# Progress of Process Monitoring for the Multi-Mode Process: A Review
## 4 Steady-State Mode Process Monitoring Methods
### Unsupervised Process Monitoring Method
#### 4.2.2 Pattern Recognition Clustering Method  
The performance of process monitoring largely depends on the clustering effect of sample data. The pattern recognition clustering method first introduces various clustering analysis methods in pattern recognition into process monitoring and then combines them with other monitoring methods for process monitoring. The clustering method tends to be limited to a predetermined number of clusters, which is difficult to realize in practice. The K-means clustering method involves first randomly classifying the data, taking the mean of all samples in each cluster subset as the center of the category, then classifying the data according to each classification center, and then iterating continuously until the cluster center converges to determine the category of each sample. [PERSON] et al. [59] used the K-means clustering method and multi-PCA model to monitor the process of variable modes. First, the modes were divided by the K-means clustering method, and then a multi-PCA model was established for each mode for process monitoring. This method has been successfully applied to monitoring the boiler process in power plants. [PERSON] et al. [60] used the K-means clustering method to monitor multi-stage batch processes, and it has been successfully applied to the process monitoring of penicillin fermentation and semiconductor manufacturing. [PERSON] [43] used the sliding window cutting data matrix to calculate the mean value, then applied the improved K-means to cluster the window mean vector to realize the fully automatic monitoring of the multi-mode. The results of the K-means clustering algorithm can be greatly affected by the initial classification and its monitoring effect is unstable. To reduce the impact of other data on the clustering process, the K-center point clustering method is used to construct data clusters by iterating the data. After randomly selecting the center point of each cluster and calculating its distance from other data, the data are assigned to the nearest center point and iterated continuously until each data point is the same as the corresponding center point. [PERSON] et al. [61] improved the distance calculation approach of the K-center point algorithm using the shared nearest neighbor distance combined with the dynamic kernel principal component analysis method for the online monitoring of fixed-wing UAVs in multi-mode. Fuzzy C-Means Clustering (FCMC) Method  
Proposed by [PERSON] in 1981, FCMC is used to calculate the C clustering centers and the membership function matrix of the sample set by a recursive iteration method according to the clustering criterion function and to determine the category of the sample set by membership [62]. [PERSON] and [PERSON] et al. [63,64] proposed an FCMC method and a distance-based fuzzy C-means clustering model (DFCM) method, respectively. The methods have been successfully applied to the process monitoring of ethylene production and cracking furnaces. [PERSON] [65] calculated the number of clusters through singular value decomposition and a K-means clustering algorithm, used FCMC to divide the process modes into steady-state and transition modes according to the membership degree, and established monitoring statistics according to modes. [PERSON] et al. [66] combined LPP and DFCM to monitor the multi-mode process by first reducing the dimensions of the historical data and then dividing the modes by clustering. This enabled retention of all clustering information and improved sensitivity to outliers. Mixture Modeling (MM) Method  
The MM method is used to estimate parameters by modeling each cluster using an EM algorithm and determining the number of modes in the multi-mode process. [PERSON] et al. [67,68] used an independent component analysis mixture model (ICAMM) based on Bayesian estimation to divide and cluster the data and introduced Bayesian reasoning to build monitoring statistics to monitor the data. This method is demanding in the selection of data parameters. [PERSON] et al.