## 3 Results and Discussion
### Fault Classification Results
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Classifiers**} & \multirow{2}{*}{**Phase**} & \multicolumn{2}{c}{**MSPCA**} \\  & & **Normalized Accuracy** & **CT (s)** \\ \hline \multirow{2}{*}{ANN} & Training & 0.9149 & 72.26 \\ \cline{2-4}  & Testing & 0.9363 & 0.45 \\ \hline \multirow{2}{*}{MNN} & Training & 0.8461 & 118.4 \\ \cline{2-4}  & Testing & 0.9419 & 0.65 \\ \hline \multirow{2}{*}{CFNN} & Training & 0.8359 & 4195.8 \\ \cline{2-4}  & Testing & 0.8362 & 0.53 \\ \hline \multirow{2}{*}{DT} & Training & 0.8436 & 11.90 \\ \cline{2-4}  & Testing & 0.8634 & 0.093 \\ \hline \multirow{2}{*}{SVM} & Training & 0.8911 & 2125.14 \\ \cline{2-4}  & Testing & 0.8660 & 218.26 \\ \hline \multirow{2}{*}{KNN} & Training & 0.8722 & 3.60 \\ \cline{2-4}  & Testing & 0.8235 & 0.40 \\ \hline \multirow{2}{*}{NB} & Training & 0.7262 & 3.27 \\ \cline{2-4}  & Testing & 0.7259 & 0.25 \\ \hline \multirow{2}{*}{DA} & Training & 0.4383 & 2.86 \\ \cline{2-4}  & Testing & 0.4317 & 0.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: MSPCA normalized accuracy values for the diverse extracted features and NN classifiers. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Classifiers**} & \multirow{2}{*}{**Phase**} & \multicolumn{2}{c}{**Normalized Accuracy**} & \multirow{2}{*}{**CT (s)**} \\ \hline \multirow{2}{*}{ANN} & Training & 0.8249 & 88.23 \\ \cline{2-4}  & Testing & 0.9166 & 0.62 \\ \hline \multirow{2}{*}{MNN} & Training & 0.6486 & 110.98 \\ \cline{2-4}  & Testing & 0.8220 & 0.68 \\ \hline \multirow{2}{*}{CFNN} & Training & 0.6611 & 4260.8 \\ \cline{2-4}  & Testing & 0.6674 & 0.40 \\ \hline \multirow{2}{*}{DT} & Training & 0.7364 & 23.18 \\ \cline{2-4}  & Testing & 0.7349 & 0.20 \\ \hline \multirow{2}{*}{SVM} & Training & 0.8569 & 3700.79 \\ \cline{2-4}  & Testing & 0.8532 & 500.31 \\ \hline \multirow{2}{*}{KNN} & Training & 0.8157 & 5.57 \\ \cline{2-4}  & Testing & 0.8212 & 0.82 \\ \hline \multirow{2}{*}{NB} & Training & 0.2143 & 5.75 \\ \cline{2-4}  & Testing & 0.2368 & 0.50 \\ \hline \multirow{2}{*}{DA} & Training & 0.3744 & 4.92 \\ \cline{2-4}  & Testing & 0.3721 & 0.46 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Normalized accuracy for the various extracted features and the NN classifiers. The established MSPCA-based NN methods are demonstrated to be efficient alternatives for fault diagnosis when compared to other existing methods. In spite of the fact that the MSPCA tool enhances and improves the overall performance of all the utilized techniques, the conventional methods still have significant drawbacks. For instance, the accuracy of the DA and NB approaches is still poor, and the SVM technique suffers from a difficult training phase and a high time complexity. In effect, it is clear that the suggested approach performs better and produces good outcomes in terms of classification accuracy compared to conventional techniques.Indeed, the accuracy of the training and testing phases of the ANN classifier increased by 9 and 1.97 percent, respectively, the training and testing phase accuracy of the MNN classifier improved by 19.75 and 11.99 percent, respectively; and indeed, for the CFNN classifier, the training mode accuracy increased by 17.48 percent and the testing mode accuracy by 16.88 percent. Besides, the evolved strategy reduces and decreases the computation time (CT), which speeds up the NN classifiers and slows down their convergence. For instance, for the ANN classifier, the CT has been decreased by 15.97 (s) and 0.17 (s) for the training and testing phases, respectively. Tables 5-7 present the obtained testing classification outcomes of diverse classes by the use of the normalized confusion matrix in order to indicate the efficiency of the developed strategies. In fact, this matrix presents the samples that were correctly classified as well as the ones that were incorrectly classified for the healthy (\(C_{0}\)) and faulty modes (\(C_{1}\) to \(C_{21}\)). Actual classes and predicted process statuses are indicated by the raw and the column, respectively.