A complex industrial process is dynamic and unpredictable, and it is impractical to prevent all abnormal conditions. In practice, the occurrence, development, and elimination of abnormal conditions take different states in different views. Traditional single-view-based methods fail to monitor all types of abnormal conditions, which can easily be disturbed and rendered useless due to the complexity and variability of industrial sites, and there is an emerging need to advance a condition monitoring system based on multiview data. In this paper, collaborative feature regression (CFR) is proposed to process multiview data in detecting abnormal working conditions, and its novelties include: (1) a unified framework to correspond both of physical variables and image matrix to the working conditions of an industrial process, (2) a new data preprocessing method to convert multiview data into the data with the same type for further consideration, and (3) a holistic feature regression model using multiview data in which sample points in are weighted based on their qualities in classifications. The above CFR-based method is implemented to classify working conditions of industrial processes and detect abnormal conditions. Compared with the single-view-based methods, the proposed method can identify abnormal conditions in a timely and effective manner, ensuring the stable operation of industrial processes. Finally, its effectiveness is proven when it is used to detect a sequence of abnormal working conditions in an electro-fused magnesia furnace (EFMF).

As an effective feature extraction and dimensionality reduction technique, nonnegative matrix factorization (NMF) has been widely applied in fault detection in recent years. The requirement for vectorization of samples causes NMF to disrupt the inherent structure of matrix data, making subsequent fault isolation and localization unachievable. In addition, existing statistical metrics used for fault detection are distance-based. Due to additional terms or other constraints, the data distribution in low-dimensional space deviates from the origin, resulting in excessively large decision boundaries and reduced fault detection performance. To directly utilize matrix data and address the issue of excessively large decision boundaries, a new method, named general semi-nonnegative matrix factorization, is proposed for statistical process monitoring. Its novelties include the following. First, the common features among the samples are extracted within a lower dimensional space, concurrently preserving the special features of the data. Second, by constructing two new statistical metrics, the latent variables extracted by GSNMF are combined with process monitoring techniques for fault detection. Third, the algorithm relieves the nonnegative restriction for original data, and allows samples to be input as vectors or matrices. On this basis, an abnormal variable isolation method named generic reconstruction-based contribution, which is suitable for matrix and variable data, is proposed for statistical process. The effectiveness of the proposed fault detection and abnormal variable isolation methods are verified on the benchmark dataset and the practical electrical-fused magnesia furnace process.

Nonnegative matrix factorization (NMF) is a widely recognized approach for data representation. When it comes to clustering, NMF fails to handle data points located in complex geometries, as each sample cluster is represented by a centroid. In this article, a novel multicentroid-based clustering method called graph-based multicentroid NMF (MCNMF) is proposed. Because the method constructs the neighborhood connection graph between data points and centroids, each data point is represented by adjacent centroids, which preserves the local geometric structure. Second, because the method constructs an undirected connected graph with centroids as nodes, in which the centroids are divided into different centroid clusters, a novel data clustering method based on MCNMF is proposed. In addition, the membership index matrix is reconstructed based on the obtained centroid clusters, which solves the problem of membership identification of the final sample. Extensive experiments conducted on synthetic datasets and real benchmark datasets illustrate the effectiveness of the proposed MCNMF method. Compared with single-centroid-based methods, the MCNMF can obtain the best experimental results.

Detecting abnormal conditions in an electrical fused magnesia furnace (EFMF) is challenging due to the difficulties in measuring ultra-high temperature, fluctuation of raw materials, uncertain boundary conditions, and numerous processing variables. In practice, images acquired from the wall of furnace are used to reflect working conditions of furnace indirectly. In this article, a supervised matrix regression algorithm is proposed to detect abnormal conditions based on the matrix data. Bilinear analysis is conducted to connect matrix data with labels and thus preserve the correlations in matrix with decreased complexity. By supervising and adjusting the weights of outliers in the modeling process, neutral and chaotic datasets can be monitored in low-dimensional spaces accurately. Moreover, a common information extraction method is proposed to eliminate redundant data. To verify proposed methods, the images recorded from an actual EFMF are used to detect abnormal conditions, and it is found that the proposed methods are able to monitor actual EFMF and issue alarms timely and effectively.

Low-dimensional representations that can fully preserve the key structural features of original process data constitute the foundation for constructing efficient process monitoring models. However, existing methods often suffer from incomplete and one-sided modeling of spatial structures and temporal dynamics when extracting the intrinsic low-dimensional manifold of process data. To address these limitations, a new method called collaborative preserving matrix factorization (CPMF) is proposed in this article and applied to process monitoring. Specifically, CPMF adaptively adjusts the spatial neighborhood size based on local data density and dynamically determines the temporal neighborhood according to the time-varying rate of change in the data. This dual-adaptive strategy enables CPMF to effectively preserve both the inherent spatial structure and dynamic characteristics of the data across spatial and temporal scales. Furthermore, by decomposing the low-dimensional representation into common and special feature components, CPMF mitigates the data point offset problem, thereby significantly improving monitoring accuracy. The effectiveness and competitive performance of CPMF are validated through experiments on the Tennessee Eastman process and a real industrial production process.

Process monitoring is essential to ensure safety, stability, and efficiency of modern industrial processes. In a monitoring method that is based on dimensionality reduction, fully exploiting intrinsic data structure is critical to improve accuracy. In this study, a novel dimensionality reduction method called adaptive preserving embedding (APE), is proposed and used in statistical process monitoring. APE is innovative in the sense that (1) a distance-driven adaptive local structure-preserving strategy is developed to determine the optimal neighborhood size for each sample, thereby enhancing the reliability of adjacency modeling and improving local feature extraction. (2) An adaptive global structure-preserving mechanism is introduced to maximize the projected variance of each sample with its adaptively defined non-neighbors; this enables the extraction of more representative and discriminative global features. (3) A unified dual-objective optimization framework is formulated to balance local and global structural preservation. A spectral-radius-based balancing parameter and orthogonality constraints are employed to ensure an appropriate trade-off while maintaining numerical stability. The effectiveness and advantages of the proposed APE are validated through experiments on the benchmark dataset and the real industrial production process.