Exact(5)
The relative error of training and testing sets were 2.11% and 2.6%, respectively.
Standard error of training and standard error of prediction were 6.28 and 5.11%, respectively, for the MLR model and 1.03 and 1.20%, respectively, for the ANN model.
Figure 20a shows the normalized absolute average error of training data per normalized forecasting length (h). Figure 20b shows the divergence between training data and network training data.
In Fig. 3 the alteration of the value of mean squared error of training data versus the epochs is depicted and in Fig. 4 the alteration of the value of adaptive training factor mu versus the epochs is plotted.
The aim of this work was to create a system that could predict the surface roughness quite accurately; it is quantified as a small value of Mean Squared Error of training and test data, respectively.
Similar(54)
Standard errors of training and prediction were 0.954 and 0.945, respectively, for the MLR model and 0.032 and 0.007, respectively, for the ANN model.
Obviously, the values of both the mean squared errors of training and test data are significantly small.
Open image in new window Fig. 15 Accuracy of ANN predictions for training, validation, and testing sets Open image in new window Fig. 16 Histogram of calculated errors of training, validation, and testing sets.
The training process was stopped when errors of training and validation data sets converged.
If the difference between training errors of current training series and previous training series is smaller than a specified threshold ε, it means the network is convergent and the training should stop.
The results showed that the statistical error values of training were obviously within acceptable uncertainties.
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