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Artificial neural network model for predicting the tensile strength of friction stir welded aluminium alloy AA1100
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 5 (2018) 16716–16723
www.materialstoday.com/proceedings
SCICON 2016
Artificial neural network model for predicting the tensile strength of friction stir welded aluminium alloy AA1100 R. Vaira Vignesh and R. Padmanaban* Department of Mechanical Engineering, Amrita School of Engineering,Coimbatore, Amrita Vishwa Vidyapeetham, Amrita University, India.
Abstract Friction stir welding (FSW) is a solid state welding technique, in which high strength weldswith minimal defects, can be obtained even with materialsthat are hardly weldable by conventional techniques. FSW is influenced by a number of process parameters. Some of the highly influential process parameters that determine the quality of the welds in FSW are tool rotation speed, welding speed, shoulder diameter and pin diameter of tool. In this study, FSW trials were conducted on AA1100 as per central composite design, with four parameters varied at five levels. The tensile strength of the joints were measured using a computerized tensile testing machine and these results were used to develop an artificial neural network model. The input parameters to the model were tool rotation speed, welding speed, shoulder diameter and pin diameter and the output was tensile strength of the joints. Levenberg Marquardt algorithm was used to establish the relationship between the process parameters and the output. The feed forward model was trained using 80% of the experimental data and the remaining 20% of the data was used for validation and testing of the model. The R2 valuesfor validation data and testing datawere found to be 0.80and0.99respectively, displaying the closeness between the experimental and predicted data. The results indicate that the generated model has high efficacy in predicting the tensile strength of friction stir welded aluminium alloy AA1100 joints. © 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Advanced Materials (SCICON ‘16). Keywords:Friction stir welding; Aluminium alloy; Tensile strength; Artificial neural network; Algorithm
1. Introduction Aluminium alloy 1100 is one of the preferred alloy for structural applications, sheet metal applications, heat exchangers, food containers etc. Conventional welding techniques when used for welding AA1100, result in poor
* Corresponding author. Tel.: 098945 68309 E-mail address: [email protected] 2214-7853© 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Advanced Materials(SCICON ‘16).
Vaira Vignesh and Padmanaban / Materials Today: Proceedings 5 (2018) 16716–16723
16717
Nomenclature FSW AA ANN TS TRS WS SD PD FSWed BHN MLP
Friction Stir Welding Aluminium Alloy Artificial Neural Network Tensile Strength Tool Rotation Speed Welding Speed Shoulder Diameter Pin Diameter Friction Stir Welded Brinell’s Hardness Number Multilayer Perceptron
quality welds due to rapid oxidation of the alloy at high temperature.Friction stir welding (FSW) is a solid state welding process, where the material is plasticized and the joining is effected by traversing a rotatingtool along the joint, under the action of axial force [1, 2]. The quality of welded joints depend on process parameters[3, 4], tool geometry[5] and the environmental conditions. Tool shoulder diameter, pin diameter and pin profile affects the welding joint efficiency [6, 7]. The major defects found in the conventional welds like porosity, segregation of alloying elements, hot cracking, poor surface finish etc. are minimized in FSW and high efficient joint is obtained[8, 9]. The joint formation by plasticizingthe material under extreme deformation results in dynamic recrystallization [10]. Sato et al., [11] produced friction stir welds with fine grained and improved mechanical properties, in accumulative roll bonded AA1100. Khorrami et al., [12] found that increase in tool rotation speed decreased the strength of friction stir welded joints in AA1100, which was imposed with severe strain by cumulative groove pressing before FSW. Sadiq Aziz Hussein et al., [13] found that the FSW process parameters greatly influence the mechanical properties of the dissimilarwelded between aluminium alloy and steel. I. Kartsonakis et al., [14] improved the corrosion resistance of dissimilar FSWed aluminium alloys by reinforcing nanophase cerium molybdate in the welds. Moosa Sajed et al., [15] optimized the two stage refilled friction stir spot welding process parameters for AA1100 and concluded that the dwell time had minimal effect in improving the strength of the weld. Sang-Won Park et al., [16] found that increasing the tool rotation speed decreased the tensile shear strength of the FSWed joint. The tensile shear strength of the material was high for specimens processed with large shoulder diameter. The main challenge in FSW lies in selecting the welding parameters that would produce an excellent weld joint. Conventional way of choosing welding parameters to produce a weld joint is a time consuming work and again each weld has to be tested for defects and mechanical properties. The experimental trials may or may not result in optimized FSW process parameter combinations. The welding parameters can be found accurately, with limited number of experimental trials using regression analysis, response surface methodology, soft computing techniques like fuzzy logic systems and support vector machines.This is achieved by establishing a relationship between the input process parameters and the desired output. Artificial neural network (ANN) is a blooming strategy for predicting the responses by training the network with the experimental data[17, 18]. ANN model imitates the basics of information processing modules of the human brain. ANN can handle complex tasks which include fitting complex models to data, multifaceted classification of data or signals, clustering the data and time series forecasting. Ghetiya et al., [19] predicted the tensile strength of FSWed aluminium alloy 8014 using ANN model and found that the predicted data were in good agreement with the experimental data. Lakshminarayanan et al., [20] compared the traditional response surface methodology technique with ANN model for predicting the tensile strength of FSWed AA7039. Hasan Okuyucu et al., developed ANN models to predict the tensile strength, yield strength and hardness of the FSWed aluminium alloy [21]. In this article, an ANN model was developed to predict the tensile strength of the FSW joint made in aluminium alloy AA1100. The model was validated using the data obtained from the experimental study.
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Vaira Vignesh and Padmanaban / Materials Today: Proceedings 5 (2018) 16716–16723
2. Materials and Methods AA1100 was used in this study and the nominal composition of the alloy is given in Table 1. The tensile strength and hardness of the alloy is 110 MPa and 32BHN respectively. The as received plates of thickness 5 mm were cut into required specimens of dimensions 150 mm x 75 mm. The sides of the workpiece were milled to ensure parallelism. Table 1. Nominal composition of the alloy Metal
Al
Mn
Zn
Cu
Fe & Si
Composition (%)
99
0.05
0.10
0.15
0.95
The FSW process parameters that greatly influence the quality of welds are tool rotation speed, welding speed, tool profile (shoulder diameter and pin diameter). So these four major FSW parameters were chosen for the study. The experiments were tailored according to face centered central composite design, with five levels of variation in each process parameter. The plan of the experiments is given in Table 2. FSW trials were performed in an automated vertical milling center. The FSW tool was positioned at the interface of the abutting workpieces, and then FSW was initiated. The workpieces were cleaned using acetone before FSW of the workpieces. The specimens for testing the tensile strength of the weld joints were prepared according to the ASTM standard - E-8M-08 (ASTM-2008). Two specimens were prepared for testing the tensile strength of each weld joint. The tests were performed in computer controlled tensile testing machine. The average tensile strength of the joints is given in Table 2.
Fig. 1. Artificial neural network model
The prediction and classification of nonlinear data can be effected by multilayer perceptron model in ANN. An example of multilayer perceptron network (feed forward model) is given in Fig. 1. As shown in Fig. 1, the inputs (FSW process parameters) are linked to the neurons and in turn the neurons are connected to the output (TS). The link between the input and output parameter with neurons is called as weighs, which facilitates the neural network to easily map the patterns in the data. In this study, ANN model was generated to predict the tensile strength of the friction stir welded joints AA1100. The modelling details are discussed in the next section of the paper. 3. ANN model development Multilayer perceptron networks (MLP) consists of three layers of neurons [22]. The first layer of neuron is the input layer, the third layer of neuron is the output layer and the middle layer of neurons is the hidden layer. In general, the intermediate stages in MLP model with r input neurons, s hidden neurons and t output neurons are constructed as given below. Equation (1) and (2) is used to map the input layer neuron with the hidden layer of neurons.
Vaira Vignesh and Padmanaban / Materials Today: Proceedings 5 (2018) 16716–16723
ui = woj ∑ wij × xi ; i = 1 to n
16719
(1)
yi = f (ui) (2) Where i and j are number of neurons in input layer and hidden layer respectively, xi is the ith input, wij is the weight associated with the input i and the neuron j, woj is the bias weightage of the hidden neuron j and f(uj) is the activation function of the jth neuron that transforms any hidden neuron input uj to hidden neuron output yj. Equation (3) and (4) is used to map the hidden layer of neurons with the output layer neurons. vk = wok ∑ wjk × yj ; j = 1 to m
(3)
zk = f (vk) (4) Where m and k are number of neurons in hidden layer and output layer respectively, yj is the jth output, wjk is the weight related with the output k and the neuron j, wok is the bias weightage of output neuron and f(vk) is the activation function of the kth neuron that transforms any weighed sum of inputs vk to the final output zk. The mean squared error (MSE) for all the training pattern of the networks with only one output neuron is given by the equation (5). MSE = ∑ (ti – zi) / 2N ; i = 1 to N
(5)
Where N is the number of training patterns, ti is the target value and zi is the predicted value. The parameter that controls the weights and bias changes in the leering of training algorithm is the learning rate, ε. In Gauss – Newton algorithm, ε is adjusted to train the network. In Levenberg Marquardt algorithm [23-26], ε is set to unity and an additional eλ term is introduced in the second derivative of the error function. It is advantageous over Gauss – Newton method that incorporates first and second derivatives of error. So Levenberg Marquardt algorithm was used to train the network. In this method, λ is chosen automatically (starting from a value), until a downhill step is produced for each epoch. This reduces the error in prediction of the developed ANN. The training of network terminates prior to the number of specified epochs, if the conditions given in the equation (6) and (7) are reached. λ > 10 × Δλ + Max [H] (6) (MSE wm – MSE wm+1 / MSE wm ) ≤ MSEmin
(7)
Where [H] is Hessian matrix. MATLAB R2015 © computing environment was used to develop the ANN model. The graphical representation of the developed neural network for this study is shown in Fig. 2. The number of neurons in input layer was 4 and output layer was 1, as the model had 4 inputs and 1 output. Thumb rule was followed for selecting number of hidden layers and number of neurons in the hidden layer. In this model, two hidden layers with 30 neurons and 15 neurons were developed. Levenberg Marquardt algorithm was used to train the network. 80% of the experimental data was used for training the network. 10% of the experimental data was used for validation and the remaining 10% of experimental data was used for testing the model.
Fig. 2. Graphical diagram of ANN model developed
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Vaira Vignesh and Padmanaban / Materials Today: Proceedings 5 (2018) 16716–16723
4. Results and Discussions The training parameters chosen for developing the ANN model were: number of epochs = 25 and minimum gradient = 10-7. The performance of the ANN model was based on the mean squared error value. Fig. 3 (a) shows the chosen levels of parameters and training progress of the ANN model. From the Fig. 3 (a), it is observed that the model converged at least gradient value.The performance plot and training state of the model are shown in the Fig. 3 (b) and Fig. 3 (c) respectively. (a)
(b)
(c)
Fig. 3 (a) Training progress window displaying the process parameters chosen for training the network; (b) Performance plot model; (c) Training state plot of model
The predicted values of tensile strength using the developed ANN model is given in Table 2. The percentage error in prediction was calculated using equation (8). % Error in prediction = ( 1 – Computed value / Experimental value) × 100
(8)
The measure that determines the fitness of the generated model is R, the coefficient of correlation. The uncertainty in training data was 0.27 (approximately). The three outliers in the input data increased the uncertainty in prediction results. The validation and testing R is almost unity, showing that the model has good efficacy in predicting the tensile strength of the joints.
Vaira Vignesh and Padmanaban / Materials Today: Proceedings 5 (2018) 16716–16723
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Table 2. Layout of experiments, experimental tensile strength, predicted tensile strength and percentage error in prediction Sl. No.
TRS
WS
SD
PD
-1
900
30
15
5
Experimental TS (MPa) 45.1
-1
1200
30
15
5
41.5
41.46
-1
900
60
15
5
48.2
46.63
3.27
-1
1200
60
15
5
42.2
42.30
-0.24
+1
-1
900
30
21
5
40.3
40.25
0.12
-1
+1
-1
1200
30
21
5
36.2
36.21
-0.02
+1
+1
-1
900
60
21
5
42.2
42.01
0.45
+1
+1
-1
1200
60
21
5
36.9
37.08
-0.50
Coded Value
Real Value
TRS
WS
SD
PD
1
-1
-1
-1
2
+1
-1
-1
3
-1
+1
-1
4
+1
+1
-1
5
-1
-1
6
+1
7
-1
8
+1
Computed TS (MPa) 44.87
% Error in prediction 0.51 0.09
9
-1
-1
-1
+1
900
30
15
7
59.3
58.74
0.94
10
+1
-1
-1
+1
1200
30
15
7
54.3
53.70
1.10
11
-1
+1
-1
+1
900
60
15
7
60.3
59.69
1.01
12
+1
+1
-1
+1
1200
60
15
7
54.3
54.21
0.17
13
-1
-1
+1
+1
900
30
21
7
55.3
55.22
0.14
14
+1
-1
+1
+1
1200
30
21
7
50.1
50.37
-0.53
15
-1
+1
+1
+1
900
60
21
7
59.4
59.27
0.22
16
+1
+1
+1
+1
1200
60
21
7
54.3
54.14
0.29
17
-2
0
0
0
750
45
18
6
60.3
60.20
0.16
18
+2
0
0
0
1350
45
18
6
48.2
48.53
-0.69
19
0
-2
0
0
1050
30
18
6
59.3
59.17
0.23
20
0
+2
0
0
1050
90
18
6
60.3
60.27
0.05
21
0
0
-2
0
1050
45
18
6
42.2
62.81
-48.84
22
0
0
+2
0
1050
45
18
6
37.9
62.81
-65.73
23
0
0
0
-2
1050
45
12
4
29
29.01
-0.03
24
0
0
0
+2
1050
45
24
8
54.3
54.32
-0.04
25
0
0
0
0
1050
45
18
6
71.1
62.81
11.66
26
0
0
0
0
1050
45
18
6
69.3
62.81
9.37
27
0
0
0
0
1050
45
18
6
69.9
62.81
10.14
28
0
0
0
0
1050
45
18
6
72.4
62.81
13.25
29
0
0
0
0
1050
45
18
6
70.5
62.81
10.91
30
0
0
0
0
1050
45
18
6
72.4
62.81
13.25
31
0
0
0
0
1050
45
18
6
70.9
62.81
11.41
The plots of experimental (target) and the predicted (output) result for the training data, validation data, test data and overall data are given in Fig. 4. The correlation coefficient for training data was found to be 0.825. The closeness of the correlation coefficient in validation and training data to one indicate that the prediction efficacy of the model is good. The overall R value of the model was found to be 0.821, which again indicated the good prediction efficiency of the ANN model
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Vaira Vignesh and Padmanaban / Materials Today: Proceedings 5 (2018) 16716–16723
Fig. 4 Plot of experimental versus predicted value of tensile strength of training data, validation data, test data and overall data
5. Conclusion Aluminium alloy AA1100 was successfully joined by friction stir welding process. Friction stir welding trials were conducted by varying the tool rotation speed, welding speed, tool shoulder diameter and pin diameter. The process parameters were varied at five levels and thirty one experimental trials were performed as per central composite design. ANN model with thirty neurons in first hidden layer and fifteen neurons in second hidden layer was developed for predicting the tensile strength of the joints. Levenberg Marquardt algorithm was used to train the model. The following inferences were made from the model obtained. Percentage error in prediction is found to be low for the model developed by Artificial Neural Network. The overall correlation coefficient of the model is 0.8214, indicating closeness of relationship between the FSW process parameters and the tensile strength. References [1] Colligan, K.J., 2 - The friction stir welding process: an overview, in Friction Stir Welding. 2010, Woodhead Publishing. p. 15-41. [2] Mishra, R.S. and H. Sidhar, Chapter 1 - Friction Stir Welding, in Friction Stir Welding of 2XXX Aluminum Alloys Including Al-Li Alloys. 2017, Butterworth-Heinemann. p. 1-13.
Vaira Vignesh and Padmanaban / Materials Today: Proceedings 5 (2018) 16716–16723
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[3] Padmanaban, R., V. Balusamy, and V.R. Kishore,Effect of axial pressure and tool rotation speed on temperature distribution during dissimilar friction stir welding, 418-420 (2012) 1934-1938 [4] Padmanaban, R., V. Balusamy, and K.N. Nouranga, Journal of Engineering Science and Technology, 10 (2015) 790-801 [5] Vignesh, R.V., R. Padmanaban, M. Arivarasu, K.P. Karthick, A.A. Sundar, and J. Gokulachandran, IOP Conference Series: Materials Science and Engineering, 149 (2016) [6] Zettler, R., 3 - Material deformation and joint formation in friction stir welding, in Friction Stir Welding. 2010, Woodhead Publishing. p. 42-72. [7] Zettler, R., T. Vugrin, and M. Schmücker, 9 - Effects and defects of friction stir welds, in Friction Stir Welding. 2010, Woodhead Publishing. p. 245-276. [8] Gibson, B.T., D.H. Lammlein, T.J. Prater, W.R. Longhurst, C.D. Cox, M.C. Ballun, K.J. Dharmaraj, G.E. Cook, and A.M. Strauss, Journal of Manufacturing Processes, 16 (2014) 56-73 [9] He, X., F. Gu, and A. Ball, Progress in Materials Science, 65 (2014) 1-66 [10] MURR, L.E., G. LIU, and J.C. McCLURE, Journal of Materials Science Letters, 16 (1997) 1801-1803 [11] Sato, Y.S., Y. Kurihara, S.H.C. Park, H. Kokawa, and N. Tsuji, Scripta Materialia, 50 (2004) 57-60 [12] Khorrami, M.S., M. Kazeminezhad, and A.H. Kokabi, Materials Science and Engineering: A, 543 (2012) 243248 [13] Hussein, S.A., A.S.M. Tahir, and A.B. Hadzley, Materials Today Communications, 5 (2015) 32-49 [14] Kartsonakis, I.A., D.A. Dragatogiannis, E.P. Koumoulos, A. Karantonis, and C.A. Charitidis, Materials & Design, 102 (2016) 56-67 [15] Sajed, M., Journal of Manufacturing Processes, 24, Part 1 (2016) 307-317 [16] Park, S.-W., T.-J. Yoon, and C.-Y. Kang, Journal of Materials Processing Technology, 241 (2017) 112-119 [17] Zurada, J.M., Introduction to artificial neural systems. Vol. 8. 1992: West St. Paul. [18] Kröse, B., B. Krose, P. van der Smagt, and P. Smagt, (1993) [19] Ghetiya, N.D. and K.M. Patel, Procedia Technology, 14 (2014) 274-281 [20] Lakshminarayanan, A.K. and V. Balasubramanian, Transactions of Nonferrous Metals Society of China, 19 (2009) 9-18 [21] Okuyucu, H., A. Kurt, and E. Arcaklioglu, Materials & Design, 28 (2007) 78-84 [22] Basheer, I. and M. Hajmeer, Journal of microbiological methods, 43 (2000) 3-31 [23] Russell, S.J., P. Norvig, J.F. Canny, J.M. Malik, and D.D. Edwards, Artificial intelligence: a modern approach. Vol. 2. 2003: Prentice hall Upper Saddle River. [24] Wang, S.-C., Artificial neural network, in Interdisciplinary Computing in Java Programming. 2003, Springer. p. 81-100. [25] Priddy, K.L. and P.E. Keller, Artificial neural networks: an introduction. Vol. 68. 2005: SPIE Press. [26] Yegnanarayana, B., Artificial neural networks. 2009: PHI Learning Pvt. Ltd.
ScienceDirect Materials Today: Proceedings 5 (2018) 16716–16723
www.materialstoday.com/proceedings
SCICON 2016
Artificial neural network model for predicting the tensile strength of friction stir welded aluminium alloy AA1100 R. Vaira Vignesh and R. Padmanaban* Department of Mechanical Engineering, Amrita School of Engineering,Coimbatore, Amrita Vishwa Vidyapeetham, Amrita University, India.
Abstract Friction stir welding (FSW) is a solid state welding technique, in which high strength weldswith minimal defects, can be obtained even with materialsthat are hardly weldable by conventional techniques. FSW is influenced by a number of process parameters. Some of the highly influential process parameters that determine the quality of the welds in FSW are tool rotation speed, welding speed, shoulder diameter and pin diameter of tool. In this study, FSW trials were conducted on AA1100 as per central composite design, with four parameters varied at five levels. The tensile strength of the joints were measured using a computerized tensile testing machine and these results were used to develop an artificial neural network model. The input parameters to the model were tool rotation speed, welding speed, shoulder diameter and pin diameter and the output was tensile strength of the joints. Levenberg Marquardt algorithm was used to establish the relationship between the process parameters and the output. The feed forward model was trained using 80% of the experimental data and the remaining 20% of the data was used for validation and testing of the model. The R2 valuesfor validation data and testing datawere found to be 0.80and0.99respectively, displaying the closeness between the experimental and predicted data. The results indicate that the generated model has high efficacy in predicting the tensile strength of friction stir welded aluminium alloy AA1100 joints. © 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Advanced Materials (SCICON ‘16). Keywords:Friction stir welding; Aluminium alloy; Tensile strength; Artificial neural network; Algorithm
1. Introduction Aluminium alloy 1100 is one of the preferred alloy for structural applications, sheet metal applications, heat exchangers, food containers etc. Conventional welding techniques when used for welding AA1100, result in poor
* Corresponding author. Tel.: 098945 68309 E-mail address: [email protected] 2214-7853© 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Advanced Materials(SCICON ‘16).
Vaira Vignesh and Padmanaban / Materials Today: Proceedings 5 (2018) 16716–16723
16717
Nomenclature FSW AA ANN TS TRS WS SD PD FSWed BHN MLP
Friction Stir Welding Aluminium Alloy Artificial Neural Network Tensile Strength Tool Rotation Speed Welding Speed Shoulder Diameter Pin Diameter Friction Stir Welded Brinell’s Hardness Number Multilayer Perceptron
quality welds due to rapid oxidation of the alloy at high temperature.Friction stir welding (FSW) is a solid state welding process, where the material is plasticized and the joining is effected by traversing a rotatingtool along the joint, under the action of axial force [1, 2]. The quality of welded joints depend on process parameters[3, 4], tool geometry[5] and the environmental conditions. Tool shoulder diameter, pin diameter and pin profile affects the welding joint efficiency [6, 7]. The major defects found in the conventional welds like porosity, segregation of alloying elements, hot cracking, poor surface finish etc. are minimized in FSW and high efficient joint is obtained[8, 9]. The joint formation by plasticizingthe material under extreme deformation results in dynamic recrystallization [10]. Sato et al., [11] produced friction stir welds with fine grained and improved mechanical properties, in accumulative roll bonded AA1100. Khorrami et al., [12] found that increase in tool rotation speed decreased the strength of friction stir welded joints in AA1100, which was imposed with severe strain by cumulative groove pressing before FSW. Sadiq Aziz Hussein et al., [13] found that the FSW process parameters greatly influence the mechanical properties of the dissimilarwelded between aluminium alloy and steel. I. Kartsonakis et al., [14] improved the corrosion resistance of dissimilar FSWed aluminium alloys by reinforcing nanophase cerium molybdate in the welds. Moosa Sajed et al., [15] optimized the two stage refilled friction stir spot welding process parameters for AA1100 and concluded that the dwell time had minimal effect in improving the strength of the weld. Sang-Won Park et al., [16] found that increasing the tool rotation speed decreased the tensile shear strength of the FSWed joint. The tensile shear strength of the material was high for specimens processed with large shoulder diameter. The main challenge in FSW lies in selecting the welding parameters that would produce an excellent weld joint. Conventional way of choosing welding parameters to produce a weld joint is a time consuming work and again each weld has to be tested for defects and mechanical properties. The experimental trials may or may not result in optimized FSW process parameter combinations. The welding parameters can be found accurately, with limited number of experimental trials using regression analysis, response surface methodology, soft computing techniques like fuzzy logic systems and support vector machines.This is achieved by establishing a relationship between the input process parameters and the desired output. Artificial neural network (ANN) is a blooming strategy for predicting the responses by training the network with the experimental data[17, 18]. ANN model imitates the basics of information processing modules of the human brain. ANN can handle complex tasks which include fitting complex models to data, multifaceted classification of data or signals, clustering the data and time series forecasting. Ghetiya et al., [19] predicted the tensile strength of FSWed aluminium alloy 8014 using ANN model and found that the predicted data were in good agreement with the experimental data. Lakshminarayanan et al., [20] compared the traditional response surface methodology technique with ANN model for predicting the tensile strength of FSWed AA7039. Hasan Okuyucu et al., developed ANN models to predict the tensile strength, yield strength and hardness of the FSWed aluminium alloy [21]. In this article, an ANN model was developed to predict the tensile strength of the FSW joint made in aluminium alloy AA1100. The model was validated using the data obtained from the experimental study.
16718
Vaira Vignesh and Padmanaban / Materials Today: Proceedings 5 (2018) 16716–16723
2. Materials and Methods AA1100 was used in this study and the nominal composition of the alloy is given in Table 1. The tensile strength and hardness of the alloy is 110 MPa and 32BHN respectively. The as received plates of thickness 5 mm were cut into required specimens of dimensions 150 mm x 75 mm. The sides of the workpiece were milled to ensure parallelism. Table 1. Nominal composition of the alloy Metal
Al
Mn
Zn
Cu
Fe & Si
Composition (%)
99
0.05
0.10
0.15
0.95
The FSW process parameters that greatly influence the quality of welds are tool rotation speed, welding speed, tool profile (shoulder diameter and pin diameter). So these four major FSW parameters were chosen for the study. The experiments were tailored according to face centered central composite design, with five levels of variation in each process parameter. The plan of the experiments is given in Table 2. FSW trials were performed in an automated vertical milling center. The FSW tool was positioned at the interface of the abutting workpieces, and then FSW was initiated. The workpieces were cleaned using acetone before FSW of the workpieces. The specimens for testing the tensile strength of the weld joints were prepared according to the ASTM standard - E-8M-08 (ASTM-2008). Two specimens were prepared for testing the tensile strength of each weld joint. The tests were performed in computer controlled tensile testing machine. The average tensile strength of the joints is given in Table 2.
Fig. 1. Artificial neural network model
The prediction and classification of nonlinear data can be effected by multilayer perceptron model in ANN. An example of multilayer perceptron network (feed forward model) is given in Fig. 1. As shown in Fig. 1, the inputs (FSW process parameters) are linked to the neurons and in turn the neurons are connected to the output (TS). The link between the input and output parameter with neurons is called as weighs, which facilitates the neural network to easily map the patterns in the data. In this study, ANN model was generated to predict the tensile strength of the friction stir welded joints AA1100. The modelling details are discussed in the next section of the paper. 3. ANN model development Multilayer perceptron networks (MLP) consists of three layers of neurons [22]. The first layer of neuron is the input layer, the third layer of neuron is the output layer and the middle layer of neurons is the hidden layer. In general, the intermediate stages in MLP model with r input neurons, s hidden neurons and t output neurons are constructed as given below. Equation (1) and (2) is used to map the input layer neuron with the hidden layer of neurons.
Vaira Vignesh and Padmanaban / Materials Today: Proceedings 5 (2018) 16716–16723
ui = woj ∑ wij × xi ; i = 1 to n
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(1)
yi = f (ui) (2) Where i and j are number of neurons in input layer and hidden layer respectively, xi is the ith input, wij is the weight associated with the input i and the neuron j, woj is the bias weightage of the hidden neuron j and f(uj) is the activation function of the jth neuron that transforms any hidden neuron input uj to hidden neuron output yj. Equation (3) and (4) is used to map the hidden layer of neurons with the output layer neurons. vk = wok ∑ wjk × yj ; j = 1 to m
(3)
zk = f (vk) (4) Where m and k are number of neurons in hidden layer and output layer respectively, yj is the jth output, wjk is the weight related with the output k and the neuron j, wok is the bias weightage of output neuron and f(vk) is the activation function of the kth neuron that transforms any weighed sum of inputs vk to the final output zk. The mean squared error (MSE) for all the training pattern of the networks with only one output neuron is given by the equation (5). MSE = ∑ (ti – zi) / 2N ; i = 1 to N
(5)
Where N is the number of training patterns, ti is the target value and zi is the predicted value. The parameter that controls the weights and bias changes in the leering of training algorithm is the learning rate, ε. In Gauss – Newton algorithm, ε is adjusted to train the network. In Levenberg Marquardt algorithm [23-26], ε is set to unity and an additional eλ term is introduced in the second derivative of the error function. It is advantageous over Gauss – Newton method that incorporates first and second derivatives of error. So Levenberg Marquardt algorithm was used to train the network. In this method, λ is chosen automatically (starting from a value), until a downhill step is produced for each epoch. This reduces the error in prediction of the developed ANN. The training of network terminates prior to the number of specified epochs, if the conditions given in the equation (6) and (7) are reached. λ > 10 × Δλ + Max [H] (6) (MSE wm – MSE wm+1 / MSE wm ) ≤ MSEmin
(7)
Where [H] is Hessian matrix. MATLAB R2015 © computing environment was used to develop the ANN model. The graphical representation of the developed neural network for this study is shown in Fig. 2. The number of neurons in input layer was 4 and output layer was 1, as the model had 4 inputs and 1 output. Thumb rule was followed for selecting number of hidden layers and number of neurons in the hidden layer. In this model, two hidden layers with 30 neurons and 15 neurons were developed. Levenberg Marquardt algorithm was used to train the network. 80% of the experimental data was used for training the network. 10% of the experimental data was used for validation and the remaining 10% of experimental data was used for testing the model.
Fig. 2. Graphical diagram of ANN model developed
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4. Results and Discussions The training parameters chosen for developing the ANN model were: number of epochs = 25 and minimum gradient = 10-7. The performance of the ANN model was based on the mean squared error value. Fig. 3 (a) shows the chosen levels of parameters and training progress of the ANN model. From the Fig. 3 (a), it is observed that the model converged at least gradient value.The performance plot and training state of the model are shown in the Fig. 3 (b) and Fig. 3 (c) respectively. (a)
(b)
(c)
Fig. 3 (a) Training progress window displaying the process parameters chosen for training the network; (b) Performance plot model; (c) Training state plot of model
The predicted values of tensile strength using the developed ANN model is given in Table 2. The percentage error in prediction was calculated using equation (8). % Error in prediction = ( 1 – Computed value / Experimental value) × 100
(8)
The measure that determines the fitness of the generated model is R, the coefficient of correlation. The uncertainty in training data was 0.27 (approximately). The three outliers in the input data increased the uncertainty in prediction results. The validation and testing R is almost unity, showing that the model has good efficacy in predicting the tensile strength of the joints.
Vaira Vignesh and Padmanaban / Materials Today: Proceedings 5 (2018) 16716–16723
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Table 2. Layout of experiments, experimental tensile strength, predicted tensile strength and percentage error in prediction Sl. No.
TRS
WS
SD
PD
-1
900
30
15
5
Experimental TS (MPa) 45.1
-1
1200
30
15
5
41.5
41.46
-1
900
60
15
5
48.2
46.63
3.27
-1
1200
60
15
5
42.2
42.30
-0.24
+1
-1
900
30
21
5
40.3
40.25
0.12
-1
+1
-1
1200
30
21
5
36.2
36.21
-0.02
+1
+1
-1
900
60
21
5
42.2
42.01
0.45
+1
+1
-1
1200
60
21
5
36.9
37.08
-0.50
Coded Value
Real Value
TRS
WS
SD
PD
1
-1
-1
-1
2
+1
-1
-1
3
-1
+1
-1
4
+1
+1
-1
5
-1
-1
6
+1
7
-1
8
+1
Computed TS (MPa) 44.87
% Error in prediction 0.51 0.09
9
-1
-1
-1
+1
900
30
15
7
59.3
58.74
0.94
10
+1
-1
-1
+1
1200
30
15
7
54.3
53.70
1.10
11
-1
+1
-1
+1
900
60
15
7
60.3
59.69
1.01
12
+1
+1
-1
+1
1200
60
15
7
54.3
54.21
0.17
13
-1
-1
+1
+1
900
30
21
7
55.3
55.22
0.14
14
+1
-1
+1
+1
1200
30
21
7
50.1
50.37
-0.53
15
-1
+1
+1
+1
900
60
21
7
59.4
59.27
0.22
16
+1
+1
+1
+1
1200
60
21
7
54.3
54.14
0.29
17
-2
0
0
0
750
45
18
6
60.3
60.20
0.16
18
+2
0
0
0
1350
45
18
6
48.2
48.53
-0.69
19
0
-2
0
0
1050
30
18
6
59.3
59.17
0.23
20
0
+2
0
0
1050
90
18
6
60.3
60.27
0.05
21
0
0
-2
0
1050
45
18
6
42.2
62.81
-48.84
22
0
0
+2
0
1050
45
18
6
37.9
62.81
-65.73
23
0
0
0
-2
1050
45
12
4
29
29.01
-0.03
24
0
0
0
+2
1050
45
24
8
54.3
54.32
-0.04
25
0
0
0
0
1050
45
18
6
71.1
62.81
11.66
26
0
0
0
0
1050
45
18
6
69.3
62.81
9.37
27
0
0
0
0
1050
45
18
6
69.9
62.81
10.14
28
0
0
0
0
1050
45
18
6
72.4
62.81
13.25
29
0
0
0
0
1050
45
18
6
70.5
62.81
10.91
30
0
0
0
0
1050
45
18
6
72.4
62.81
13.25
31
0
0
0
0
1050
45
18
6
70.9
62.81
11.41
The plots of experimental (target) and the predicted (output) result for the training data, validation data, test data and overall data are given in Fig. 4. The correlation coefficient for training data was found to be 0.825. The closeness of the correlation coefficient in validation and training data to one indicate that the prediction efficacy of the model is good. The overall R value of the model was found to be 0.821, which again indicated the good prediction efficiency of the ANN model
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Vaira Vignesh and Padmanaban / Materials Today: Proceedings 5 (2018) 16716–16723
Fig. 4 Plot of experimental versus predicted value of tensile strength of training data, validation data, test data and overall data
5. Conclusion Aluminium alloy AA1100 was successfully joined by friction stir welding process. Friction stir welding trials were conducted by varying the tool rotation speed, welding speed, tool shoulder diameter and pin diameter. The process parameters were varied at five levels and thirty one experimental trials were performed as per central composite design. ANN model with thirty neurons in first hidden layer and fifteen neurons in second hidden layer was developed for predicting the tensile strength of the joints. Levenberg Marquardt algorithm was used to train the model. The following inferences were made from the model obtained. Percentage error in prediction is found to be low for the model developed by Artificial Neural Network. The overall correlation coefficient of the model is 0.8214, indicating closeness of relationship between the FSW process parameters and the tensile strength. References [1] Colligan, K.J., 2 - The friction stir welding process: an overview, in Friction Stir Welding. 2010, Woodhead Publishing. p. 15-41. [2] Mishra, R.S. and H. Sidhar, Chapter 1 - Friction Stir Welding, in Friction Stir Welding of 2XXX Aluminum Alloys Including Al-Li Alloys. 2017, Butterworth-Heinemann. p. 1-13.
Vaira Vignesh and Padmanaban / Materials Today: Proceedings 5 (2018) 16716–16723
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