## 4 Test Results and Discussion
There were a total of 18 errors, with 15 errors during training and only 3 errors during validation, demonstrating the effectiveness of the model. As a result, the following confusion matrix, Figure 9, was obtained. On the confusion matrix plot, the rows correspond to the predicted class (\(\mathbf{Y_{ob}}\)--obtained via ANN), and the columns correspond to the true class (\(\mathbf{Y_{des}}\)--Target). The cells along the diagonal represent instances that are accurately classified, while those of the diagonal denote misclassified observations. Each cell displays both the count and the percentage of observations relative to the total. The rightmost column provides the percentages of all predicted examples for each class that are correctly and incorrectly classified. These metrics are commonly known as precision (or positive predictive value) and false discovery rate, respectively [20]. Similarly, the bottom row displays the percentages of all examples belonging to each class that are correctly and incorrectly classified. These metrics are often referred to as recall (or true positive rate) and false negative rate, respectively. Finally, the cell in the bottom right corner of the plot indicates the overall accuracy [26]. In Figure 9, the first three diagonal cells show the number and percentage of correct classifications after the training (Figure 9a) and validation (Figure 9b) of the network, respectively. For example, in Figure 9a, 616 samples are correctly classified as class 1 (normal operation). This corresponds to 84% of all 733 samples. Similarly, 46 cases are correctly classified as class 2 (thermal faults). This corresponds to 6.3% of all samples. Finally, 56 samples were classified as class 3 (electrical faults), corresponding to 7.6% of all samples. Overall, 97.9% of the predictions are correct, and 2.1% are wrong for training. Similar results are presented for validation in Figure 9b: it is observed that 96.3% of the predictions are correct and 3.7% are wrong. In both phases, the network achieved an accuracy of 97.8%, hitting 797 samples and an error rate of just 2.2%, as shown in Figure 9c. \begin{table}
\begin{tabular}{c c c} \hline \hline
**PRN (5, 5, 3)** & **Specified Values** & **Achieved Values** \\ \hline Iterations & 1000 & 113 \\ Time (s) & 20 & 2 \\ Performance (**MSE**) training & 0.001 & 0.0456 \\ Correlation (R\({}^{2}\)) & 1.0 & 0.8769 \\ Performance (**MSE**) validation & 0.001 & 0.0595 \\ Correlation (R\({}^{2}\)) validation & 1.0 & 0.7599 \\ Validation checks & 10 & 10 * \\ \hline
**PRN (5, 10, 3)** & **Specified Values** & **Achieved Values** \\ \hline Iterations & 1000 & 861 \\ Time (s) & 20 & 10 \\ Performance (**MSE**) training & 0.001 & 0.0179 \\ Correlation (R\({}^{2}\)) & 1.0 & 0.9252 \\ Performance (**MSE**) validation & 0.001 & 0.0057 \\ Correlation (R\({}^{2}\)) validation & 1.0 & 0.9718 \\ Validation checks & 10 & 10 * \\ \hline \hline \end{tabular}  
* Achieved criterion.  
\end{table} 
Table 2: Values specified and achieved in training and validation of PRN with 5 and 10 neurons in the hidden layer compared to \(\mathbf{Y_{des}}\) output. Figure 8: **MSE** performance for PRN with 5 neurons in hidden layer, **(a)** training phase with 90% of samples (733), **(b)** validation phase with 10% of samples (82), **(c)** 100% of samples (815). Figure 10 presents results for the PRN network with 10 neurons in the hidden layer. Better outcomes were achieved for both training and validation, as shown in Figure 10a,b. During network training, there were a total of 16 errors, resulting in an accuracy rate of 97.8%, as illustrated in the confusion matrix presented in Figure 11a. During the model validation, the ANN (PRN) classified with 100% accuracy the samples that were not included in the training.