Multivariate statistical process monitoring (MSPM) methods are significant for improving production efficiency and enhancing safety. However, to the authors’ best knowledge, there is no survey paper providing statistics of published papers over the past decade. In this paper, several issues related to MSPM methods are reviewed and studied. First, the annual publication numbers of journal articles concerning MSPM are provided to show the active development of this important research field and to point out several promising directions in the future. Second, the annual numbers of patents are also shown to demonstrate the practicality of different MSPM methods. Particularly, this paper also lists and analyzes the number of MSPM‐related publications in China. The statistics indicate that Chinese researchers and engineers may have different viewpoints from those of other countries, which results in different development trends of MSPM in China.

In this study, a two-step principal component analysis (TS-PCA) is proposed to handle the dynamic characteristics of chemical industrial processes in both steady state and unsteady state. Differently from the traditional dynamic PCA (DPCA) dealing with the static cross-correlation structure and dynamic auto-correlation structure in process data simultaneously, TS-PCA handles them in two steps: it first identifies the dynamic structure by using the least squares algorithm, and then monitors the innovation component by using PCA. The innovation component is time uncorrelated and independent of the initial state of the process. As a result, TS-PCA can monitor the process in both steady state and unsteady state, whereas all other reported dynamic approaches are limited to only processes in steady state. Even tested in steady state, TS-PCA still can achieve better performance than the existing dynamic approaches.

Several studies have applied the hidden Markov model (HMM) in multimode process monitoring. However, because the inherent duration probability density of HMM is exponential, which is inappropriate for modeling the multimode process, the performance of these HMM-based approaches is not satisfactory. As a result, the hidden semi-Markov model (HSMM), which integrated the mode duration probability into HMM, is combined with principal component analysis (PCA) to handle the multimode feature, named as HSMM-PCA. PCA is a powerful monitoring algorithm for the unimodal process, and HSMM specializes in mode division and identification. HSMM-PCA inherits the advantages of these two algorithms and hence it performs much better than the existing HMM-based approaches do. In addition, HSMM-PCA can detect the mode disorder fault, which challenges the most multimode approaches.

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Nonlinearity is extremely common in industrial processes. For handling the nonlinearity problem, this paper combines artificial neural networks (ANN) with principal component analysis (PCA) and proposes a new neural component analysis (NCA). NCA has a similar network structure as ANN and adopts the gradient descent method for training, hence it has the same nonlinear fitting ability as ANN. Furthermore, NCA adopts PCA's dimension reduction strategy to extract the uncorrelated components from the process data and constructs statistical indices for process monitoring. The simulation test results show that NCA can successfully extract the uncorrelated components from the nonlinear process data, and it has better performance than other nonlinear approaches.

Outliers may cause model deviation and then affect the monitoring performance and hence it is a challenging problem for process monitoring. The robust principal component analysis (RPCA) approach, which describes outlier components with a sparse matrix and identifies these components using the sparse matrix recovery approach, is the most commonly used method to solve the model deviation problems caused by outliers. However, because the existing mathematical tools can only obtain a nonsparse matrix with small element values, RPCA performs poorly during process monitoring. In this paper, we propose a novel robust PCA scheme called moment-based RPCA (MRPCA). In the offline training stage, MRPCA adopts a novel outlier selection mechanism based on the difference between the higher-order and second-order central moments to select outlier samples; in the online monitoring stage, MRPCA adopts an outlier detection mechanism to distinguish outliers from fault data. Using the aforementioned mechanisms, MRPCA achieves high fault detection and low false alarm rates in tests of a numerical model and the Tennessee Eastman process.

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