Nonstationarity in industrial processes, guided by factors, such as equipment aging and changing upstream load demands, inherently exhibits heterogeneous characteristics. This complex overlay of homogeneous stationarity poses great difficulty in process monitoring and analysis. Therefore, this study presents a new model (Hs- ${\mathrm {H}}_{\mathrm {n}}$ ) that peels the homogeneous and heterogeneous nonstationarity, which has four components: a differentiated learning network (DL-Net), a peeling network (Pe-Net), an adaptive reweighting network (AR-Net), and a global decoder network. DL-Net obtains the differentiated representation by leveraging a new differentiated learning approach to unique inputs, which is based on the cognitive understanding and derivation of functional specialization and content learning during network training. The aim is to maximize functional diversity and minimize content overlap. Furthermore, Pe-Net extracts the stationarity and nonstationarity (S-N) components from each differentiated scale, formulated as an encoder-decoder-encoder architecture with an integrated identity subtraction skip connection. A min-max S-N constraint regulates the peeling process and controls the extracted content. AR-Net additionally refines homogeneous stationarity across each scale and reweights the individual components to adaptively adjust their contributions. Last, reweighted components are fused and input into the global decoder to facilitate unsupervised learning. Experimental results on three processes demonstrate the effectiveness of Hs-Hn.

Due to the scarcity of fault samples in real-world industrial scenarios, few-shot fault diagnosis (FSFD) has attracted increasing attention, as it is vital for ensuring industrial safety and engineering reliability. However, existing metrics-based meta learning approaches generally calculate fault similarity relying on global pairwise, which insufficiently exploit fault information and thus limit discrimination among fault types. To address the insensitivity to buried fault information in complete processes, we propose a novel framework called the Local-Global Consistency Relation Network (LGCRN). The framework captures more comprehensive fault feature information through two components: the global branch, which focuses on macro-information involving all join process units, and the local branch, which emphasizes finer granularity from specific units. Additionally, a local-global alignment loss is utilized to optimize LGCRN, where self-cross relation improves the discriminability and stability of fault features by maintaining consistency between local and global branches. The self-cross relation comprises self-sample relation, ensuring consistency within the same sample at different granularities, and cross-sample relation, maintaining consistency across samples within the same class. Experiments on two benchmarks and a real semiconductor process demonstrate the feasibility and superiority of the proposed method, confirming its effectiveness in addressing limited-sample industrial fault diagnosis tasks and enabling timely maintenance crucial for operational safety in real-world scenarios.

Classical regression is a supervised task that uses target output to guide the modeling. Generally, the original input contains both output relevant and irrelevant information, whereas the latter may decrease the predictive performance to a certain extent. Without prior information about what information contributes to the prediction, the predictive performance of regression models can be improved based on such output relevant information as input. Thus, a joint autoencoder (JAE) combining the supervised and unsupervised mechanisms is proposed to learn output relevant features from the original input. In this way, both predictive and reconstructive performance are considered to learn the essential characteristics and avoid poor generalized performance on untrained instances. Meanwhile, hierarchy representations can be learned by successive JAEs with a local parameter embedding strategy, which is presented to preserve the predictive performance in this structure. In the experiments, the predictive performance and robustness of the proposal are verified on nine datasets with different sample sizes.

Plant-wide multiunit processes generally contain numerous variables, complex relations, and strong nonlinearity, making the monitoring of such processes challenging. This work proposes a new Gaussian-process-based probabilistic latent variable (GPPLV) modeling framework for distributed monitoring of multiunit nonlinear processes. A Gaussian-process latent variable model is first established to extract the dominant features of a local unit. Using the extracted features, a correlation between the local unit and its neighboring units are then modeled through a Gaussian-process regression (GPR) model. The genetic algorithm is used to determine the ideal independent variables from the neighboring units and optimize the hyperparameters of the GPR model simultaneously. Residuals are generated and monitoring statistics are constructed using an established GPPLV model. Experimental studies on three processes: 1) a numerical example; 2) the Tennessee Eastman benchmark process; and 3) a laboratory distillation process show that compared to some common distributed process monitoring models, the proposed method performs better in showing the nature of different faults and shows higher fault detection rate for large-scale multiunit processes.

This study develops a novel data-driven latent variable correlation analysis (LVCA) framework to achieve communication efficient distributed monitoring for industrial plant-wide processes. Process data of a local unit are first projected into a dominant latent variable subspace and a residual subspace to characterize the correlation within the local unit. Then, least absolute shrinkage and selection operator is used to determine communication variables from neighboring units that are beneficial for monitoring the local unit. Thereafter, canonical correlation analysis is performed between the dominant subspace and communication variables to characterize the correlation between units. Finally, a distributed monitor is established for each unit, which considers the correlation within the local unit and the correlation between different operation units. The proposed LVCA-based distributed monitoring scheme is applied on a numerical example, the Tennessee Eastman benchmark process, and a lab-scale distillation process. Comparison results with some state-of-the-art methods verify the effectiveness.Note to Practitioners—In the monitoring of a local operation unit, it is important to characterize the relationship among variables within the local unit and the relationship between the local unit and its neighboring units. However, not all variables from neighboring units are beneficial for the monitoring. Including nonbeneficial variables may cause considerable communication cost and model interpretation difficulty. Here a novel latent variable correlation analysis (LVCA)-based distributed local monitoring method, which considers simultaneous correlation within the local unit and between units, is proposed. The LVCA-based distributed monitoring preserves the fault detection ability and is more computationally efficient than the existing stochastic optimization-based methods, and therefore is more suitable for practical application. The superiority and characteristics are theoretically discussed and experimentally studied. MATLAB code is available upon request.

The complexity of an optimization problem is determined by its decision and objective spaces. Over the past few decades, a large number of works have focused on the performance improvement of metaheuristic algorithms via the objective space, whereas studies related to the decision space have attracted little attentions. Moreover, metaheuristic algorithms may not obtain satisfactory results within an entire feasible region, even if sufficient computational resources are available. Therefore, reducing the search space (i.e., finding a trust region) may be an effective method to ensure that the convergence is sufficiently close to the global optimal region. However, inappropriate subspace size may also weaken the performance of algorithms except for ones with a sufficiently small search space. To alleviate aforementioned problems, a variable search space (VSS) strategy based on a sequential trust region determination approach is proposed in this paper. In the VSS, the entire optimization process is divided into two stages: the first stage is to use an optimization approach for sequentially finding the trust domain of each variable and then determine the best-matched subspace; the second stage is to employ the optimization method for searching an optimal/near-optimal solution within the found trust region. The effectiveness of the VSS is evaluated using two widely used test suites, that is, IEEE CEC2014 and BBOB2012. Experimental results indicate that improving the algorithm performance is an important method for tackling problems, but locating a trust region is also beneficial for metaheuristic algorithms to improve the solution precision, especially for complex optimization problems.

Visual process monitoring is the application of a visualization method to map the real-time operating information of an industrial process to a 2-D map, followed by process monitoring. However, owing to the complexity of industrial production processes and the complex correlations among industrial process variables, the structure and distribution of high-dimensional industrial data are very complicated. Therefore, a general visualization method cannot effectively separate the different fault data in a 2-D map for process monitoring. Accordingly, in this article, a deep double supervised embedding neural network (DDSE) is proposed for visualizing high-dimensional industrial data. The DDSE consists of two supervised deep neural networks: a deep class centres uniform distribution neural network (DCCUD), and a deep supervised t-stochastic neighbor embedding neural network (DSSNE). The DCCUD maps the high-dimensional industrial data to a new feature space in which the class centres obey a uniform distribution, promoting a good and separable situation for subsequent visualization procedures. The DSSNE then maps these high-dimensional features into a 2-D space. The training of the DDSE can be conducted through pre-training and fine-tuning. A proposed visual process monitoring approach combines the DDSE with the local outlier factor and k-nearest neighbor approaches. The proposed approach is tested on a Tennessee Eastman process, and the results illustrate that the proposed approach outperforms traditional methods in terms of visualization and visual process monitoring.

Synthetic minority oversampling technique (SMOTE) has been widely used in dealing with the imbalance classification problem in the machine learning field. However, classical SMOTE implements the oversampling by linear interpolation between adjacent minority class samples, which may fail to consider the uneven distribution of the samples. This article proposes a minority clustering SMOTE (MC-SMOTE) method that involves the clustering of minority class samples to improve the imbalance classification performance. First, samples from the minority class are clustered into several clusters. Second, oversampling is performed by linear interpolation between adjacent clusters to create new samples from different clusters that contain additional information of the entire minority class. Then classical classification techniques can be employed to achieve efficient classification. The superiority of the MC-SMOTE is first verified by experiments on some benchmark datasets from various application domains. The proposed method is then applied to the real industrial SCADA data of wind turbine blade icing. Classification results indicate that the MC-SMOTE exhibits a better performance than that of the classical SMOTE.

Industrial big data and complex process nonlinearity have introduced new challenges in plant-wide process monitoring. This article proposes a local-global modeling and distributed computing framework to achieve efficient fault detection and isolation for nonlinear plant-wide processes. First, a stacked autoencoder is used to extract dominant representations of each local process unit and establish the local inner monitor. Second, mutual information (MI) is used to determine the neighborhood variables of a local unit. Afterward, a joint representation learning is then performed between the local unit and the neighborhood variables to extract the outer-related representations and establish the outer-related monitor for the local unit. Finally, the outer-related representations from all process units are used to establish global monitoring systems. Given that the modeling of each unit can be performed individually, the computation process can be efficiently completed with different CPUs. The proposed modeling and monitoring method is applied to the Tennessee Eastman (TE) and laboratory-scale glycerol distillation processes to demonstrate the feasibility of the method.

Finding a good Pareto front (PF) approximation and locating sufficient equivalent Pareto optimal solutions are two important goals of the multimodal multiobjective optimization (MMO). Preserving the diversity in decision and objective spaces is a core task in the MMO accordingly. Although various “soft isolation” approaches, such as niching methods, have been proposed to promote the diversity and find multiple Pareto optimal solutions in the decision space, they may perform poorly on complex MMO problems (MMOPs) due to high environmental selection pressure and complex geometry of Pareto optimal sets (PSs). To alleviate the above-mentioned challenging task, a “hard/physical isolation” method called zoning search (ZS) is proposed to maintain the diversity in the decision space and reduce the problem complexity in this article. In the ZS, some decision variables of MMOPs are selected randomly and then divided into several segments, i.e., the entire search space is partitioned into many subspaces. Clearly, the population diversity can be naturally maintained in the decision space and the problem complexity is reduced by the ZS in each subspace. The effectiveness of the ZS is systematically evaluated by 11 recently proposed MMOPs. The experimental results demonstrate that the ZS can effectively assist a selected multimodal multiobjective evolutionary algorithm (MMOEA) in finding more and better distributed equivalent Pareto optimal solutions in the decision space, and keep its performance in the objective space unchanged. Additionally, if additional computational resources are given, the ZS can further help the selected MMOEA to improve its performance in the decision space when compared with a soft isolation method used in the corresponding MMOEA. Overall, the ZS is a simple and promising approach to balance the broad search and the deep search in solving MMOPs.

Nonlinear process fault detection remains a challenge, with representation learning being a key step. In this article, a deep neural network (DNN)-based discriminative representation learning approach is proposed to achieve efficient fault detection for nonlinear plant-wide processes. An early-stage fault rarely affects several independent variables concurrently; hence, mutual information-based block division and randomized fault construction are performed to generate faulty validation data. By using the training data from the normal operation training data and the constructed validation data, a DNN with stacked autoencoders and a softmax classifier is trained to generate discriminative representations that maximize the capability of discriminating normal and abnormal statuses. Finally, on the basis of the learned deep discriminative representations, support vector data description is employed to discriminate the normal and abnormal process statuses. The proposed monitoring approach is tested on a numerical example and an industrial tail-gas treatment process, through which the efficiency is verified.

Process monitoring based on deep learning has attracted considerable attention. Generally, several hidden layers exist in the deep-learning model, and only the output information of the last hidden layer neurons extracted by deep learning is applied. Considering that each hidden layer is a kind of information representation of the original data, the information of different hidden layers may contain positive elements for process monitoring. In this article, we found that when a fault occurs, there are some neurons in each hidden layer that the information they output are different, compared with the normal condition. These neurons are called unstable neurons. Obviously, the information they output are beneficial for process monitoring. Motivated by theoretical analysis and experimental studies on unstable neurons, a novel method (UN-DBN) based on the unstable neurons in hidden layers is proposed to integrate the useful information for process monitoring, the Euclidean metric, the moving average filter, and the kernel density estimation technique are employed to provide an intuitionistic expression of the working state. The comparable result applied on a mathematic simulation process and the TE process with other advanced monitoring methods confirms the superiority and feasibility of the proposed method UN-DBN in this article.

Dynamics and nonlinearity may exist in the time and batch directions for batch processes, thereby complicating the monitoring of these processes. In this article, we propose a two-dimensional deep correlated representation learning (2D-DCRL) method to achieve the efficient fault detection and isolation of the nonlinear batch processes. Three-way historical data are first unfolded as two-way time-slice data. Second, a stacked autoencoder based deep neural network is constructed to characterize the correlation among the process variables. Considering that the time and batch directions may be dynamic, for each time-slice measurement, a constructed 2-D measurement containing samples from the previous time instants and batches is then obtained. Subsequently, DCRL is performed between the current running-batch measurements and the constructed 2-D measurements to characterize the 2-D dynamics and nonlinearity. The 2D-DCRL-based monitoring examines the status of a sample by considering the 2-D nonlinear and dynamic information, providing improved monitoring performance. Applications on two typical batch processes demonstrate the effectiveness of the proposed 2D-DCRL monitoring scheme.

In modern plants, industrial processes typically operate under different states to meet the different requirements of high-quality products. Many monitoring models for industrial processes were constructed based on the prior knowledge (the mechanism's model or the process data characteristics) to monitor such processes (called multimode processes). However, obtaining this prior knowledge is difficult in practice. Efficiently monitoring nonlinear multimode processes without any prior knowledge is an open problem that demands further exploration. Since data from different modes follow different distributions while data from the same mode are considered to be sampled from the same distribution, the modes of multimode processes can be uncovered based on the characteristics of the process data. This article proposes using a Dirichlet process Gaussian mixed model to classify the modes of multimode processes based on historical data, and then, determine the mode types of the monitored data. A nonlinear monitoring strategy based on the t-distributed stochastic neighbor embedding is then proposed to achieve nonlinear dimensionality reduction and visualize the data. Finally, a monitoring index that is integrated with support vector data description is constructed for comprehensive monitoring. The proposed nonlinear multimode framework completely realizes data-driven mode identification and unsupervised fault detection without knowing any prior knowledge. The effectiveness and feasibility of the proposed model are demonstrated using data from a simulated wastewater treatment plant.

Industrial processes generally have various operation modes, and fault detection for such processes is important. This paper proposes a method that integrates a variational Bayesian Gaussian mixture model with canonical correlation analysis (VBGMM-CCA) for efficient multimode process monitoring. The proposed VBGMM-CCA method maximizes the advantage of VBGMM in automatic mode identification and the superiority of CCA in local fault detection. First, VBGMM is applied to unlabeled historical process data to determine the number of operation modes and cluster the data in each mode. Second, local CCA models that explore input and output relationships are established. Fault detection residuals are generated in each local CCA model, and monitoring statistics are derived. Finally, a Bayesian inference probability index that integrates monitoring results from all local models is developed to increase the monitoring robustness. The effectiveness of the proposed monitoring scheme is verified through experimental studies on a numerical example and the multiphase batch-fed penicillin fermentation process.

Deep neural network (DNN) extracts hierarchical representations from process data and is promising for nonlinear process monitoring. Obtaining meaningful representations and generating efficient fault detection residual are the main challenges in DNN-based monitoring. This study proposes a regularized deep correlated representation (RDCR) method that incorporates deep belief networks (DBNs) and canonical correlation analysis (CCA) for nonlinear process monitoring. Hierarchical representations are initially extracted using DBN to process input and output variables. Second, hierarchical representations from process input and output are modeled through CCA to characterize the relationship between them. Efficient fault detection residuals are then generated, and monitoring statistics are established. CCA-based monitoring relies on the most correlated representations; thus, a multiobjective evolutionary optimization-based regularization is performed to select the most correlated representations and eliminate the influence of unrelated representations. The advantages of the RDCR monitoring are verified through experimental studies on a numerical example and the Tennessee Eastman process.

The performance of the differential evolution (DE) algorithm is significantly affected by the choice of mutation strategies and control parameters. Maintaining the search capability of various control parameter combinations throughout the entire evolution process is also a key issue. A self-adaptive DE algorithm with zoning evolution of control parameters and adaptive mutation strategies is proposed in this paper. In the proposed algorithm, the mutation strategies are automatically adjusted with population evolution, and the control parameters evolve in their own zoning to self-adapt and discover near optimal values autonomously. The proposed algorithm is compared with five state-of-the-art DE algorithm variants according to a set of benchmark test functions. Furthermore, seven nonparametric statistical tests are implemented to analyze the experimental results. The results indicate that the overall performance of the proposed algorithm is better than those of the five existing improved algorithms.