## 4 Results and Discussion  
In this section, the criteria through which the neural networks were optimized are demonstrated along with the performance of two data preprocessing methods. The D-value and PCA were computed as discussed in the previous section. An example of performing these methods on the CHEM 1 loop of ISDB data is shown in Figures 9 and 10. Interestingly, when all the generated data were used, the ability of the network to detect nonstiction data was considerably low. This indicated that samples from different sources were highly similar between the stiction and nonstiction groups. Since overfitting of the stiction data was present, the prediction accuracy of the individual noise level was tested, as shown in Table 4.  
Table 4 shows that using only the noise level with a variance of \(0.04^{0.5}\) gave the best result, followed by a variance of \(0.05^{0.5}\). Surprisingly, when noise with both of these variances was combined, an accuracy of \(76.38\%\) was obtained. Once the dataset used to train the neural network was determined, the performances of the different training algorithms were analyzed. The results are shown in Table 5. The scaled conjugate gradient was found to yield the highest accuracy for the detection of stiction. Even though a total performance of \(76.28\%\) was achieved, the ability of the network to accurately detect nonstiction loops did not reach the mark. Although stiction detection had a prediction accuracy of \(86.11\%\), the nonstiction prediction accuracy was only \(66.66\%\). A comparison of the results obtained using the different learning algorithms mentioned in Table 5 is shown in Figure 14.  
A similar test was also performed on the data that were reduced by PCA to determine which learning algorithm and set of training data yielded the highest results. Through this test, it was found that the combination of datasets involving variances of \(0.01^{0.5}\), \(0.04^{0.5}\), and \(0.05^{0.5}\) gave the best results. By comparing their performances to those of the learning algorithms, a similar prediction in terms of accuracy was achieved when using SCG or the conjugate gradient with Powell/Beale restart (CGB), as shown in Table 6. Although their overall prediction accuracies were similar, the abilities of both methods to detect stiction and nonstiction loops were different. While SCG had a prediction accuracy of \(50\%\), CGB achieved even worse results, with a performance of \(38.88\%\). However, the nonstiction prediction performance of CBG was higher than that of SCG, with the former having a prediction accuracy of \(83.33\%\) and the latter having a prediction accuracy of \(73.80\%\), as shown in Figure 15. \begin{table}
\begin{tabular}{c c} \hline \hline
**Variance** & **Performance \%** \\ \hline \(0.05^{0.5}\) & 69.24 \\ \hline \(0.04^{0.5}\) & 73.4 \\ \hline \(0.03^{0.5}\) & 65.9 \\ \hline \(0.02^{0.5}\) & 65.8 \\ \hline \(0.01^{0.5}\) & 62.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of each noise level for the D-value. \begin{table}
\begin{tabular}{c c} \hline \hline
**Learning Algorithm** & **Performance \%** \\ \hline Conjugate Gradient with Powell/Beale Restart (CGB) & 60.317 \\ \hline Fletcher–Powell Conjugate Gradient (CGF) & 60.31 \\ \hline Polak–Ribere Conjugate Gradient (CGP) & 57.53 \\ \hline Scaled Conjugate Gradient (SCG) & 76.38 \\ \hline One Step Secant (OSS) & 65.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance of various learning algorithms for D-values. Figure 14: Performance of different learning algorithms for D-values. Figure 15: Performance of different learning algorithms for PCA. A neural network that can identify stiction in control valves was designed and tested on a real industrial benchmark control loop to verify the validity of the network. The data used to train the network were obtained artificially using a data-driven Choudhury's stiction model. The model used two variables, S and J, to model the network. The data obtained from these data were used to train the neural network.