OBRABOTKAMETALLOV Vol. 24 No. 3 2022 TECHNOLOGY from the input data and initialized weights which lead to the fi nal output prediction of the network. Then, the error at output node is calculated and based on an error the weights are modifi ed. And weights in the previous layers are modifi ed by back-propagating errors calculated at output layer nodes [18]. This process is repeated for a set of input and output of training data. The training stops when the ANN output is suffi ciently close to the expected output for each set. ANN model is built to obtain the wear considering the input parameters as the normal load, interface temperature, and sliding speed using MATLAB Toolbox. The ANN architecture has three layers namely input, output, and hidden layers (Fig. 4). The input layer has 3 neurons, the output layer has 1 neuron, and there is appropriate number of neurons on the hidden layer. The neurons are selected by checking the network accuracy. The number of neurons on the hidden layer can be changed if the network does not perform well after training. Fig. 4. ANN architecture to obtain wear rate A feed-forward neural network maps a data set of numeric inputs with a set of numeric targets. The Neural Fitting app of MATLAB Toolbox helps to select data and create and train a network and evaluate its performance using mean square error and regression analysis. A two-layer feed-forward network with sigmoid hidden neurons and linear output neurons is selected that fi ts multi-dimensional problems arbitrarily well, given consistent data and enough neurons in its hidden layer. The network has been trained with the Levenberg-Marquardt backpropagation algorithm. In a neural network, three kinds of samples are used for the training and validation of test data. In the present work, around 70 % of the data is used for training the neural network. The network is adjusted according to its error. Around 15 % of the data is used for validation of the results predicted by the trained neural network. These validation data sets are used to measure network generalization, and to halt training when generalization stops improving. And around 15 % data is used for testing the results predicted by the neural network. These data sets do not affect training and so provide an independent estimation of network performance during and after training. The next important step is to determine network architecture to obtain better accuracy of the predicted results. In this study, a better-predicted accuracy of 0.9747 has been observed with eight neurons in the hidden layer. Further, the network is to be trained using either the Levenberg-Marquardt algorithm or Bayesian Regularization, or Scaled Conjugate Gradient algorithm. However, the researchers have mostly used the Levenberg-Marquardt algorithm. This algorithm is comparatively faster than other algorithms. However, this algorithm requires more memory. Neural network training performance is measured in terms of mean squared error (the average squared error between targets and outputs). Lower values are better. Regression (R) values measure the correlation between outputs (predicted values) and targets (inputs). Neural network regression graphs with regression coeffi cients obtained while training the model, during validation, testing, and for the entire data set are shown in Figs. 5, a–d respectively. The values of regression coeffi cients close to one for training, validation, testing, and for the entire data set shows that the developed neural network model could be reliably used for predicting PTFE composite wear rate reinforced with carbon fi bre (35 wt.%) against SS304 stainless steel within the domain of the parameters selected in this study.
RkJQdWJsaXNoZXIy MTk0ODM1