Objective needs of development of different technical areas are the reason for creation of new constructional materials with high durability and high elastic coefficient. Using of composites on polymer basis has allowed rapid decreasing of articles' weight. The leading place by volume of manufacturing in the world, currently, belongs to carbon fiber composites, due to, in the first rate, high mechanical properties of the fibers and their comparably low cost.
High technology of construction of composite materials combines with high sensibility to technological parameter deviations. The construction elements are mostly made according to those technological schemes which lead to appearing of initial stresses inside the material. Often their level reaches 50-60% out of destructive ones. It is natural for the structure of the composite to have pores, microcracks of internal borders of phase division, which are, as a rule, the centers of defect's birth and development.
The capability of carbon fiber to conduct electrical current enables using the eddy current method for composites, which turned out to be useful for testing of metal objects. But there are some problems, specific for the composite, connected with a comparatively small value of its specific electrical conductivity, non-constant volume conductivity of the material, presence of complex periodical structure with distortions, complex configuration and presence of specific defects of solidity and also due to considerable roughness of the surface.
Modulation impulses of the most widespread and dangerous defects of solidity of composites, such as cracks obtained at scanning of a product surface with an eddy current transformer, are comparable in amplitude and width with drawback impulses, which are created because of inclinations of the eddy current transformer on surface's roughs. Besides, noise is added to the modulation impulse. The high-frequency noise is mostly caused by roughness of the surface and low-frequency noise is due to changing of volume and surface conductivity of the composite.
Investigations of metric characters of roughness of carbon fiber composites with a different type of forming tissue, as well as an investigation of eddy current transformer signal sequences, obtained via scanning a non-defective surface, showed that high-frequency noise was completely adequate to the model of white gaussian noise. At this point, the mechanism of mixing the signal with high-frequency noise as well as with low-frequency noise is mostly the additive one.
The modulation crack impulse is pretty well described by bell-shaped gaussian curve, while the signal of inclination of the eddy current transformer (a drawback) is of a parabolic character.
The threshold of device sensibility for defectoscopy and defectometrology of articles has been constantly decreasing. Nowadays, it is on the level of 0,1-0,2mm in surface crack's depth.
Numerous experiments, carried out by us, show that the amplitude of the false impulse (a drawback) in the most cases is comparable and exceeds the amplitude of the defect modulation impulse. The width of the crack modulation impulse in the whole is determined by 2 factors: the 1st, it is radial measurements of the area localization of the eddy current transformer probe field; the 2nd, it is a value of the angle between a scanning trajectory and the plane of defect symmetry. The width of the false impulse can be changed occasionally in a quite wide range. It can be both wider and narrower than the defect modulation impulse.
Today, to lessen the influence of the gap and the inclination of the eddy current initial transformers the most often phase and amplitude-phase method are used, based upon the idea that "allotment" lines of the eddy current transformers on the complex plane of inserted resistances or voltages on a definite area are close to straight lines. However, the diapason of tuning is not large and does not satisfy the demands of the control of composite materials, surfaces of which are characterized by considerable level of roughness.
It is supposed to use the next two methods for solving the task of defect modulation impulse identification.
The first method is based on the analysis of impulse's form. For this, the points of the impulse start and maximum are connected with a virtual straight line. Further, we analyze discretes obtained along a scanning trajectory, counting the amount of points lying higher or lower than the virtual straight line. Ratio of, e.g., the number of points located lower than the line to the whole amount of points, gives likelihood that the investigated signal is a defect modulation impulse. The situation here dramatically deteriorates with a level of noise rises, when it becomes difficult to define the initial and the maximum points of the impulse. For solving this problem, algorithms of linear and non-linear smoothing are used in the vaccinates of the fulcrums of the virtual line.
The results of identification of noised signals of the defect and the drawback, obtained by using this method, is shown in the table 1. The results were averaged by 100 experiments.
| Noise level (%) | Likelihood of identification
|
| For defect signals
| For drawback signals
|
| 0
| 100
| 100
|
| 1
| 100
| 100
|
| 5
| 99
| 99
|
| 7
| 91
| 96
|
| 10
| 78
| 93
|
| 15
| 65
| 80
|
| Table 1: Likelihood of identification of drawback and defect impulses at different noise levels. |
According to the second method, we choose the ideal signal of the 1st type (bell-shaped gaussian signal) as a test signal. Changing signal's amplitude with a step 0,1 in the range 0,3-1,5 and its width with the same step in the range 0,7-4, estimate root mean square deviation of the test signal from the investigated one and memorize the minimum from obtained values. This value is checked on belonging to the one out of two known, estimated by results of preliminary experiments, diapasons that corresponds to the signal of a drawback and a defect accordingly.
When making up such a database for pairs of diapasons, noise levels should be defined so that every pair of values of root mean square deviation of test signal from the defect signal and the drawback signal corresponds to the certain noise level. The raising of noise level can lead to the overlapping of diapasons of a pair, and, as result, to the errors of identification process.
Table 2 shows averaged by 100 experiments values of least root mean square deviations of the test signal from the defect and drawback signals at different levels of white gaussian noise. In the table as the level of noise, values of root mean square deviation of noise for selection N=100 values, averaged by 100 selections are shown. The width of impulses of a surface crack and a drawback is chosen to be the same and it equals to 50 points alone the scanning trajectory. At the diameter of the control spot of the eddy current transformer equaled 2mm this corresponds to the width of the defect modulation impulses equaled approximately 4mm.
| Noise level (%)
| For defect signals
| For drawback signals
|
| 5
| 0.05
| 0.14
|
| 10
| 0.09
| 0.17
|
| 15
| 0.14
| 0.20
|
| 20
| 0.19
| 0.236
|
| Table 2: Averaged values of minimum root mean square deviations at different noise levels |
For more qualitative identification of noised signals artificial neural networks were used. Comparative analysis of topologies and algorithms of multilayer neural networks showed that the most suitable for this task is using a "back propagation" paradigm. In this case, the inputs of the net's neurons either plug to the output of the preceded layer or come from outside. The activation function takes the form:
z = 1/1(1 + e-y)
When teaching the net it is surmised that for every input vector there exists, coupled to it, aimed vector, defining required output. Before the inception of teaching, small initial values, randomly chosen in the range from 0 to1, are assumed to all weights of the net's neurons. During the teaching next operations are performed:
- Give the next vector, represented the noised signal, on the input of the net. Estimate the output signal of the net:
| (1) |
where Xk and Zk are input and output layer vectors accordingly and Wk - is the matrix of weights.
Applying equation (1) sequentially to the every layer, receive:
where M - the number of layers in the net.
| (2) |
- Estimate the difference between the received signal and the required one, which forms when the aimed vector is given.
Take a look at the process of teaching of the connection weight of the neuron p in the hidden (i.e. internal) layer j with the neuron q in the output layer k. The output of q neuron of the output layer k, subtracted from the aimed vector D, gives the error signal D. It is multiplied by the first derivative of the squeezing function:
that was estimated for this neuron of k -layer. Thus, get:
- After that s is mult
iplied by zpj of p neuron, that lies in the hidden j layer,
| (3) |
for which the connection weight is analyzed. This product, in its turn, is multiplied by the learning rate coefficient η (usually from 0.01 to 1) and the result is added to the weight:
| (4) |
| (5) |
where wpq,k(n) - the value of connection weight between p neuron in the hidden layer to q neuron in the output layer, on the n step (before the correction applies); wpq,k(n+1) - the value of connection weight on n+1th step (after the correction applies).
That is how the third stage - correction of the network's weights with the aim of minimizing the net error is fulfilled. The same to (4) ,(5) ways, weights for every neuron in the hidden layers are corrected. The bias of the activation function was made via inculcation of the neuron bias.
Carried out experiments showed that the most rationally is using a 3-layer network with 1 neuron in the output layer. The amount of inputs of every neurons in the input layer is accepted to be equal to 50, according to the amount of points per length of the defect modulation signal.
Configurations of the 3-layer net, that were tested, is shown in the table 3. The amount of operations that were needed to successfully teach the net (i.e. the amount of cycles of forward and backward propagation) is also shown here. The teaching was stopped if changing of every weight in the net at the given iteration was less than S=10-4.
The net was being taught on 30 test signals of defects with different noise levels within the diapason of the value of the root mean square deviation up to 20% and on 30 signals of drawbacks with tantamount noising. The net's error was defined by averaging through all signals. Table 3 shows these errors, additionally averaged by 10 experiments for every net configuration and a given noise level.
| Configuration
| Amount of operation to teach | The net error
|
| 7%
| 10%
| 15%
| 20%
|
| 1x1x1
| 135569
| 0.053
| 0.071
| 0.087
| 0.160
|
| 2x1x1
| 107602
| 0.044
| 0.056
| 0.069
| 0.123
|
| 3x2x1
| 98103
| 0.038
| 0.045
| 0.065
| 0.102
|
| 5x3x1
| 88717
| 0.032
| 0.038
| 0.059
| 0.094
|
| 10x5x1
| 62913
| 0.028
| 0.032
| 0.056
| 0.084
|
| 10x7x1
| 62261
| 0.025
| 0.028
| 0.049
| 0.065
|
| 15x5x1
| 56135
| 0.023
| 0.027
| 0.046
| 0.069
|
| 20x10x1
| 43662
| 0.019
| 0.025
| 0.039
| 0.058
|
| Table 3: The results of investigating the net with different configurations |
In detail, proceeding from the satisfactory error, saving quite high speed of work, the net with 10x5x1 configuration was investigated. The program corresponding to all demands of neural network modeling was created to run with the value of S=10-6. The time of teaching on earlier used test signals was 90 minutes with Pentium MMX 200MHz. The results of the net's work are presented in table 4. While teaching noised test signals of defects and drawbacks with the whole and the half of amplitude in the amount of 120 were introduced to the net. The likelihood of signal recognition was averaged for both types of signals.
| Noise(%)
| Likelihood of recognition
|
| 0
| =100
|
| 1
| ~100
|
| 5
| ~99
|
| 7
| ~99
|
| 10
| ~98
|
| 20
| ~97
|
| 50
| ~85
|
| 100
| ~72
|
| Table 4: The likelihood of signal recognition by neural network with configuration 10x5x1. |
As it can be seen from the applied table, the likelihood of recognition of defect and drawback signals by neural network is much higher than that in the presented earlier algorithms, especially at high values of root mean square deviation of the noise.
