## 3 Results and Discussions
### Tennessee Eastman Process
#### 3.2.1 Influence of Different Feature Selection Algorithms on the Performance of Fault Diagnosis  
TE datasets are high-dimensional, small imbalanced samples, and three basic feature selection methods exist filter, wrapper, and embedding. SVM-RFE, an embedded feature selection method, was utilized by [PERSON] et al. [47] to score and sort the features, and the best five features were then selected for classification studies. Table 3 shows the feature selection results. [PERSON] et al. [48] utilized the filtered feature selection method random forest three-bagger (RFtb), randomly divided the dataset, incrementally grew the decision tree set from the given dataset, and measured and sorted the relative value of 52 features. The initial five characteristics are chosen for categorization experiments. The results of the feature selection are shown in Table 4. This study offers a packaged feature selection approach, PSO-SVM-RFE, which employs PSO-SVM and SVM-RFE to analyze the original dataset and produce a dataset with five features. The results of the feature selection are shown in Table 5.  
First, the training samples under normal state and 21 fault categories are fed into the PSO-SVM-RFE model for feature selection, and the five highest-priority feature ranking sets are produced. The training and test samples are then simplified using our feature selection \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Category** & **Feature** & **Category** & **Feature** & **Category** & **Feature** \\ \hline
1 & 1,20,22,44,46 & 8 & 16,29,38,40,41 & 15 & 16,19,20,39,40 \\
2 & 10,34,39,46,47 & 9 & 19,25,31,38,50 & 16 & 18,19,38,46,50 \\
3 & 18,20,37,40,41 & 10 & 18,19,31,38,50 & 17 & 21,38,46,50,51 \\
4 & 19,38,47,50,51 & 11 & 7,9,13,38,51 & 18 & 16,19,22,41,50 \\
5 & 17,18,38,50,52 & 12 & 4,11,18,19,35 & 19 & 5,13,20,46,50 \\
6 & 1,20,37,44,46 & 13 & 7,18,19,39,50 & 20 & 19,39,41,46,50 \\
7 & 19,38,45,46,50 & 14 & 9,11,21,38,50 & 21 & 7,16,19,45,50 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Feature selection results of RFtb. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Category** & **Feature** & **Category** & **Feature** & **Category** & **Feature** \\ \hline
1 & 18,16,7,46,44 & 8 & 50,19,18,13,16 & 15 & 17,52,18,7,20 \\
2 & 10,7,47,20,19 & 9 & 52,17,13,7,19 & 16 & 17,52,48,12,7 \\
3 & 52,17,11,19,18 & 10 & 13,7,50,19,18 & 17 & 21,7,13,9,51 \\
4 & 51,9,21,18,19 & 11 & 52,17,48,12,16 & 18 & 52,17,50,18,20 \\
5 & 52,17,11,19,18 & 12 & 7,13,50 sort set and [PERSON] and [PERSON]'s feature selection sort sets. Lastly, the three simplified samples and the original samples without simplification are entered into the optimization model MSSA-PNN established in this research to compare the performance of various feature selection approaches. The population of the model is set at 20, and the maximum number of iterations is 30. Feature selection techniques such as PSO-SVM-RFE and others are shown in Table 6. As a result of the optimization, the diagnostic rate for the 21 faults was 91% for PSO-SVM-RFE, 88.8% for SVM-RFE, and 90% with RFtb. After feature selection with PSO-SVM-RFE, the smaller dataset is more accurate because of the following. 1. The PSO-SVM-RFE model offers a considerable advantage in feature selection for categories 3, 9, 11, 13, 14, 17, and 19, compared to the SVM-RFE model for these seven fault categories. Despite the fact that the PSO-SVM-RFE model does not outperform the SVM model in categories 8, 10, 15, and 16, its diagnosis rate is still higher than 80%. In the remaining categories of defects, the differences between them are insignificant. Thus, when it comes to selecting features, the PSO-SVM-RFE model with initial pre-screening by PSO-SVM does better than the SVM-RFE model. 2. For categories 3, 9, 11, 13, 14, 17, and 19, the PSO-SVM-RFE model has a significant advantage over the SVM-RFE model in feature selection for these seven fault categories.