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ANN model is proposed, developed and validated to predict residual stress (Fig. 4). It is feed forward back propagation network trained with Levenberg- Marquardt back propagation algorithm. The data required for training and testing the ANN model is obtained from finite element analysis simulation (Table 1). The learning function is gradient descent algorithm with momentum weight and bias learning function. The number of hidden layers and neurons are determined through a trial and error method, in order to accommodate the converged error. The structure of the proposed neural network is 4-12-13-1 (4 neurons in the input layer, 12 neurons in 1“ hidden layer and 13 neurons in 2™ hidden layer and 1 neuron in the output layer). With a learning rate of 0.55 and a momentum term of 0.9, the network is trained for 10000 iterations. The error between the desired and the actual outputs is less than 0.001 at the end of the training process and the command window shows the input test data and output obtained from the developed ANN model (Fig. 5). Fig. 3—Stress distribution over butt-welded structure under study

Figure 4 ANN model is proposed, developed and validated to predict residual stress (Fig. 4). It is feed forward back propagation network trained with Levenberg- Marquardt back propagation algorithm. The data required for training and testing the ANN model is obtained from finite element analysis simulation (Table 1). The learning function is gradient descent algorithm with momentum weight and bias learning function. The number of hidden layers and neurons are determined through a trial and error method, in order to accommodate the converged error. The structure of the proposed neural network is 4-12-13-1 (4 neurons in the input layer, 12 neurons in 1“ hidden layer and 13 neurons in 2™ hidden layer and 1 neuron in the output layer). With a learning rate of 0.55 and a momentum term of 0.9, the network is trained for 10000 iterations. The error between the desired and the actual outputs is less than 0.001 at the end of the training process and the command window shows the input test data and output obtained from the developed ANN model (Fig. 5). Fig. 3—Stress distribution over butt-welded structure under study

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where q, and q, are the components of heat flow rate vector per unit area in the plate (x; y), Q the heat Fig. 1—Developed scheme to predict weld residual stress
where q, and q, are the components of heat flow rate vector per unit area in the plate (x; y), Q the heat Fig. 1—Developed scheme to predict weld residual stress
Fig. 2—Material properties of mild steel
Fig. 2—Material properties of mild steel
Every rule has a weight (a number between 0 and 1), which is applied to the number given by the antecedent. Once proper weighting has been assigned o each rule, the implication method is implemented. The result is a fuzzy set represented by a membership function, which weights the linguistic characteristics hat are attributed to it. The decisions are based on he testing of all the rules in fuzzy inference system. The input of the aggregation process is the list of runcated output functions returned by the implication process for each rule. The input for the defuzzification process is a fuzzy set and the output is a single number. Fuzziness helps the rule evaluation during he intermediate steps, the final desired output for each variable is a single number. However, the Fig. 4—Developed ANN architecture for residual stress prediction
Every rule has a weight (a number between 0 and 1), which is applied to the number given by the antecedent. Once proper weighting has been assigned o each rule, the implication method is implemented. The result is a fuzzy set represented by a membership function, which weights the linguistic characteristics hat are attributed to it. The decisions are based on he testing of all the rules in fuzzy inference system. The input of the aggregation process is the list of runcated output functions returned by the implication process for each rule. The input for the defuzzification process is a fuzzy set and the output is a single number. Fuzziness helps the rule evaluation during he intermediate steps, the final desired output for each variable is a single number. However, the Fig. 4—Developed ANN architecture for residual stress prediction
Table 1—Training data set obtained from finite element analysis
Table 1—Training data set obtained from finite element analysis
Fig. 5—Command window showing the input test data and outputs obtained from the developed ANN model for weld residual stress prediction
Fig. 5—Command window showing the input test data and outputs obtained from the developed ANN model for weld residual stress prediction
Fig. 6—Membership function for arc efficiency
Fig. 6—Membership function for arc efficiency
Fig.7—Membership function for weld speed Fig. 8—Membership function for arc voltage
Fig.7—Membership function for weld speed Fig. 8—Membership function for arc voltage
Fig. 9—Membership function for weld current
Fig. 9—Membership function for weld current
Fig. 10—Membership function for weld residual stress
Fig. 10—Membership function for weld residual stress
Table 2—Crisp input values used for fuzzy logic modeling aggregate of a fuzzy set encompasses a range of output values and so must be defuzzified in order to resolve a single output value from the set. Centroid method of defuzzification is used in developing the model.
Table 2—Crisp input values used for fuzzy logic modeling aggregate of a fuzzy set encompasses a range of output values and so must be defuzzified in order to resolve a single output value from the set. Centroid method of defuzzification is used in developing the model.
Fig. 11—An example from fuzzy logic modeling for prediction of weld residual stress
Fig. 11—An example from fuzzy logic modeling for prediction of weld residual stress
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