UDK 666.3/.7:004.032.26	ISSN 1580-2949
Original scientific article/Izvirni znanstveni članek	MTAEC9, 48(4)453(2014)
APPLICATION OF A NEURAL NETWORK FOR ESTIMATING THE CRACK FORMATION AND PROPAGATION IN SOL-GEL CeO2 COATINGS DURING PROCESSING AT TEMPERATURE
UPORABA NEVRONSKE MREŽE ZA UGOTAVLJANJE NASTANKA IN ŠIRJENJA RAZPOKE V SOL-GEL PREMAZU CeO2 MED POSTOPKOM OGREVANJA
Aydogan Savran1, Musa Alci1, Serdar Yildirim2,3, Recep Yigit3'4 5, Erdal ^elik2'3,5
1Ege University, Dept. of Electrical and Electronics Engineering, 35100 Bornova, Izmir, Turkey 2Dokuz Eylul University, Dept. of Metallurgical and Materials Engineering, 35160 Buca, Izmir, Turkey 3Dokuz Eylul University, Center for Production and Applications of Electronic Materials (EMUM), 35160 Buca, Izmir, Turkey 4Dokuz Eylul University, Izmir Vocational School, Department of Technical Programs, 35150 Buca, Izmir, Turkey 5Dokuz Eylul University, Dept. of Nanoscience and Nanoengineering, 35160 Buca, Izmir, Turkey
recep.yigit@deu.edu.tr
Prejem rokopisa - received: 2012-09-21; sprejem za objavo - accepted for publication: 2013-10-28
In this study the application of a neural network to estimate the crack propagation and crack size in CeO2 coatings on a Ni substrate during processing at temperature was evaluated as a function of the Ce content in solutions with increasing processing temperatures from 24 °C and 700 °C. In this respect, CeO2 coatings were prepared on Ni tapes from solutions derived from Ce-based precursors using a sol-gel method for YBCO-coated conductors. The crack size of the coating was determined using an in-situ Hot-Stage ESEM depending on the temperature at a certain time in vacuum conditions. It was determined that the crack size of the coating increased with the increasing processing temperature. Measuring the crack sizes of the coatings using Hot-Stage ESEM is an expensive and time-consuming process. In order to eliminate these kinds of problems a neural-network approach was used to estimate the crack sizes of the coatings at different temperatures. The neural network was constructed directly from the experimental results. It was concluded that the estimation of the crack propagation of CeO2 coatings on a Ni tape substrate are reasonable for the processing temperatures. Keywords: CeO2, sol-gel, neural network, crack
V tej študiji je bila ocenjena uporaba nevronske mreže za določanje širjenja razpoke in velikosti razpoke v premazu iz CeO2 na podlagi iz Ni med ogrevanjem kot funkcija vsebnosti Ce v raztopini med ogrevanjem od 24 °C do 700 °C. Za ta namen je bil pripravljen premaz iz CeO2 na traku iz Ni iz predhodne raztopine Ce z uporabo sol-gel metode za premaz na prevodniku YBCO. Velikost razpoke v premazu je bila določena v vročem z in-situ ESEM v odvisnosti od temperature po določenem času v vakuumu. Ugotovljeno je bilo, da velikost razpoke v premazu narašča z naraščanjem temperature procesa. Merjenje velikosti razpoke v vročem z uporabo ESEM je drag in časovno zamuden postopek. Za odpravo teh težav je bila za določanje velikosti razpoke v premazu pri različnih temperaturah uporabljena nevronska mreža. Ta je bila postavljena na podlagi eksperimentalnih rezultatov. Ugotovljeno je bilo, da je mogoče določanje širjenja razpoke v premazu CeO2 na traku iz Ni pri različnih temperaturah procesa.
Ključne besede: CeO2, sol-gel, nevronska mreža, razpoka
1 INTRODUCTION	of magnetic, electronic and microwave technologies.
Ceramic superconductors have been deposited as thin
Neural networks (NNs) possess massive parallelism,	films using various methods, e.g., electron-beam co-eva-
a powerful mapping capacity, and a learning property.1	poration, chemical vapor deposition, ion-beam sputter-
They are capable of making decisions based on incom-	ing, pulsed-laser deposition and the sol-gel technique on
plete, noisy and disordered information. In addition, they	many buffered substrates.6 CeO2 is one of the buffer
can provide reasonable outputs for inputs not encoun-	layers frequently used for surface-coated YBCO super-
tered during training. Because of these properties they	conductors on textured nickel substrates.7 The sol-gel
have gained the attention of scientist from many different	process offers a new possibility for the synthesis of oxide areas. There are a huge number of papers in the area of layers by applying liquid precursors to substrates by
control, identification and estimation.2-5 Most of the	dipping, spinning or spraying methods.8 The major fac-
industrial productive processes exhibit a certain degree	tors affecting the CeO2 sol-gel coatings are the nature of
of nonlinearity. By means of their nonlinear mapping	the coating and the substrate, and the reaction parameters
and learning properties, neural networks have been	at the temperature of YBCO formation.9 The nature of
employed in the identification of unknown nonlinear	the coatings are influenced by sol-gel parameters such as
systems.	types of precursor, solvent and chelating agents, visco-
The development of the new, high-temperature super-	sity, Ce content, dilution, chelation, complexation, with-
conductors has resulted in many applications in the fields	drawal rate, coating thickness and annealing conditions.
In particular, the cracks of buffer layers are the main problem in sol-gel processing.10
In our initial attempts11 we determined the crack-propagation rate and the crack size of CeO2 buffer layers on Ni tapes for YBCO-coated conductors using an in-situ, hot-stage, environmental scanning electron microscope (ESEM). In the present investigation, in order to determine the crack size of the CeO2 sol-gel coatings by avoiding time-consuming and expensive experimental works, we propose to use a multilayer feed-forward NN to estimate the crack size at the processing temperatures.
2 NEURAL NETWORKS
Neural Networks (NNs) are massively parallel, distributed, adaptive, nonlinear information processing tools. They consist of simple nonlinear processing elements (PEs), referred to as neurons. Each neuron receives connections from other PEs and/or itself. The block diagram of a neuron is shown in Figure 1.
The neuron collects the values from all of its input connections, performs a predefined mathematical operation, and produces a single output value computed as:
f( x) =
n
yj = f E+ bj
(1)
Figure 1: Artificial neuron model Slika 1: Model umetne nevronske mreže.
1+e
(2)
The interconnectivity defines the topology of the NN. An important class of NNs is the multilayer feed-forward neural network, as shown in Figure 2. They consist of simple nonlinear processing elements (PEs) and weighted connections in a layered structure. The input signal propagates through the network in a forward direction from one layer to the next. The neurons are connected with weighted connections represented by the arrows in Figure 2.
The training of the NN is performed by adjusting the connection weights. It is performed by iteratively adjusting the weights (w) of the connections and biases (b) in the network in order to minimize a predefined cost function. A popular cost function is the sum of the squared error between the actual output and the desired output value for each unit in the output layer:
1
E = -E (tk -
■yk)
(3)
where ui is the input value, wji is the connection weight between the ith input and the jth neuron, and f is the activation function. The sum of the weighted inputs and the bias forms the input to an activation function f. The neurons may use any differentiable activation function f to generate their output. The sigmoid function is the one of the most common activation functions, as follows:
where tk is the desired or target response on the kth unit and yk is the produced network output on the same unit.
In order to perform training, a training set, including the input and desired response vectors, is prepared. The training is performed in two phases referred to as the forward and backward phases. In the forward phase, the input patterns from the training set are applied to the input layer. These inputs are multiplied by the associated weights, passed through the activation functions and transferred to the next layer. They propagate through the network, layer by layer. Finally, the actual response of the network is produced at the output layer. The errors between the desired and the network outputs are found. In the backward phase, the error signal propagates backwards through the network and the gradients are computed. These are then used to determine the weight changes in the net according to used learning rule. A more common learning algorithm is the back-propagation algorithm, which is introduced in12.
The standard back-propagation implements the steepest-descent method (also called the gradient-descent method). At each step of the steepest-descent method the weights are adjusted in the direction in which the error function decreases most rapidly. This direction is determined by the gradient of the error surface at the current point in the weight space. The weights are updated in a negative direction to the gradient with a certain rate, as given by:
dE
Figure 2: Multilayer feed-forward neural network Slika 2: Večplastno napajanje nevronske mreže
W °ew = W - M
w new = w old - M
w nrw = wo!d - M
dE
dwij dE
dw
(4)
1

in which ^ is the learning rate that determines the step size through the gradient direction. Similarly, the biases are updated as follows:
=br - n
bnew =	- n
b-w = bf^ - n
dE_ db,
dEL db,.
(5)
More details regarding the NN training can be found elsewhere.13
3 EXPERIMENTAL AND NUMERICAL PROCEDURES
Ce-based solutions were prepared from cerium nitrate precursors (Ce(NO3)3 ■ 6H2O). The powder precursors were first dissolved in glacial acetic acid, which is used as a chelating agent. Eleven different amounts of Ce precursor, including (0.0499, 0.1990, 0.3490, 0.7500, 1.4900, 2.9900, 4.2500, 4.9900, 5.9900, 7.0080, 43.4000) g, which are called as concentration indexes, were used to estimate the effects on the crack formation and propagation of the coatings in the solutions as a processing parameter. The obtained solutions were subsequently diluted with isopropanol. All the solutions were stirred at room temperature for 60-120 min in order to yield transparent solutions. The thickness of the CeO2 thin films measured by ESEM varied between 0.4 ^m and 7 ^m, depending on the Ce concentration in the solution. More details regarding the preparations of Ni tape and CeO2 thin films were given in111415.
In order to investigate the surface morphology, the crack formation and the propagation of CeO2 films, in-situ hot stage ESEM was used. For this procedure, Ni tape substrates were separately dipped into the eleven different Ce-based solutions at room temperature in air. Ce-based gel coatings were obtained from this process. These gel coatings were then placed in the hot-stage ESEM. The gel coatings were examined in the temperature range 24 °C to 700 °C for 5 min in vacuum conditions. After placing the Ce-based gel coatings contain-
Figure 4: ESEM microstructures of Ce-based gel and CeO2 coatings on Ni tape at: a) 25 °C and b) 600 "C11
Slika 4: ESEM-posnetka koloida na osnovi premaza Ce in CeO2 na traku iz Ni pri: a) 25 °C in b) 600 "C11
ing a bubble structure in the ESEM, they were dried and heat treated from room temperature to 700 °C. The crack length and the size of the coatings were measured in the ESEM at several temperatures, i.e., (25, 100, 200, 300, 500, 600 and 700) °C, for a period of 5 min under vacuum conditions. However, here we utilized the temperatures 400 °C and 700 °C. A computer program of an in-situ hot-stage ESEM was used to measure the crack
Figure 3: The used NN structure Slika 3: Uporabljena NN-struktura
size of the coating as a function of concentration index (Ce content in the solutions) and processing temperature. In as much as the coating is a gel-like structure at 25-100 °C, and amorphous at 100-350 °C, the CeOi coating was formed on Ni tape at 420 °C and densified at 700 °C. For these reasons, the crack size of the CeO2 coatings was also measured at 400 °C and 700 °C in detail. When measuring the crack sizes of the gel and oxide coatings, ESEM micrographs were taken with the scale bar 20 ^m.
The NN used in this study is shown in Figure 3. Where v and w represent the weights, and b represents the biases. The NN has two inputs (ui, U2) and 1 output (j). There are six neurons in the hidden layer. f(.) and g(.) are the hidden-layer and the output-layer activation functions, respectively. The sigmoid-type activation functions are used by both layers. All the programs for the NN were developed under Matlab. The inputs of the NN represent the amount of material and the processing temperature at which the experiment was performed. The output of the NN represents the crack sizes of the coatings. The training data set contains 66 elements, includ-
Figure 5: The NN estimation and experimental results for CeO2 coatings on Ni tape at 400 °C. In this figure, the x and j axes indicate the crack size of the coating and the concentration index, respectively. Slika 5: Določanje NN in rezultati preizkusov za premaz CeO2 na traku iz Ni pri 400 °C. Na sliki x- in j-os pomenita velikost razpoke in indeks pogostosti.
Table 1: NN estimated and experimental crack sizes for 400 °C Tabela 1: Določen NN in eksperimentalna velikost razpok pri 400 °C
Concentration index
1 2
3
4
5
6
7
8
9
10 11
NN inputs
Amount of precursor material (g)
0.0499 0.1990 0.3490 0.7500 1.4900 2.9900 4.2500 4.9900 5.9900 7.0080 43.4000
Temperature (oC)
400 400 400 400 400 400 400 400 400 400 400
NN output
NN estimated crack size (um)
1.6309 1.6980 1.9820 10.2419 14.5338 14.8854 15.2480 15.6821 18.7295 9.6382 33.5412
Experimen tal crack size (um)
2.4133 2.4345 2.5000 9.7605 15.0000 15.6250 17.6410 15.7140 25.0500 16.8900 30.5000
Table 2: NN estimated and experimental crack sizes for 700 °C Tabela 2: Določen NN in eksperimentalna velikost razpok pri 700 °C
Concentration index
1 2
3
4
5
6
7
8
9
10 11
NN inputs
Amount of precursor material (g)
0.0499 0.1990 0.3490 0.7500 1.4900 2.9900 4.2500 4.9900 5.9900 7.0080 43.4000
Temperature (oC)
700 700 700 700 700 700 700 700 700 700 700
NN output
NN estimated crack size (um)
2.2660 2.8976 5.4302 17.2949 18.5257 22.9032 55.6694 71.0257 75.8715 110.6222 1422619
Experimen tal crack size (um)
2.6886 2.6547 3.0000 13.8090 15.6000 17.5000 26.4710 44.4700 71.4200 73.9000 140.0000
ing the data for temperatures (25, 100, 200, 300, 500 and 600) °C. We left the data for temperatures 400 °C and 700 °C as the testing data sets. Both test sets contain 11 elements. A batch-training procedure was applied to train the NN using the Steepest Descent (SD) method and then the crack size of the CeO2 buffer layer was estimated for 400 °C and 700 °C. The details of test data sets and the NN estimation results are shown in Tables 1 and 2.
4 RESULTS AND DISCUSSION
In-situ, hot-stage ESEM, depending on the temperature, the crack formation and propagation of the coatings were evaluated as a function of the Ce content in the solutions. Figure 4 shows ESEM microstructures of the Ce-based gel and CeO2 coatings on Ni tape at 25 °C and 600 °C, respectively.11 The ESEM observations revealed that the crack surface of the Ce-based films changed slightly with increasing temperatures, from 25 °C to 500 °C, when compared with the other thin films. After CeO2 formation at about 420 °C, microcracks were observed on the surface. It is interesting to note here that the bubbles and micro-bubbles were produced on the surface once the precursor material increased in this solution. The bubbles showed characteristic properties that caused the cracks to start on the surfaces of the gel films of the nitrate-salt-based precursors. Note that there are many factors influencing the bubbling problem, such as types of precursors, solvent and chelating agent, viscosity, dilution, Ce content in solution and so on. It was found that the size and propagation rate of the cracks increased with the increasing Ce content. It is clear from the ESEM observations that the measured values of the
Figure 6: The NN estimation and experimental results for CeO2 coatings on Ni tape at 700 °C. In this figure, the x and y axes indicate the crack size of the coating and the concentration index, respectively. Slika 6: Določanje NN in rezultati preizkusov za premaz CeO2 na traku iz Ni pri 700 °C. Na sliki x- in y-os pomenita velikost razpoke in indeks pogostosti.
crack-propagation rate altered slightly at (300, 400 and 500) °C, whereas at 600 °C they changed considerably.
Figure 5 shows the NN estimation and the experimental results for CeO2 on Ni tape at 400 °C. In this figure, the x and y axes indicate the crack size of the coating and the concentration index, respectively. The concentration index corresponds to eleven type solutions, including several Ce(NO3)3 • 6H2O contents. As mentioned just previously, the Ce(NO3)3 • 6H2O precursors were dissolved using a solvent and a chelating agent. The eleven solutions were prepared by changing the amount of precursors and thus eleven type coatings were obtained using the hot-stage ESEM. As a result of this, the crack sizes were measured at 400 °C in the ESEM and the concentration index was taken as numerical values, such as from 1 to 11. Actually, the concentration indexes are not real values indicating the amount of precursor. It is clear from Figure 5 that the estimated crack size of the coating is close to the experimental results for 400 °C. Similarly, the NN estimation and the experimental results of the crack size for 700 °C are presented in Figure 6. It is worth noting that the predicted result approaches the mean values when the standard deviation associated with the measurements is small. Now that the goal is to fabricate low-cost, high-quality products in a short time in a modern industry, the optimization of the processing temperature can be estimated using the NN technique. The key feature of this research is that the NN approach is useful for the prediction of the cracks size and the crack-propagation rate during the heat treatment of the sol-gel coatings. This study can be extended by using other buffer layers, depending on the sol-gel parameters. This technique is quite likely to be a key area for the development of all sol-gel films in the future, prior to the coating processes.
5 CONCLUSIONS
In summary, the NN-based approach was developed to estimate the crack sizes of a CeO2 coating on a Ni tape for YBCO-coated conductors, depending on processing temperatures such as 400 °C and 700 °C using a hotstage ESEM. A multilayer feed-forward NN was trained to estimate the crack size of the coating during processing at temperature in the range 24-700 °C. The experimental measurements of the crack size on the coating on the Ni tape substrate are a very expensive and a time-consuming process. The approach proposed in the present study provides simplicity and is cost-effective for preparing the new solutions and subsequent processing in the sol-gel technique.
Acknowledgements
The authors would like to thank Dr. Y. S. Hascicek and R. E. Goddard for their assistance in obtaining the ESEM micrographs at the National High Magnetic Field Laboratory of Florida State University in Tallahassee, Florida USA.
6	REFERENCES
1	K. Hornik, M. Stinchocombe, H. White, Neural Networks, 2 (1989), 359-366
2	K. J. Hunt, D. Sbarbaro, R. Zbikowski, P. J. Gawthrop, Automatica, 28 (1992), 1083-1112
3M. Agarwal, IEEE Control Systems Magazine, 17 (1997), 75-93
4	K. S. Narendra, K. Parthasarathy, IEEE Transactions on Neural Networks, 1 (1990), 4-27
5	A. G. Parlos, S. K. Menon, A. F. Atiya, IEEE Transactions on Neural Networks, 12 (2001), 1411-1432
61. H. Mutlu, E. Celik, M. K. Ramazanoglu, Y. Akin, Y. S. Hascicek, IEEE Transactions on Applied Superconductivity, 10 (2000), 1154-1157
7	E. Celik, I. H. Mutlu, Y. S. Hascicek, IEEE Transactions on Applied Superconductivity, 10 (2000), 1162-1166
8E. Celik, H. Okuyucu, I. H. Mutlu, M. Tomsic, J. Schwartz, Y. S. Hascicek, IEEE Transactions on Applied Superconductivity, 11
(2001),	3162-3165
9	H. Okuyucu, E. Celik, M. K. Ramazanoglu, Y. Akin, I. H. Mutlu, W. Sigmund, J. E. Crow, Y. S. Hascicek, IEEE Transactions on Applied Superconductivity, 11 (2001), 2889-2892
10	X. D. Wu, S. R. Foltyn, P. Arendt, J. Townsend, I. H. Campbell, P. Tiwari, Q. X. Jia, J. O. Willis, M. P. Maley, J. Y. Coulter, D. E. Peterson, IEEE Transactions on Applied Superconductivity, 5 (1995), 2001-2006
11E. Celik, Y. S. Hascicek, Materials Science & Engineering B, 94
(2002),	176-180
12	P. J. Werbos, Beyond Regression, New Tools for Prediction and Analysis in the Behavioral Sciences, PhD. Dissertation, Harvard University, Boston, USA, 1974
13	M. S. Al-Haik, H. Garmestani, A. Savran, International Journal of Plasticity, 20 (2004), 1875-1907
14	E. Celik, J. Schwartz, E. Avci, H. J. Schneider-Muntau, Y. S. Hasci-cek, IEEE Transactions on Applied Superconductivity, 9 (1999), 2264-2268
15	E. Celik, H. I. Mutlu, E. Avci, Y. S. Hascicek, Advances in Cryogenic Engineering (Materials), 46 (1999), 895-900