EUROCON 2007 The International Conference on “Computer as a Tool”
Warsaw, September 9-12
Thermographical Investigation of Crack Initiation Using Artificial Neural Networks M. Selek*, Ö. S. Şahin† and Ş. Kahramanlı* * Selcuk University, Technical Sciences Vocational High School, Konya, Turkey, e-mail:
[email protected] † Selcuk University, Department of Mechanical Engineering, Konya, Turkey, e-mail:
[email protected] * Selcuk University, Department of Computer Engineering, Konya, Turkey, e-mail:
[email protected] temperature profiles of the specimen under testing taken by thermal camera at 1Hz were digitalized and transferred to the image processing program through the graphical interface both of which we have developed in MATLAB 7.1 environments. The image processing program realizes the function of certain artificial neural network (ANN) that handles thermal images (TI) in one by one manner. It obtains the hottest, coldest and medium heat spots of the specimen for each TI. Using temperatures of these spots, we fit the curve demonstrating spot temperatures of the specimen at moment when given TI is taken. This curve allows us to obtain the temperatures of all spots of the specimen surface at corresponding moment. By handling obtained temperatures, we fix most probable crack regions of the specimen. At once, we capture these regions; we stop observing the specimen wholly and continue with only probable crack regions until the specimen is fractured.
Abstract—In this study, a thermographic infrared imaging system was used to detect the temperature rise of AISI37 steel specimen under reverse bending fatigue. Fatigue behavior of metals shows temperature profiles with three stages: an initial increase of the specimen mean temperature region, a constant (equilibrium) temperature region, an abrupt temperature increase region at end of which the specimen fails and its temperature falls instantly. In order to recognize critical third region, it is necessary to observe endurance state of the specimen being tested. In this study, the temperature profiles of the specimen under testing are recorded by thermal camera and transferred to the image processing program. The artificial neural networks obtain spot temperatures of the inspected specimen by using its temperature profiles. By analyzing the values of obtained data, we detect spots of highest temperatures as ones that are exposed to most intensive deformation. These regions considered to be probable crack initiation sites. Keywords—Image processing, infrared thermography, neural networks, fatigue.
II. OBTAINING SPOT TEMPERATURES OF A SPECIMEN BY PROCESSING ITS THERMAL IMAGES In this section, we explain the method of obtaining the pre-fracture state of a specimen. For this aim, we use TIs of the specimen taken at frequency 1 image per second. We fixed the temperatures of a lot of spots of each TI. By analyzing these data, we obtained that the relation between the temperatures of image spots and its gray level is significantly nonlinear. To avoid this computational negativity, we fit a curve to obtain the real temperature of each spot on its gray level. This curve is expressed by following quadratic function.
I. INTRODUCTION The detection of the damage accumulation and crack nucleation in metals has great importance in practical applications [1]. For this aim, a few Nondestructive Evaluation (NDE) techniques such as acoustic emission, eddy currents, ultrasonic and X-ray have been developed [2-6]. But these techniques have some shortcomings restricting their practical applications. In contrast, Infrared (IR) Thermography has found to be applicable not only to mechanical applications but also to many disciplines including medical sciences [7]. Thermoelasticity and thermoplasticity theories relate the heat generation with the material internal stress state [8]. The applied stress is converted into heat generation by means of strain energy. Hence, as the damage accumulates and localizes, a local temperature increases. Up to date, relatively little work has been conducted to investigate the fatigue behaviors using the thermography technique [7-11] and all of them use the digital thermal images generated by high resolution thermal camera. But in practice are used a lot of thermal cameras with analogue video output. In order to use a camera of this kind in computer aided fatigue control system it is necessary to convert analogue thermal images to digital form and subject them to some image processing clearing the weakness region of the specimen. For this aim, three different loads were applied on AISI37 steel specimen at frequency 25Hz. The
1-4244-0813-X/07/$20.00 2007 IEEE.
T ( x) = ax 2 + bx + c .
(1)
Where T(x) is temperature of given spot, x is the gray level of given spot and a, b and c are the values significantly varying from image to image. A. Obtaining Temperatures of Characteristic Spots Using ANN We obtain the temperatures of all spots of the specimen under loading by using its characteristic spots temperatures consisting of hottest, coldest and medium heat ones. First, by special testing, we fix the spot to be one of approximately medium temperature for all experiments. Next, in each experiment, we determine TI fields containing the numbers expressing temperatures of the hottest, coldest and medium heat spots of the specimen and cut these fields from TI (Fig.1). Then, we
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S1 = {d: d< H} and
decompose them into R (RED), G (GREEN), B (BLUE) components. The color matrix RGB belonging to a cut field can be decomposed as follows.
S2 = {d: d≥H}, ∀ i ∈{1, 2,.., n} and j ∈{1,2,..,m}. Where d is an element of the normalized matrix N. Based on this rule, we replace each element of the matrix N by 0 if its value is less than H and by 1 if its value is equal or high than H. Finally, as result of this transformation, we get the following Binary matrix.
rgb11 .. rgb1n RGB = .. .. .. rgbm1 .. rgbmn mxn
x11 ... x1n Binary = ... ... ... x m1 ... x mn mxn
b11 .. b1n r11 .. r1n g11 .. g1n R = .. .. .. G = .. .. .. B = .. .. .. bm1 .. bmn mxn rm1 .. rmn mxn g m1 .. g mn mxn
Where, xij ∈ {0.1}, ∀ i ∈ {1,2,...., n} and
Where, R, G and B are red, green and blue components matrices of the RGB matrix. We can transform these matrices to the single unit-8 gray image, satisfying NTSC (National Television Systems Committee) standard [12], by using the following formula. Gray = 0 , 2989 R + 0 , 587 G + 0 ,114 B .
j ∈ {1,2,...., m}.
In literature, this type of problems is known as image recognition and classification [13]. For solving these problems, generally the supervised and unsupervised networks are used [14]. These networks are characterized by such important features as the ability to learn and generalize, smaller training, set requirements, fast operation, easy of implementation and tolerance of noisy data. However, among a lot of network structures, the Multi Layer Perceptron (MLP) ANN structure with feedforward (FF) – backpropagation (BP) training algorithm is most commonly adopted for solving this type of problems [14]. Based on above-mentioned, we preferred MLP network to recognize numerical values of hottest, coldest and medium heat spots temperatures of TIs generated by the thermal camera. For this aim, the rows of the Binary matrix (22x28 or 23x28 or 25x28 or 35x45) of the number to be recognized are concatenated into the single Vector= ( x1 , x 2 , x 3 ,...................., x mxn ) of length 616 or 644 or 700 or 1575. According to this, we designed four MLPs of common structure consisting of one input, one hidden and one output layers but differing in numbers of elements in these layers. The general structure of these networks is shown in Fig.2.
(2)
Fig. 1. The thermal image (on the left) and cut fields (on the right).
Next to normalize Gray matrix, we divide each of its elements by 255. y11 .. y1n Gray = .. .. .. y m1 .. y mn mxn d 11 .. d1n y11 .. y1n N = Gray : 255 = .. .. .. : 255 = .. .. .. d m1 .. d mn mxn y m1 .. y mn mxn
We analyzed the statistics of values of elements of many normalized matrices and found that these values are divided into two categories. The first category consists of values that less than a threshold H and second one consist of values equal or high than this threshold. In particular, our experiments showed that the threshold is H = 0.9 for the normalized matrices produced from the images of numerical dates generated by the thermal camera FLIR E45. This is because of different colored backgrounds of the white images of the numbers. Therefore, we divide the elements di,j of each normalized matrix N into two sets defined as follows.
Fig. 2. The MLP with one input layer, one hidden layer and one output layer.
We have evaluated the performance of the designed MLPs for such standard and most used BP algorithms [14] as Scaled Conjugate Gradient Backpropagation (SCGBP), Resilient Backpropagation (RBP) and Gradient
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medium heat) spots on each TI, MLPs trained by SCGBP training algorithm are used.
Descent with Momentum and Adaptive Learning Rate Backpropagation (GDMBP). As well known, for the activation of neurons in hidden and output layers of MLP, the different combinations of the functions such as a simple threshold function, a linear function, a sigmoid function, a hyperbolic tangent function and a radial basis function may be used [15]. We have preferred the hyperbolic tangent function for the hidden layer and the sigmoid function for the output layer due to relatively low error rate provided by these functions in a lot of experiments that we carried out. As result of these experiments, we have obtained the optimal values of training parameters for above-mentioned algorithms. These values are given in Table 1.
TABLE III. TRAINING AND TEST RESULTS FOR D IFFERENT MLPS
TABLE I. THE OPTIMAL VALUES OF TRAINING PARAMETERS FOR DIFFERENT TRAINING ALGORITHMS Training Algorithms Momentum Coeff. (mc) Learning Rate (lr) Increase Factor ( η ) Decrease Factor ( µ )
σ) Lambda ( λ ) Sigma (
GDMBP 0.01 0.6 -
RBP 1.2
SCGBP -
-
0.5
-
-
-
5.10-5 5.10-7
TABLE II. ARCHITECTURES OF MLPS Element numb. Element numb. of of Input Layer Hidden Layer 616 50 644 50 700 100 1575 100
Epoch
MLP1 MLP1 MLP1 MLP2 MLP2 MLP2 MLP3 MLP3 MLP3 MLP4 MLP4 MLP4
20 20 105 64 171 31 146 112 38 110 75 225
Train Train Error Algorithms (mse) SCGBP GDMBP RBP SCGBP GDMBP RBP SCGBP GDMBP RBP SCGBP GDMBP RBP
0.0001 0.008 0.047 0.0006 0.0922 0.0726 0.000045 0.089 0.045 0.0017 0.0937 0.0674
Test Error (mse) 0.0001 0.008 0.049 0.0007 0.0907 0.0774 0.0045 0.0908 0.0664 0.0074 0.0948 0.0706
Train Accu. (%) 100 100 84 100 92 88 100 90 84 100 92 86
Test Accu. (%) 100 100 86 100 92 90 100 92 88 100 94 88
B. Obtaining Temperature Distribution on The Thermal Image We obtain the temperatures of all spots of the specimen under loading by using its characteristic spots temperatures consisting of hottest, coldest and medium heat ones. As above-mentioned, the dependence of TI’s spot temperature on its gray level has somewhat nonlinear relation and hence we fit curves expressing the spots temperatures on TIs of the inspected specimen. In order to obtain these curves, we use the temperature values of the hottest, coldest and medium heat spots generated by MLPs and the pixel gray level of the hottest, coldest and medium heat points generated by image processing program. By analyzing these data, we have obtained that the dependence between the pixel value xi and temperature Ti of a spot can be expressed a quadratic function as follows.
The hidden layer enables the MLP to extract higherorder statistics especially when the size of the input layer is large [16]. The number of hidden layer element is derived from the best results obtained by trial and error method [14]. The input layer consists of elements the number of which is equal to the element number of input vector. The number of output layer element is dependent on maximal value that can be correctly detected by IR camera. The optimum architectures of four different MLPs are shown in Table 2.
MLPs MLP1 MLP2 MLP3 MLP4
MLPs
T j = ax 2j + bx j + c
j ∈ {1,2,3} .
Where x1, x2 and x3 are gray levels of hottest, coldest and medium heat spots of the TI at hand and T1,T2 and T3 are the temperature of these spots, respectively. In general, the coefficients a, b and c are different for each TI due to different colored backgrounds. Such expressions are composed for the hottest, coldest and medium heat spots of given TI and by handling these expressions as a system of three linear equations [18], we obtain values of a, b and c for each TI at hand. Thus, we get the single quadratic equation to obtain the temperatures of spots of desired points of the specimen as follows.
Element numb. of Output Layer 2 10 10 10
To train MLPs in Table 2, we composed the sample sets of images obtained by thermal camera. For MLP1, MLP2, MLP3 and MLP4, each of the training and test sets were composed 50 images. For capable of a good generalization of trained MLPs, training and test sets were arranged in a form that problem space will be able to represent by its whole futures [17]. In the beginning of training phase, weights and biases of MLPs were selected randomly in the range -0.1 to 0.1 [14]. Minimum error rate was given 1.10-5 as stop threshold of training. In the end of training process performed with these parameters, results in Table 3 were obtained for three different training algorithms. As shown in Table 3, low error rate and high accuracy are obtained in MLPs trained by SCGBP training algorithm. For this reason, in this study, to determine temperatures of the characteristic (hottest, coldest and
T ( x) = ax 2 + bx + c .
Where x is gray level of given pixel on TI at hand, and T(x) is the temperature of the point indicated by this pixel. All of these processes are performed by the image processing programs that we have developed in MATLAB 7.1 environment. III. EXPERIMENTAL STAND SETUP The material used in the low cycle bending fatigue tests was the steel (AISI37) which is composed of %0.2C,
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%Impurities < 0.045. The yielding strength of the steel was 230 MPa, ultimate strength of 550 MPa, young modulus of 200 GPa, Poisson’s ratio of 0.3 and percentage elongation (%) of 4,2. The geometry of the test specimen is shown in Fig.3.a. As seen in this figure, all test specimens of dimensions of 90x25x3 mm were perforated by forming side grooves. So, the highest bending stress occurs at the perforated region that can be easily observed. The bending fatigue test stand is shown in Fig.3.b. It consists of an electric motor of 1,5kW coupled with an axle. A crank converts the rotation motion into the linear motion. The displacement of the end of the specimen is set by making use of the crank rig. The tests were performed at three different loads. The low cycle bending fatigue tests were performed by applying sinusoidal wave form loads by using displacement values of ±3, ±4 and ±5 mm to the free end of the specimen. In order to get the TIs of the specimen during the lowcycle bending fatigue testing, the FLIR E45 IR camera was used. The detector type of this camera is Focal Plane Array (FPA) of 160x120 Pixels, spectral range of 7.5 to 13 µm, thermal sensitivity of 0.1 ˚C at 30 ˚C, image frequency of 50/60 Hz.
IV. RESULTS AND DISCUSSIONS For example, below we explain the results of the test on the specimen under three different sinusoidally varying loads with peak values of ±503, ±515 and ±524 MPa at 25 Hz displacing the free end of the specimen to ±3, ±4 and ±5 mm, respectively. For instance in Figure 4 is given one TI for each loading. We took 230, 71 and 30 TIs and for these loadings, respectively and subject them to the processing by above-mentioned method. The results of these processing are shown in Figure 5 as the fracture lines of the specimen. These lines are explain the timetemperature dependence of the probably fracture region spots of the specimen under testing.
a)
b)
a)
c) b)
Fig.4. Thermal images of test specimens a) for δ = ± 3mm, b) for δ = ± 4mm, c) for δ = ± 5mm.
Fig.3. a) Geometry of the test specimen b) Bending fatigue test stand.
As seen in this figure, as the displacement (δ) increases, the maximum temperature values increase. For instance, the spots temperatures of hottest region of the specimen
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tested at δ = ± 5mm are significantly higher than ones that at δ = ± 3mm. This is because of the increase of plastic deformation leading to heat generation. The fatigue life decreases dramatically as the end displacements (δ) increases. The spot temperatures begin to increase linearly from ambient temperature depending on heat generation, due to the irreversible plastic deformation. The sharpest temperature increase is obtained at δ = ± 5mm, since the highest degree of plastic deformation occurs at this loading.
c) Fig.5. Temperature-time variations of fracture lines a) for (δ = ±3 mm), b) for (δ = ±4 mm), c) for (δ = ±5 mm).
The increase rate of temperature at the ends of the fracture line begins to decrease at approximately 15 % of the fatigue life. This is because of the most of the strain is located in the front of microcracks formed at the free surfaces of the side groove region on the specimen such that the volume under inelastic deformation decreased greatly and leads the hysteresis energy to decrease. So, the temperature dropped significantly until the failure of the specimen. At this point, the temperature alterations also observed for all loadings. The temperature alterations may be related to microcrack formation. Because, when a microcrack is formed, the local strain energy releases at that point leading the decrease in heat generation. The apparently decrease in dissipation may also be associated with the transient thermal regime leading to a steady temperature field [19] or may be due to the thermoelastic effect [20]. After the spots temperatures reach the maximum, the temperature begins to decrease. This decrease indicates that the fatigue microcracks have converted to macrocracks.
a)
V. CONCLUSION In this study, the infrared thermography method was used to detect the temperature rise of reverse bending fatigued AISI37 steel at 25 Hz and three different loadings. By using IR camera, the temperature profiles of the test specimens were recorded. The data were evaluated by using the image processing and graphical interface programs that we have developed in MATLAB 7.1 environment. The spot temperatures were obtained from thermal images by using artificial neural networks. By analyzing the results of these experiments we found that the damage in the region to be fractured is gradually accumulated with increasing its temperature. The fracture occurs on a fracture line appeared in the location where the bending stress is maximal. When the fatigue macrocrack is formed, spots temperatures of the fracture line show a sharp decrease.
b)
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ACKNOWLEDGMENT This study is supported by the Coordinatorship of Selcuk University’s Scientific Research Projects. REFERENCES [1]
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