## 3 Results and Discussions
### Tennessee Eastman Process
#### 3.2.2 Performance Analysis of Fault Classification for Different Optimized PNN Schemes
SSA-PNN and SOA-PNN do not identify the normal state data very well, and the CS-PNN does not identify the fault state data very well. MSSA-PNNN, PSO-PNN, and MOV-PNN are generally close to each other in terms of fault detection performance. However, a closer look reveals that MSSA-PNN is more sensitive than PSO-PNN for fault state data and more sensitive than MOV-PNN for normal state data. Similar to category 12, category 13 has a detrimental effect on the overall quality of the product. As can be seen in Figure 7, the CS-PNN, GA-PNN, PSO-PNN, MOV-PNN, and the original PNN fail to achieve the desired results for monitoring category 13 faults. The fault detection capabilities of the MSSA-PNN, SSA-PNN, and SOA-PNN are generally equal. However, MSSA-PNN and SSA-PNN have a slightly higher recognition rate for fault state data than SSA-PNN, with almost the same recognition rate for normal state data. Although SOA-PNN has a slightly higher recognition rate for normal state data than MSSA-PNN, its recognition rate for fault state data is significantly lower than that of MSSA-PNN. In summary, MSSA-PNN has high robustness and good diagnostic accuracy. Moreover, it is more sensitive than other optimization models and can accurately classify fault and non-fault data. It is also not prone to overfitting problems that degrade the model's performance. Therefore, on the whole, the fault detection performance of MSSA-PNN is superior. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Category** & **MSSA-PNN** & **SSA-PNN** & **CS-PNN** & **GA-PNN** & **PSO-PNN** & **MOV-PNN** & **SOA-PNN** & **PNN** \\ \hline
1 & 1.00 & 1.00 & 1.00 & 0.99 & 0.99 & 0.99 & 0.96 & 0.99 \\
2 & 0.98 & 0.98 & 0.98 & 0.98 & 0.98 & 0.96 & 0.97 & 0.97 \\
3 & 0.98 & 0.94 & 0.7  
Figure 6: Monitoring performances for Fault 12. Figure 7: Monitoring performances for Fault 13. 3.2.3. Analysis of Fault Diagnosis Performance Indicators of Different Classifiers  
In the third experiment, the performance of the MSSA-PNN classification model was evaluated by diagnosing 21 types of errors in the TE process. The matching simplified data samples were generated based on the feature selection sorting set provided in Table 5 and then fed into the MSSA-PNN model and other commonly used classifiers to compare the classification outcomes. Similar to linear discriminant analysis (LDA) are quadratic discriminant analysis (QDA), KNN, SVM, and maximum entropy model (MaxEnt), which are used a lot in the literature [49; 50; 51; 52; 53]. In addition, we compare it to the hybrid back propagation (BP) neural network model described in the literature, such as (CS)-BP [54]. Moreover, the MSSA algorithm's parameters are consistent with those established in the initial experiment. K in the KNN model has a value of 7. The MaxEnt model's maximum step length is set to 10 (Max step = 10), and the probability distribution adopts empirical edge distribution probability, which is optimized by a geographic information system (GIS) algorithm. In the CS-BP model, the population size is set to twenty, and the probability of discovery is set to 0.25. Other models' parameters retain the default values of MATLAB tools. It is important to avoid individual classifiers from achieving the local optimum, i.e., [normal, fault] = [0, 1], and thus, producing \"false positives\" for the fault categories. This experiment also provides the expected diagnosis rate for the normal condition. Table 8 shows the expected diagnosis rates of different classifiers for both normal and problem states. Table 8 shows that the fault diagnosis rate for MSSA-PNN is 91%, and 68% for LDA, 78% for QDA, 83% for KNN, 96% for SVM, 35% for MaxEnt, and 91% for CS-BP. If we only look at the rate of diagnosing each fault state, the diagnostic performance of the MSSA-PNN model is almost the same as that of the CS-BP model and is even worse than that of the SVM model. Table 8 also shows that SVM has \"false positives\" in 14 fault categories, such as categories 3, 8, 9, 10, and 11.