In order to improve the performance of fault isolation and diagnosis of Principal Component Analysis (PCA) based methods, this article proposes a novel fault detection and isolation approach using the Structured Joint Sparse PCA (SJSPCA). The objective function involves two regularization terms: the $l_{2,1}$ norm(sum of the Euclidean norms of the rows of a matrix) and the graph Laplacian. By imposing the $l_{2,1}$ norm, SJSPCA is able to achieve row-wise sparsity, and the graph Laplacian incorporates variable correlation information. The row-sparsity property of $l_{2,1}$ norm ensures that the score indices associated with normal variables approach zero and the graph Laplacian helps the isolation of correlated faulty variables. Once a fault is detected, a two stage fault isolation strategy is considered and a score index is calculated for each variable. It is proved that the proposed two stage strategy is capable of isolating faulty variables. The improved fault isolation performance of SJSPCA is illustrated by a simulation example and a gas flow fault observed in an industrial blast furnace.

It is of critical importance to keep a steady operation in the blast furnace to facilitate the production of high quality hot metal. In order to monitor the state of blast furnace, this article proposes a fault detection and identification method based on the multidimensional Gated Recurrent Unit (GRU) network, which is a kind of recurrent neural network and is highly effective in handling process dynamics. Comparing to conventional recurrent neural networks, GRU has a simpler structure and involves fewer parameters. In fault detection, a moving window approach is applied and a GRU model is constructed for each process variable to generate a series of residuals, which is further monitored using the support vector data description (SVDD) method. Once a fault is detected, fault identification is performed using the contribution analysis. Application to a real blast furnace fault shows that the proposed method is effective.

This article develops a novel probabilistic monitoring framework for industrial processes with multiple operational conditions. The proposed method is based on the probabilistic linear discriminant analysis (PLDA), which relies on two sets of latent variables, i.e., the between-class and within-class latent variables. In order to deal with the large within-class variations in multi-mode industrial processes, this approach modifies the original PLDA by introducing a separate within-class loading matrix for each operational mode and designs an expectation maximization (EM) algorithm to estimate the model parameters from the training samples. Mode identification for test samples is achieved by investigating the cosine similarity in the between-class latent variables and two monitoring statistics corresponding to within-class latent variables and the residuals are considered for fault detection. To diagnose the process fault, this article further develops a sparse probabilistic generative model based on PLDA for fault isolation. The enhanced performance of the proposed method is illustrated by applications to numerical examples and industrial processes.

Principal Component Analysis (PCA) is a widely used technique in process monitoring, fault diagnosis, and soft sensing of industrial systems. Despite its popularity, PCA suffers from the limitations of poor interpretability and robustness. In order to improve the PCA model, this article considers a structured sparse method—Laplace sparse principal component analysis (LSPCA), by integrating domain knowledge and sparsity constraint in the form of Laplace matrix and elastic net regularization constraint. Different from previous work, this article focuses on the advantages brought by the Laplace matrix and sparsity constraint on revealing the true latent process structure. When variable correlations are known in advance, the Laplace matrix can help extract sparse principal components that are consistent with the variable correlations. The increased accuracy of extracted latent process structure enhances the capability of PCA in soft sensing. The performance of the proposed method is verified by a simulation example and an application study to a distillation process.