## 4 Conclusions  
This paper develops a basic fault diagnosis model based on feature selection and PNN. The main innovation of this paper is to use PSO-SVM to pre-screen the SVM-RFE feature selection and MSSA to optimize the PNN. PSO-SVM-RFE performs feature selection by two \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Category** & **MSSA-PNN** & **LDA** & **QDA** & **KNN** & **SVM** & **MaxEnt** & **CS-BP** \\ \hline  
Mean & 0.88 & 0.69 & 0.81 & 0.70 & 0.75 & 0.52 & 0.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The F1-score of MSSA-PNN and other classification models. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Category** & **MSSA-PNN** & **LDA** & **QDA** & **KNN** & **SVM** & **MaxEnt** & **CS-BP** \\ \hline  
Mean & 0.91 & 0.74 & 0.83 & 0.79 & 0.84 & 0.46 & 0.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The accuracy of MSSA-PNN and other classification models. level screening, which can remove redundant features, simplify the samples, and indirectly improve the classification performance. MSSA uses a unique optimization mechanism to update the parameters, giving the algorithm better global search capabilities. In this paper, the fault diagnosis performance of the PSO-SVM-RFE-MSSA-PNN model is experimentally validated using experimental data provided during the TE chemistry process. The analysis of the experimental results shows that the PSO-SVM-RFE feature selection method can improve the classification accuracy, and MSSA can enhance the local convergence of PNN, making the combined model have better fault diagnosis performance. Therefore, PSO-SVM-RFE-MSSA-PNN is suitable for fault prediction and diagnostic classification of the Tennessee Eastman process. Although the model proposed in this paper has achieved good results to some extent, there are still some limitations that need further improvement in future work:  
1. This paper uses a two-stage feature selection algorithm to delete redundant features. Experiments verify the practicability and superiority of the algorithm, but the influence of operation time is ignored in the experiments. In future work, further simplification of the structure of the feature selection algorithm, such as adopting NSGA-II, should be considered to achieve simplification in the data preprocessing stage. 2. The quality of the original data of the TE process directly affects the diagnostic performance of the fault diagnosis model. By observing the sample data, it can be seen that each characteristic variable of the TE process fluctuates in a normal state, which can easily cause misjudgment, which may be the reason for the low diagnosis rate of some fault types. Therefore, it is necessary to scale out abnormal data before feature selection in practical applications. 3. The feature selection algorithm in this paper only filters redundant features at the data level. Next, we can combine the characteristics of the TE chemical process itself, explore the chemical connection between the characteristic variables, and ignore unnecessary variables from the chemical direction, which will be a new cross-optimization direction. 4. In a natural chemical process, faults can be divided into process and sensor faults. Process faults are characterized by multivariate coordination, while sensor faults are variable independent, and the fault variable is unique. The occurrence of a process fault means that the system's operating state deviates from its normal value. In contrast, sensor faults interfere with the system's stability and affect the operator's judgment, which may lead to failures. Examples are drift, jitter, and stepping of data. This paper makes no distinction between the two, but they are uniformly classified as faults. Therefore, we should distinguish and differentiate between process and sensor faults in chemical processes in subsequent research. Conceptualization, H.X. ; methodology, H.X. ; software, H.X. ; validation, Z.M. and T.R. ; formal analysis, H.X. ; writing--original draft preparation, H.X.