## 3 Results and Discussions
### Tennessee Eastman Process
#### 3.2.2 Performance Analysis of Fault Classification for Different Optimized PNN Schemes  
To compare the optimization performance of various heuristic methods on the smoothing factor of PNN, the training sample set and the test sample set are generated using the simplified feature set resulting from PSO-SVM-RFE feature selection, as shown in Table 5. The training set is then inputted into the MSSA-PNN, SSA-PNN, genetic algorithm (GA)-PNN, cuckoo algorithm (CS)-PNN, PSO-PNN, seagull optimization algorithm (SOA)-PNN, multi-verse optimizer (MVO)-PNN, and Unoptimized PNN models. Lastly, the test set is utilized to compare the respective fault correctness rates. All models have 20 populations and 50 iterations. GA-PNN sets the crossover probability to 0.7 and the mutation probability to 0.01. The CS-PNN sets the discovery probability Pa to 0.25, \(\lambda\) to 1, and the step size \(\alpha\) to 0.4. PSO sets the maximum speed to 1, the minimum speed to 1, the solution space to \([-5,5]\), and the learning factor to 1.49445 [48]. The smoothing factor of the Unoptimized PNN is 0.8. The results of the classification are provided in Table 7. As shown in the table, the average MSSA-PNN diagnostic rate is 88%, which is more than other approaches: 77% for the PNN, 86% for the SSA-PNN, 83% for the CS-PNN, 81% for the GA-PNN, 84% for the PSO-PNN, 82% for the MOV-PNN, and 86% for the SOA-PNN. The results are analyzed as follows. 1. Compared to the other optimization models, the diagnostic rate of PNN is lower on average, which demonstrates the inadequacies of the common PNN and the importance of the optimization model. 2. MSSA-PNN has a higher average diagnostic rate than SSA-PNN, demonstrating the advantages of optimized SSA and the soundness of this theory. 3. MSSA-PNN has the highest average diagnosis rate among the aforementioned optimization models, and its fault diagnosis rate is superior than those of other optimization models. In addition, categories 3, 9, 13, and 17 outperform all other categories. Although it is inferior in a few defect categories, the difference is minor. Further evidence demonstrates that utilizing MSSA to optimize PNN can boost performance. \"G at reactor feed\" (characteristic 35) can indicate product quality. Failure categories 1, 2, 5, 6, 7, 8, 12, 13, 20, and 21 have a stronger influence on product quality than other failure categories [48]. The actual TE process is imitated, i.e., the actual situation is reproduced when the chemical process fails under normal circumstances. In this paper, 270 random samples are taken from the original dataset, and 570 random samples are taken from 12(13) categories of faults to make a \"simulated sample set.\" The chemical process with this set of samples is as follows: the sampling interval is 3 minutes, and the TE process is carried out normally when \(t\in(0,3\times 270)\) min; the TE process is carried out under normal  
Figure 5: Stability comparison of PSO-SVM-RFE and RFtb for 21 fault diagnosis rates. conditions. \(t=(3\times 270+1)\) min marked the beginning of the category 12(13) fault, which persisted until \(t=3\times(270+570)\) min was reached. Figures 6 and 7 show detailed process monitoring graphs for two typical faults (category 12 and category 13). These graphs combine the raw time trends with the dynamics of the TE process. Because of this, it is easier to see how well the various optimization models monitor the dynamics of the TE process for the category 12(13) failure, which has a significant impact on the product quality, and it is possible to visualize the data in Table 7, making the \"numerical\" experimental results more informative. For category 12, Figure 6 shows that the original PNN has an overfitting phenomenon in diagnosing category 12 faults and failing to separate the normal state data. The GA-PNN also suffers from overfitting when optimizing the smoothing factor but behaves exactly opposite to the original PNN, failing to isolate the fault state data.