only analyze signal in frequency range. In recent years, some joint time-frequency transform techniques are studied more and more intensively[1]. Among these, wavelet transform is the most popular one. It can perform joint time-frequency distribution under the principal of multiresolution analysis. Besides the above mentioned signal processing techniques, some artificial intelligence approaches, especially artificial neural network technique are playing more and more important roles in the field of signal processing. One of the feed forward neural networks - multilayer perceptron, is very suitable to act as classifier or predictor in most application of NDT signal processing [2-4].
In this paper, we combine wavelet transform and artificial neural network to locate the ultrasonic NDT flaw echo of fiber reinforced composites. To represent the signal more finely, we employ fully sampling discrete wavelet transform. Two special neural network methods - segmental mapping and continuous mapping are proposed to locate the flaw echo. Besides, We also propose an approach called complex amplitude method to extract depth information and to connect the wavelet transform and artificial neural network.

2. Wavelet transform and feature extraction

Suppose discrete signal x(n), n=1,2,...,N, then the algorithm of fully sampling discrete wavelet transform can be described as follows:

(1)

where, k is shift factor, g_j is orthonormal bases of compactly supported wavelets. g_j should be iterated as follows:

	(2)
	(3)

where, g[n] and h[n] are high pass and band pass filter series respectively, given independently and S.Mallat as multiresolution analysis theory[5].
It should be noted that, in conventional fast algorithm of discrete wavelet transform, the shift factor is 2^j k rather than k[6]. It gives diadic sampling results and thus usually cannot give us enough useful signal information. While in the fully sampling algorithm described by equation (1), to each scale j, the sampling rate maintain same with that of original signal x[n]. Thus the results contain maximum volume of useful information.
Two example of ultrasonic NDT signals detected from fiber reinforced composites and their fully sampling discrete wavelet transform are illustrated in figure 1. The original signal is detected by ultrasonic transducer with 7.5MHz central frequency and sampling rate is 50MHz.

Fig 1: wavelet transform and complex enveloge of two ultrasonic NDT signals

From figure 1 we can see that flaw echoes are usually reflected in wave amplitudes of some scale of wavelet transform, at least in one scale. So we use complex envelope method to extract wave amplitude of each scale as flaw depth feature. We get the complex envelope by taking the Hilbert transform with some computations in frequency range. Figure 1 also shows the complex envelops of each scale. We can see that the peak positions of complex envelope in some scales, especially in scale 4 and 5 have stable mapping relationship with the flaw echo position. So we join the complex envelope in scale 4 and 5 as input signal of artificial neural network. The input signals computed from figure 1 are shown in figure 2.

Fig 2: input signal of ANN relating with figure 1. A,B respectively

3. Artificial neural network methods

Multi-layer perceptron, which is one of the most popular feed forward networks, is employed as our model of artificial networks. Its architectural graph is shown in figure 3. The individual perceptrons in the network are called nodes or nets, every node in layer 1 is connected to every node in layer 1+1. Each neural net has the architecture as depicted in figure 4. In figure 4 w_ki(i=1,2,...,p) is the connection weight from input k to node i. The sigmoid function such as logistic function F(*) is usually applied as the nonlinear activation function[7]. While, in this paper, in order to accelerate convergence we replace logistic function by hyperbolic tangent function and have achieved good effect. The convergence time is shortened by about a factor of four. The Hyperbolic tangent function is shown in figure 5. The back propagation (BP) algorithm is used to train multi-layer perceptron[7].

Fig 3: architectural graph of multilayer perceptron

Fig 4: architectural graph of neural net

Fig 5: Hyperbolic tangent function

A multilayer perceptron trained with the BP algorithm may be viewed as a practical vehicle for performing a nonlinear input-output mapping of a general nature. In this paper, we propose the following specific methods - segmental mapping and continuous mapping to locate the flaw echo.

4. Experimental results

Segmental mapping
Here the multilayer perceptron works as classifier. The output layer has 3 nodes and therefore the multilayer perceptron has 8 target outputs, {-1,-1,-1}, {-1,-1,1}, {1,1,1}. At the same time each ultrasonic NDT signal is separated linearly into 8 segments. From head to end, the 8 segments connect with the 8 target outputs sequentially. The segment which contain the starting point of flaw echo is also marked. Therefore each signal is connected with one of the target outputs. We can see that this method can only locate the flaw echo segmentally, which is why it is called segmental mapping.
The multilayer perceptron has only one hidden layer with 20 neural nodes. The input layer has 150 nodes, which is same with the length of input signal. We have totally prepared 186 samples of ultrasonic NDT signal of fiber reinforced composites. 60 samples are randomly selected out to train the neural network. The left 126 samples are used to test the network. After 315 epochs of training, the mean-squared error reaches the stop criterion 3.0 × 10^-4 and the training is halted. The testing result is present in table 1.

Number of samples	correct	failure	probability of correct classification
126	108	17	85.7%
Table 1: result of segmental mapping

We can see from table 1 that the performance of segmental mapping is not very good. One of the reasons is that segmental mapping cannot locate flaw echo precisely. To avoid this shortcoming, we have developed another neural networks methods - continuous mapping.

Continuous mapping
The conventional application of multilayer perceptron, including segmental mapping, demand the target outputs lie in saturation area of nonlinear activation function of neural nets. And in most situations act then to be one of two value of activation function - 1 and -1. While continuous mapping permits the object values to be any continuous value between 1 and -1. It establishes linear mapping between neural network output and the start point of flaw echo. That is to say, it's let the neural network output value denote the depth of the flaw echo. No doubt that there is only one neural net in the output layer.
Before the use of multilayer perceptron, we first translate the flaw echo's start point of every signal linearly to the value between 1 and -1 and let it to be target output of that signal. We select the 60 samples to train the neural network. After 1157 epochs of training, the network converges to the same mean square value.
The test result is shown in table 2. The absolute error denote the absolute value of difference between actual output and target output. As the wide of output range is 2, we divide the absolute error by 2 to get the relative error.
From table 2 we can see that the average relative error reaches a very low value 5.1%. And the average errors of 90.5% samples are less than 10%. We conclude that this method performs better than segmental mapping.

number of samples	average error		maximum error		of the relative error within 10%
	absolute	relative	absolute	relative	number	percentage
126	0.102	5.1%	0.459	23%	114	90.5%
Table 2: result of continuous mapping

5. Conclusions

We have used discrete sampling wavelet transform and multilayer perceptron to determine the depth of flaw echo. A complex envelope method is successfully used to extract depth information as input signal of multilayer perceptron. We have also proposed two neural network methods -segmental mapping and continuous mapping to predict the depth of flaw echo. Experiment results have shown that the continuous mapping is the better method.

Acknowledgement

This research was supported by the National Science Foundation of China, grant No. 19574039

References

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