## 1 Introduction
As a supervised network classifier based on the Bayesian minimal risk criterion, the probabilistic neural network (PNN) does not require weight adaption, the learning process is straightforward, the training speed is quick, and it possesses more robustness and fault tolerance. In addition, even with fewer training data, the insensitivity to noisy data maintains an excellent diagnostic accuracy. It has been applied successfully to photovoltaic array fault diagnosis [18], circuit breakers fault diagnosis [19], and distributed generation fault diagnosis [20]. However, PNN has significant limitations, such as a low recognition rate and misclassification due to the usage of the same smoothing factor in the iterative process and a complex network structure when the sample set is large. In recent years, meta-heuristic algorithms, such as grey wolf optimizer (GWO) [21], particle swarm optimization (PSO) [22], and sparrow algorithm (SA) [23], have grabbed the attention of researchers and been widely applied to improve the diagnostic performance of PNN further. However, the recently created salp swarm algorithm (SSA) in 2017 has some advantages over conventional optimization algorithms, including a straightforward theory and a rapid search rate. In addition, it has the unique benefit that exploration and production are balanced by a single parameter (\(c_{1}\)) [24; 25]. Although research into chemical process fault identification has made tremendous strides thanks to machine learning techniques, there are still some issues to be resolved. Numerous studies have demonstrated that, due to noisy features, computations with all feature sets in chemical processes may not always yield ideal results. Feature selection algorithms can be used to remove these superfluous features. The features election problem in classification can be characterized as \"identifying the smallest subset of features from the whole collection of features that achieves the highest classification accuracy.\" However,this frequently needs exponential calculation time, which is challenging. To improve classification, researchers employ evolutionary and heuristic methods to feature selection, such as genetic algorithm (GA) [26], ant colony optimization (ACO) [27], particle swarm optimization (PSO) [28], etc. In this feature selection method, the particle swarm algorithm is combined with the support vector machine, which is used to evaluate the fitness value of the particle swarm. This allows for more effective implementation of the feature selection process, as well as improved processing speed and accuracy. When used to classify issues, the method can improve accuracy by 2 to 4% [29]. SVM is not only a data-driven classification technique, but also an excellent machine learning technique. Numerous novel techniques combine data dimensionality reduction with SVM for process monitoring, defect information extraction, and variable elimination. SVM can give their dimension reduction techniques. For example, recursive feature elimination approaches choose the most important features by using accurate category rankings, getting important and useful information from samples, rebuilding samples for classification, and using this method to successfully diagnose chemical faults [30]. This work provides a novel chemical process defect diagnosis model based on Tennessee Eastman (TE) data and prior research expertise. The establishment of the model involves three sequential steps: establishing a two-stage feature selection approach with PSO-SVM and SVM-RFE, updating SSA with Levy flight, and developing a fault detection method based on PNN with an optimum smoothing factor. The steps are as follows:  
1. When there are nonlinear, high-dimensional TE process datasets, we use a two-stage feature selection method to eliminate duplicate features and reduce memory needs. This makes fault diagnosis more accurate and effective. 2.