CHAPTER 6 OPTIMIZATION OF WELDING SEQUENCE

88 CHAPTER 6 OPTIMIZATION OF WELDING SEQUENCE 6.1 INTRODUCTION The amount of distortion is greatly influenced by changing the sequence of welding in a structure. After having estimated optimum GMAW process parameters for a single sequence provided in chapter 5, an attempt was made to further minimize the distortion in the T-joint on the basis of welding sequence, by simulating welding of T-joint at various combinations of welding sequences, using the same optimized GMAW process parameters in all the simulations. The later part of this chapter covers the development of ANN model used to optimize welding sequences to minimize distortion in the T-joint. 6.2 DESCRIPTION OF INPUT PARAMETERS The fillet welding to be carried out on anyone side of the T-joint for a length of 210 mm is divided into three step welding sequence each of which has a length of 70 mm. Figure 6.1 shows the divisions and notations of the step welding sequence in the T-joint. In order to complete the fillet welding on both the sides of T-joint, there are six step welding sequences. Each step welding sequence can be done either in forward direction (shown in Figure 6.1) or in reverse direction. Thus, for example, if the welding pattern is specified as 14362-5, then it means that the step welding sequence 1 has to be welded first in the position and direction as shown in Figure 6.1, followed by the step welding sequences 4, 3, 6, 2 and -5. It is to be noted that

89 only the step welding sequence 5 in this example, needs to be welded in the opposite direction. According to this, the same step welding sequence should not reappear either in the forward or reverse direction. Thus, for example, the pattern 34621-2 is considered to be invalid due to the reason that the step welding sequence 2 appears again. Figure 6.1 Representation and position of step welding from the end A 6.3 SELECTION OF COMBINATIONS OF WELDING SEQUENCES When the fillet welding in the T-joint can be completed by six different step welding sequences in any order and direction, the total possible welding sequences work out to be equal to 46080 ( = 2 6 x 6!). For each welding sequence in these 46080 combinations, there is another sequence which results n the same distortion, if the reference for the representation is made from the end B of the T-joint as shown in Figure 6.2. Since the T-joint is symmetric about vertical plane and has a uniform cross section, the same

90 divisions and notations of step welding sequence can be made about the end B as that about the end A. Hence, for example, if the given welding sequence is 1-24-536 with reference to the end B, its corresponding welding sequence with reference to the end A is -65-32-4-1. Hence, for every welding sequence in which the first step welding sequence is positive, another welding sequence in which the first step welding sequence is negative, will result in the same output of distortion. Hence it was decided to consider only the welding sequences in which the first step welding sequence is positive. Therefore, the total number of possible combinations of welding sequences which can result in distinct distortions is 23040. Since the FE computation of distortion of T-joint for any given welding sequence takes about 30 hours, it is impractical to simulate for all the 23040 welding sequences. Hence, it was decided to consider a reasonable number of welding sequences from among the 23040 combinations. The distortion of T-joint gets affected by the intensity and the extent of spread of the arc heat, while other factors such as mechanical constraints, preheating etc, remain constant. As all the welding sequences are carried out using the same optimized GMAW process parameters, the intensity of arc heat is almost same in all the welding sequences. Therefore, the selection of the welding sequences should be made on the basis of the extent of spread of arc heat. The one thing which changes the extent of spread of arc heat is the immediate laying of subsequent step welding sequence in a particular welding sequence. After a particular step welding sequence has been welded, the next step welding sequence should not be adjacent or from the same side of the T-joint. For example, the welding sequence 1243-5-6 was not considered due to the reason that after the step welding sequence 1, the next step welding sequence was 2, which was adjacent as well as from the same side of the joint. It was also not considered for the same reason in respect of the step welding sequence -5 and -6. After avoiding the welding sequences on the basis of similar and two consecutive step welding sequences, the remaining welding sequences were

91 found to be 2304. In order to run FE simulations in a systematic way, those welding sequences were divided into six groups. Each group consisted of welding sequences with the same first step welding sequence. Thus, Group 1 consisted of 384 welding sequences in which the first step welding sequence was 1. Similarly, Group 2 consisted of 384 welding sequences which started from the step welding sequence 2. Figure 6.2 Representation and position of step welding from the end B 6.4 FINITE ELEMENT COMPUTATION OF DISTORTIONS The same finite element modelling as described in section 3.3 of Chapter 3 was used for the computation of distortions of T-joint for various welding sequences. The GMAW process parameters which were optimized in the previous chapter (welding current 190 A, arc voltage 28 V and welding speed 5.567 mm/s) were used in the simulation of distortion for all combinations of welding sequences. No time interval was assumed in between the step welding sequences. The simulation was carried out until the

92 welded T-joint reached the room temperature for all combinations of welding sequences. After the simulation, the maximum distortion in the T-joint was obtained for all the welding sequences considered. The results of FE computation of distortions for all the 2304 (=384 x 6) welding sequences were obtained. The maximum and minimum distortion values obtained for these welding sequences are shown in Table 6.1. Figures 6.3-6.5 show typical deformed shape of T-Joint for the sequences 152634, 425361 and 4-263-5-1 respectively. Figure 6.3 Deformed shape of T-Joint simulated with welding sequence 152634

93 Figure 6.4 Deformed shape of T-Joint simulated with welding sequence 425361 Table 6.1 Minimum and maximum values of distortion Description Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 * Overall Minimum Distortion Welding Sequence Distortion (mm) Minimum/Maximum 1-5 3 6-2-4 0.670878995 Minimum 1 5 2 6 3 4 0.764286047 Maximum 2 6 3 5-1-4 0.671629339 Minimum 2 5 3 6 1 4 0.736048836 Maximum 3 6 2-4-1 5 0.665213072 * Minimum 3 4 2 5 1 6 0.748373420 Maximum 4-2 6 3-5-1 0.67030810 Minimum 4 2 5 3 6 1 0.75748730 Maximum 5 3 6 2-4-1 0.67147475 Minimum 5 2 6 3 4 1 0.74228176 Maximum 6 3 5-1-4 2 0.665355880 Minimum 6 1 5 2 4 3 0.751267832 Maximum

94 Figure 6.5 Deformed shape of T-Joint simulated with welding sequence 4-263-5-1 6.5 DEVELOPMENT OF ANN MODEL With the computed distortion data available for the welding sequences, it was decided to develop an ANN model for the optimization of welding sequences. Once an ANN model is trained with the available distortion data, it can be simulated for the optimization purpose. Since the computed distortion data are available under six groups, it was decided to train the ANN model separately. 6.5.1 Architecture of ANN Model An ANN model is characterized by (1) its pattern of connections between the neurons, (2) its method of determining the weights on the connections (called its training, or training, algorithm) and (3) its activation

95 function. After many trials with the different numbers of neurons and hidden layers, it was decided to use two hidden layers, in addition to input and output layers. As the first step welding sequence in each group of welding sequences is common, it was decided to use 15 neurons to represent a particular welding sequence at the input layer, the details of which are presented in the following section. The first and second hidden layers had 15 and 5 neurons respectively. Since each welding sequence is mapped to a single distortion value, only one neuron was used in the output layer. 6.5.2 Representation of Input Parameters It is essential to use correct representation for the welding sequences, as there should not be any misrepresentation between the welding sequences. In other words, the representation to be used for the input parameters should be unique. In order to achieve this, the method shown in Table 6.2 is followed to represent the welding sequences at the input layer. Since the first step welding sequence is same for all the welding sequences in each group, only the remaining five step welding sequences in a welding sequence is considered to be represented in the input neurons. Hence, each step welding sequence in a welding sequence is represented by three neurons. The first neuron is used to specify the position of a step welding sequence in either side of the T-joint. Similarly, the second neuron is used to specify whether the position of a step welding sequence is in the right or the left fillet of the joint. The third neuron is used to specify the direction of a step welding sequence. For quicker update of weights, the values of neurons at the input layer are modified as given in Table 6.2.

96 Table 6.2 Representation of input step welding sequence Step Welding Sequence Bipolar Representation Modified Bipolar Representation 1 ( 1-1 1 ) ( 0.8-0.8 0.8 ) 2 ( 0-1 1 ) ( 0.01-0.8 0.8 ) 3 ( -1-1 1 ) ( -0.8-0.8 0.8 ) 4 ( 1 1 1 ) ( 0.8 0.8 0.8 ) 5 ( 0 1 1 ) ( 0.01 0.8 0.8 ) 6 ( -1 1 1 ) ( -0.8 0.8 0.8 ) -1 ( 1-1 -1 ) ( 0.8-0.8-0.8 ) -2 ( 0-1 -1 ) ( 0.01-0.8-0.8 ) -3 ( -1-1 -1 ) ( -0.8-0.8-0.8 ) -4 ( 1 1-1 ) ( 0.8 0.8-0.8 ) -5 ( 0 1-1 ) ( 0.01 0.8-0.8 ) -6 ( -1 1-1 ) ( -0.8 0.8-0.8 ) 6.5.3 Training and Testing of ANN model Training of ANN model was carried out separately for the individual groups of welding sequences. The training parameters considered for weights update during training are: learning rate = 0.9 and momentum = 0.9. The sigmoid function, f(x) as given in equation (6.1) was used as the activation function with the lower and the upper ranges of -1 and 1 respectively. The activation function has a slope parameter (σ) of 0.05. The weights are initialized according to the formulation given by Nguyen-Widrow (Laurene Fausett 1994) to achieve faster learning. According to this formulation, the initial weights are random values in the range from -0.5 to 0.5. As each group consists of 384 welding sequences, 50% of them were selected at random and trained with their corresponding target distortion

97 values, in batch mode. When the sum of squares of errors between the ANN output and the target was below a specified tolerance of 0.01 in the training batch, then the training of ANN model was stopped. Afterwards, the trained network was tested with the remaining 50% of welding sequences against their corresponding distortion values. The percentage of error as described in equation (6.2) was calculated for each welding sequence in the testing lot. Root mean square value for these percentage errors was computed. This process of training the network was repeated many times from the beginning by selecting another set of 50% of welding sequences at random, until the root mean square value of percentage errors in the current testing lot was better than the previous lot. 2 f (x) - 1 (6.1) - x 1 e target value - net value % Error x 100 (6.2) target value 6.6 RESULTS AND DISCUSSIONS Each group of welding sequences was trained and tested in the manner described above. The consolidated results of testing the network for all the six groups of welding sequences are presented in Table 6.3. The results of testing the ANN model for all 6 groups of welding sequences are presented separately in Appendices 1-6. The final weight matrices between different layers after the training of the ANN model for the welding sequences in Group 1-6 are presented in Appendices 7-12. Another parameter for testing the correlation between the ANN values and the target values is R 2, which is calculated as follows:

98 SS SS 2 Error %R 1 - x 100 (6.3) Target where SS Error is sum of squares of errors and SS Target the sum of squares of target (FE values). The calculated R 2 values are provided in Table 6.3. Table 6.3 Results of testing of ANN model Name of the Group Number of sequences tested Range of % Error R 2 Group 1 192-2.97273 to 1.79443 0.9999110 Group 2 192-2.78476 to 2.75832 0.9998778 Group 3 192-3.87210 to 3.23585 0.9998423 Group 4 192-3.02658 to 2.60696 0.9998973 Group 5 192-2.67335 to 3.74498 0.9998651 Group 6 192-3.07170 to 2.47957 0.9998968 6.7 OPTIMIZATION OF WELDING SEQUENCE USING ANN MODEL After having tested the predictive capability of the ANN model, the next task would be to simulate the developed ANN model for the purpose of determining the optimum welding sequence which would result in minimum distortion. The simulation of the ANN model was carried out as follows: The net input to neuron i in layer k+1 is k k 1 1 1 k k k i ij j i j1 n w a bb (6.3) where w ij is the weight of i th neuron at j th layer, a is the neuron value and bb is the bias. The output of i th neuron will be

99 a f (n ) (6.4) k 1 k 1 k 1 i i where f is the activation function of neurons in (k+1) th layer. The welding sequences from Group 1 to Group 6 were given as inputs to the first layer of the ANN model of each group and the outputs of the ANN model were obtained using equations (6.3) and (6.4). The welding sequence which resulted in minimum distortion during the simulation of the ANN model was found out from among the ANN output for the individual groups of welding sequences. The results of optimization of welding sequences for each group are presented in Table 6.4. It is evident that the developed ANN model is capable of predicting the distortion in the T-joint with reasonable accuracy. The overall optimum welding sequence can be found from the individual optimum welding sequence of each group. Thus, the overall optimum welding sequence from the simulation of the ANN model is found to be 6 2 4-3 -5-1 which results in the minimum distortion value of 0.6652 mm. But, the overall minimum distortion value of 0.66521 mm from the FE predictions in Table 6.1 was obtained for the welding sequence 3 6 2-4 -1 5 which is shown in Figure 6.6. Though the minimum distortion value predicted by both ANN model and FEM is equal, but there is a difference between the sequences predicted by ANN model and FEM. This is due to the reason that the difference between distortion values obtained for various sequences is narrow, as there are 2304 welding sequences producing distortions ranging from a minimum of 0.66535 mm to a maximum of 0.764286 mm. In addition, the error in the predictive ability of ANN model is about ± 3.8 %. Besides, the ANN model is trained on the basis of the distortion values obtained by FEM. Hence, there occurs a difference in optimum sequences predicted by ANN model and FEM. The optimum sequence obtained by ANN model can be considered as an alternative solution with an error margin of about 3.8%.

100 Table 6.4 Results of optimization of welding sequence Description Optimum Sequence Distortion, (mm) ANN FE % Error Group 1 1-5 3 6-2-4 0.6696 0.67088-0.1908 Group 2 2-4-1-5 3-6 0.6739 0.68095-1.0353 Group 3 3 5-1-4 2 6 0.6630 0.67474-1.7399 Group 4 4 2 6-3-5-1 0.6762 0.68363-1.0868 Group 5 5 3-6-2-4-1 0.6726 0.68691-2.0832 Group 6 6 2 4-3-5-1 0.6652 * 0.67531-1.4971 * Overall Minimum Distortion Thus, with the distortion values of 50% of welding sequences used for training the ANN model, the distortion of T-joint for the remaining 50% can be predicted with reasonable accuracy. The deformed shape of the T-joint welded with optimum welding sequence is shown in Figure 6.7. It is evident that the distortion of T-joint is reduced considerably. Figure 6.6 Optimum welding sequence

Figure 6.7 Deformed shape of T-Joint simulated with optimum sequence 101