Prediction of the vertical force during FSW of AZ31 magnesium alloy sheets using an artificial neural network-based model

A multivariable empirical model based on an artificial neural network (ANN) was developed in order to predict the vertical force occurring during friction stir welding (FSW) of sheets in AZ31 magnesium alloy. To this purpose, FSW experiments were performed at different values of rotational and welding speeds, and the vertical force versus time curve was recorded during the different stages of the process by means of a dedicated sandwich dynamometer. Such results were used in the training stage of the artificial neural network-based model developed to predict vertical force versus time curves. A multi-layer feed forward ANN, using the back-propagation algorithm, consisting of the input layer with four input parameters (rotational speed, welding speed, rotational speed to welding speed ratio and processing time), two hidden layers with four neurons each, and the output layer with the vertical force as output, was built and trained. The generalization capability of the ANN was tested using a two-step procedure: in the former, the leave-one-out cross-validation method was used whilst, in the latter, curves not included in the training dataset were taken into account. The low values of the relative error and average absolute relative error, and the high correlation coefficients between predicted and experimental results have proven the excellent capability of the artificial neural network in modeling complex shape of the curve and in capturing the effect of the process parameters on the vertical force without a priori knowledge of the complex microstructural and mechanical mechanisms taking place during friction stir welding. Finally, the relationship between vertical force and processing time, at different welding and rotational speeds, was also predicted using the support vector machine algorithm and the results were compared with those given by the ANN-based model.