With the growing demand for remote sensing observations, massive high-resolution data generated by low Earth orbit (LEO) remote sensing satellites (RSSs) urgently needs to be transmitted to ground stations (GSs) through a three-layer space information network composed of RSSs, communication satellites, and GSs. However, limited communication resources and complex system structures pose severe challenges for efficient scheduling of massive remote sensing data. This paper addresses the dual-layer inter-layer link scheduling in remote sensing problem (DILLS-RSP) and establishes a scheduling model that aims to maximize download task benefits while comprehensively considering energy constraints, time window constraints, and the dependency relationship between task upload and download phases. To tackle the DILLS-RSP, a proximal policy optimization based hierarchical distributed auction algorithm (PPO-HDAA) is designed, the proposed PPO-HDAA introduces a learning-assisted adaptive strategy selection mechanism and designs a task splitting mechanism to optimize scheduling schemes through hierarchical interactive auction mechanisms in both upload and download phases. Extensive experimental results demonstrate that PPO-HDAA outperforms various comparative methods in both solution quality and computational efficiency, while exhibiting robustness.

Accurate online detection or prediction of key quality variables provides critical reference information for optimizing and controlling operating variables in industrial processes. However, frequent fluctuations in raw material properties and environmental conditions often give rise to multiple data distribution modes within the same production process. Moreover, the inherent uncertainties and the energy-material coupling characteristics of industrial processes make it particularly challenging to uncover the underlying topological relationships among process variables. To address these issues, this article proposes a novel jointly shared-specific variational graph attention autoencoder (JSS-VGATE) model for spatial topological feature extraction and key quality variable prediction in multimode industrial processes. Specifically, a variational graph attention autoencoder is first constructed, which combines graph attention mechanisms with the variational inference architecture to adaptively learn the dynamic correlation strengths between adjacent nodes, thereby capturing complex variable interactions. Subsequently, a comprehensive loss function is designed to achieve high-fidelity extraction of representative latent feature distributions. Furthermore, a cross-mode jointly shared-specific learning framework is developed to simultaneously capture global shared features across modalities and preserve local specific features of each modality, while a learnable gated fusion mechanism is introduced to balance modality invariance and heterogeneity, thereby enhancing cross-mode information integration. Finally, the effectiveness and superiority of the proposed JSS-VGATE are validated on two representative real-world industrial datasets compared to other state-of-the-art methods.

In this article, we investigate the problem of adaptive safe critic control design for stochastic multiagent systems (MASs) subject to asymmetric state and input constraints. To systematically address asymmetric state constraints, a unified transformation function (UTF) is proposed to convert the constrained consensus control problem into the stability analysis of an unconstrained error system. In addition, a nonquadratic cost function is incorporated to address input limitations effectively. Building upon these developments, a time-varying Hamilton-Jacobi-Bellman equation (HJBE) is formulated by integrating the Bellman optimality principle with Itô's lemma, thereby accommodating stochastic disturbances and enhancing controller robustness. To improve data utilization and eliminate reliance on explicit drift dynamics, an integral reinforcement learning (IRL) algorithm is developed within this framework. Furthermore, a time-varying single-critic network is designed to approximate the solution to the HJBE and generate optimal control policies, thereby considerably reducing computational complexity. To further enhance learning efficiency and relax the persistent excitation (PE) condition, the experience replay (ER) technique is incorporated into the update process of the critic weight. Finally, two simulation examples are provided to verify the feasibility and effectiveness of the proposed approach.

Belief rule based classification system (BRBCS) is a useful model to handle classification problems. However, there are two problems that limit its applications. On the one hand, existing non-optimization based offline generation method can not fully extract information contained in historical data. On the other hand, there is lack of non-optimization based online modification method. In some applications, optimization based online modification can be inapplicable because of its high computational expense. Non-optimization based online modification is indispensable. In this paper, the efficient data-driven methods of belief rule offline generation and online modification are proposed, which belong to non-optimization based scope. The former changes traditional one-by-one observation into batch-by-batch observation. It directly generates a belief rule from a batch of historical data without batch fusing, so that more information can be extracted from a batch of historical data. The latter is based on multi-weight extension and actual meaning of rule parameter. The multi-weight extension is to handle the drawback that single weight is easy to cause quality degeneration of belief rules during process of online modification. The actual meaning of rule parameter is used to establish a heuristic mechanism of online parameter adjustment. The related experiments have demonstrated the effectiveness and advancement of proposed methods. BRBCS equipped with proposed methods can become more useful in some industrial applications.

Industrial multiprocess collaborative optimization presents significant challenges due to the intricate spatiotemporal dependencies inherent in modern process industries. Traditional optimization and reinforcement learning often treat subprocesses as independent entities, neglecting the fine-grained interdependencies among operational variables across different subprocesses. To fundamentally address this limitation, we introduce, a novel spatiotemporal topology-informed multiprocess collaborative optimization (STI-MCO) framework, which pioneers action-level interdependency modeling through an innovative spatiotemporal graph architecture. Rather than treating subprocesses as monolithic entities, STI-MCO operates at the operational variable level, enabling precise representation of both interprocess relationships and intraprocess dependencies through a hierarchical two-stage decision framework. This approach enables more precise coordination through fine-grained variable interactions, better temporal consistency via dynamic graph structures, and enhanced scalability compared with conventional agent-level methods. This paradigm shift from subprocess-level to variable-level collaboration, combined with dynamic graph-based coordination, enables extensive simulations and experiments conducted across three benchmark environments with progressively complex topologies to demonstrate that STI-MCO consistently outperforms baseline methods, achieving up to 38.9% improvement over centralized methods and 171.9% improvement over existing multiagent strategies. In addition, STI-MCO exhibits superior convergence efficiency, requiring significantly fewer training steps to achieve high performance. Its practical applicability is further validated through deployment in a real-world Salt Lake chemical process. By fundamentally shifting the optimization paradigm from holistic subprocess control to fine-grained variable-level collaboration, this work establishes a new framework for more effective optimization in complex industrial processes, particularly those with strong interunit coupling.

In recent years, there has been a notable increase in demand for pickup and delivery services, mainly driven by the expansion of e-commerce. These services can be conceptualized as pickup and delivery problems (PDPs), which are important variants of vehicle routing problems (VRPs). While neural methods based on deep reinforcement learning (DRL) have demonstrated success in solving VRPs, current neural methods for PDP predominantly depend on customer coordinates and Euclidean distances. This heavy reliance can diminish their practical value, given the intricacies of real-world road networks and inherent asymmetries. This paper presents a novel learning-based method, i.e., HA-GCN, that couples heterogeneous attention (HA) and a graph convolutional network (GCN) to tackle the asymmetric pickup and delivery problem (APDP). The HA-GCN model utilizes HA to comprehend the innate pairing and precedence constraints between nodes in APDP. Concurrently, it employs GCN to amalgamate features of nodes and edges, facilitating the extraction of asymmetric attributes. Additionally, to augment the real-world relevance of HA-GCN, we train the model grounded in a dataset drawn from real geographic information. Comprehensive experiments suggest that our proposed method performs favorably against both traditional and learning-based state-of-the-art approaches, while demonstrating robust generalization capabilities. Note to Practitioners—Research on the pickup and delivery problem (PDP) addresses challenges in the rapidly growing field of end-to-end delivery services, such as food and parcel delivery. This study focuses on the asymmetric pickup and delivery problem (APDP), a variant of PDP reflecting real-world road networks with one-way streets and varying distances between locations. However, due to the exponential complexity and asymmetric nature of APDP, existing traditional methods and deep reinforcement learning (DRL) approaches struggle to effectively address this challenge. To address this, we propose HA-GCN, a DRL-based model compling heterogeneous attention and a graph convolutional network. HA-GCN effectively distinguishes pickup and delivery nodes in APDP, capturing differences in asymmetric distances in real-world road networks. Experimental results based on instances of different scales show that HA-GCN outperforms learning-based and traditional baselines, exhibiting satisfactory generalization capabilities. Given these confirmed advantages, our HA-GCN has great potential to not only offer the practitioners effective alternative approaches, but also improve the solution quality for the pickup and delivery in the operation of express hubs or logistics centers in specific regions of the real world.

This article is concerned with the stochastic finite-timeL1control problem of multi-loop networked control systems (NCSs) with network-induced delay, random packet loss, and external interference. Firstly, considering the data processing mode jumping, data transmission channel switching, and positive total amount of data, the multi-loop NCSs with network-induced delay, random packet loss, and external interference are modeled as a more general class of variable dual switching positive time-delay systems (VDSPTDSs) for the first time. Secondly, a new scheduling strategy that fully considers the random packet loss and the total amount of data, named positive minimum state expectation (PMSE), is proposed. Under this scheduling strategy, the channel with the smaller expectation of the total amount of data is selected to reduce the communication overhead. Subsequently, a stochastic multiple co-positive Lyapunov-Krasovskii functional (SMCPLKF) is constructed to establish the criteria of stochastic finite-time bounded (SFTB) and finite-timeL1-gain performance. A mode-dependent finite-timeL1-gain state feedback controller is further designed such that the closed-loop VDSPTDSs are positive and SFTB withL1-gain characterization. Finally, a multi-loop data communication NCS model is given to demonstrate the validity and generality of the proposed methods.

As the new generation of power systems, cyber-physical power systems (CPPSs) become more intelligent and convenient with the application of communication networks. However, the existence of time delays and cyber attacks brings challenges to the control of the system. In this article, the load frequency control (LFC) problem in the CPPS under false data injection (FDI) attacks is investigated and the sliding mode control scheme is applied to address the LFC problem based on an adaptive event-triggered mechanism. First, a dynamic multiarea LFC model with adaptive event-triggered sliding mode control (AET-SMC) scheme is established considering time delays and FDI attacks. Then, a novel Lyapunov–Krasovskii functional is constructed based on the delay-product-term-based looped functional to analyze the stability of the system. Furthermore, the AET-SMC scheme design method is developed by solving linear matrix inequalities. It is also proved that the control law can drive the system state trajectory to the designed sliding surface within a limited time. Finally, two LFC systems are employed to demonstrate the effectiveness and superiority of the proposed control scheme in MATLAB/Simulink. The steady-state error is decreased by about 95% and the transmission frequency is decreased by about 50% compared with the time-triggered scheme. The simulation results verify that the proposed scheme can improve the control performance and save the communication resources for the LFC system under FDI attacks. In addition, the real-time simulation is done based on OPAL-RTLAB 5707 to verify the feasibility of the proposed method.

In [1], to maintain the integrity of the publication and uphold academic standards, a correction is requested for an identified error. Fig. 12 in the article is a duplicate of Fig. 13 due to an inadvertent mistake during the final stages of manuscript preparation.

Granger causality has emerged as a valuable tool in comprehending industrial processes and facilitating data modeling by unveiling the inherent relationships within the data. However, the characteristic of causality discovery tasks results in a lack of validation sets, making hyperparameter tuning reliant solely on intuition. Existing nonlinear Granger causality discovery methods suffer from insufficient accuracy and robustness due to the significant impact of hyperparameters. Hence, this article proposes an attribution-aided nonlinear Granger causality discovery method (Attri-NGC) for accurate and robust inference of Granger causality. Attri-NGC comprises two stages. In the first stage, a novel strategy is proposed to assess whether the variability in contributions, derived from deep learning-based attribution, can significantly reflect causality. This assessment transfers the robust advantage of attribution to causal discovery. In the second stage, a sparsity-inducing penalty targeted at ambiguous causality is defined to fine-tune the deep networks used for attribution. Our method transforms the paradigm of Granger causality discovery from a challenging deep networks training problem to a fine-tuning problem, leading to a substantial enhancement in the accuracy and robustness of causality discovery. The effectiveness of the proposed method is comprehensively validated on four public datasets and two industrial process datasets. The superior performance of Attri-NGC in supporting industrial process modeling effectively promotes the integration of Granger causality into practical applications for more interpretable process modeling.

Temporal feature representation is critical for soft sensor modeling in industrial time sequences. Deep learning networks like long short-term memory are often used to model the temporal dynamics of data sequences. However, the data collected from industrial plants are usually sampled with irregular frequency, making it challenging for traditional methods to handle these temporally changeable relationships. Therefore, a Gaussian-based interval-aware transformer (GIA-Trans) with interval embedding is proposed in this article to model industrial data with irregular sampling frequency. In GIA-Trans, positional and temporal embedding layers are established to take positional distances and time intervals of samples into account. Then, Gaussian-based time-aware attention is proposed to tackle the changeable time intervals with adaptive weights. In this way, the temporal correlations between samples can be adaptively captured. The GIA-Trans is applied to an industrial hydrocracking process to predict the C5 and C6 content of light naphtha.

Accurate feature extraction and quality variable prediction are critical problems for time sequences in industrial processes. However, industrial samples often exhibit strong temporal correlations with each other that have different positional distances, making it challenging for conventional data-driven models like long short-term memory (LSTM) and Vanilla transformer to capture these underlying features. In this article, a difference metric attention with position distance-based weighting is proposed for transformer (DMA-trans) in industrial time series modeling. First, the DMA is established to calculate the difference of query-key vector pair in transformer to measure the spatial similarity. In this fashion, the difference can accurately represent the spatial similarity of vectors, compared with the original dot product directly on two vectors. Then, positional distance-based weights are designed to capture the sample relevance that has different positional distances. This may help to extract more potential features because the closer samples tend to have higher relevance while there may be weak correlations if two samples are far in positional distance. The effectiveness of the DMA-trans model is validated in industrial hydrocracking processes for C5 content of the light naphtha and the final boiling point of the jet fuel.

With the development of e-commerce, the types of logistics services have become diverse. In response to the logistics requirements in urban environments, this paper introduces a logistics system that multiple drones and smart parcel lockers (SPLs) collaborate to provide package pickup, delivery and intra-city on-demand delivery services for customers. Different from pickup and delivery services, the intra-city on-demand delivery services need drones to pick up a package from a customer and deliver it to another customer. The multi-drone collaborative routing problem is crucial to find a reasonable tour over customers with flexible time-window. A multi-objective mixed-integer programming model is formulated to describe the proposed problem with simultaneously minimizing transportation costs and maximizing customer satisfaction. The model integrates dynamic energy consumption, soft time-windows, and task precedence constraints arising from the single unit capacity of drones. To tackle this problem, an adaptive-large-neighborhood-search based multi-objective algorithm (ALNSMO) is devised. CPLEX is used to verify the accuracy of the model and the quality of the proposed algorithm. Meanwhile, numerous experiments and analyses are conducted to demonstrate the superiority and practicability of the proposed mode and ALNSMO.

The growth of data collection in industrial processes has led to a renewed emphasis on the development of data-driven soft sensors. A key step in building an accurate, reliable soft sensor is feature representation. Deep networks have shown great ability to learn hierarchical data features using unsupervised pretraining and supervised fine-tuning. For typical deep networks like stacked auto-encoder (SAE), the pretraining stage is unsupervised, in which some important information related to quality variables may be discarded. In this article, a new quality-driven regularization (QR) is proposed for deep networks to learn quality-related features from industrial process data. Specifically, a QR-based SAE (QR-SAE) is developed, which changes the loss function to control the weights of the different input variables. By choosing an appropriate inductive bias for the weight matrix, the model provides quality-relevant information for predictive modeling. Finally, the proposed QR-SAE is used to predict the quality of a real industrial hydrocracking process. Comparative experiments show that QR-SAE can extract quality-related features and achieve accurate prediction performance.

For industrial processes, it is significant to carry out the dynamic modeling of data series for quality prediction. However, there are often different sampling rates between the input and output sequences. For the most traditional data series models, they have to carefully select the labeled sample sequence to build the dynamic prediction model, while the massive unlabeled input sequences between labeled samples are directly discarded. Moreover, the interactions of the variables and samples are usually not fully considered for quality prediction at each labeled step. To handle these problems, a hierarchical self-attention network (HSAN) is designed for adaptive dynamic modeling. In HSAN, a dynamic data augmentation is first designed for each labeled step to include the unlabeled input sequences. Then, a self-attention layer of variable level is proposed to learn the variable interactions and short-interval temporal dependencies. After that, a self-attention layer of sample level is further developed to model the long-interval temporal dependencies. Finally, a long short-term memory network (LSTM) network is constructed to model the new sequence that contains abundant interactions for quality prediction. The experiment on an industrial hydrocracking process shows the effectiveness of HSAN.

In cloud manufacturing of industrial processes, the accurate online prediction of product quality is the basis for realizing decision-making and control of the manufacturing process. However, frequent fluctuations in working conditions and data noise restrict the application of data-driven methods in industrial sites. In addition, the constrained resources on edge devices limit their ability to automatically update or deploy complex models. To address these issues, this study proposes a Koopman-constrained hierarchical deep state-space model (KHSSM) and incorporates it into the innovative cloud-edge collaboration framework for industrial quality prediction. First, KHSSM integrates a state-space model, leveraging its advantage in modeling noisy dynamic data. Second, the Koopman operator is introduced to constrain the latent variables in the measurement space, enabling it to interpretably reflect the evolution dynamics of the system. In addition, novel strategies for model mismatch detection and model simplification are designed and deployed to improve the predictive accuracy and real-time efficiency of the cloud-edge collaboration framework. Finally, the effectiveness of the proposed method is verified by extensive experiments in a numerical simulation and a real-world industrial process.

In industrial processes, frequent communication failures and information corruption may result in the loss of entire blocks of industrial process data, which is also known as blackout missing data. The imperfect data of industrial time series impede the performance of subsequent modeling and control tasks. However, traditional matrix factorization or supervised learning data imputation methods are hardly applicable to the challenging task of recovering blackout missing data. The difficulty in imputing the blackout data stems from two major factors: the imputation process lacks the reference of co- evolutionary variables, and the blackout data have strong autocorrelation and drift in distribution. To address these issues, this paper develops a novel hierarchical imputation framework for recovering blackout data based on the masked transformer network (Masked-Former). First, a reconstruction block strategy with random masked points is innovatively proposed to improve the ability of the model to recover missing values under different working conditions for incomplete datasets. Then, based on the masked incomplete data set, the proposed method utilizes the local feature capture capability of convolutional networks and the sample-level long-range dependency capture capability of the self-attention mechanism to complete coarse-grained and fine-grained missing data imputation, respectively. Finally, extensive experiments are conducted to verify the superior performance of the proposed method on two real-world industrial data sets. Note to Practitioners—Inspired by the phenomenon that industrial process data often have missing data, this paper proposes a novel hierarchical imputation Masked-Former method for blackout missing data recovery. The method combines local data features with long-term time series dependency performance to improve completion performance. Then, the obtained completed data can help practitioners monitor the status of industrial field conditions. In addition, it is helpful to perform subsequent quality prediction and process monitoring tasks, allowing practitioners to quickly take preventative measures to avoid disasters and take corrective operations to return the plant to its normal operating range.

In conventional process monitoring, a latent variable model (LVM) is first learned in offline training and the statistics related to extracted latent features and residuals are then used for online monitoring. However, such a practice ignores the dynamic interaction between modeling and monitoring, rendering useful online samples underexplored. This study proposes a novel LVMs-based monitoring framework that exploits the interaction using a weighting strategy and the maximum likelihood method to improve the monitoring performance with online information. The key idea is to integrate a weighting vector to components which contribute to the fault detection indices for more effective online fault information extraction. We use the maximum likelihood ratio to optimize the weighting vector and construct a new fault detection index accordingly. Case studies on a numerical example and a three-phase flow facility demonstrate the effectiveness of our approach.Note to Practitioners—A large number of anomaly detection methods in industrial systems has emerged in recent years. Latent variable models are the dominant branch of anomaly detection methods with substantial research and practice. However, fault detection performance is still unexpected especially for some minor faults that cause underwhelming fluctuation. Based on LVM models, we investigate the performance maximization method of industrial fault detection. The main mechanism is a weighting strategy that connects the normal data and the online sample to be monitored. We do not attach any additional conditions besides the existing requirements for LVM models. Also, it is the class of LVM methods that can be benefited from this novel strategy rather than a specific approach, which has been verified using principal component analysis and canonical correlation analysis. Moreover, the fault detection performance has boosted for all kinds of fault types. Notice we use general linear LVM models for deriving the methodology. Extension to nonlinear methods is still an open question for the sake of the introduced non-convex optimization.

This article studies the performance monitoring problem for the potassium chloride flotation process, which is a critical component of potassium fertilizer processing. To address its froth image segmentation problem, this article proposes a multiscale feature extraction and fusion network (MsFEFNet) to overcome the multiscale and weak edge characteristics of potassium chloride flotation froth images. MsFEFNet performs simultaneous feature extraction at multiple image scales and automatically learns spatial information of interest at each scale to achieve efficient multiscale information fusion. In addition, the potassium chloride flotation process is a multistage dynamic process with massive unlabeled data. To overcome its dynamic time-varying and working condition spatial similarity characteristics, a semi-supervised froth-grade prediction model based on a temporal-spatial neighborhood learning network combined with Mean Teacher (MT-TSNLNet) is proposed. MT-TSNLNet designs a new objective function for learning the temporal-spatial neighborhood structure of data. The introduction of Mean Teacher can further utilize unlabeled data to promote the proposed prediction model to better track the concentrate grade. To verify the effectiveness of the proposed MsFEFNet and MT-TSNLNet, froth image segmentation and grade prediction experiments are performed on a real-world potassium chloride flotation process dataset.

Soft sensors have been increasingly applied for quality prediction in complex industrial processes, which often have different scales of topology and highly coupled spatiotemporal features. However, the existing soft sensing models usually face difficulties in extracting the multiscale local spatiotemporal features in multicoupled complex process data and harnessing them to their full potential to improve the prediction performance. Therefore, a multiscale attention-based CNN (MSACNN) is proposed in this article to alleviate such problems. In MSACNN, convolutional kernels of different sizes are first designed in parallel in the convolutional layers, which can generate feature maps containing local spatiotemporal features at different scales. Meanwhile, a channel-wise attention mechanism is designed on the feature maps in parallel to get their attention weights, representing the significance of the local spatiotemporal feature at different scales. The superiority of the proposed MSACNN over the other state-of-the-art methods is validated through the performance evaluation in two real industrial processes.

The real-time recognition of operating conditions is always critical to ensuring the efficient and stable operation of industrial flotation processes. Although the widespread use of smart devices enables the availability of multimodal data in flotation processes, recognizing operating conditions using cross-modal data information is still challenging due to the modality gap. To address this issue, this article first proposes an innovative bimodal manifold autoencoder model to predict interested quality variables from the perspective of visual modality and auditory modality. Specifically, the well-designed intra- and intermodal manifold regularization constraints are introduced to fully learn the intrinsic manifold features within each modality and the interdependencies across modalities, thereby enhancing the cross-modal data representation ability of the developed prediction models. Then, based on the prediction values of quality variables, an adaptable multimodal fuzzy decision inference module is designed to recognize the operating conditions while counteracting the influence of fluctuations in feedstock properties. Finally, extensive experiments are conducted on two industrial flotation process datasets at distinct periods to validate the superiority of the proposed methods in terms of quality prediction and operation condition recognition tasks.

In complex process industries, multivariate time sequences are omnipresent, whose nonlinearities and dynamics present two major challenges for soft sensing of important quality variables. Consequently, due to the potent representational capabilities, nonlinear dynamic models like gated recurrent unit (GRU) and long short-term memory (LSTM) networks have been used for data sequence modeling. Though it is a common occurrence in many industrial plants, data series with heterogeneous sample intervals and missing values cannot be directly handled by these dynamic algorithms. To this end, attention-based interval-aided networks (AIA-Net) are proposed in this article to adaptively model the temporal information for heterogeneous sampling sequences with missing values in the processes industry. It includes two main mechanisms, which are named attention-based time-aware dynamic imputation and interval-aided time-aware network, respectively. The reduction rate is introduced by the attention-based time-aware dynamic imputation to apply the effects of time intervals and is used in the imputation of missing data. The interval-aided time-aware network includes time intervals in the model structure and uses a sampling interval gate to correct the temporal correlations in time series. The proposed AIA-Net is successfully applied to a real hydrocracking process to predict the C5 and C6 content in the light naphtha.

Missing data is a common phenomenon in the industrial field. The recovery of missing data is crucial to enhance the reliability of subsequent data-driven monitoring and control of industrial processes. Most existing methods are limited by the confined scope of feature extraction, which makes it impossible to rely on global information to impute missing data. In addition, they usually assume that industrial data is a uniform distribution across all working conditions, ignoring the differences in data evolution patterns across different conditions. To address these issues, this paper proposes an innovative scope-free global multi-condition-aware imputation framework based on diffusion transformer (SGMCAI-DiT). First, it extends the diffusion model by introducing conditional probability to capture the condition distribution of the entire data. Then, a noise prediction model is designed based on a novel double-weighted attention mechanism (DW-SA) to broaden the horizons of feature extraction. By discerning the inter-conditional interactions and the intra-conditional local information, the missing data imputation performance can be improved. Finally, the effectiveness and suitability of the proposed SGMCAI-DiT are verified on four real datasets sourced from industrial processes and two public non-industrial datasets. Extensive experimental results demonstrate that the proposed method outperforms several state-of-the-art methods in different missing data scenarios.

Latent variable-based process monitoring (PM) models have been generously developed by shallow learning approaches, such as multivariate statistical analysis and kernel techniques. Owing to their explicit projection objectives, the extracted latent variables are usually meaningful and easily interpretable in mathematical terms. Recently, deep learning (DL) has been introduced to PM and has exhibited excellent performance because of its powerful presentation capability. However, its complex nonlinearity prevents it from being interpreted as human-friendly. It is a mystery how to design a proper network structure to achieve satisfactory PM performance for DL-based latent variable models (LVMs). In this article, a variational autoencoder-based interpretable LVM (VAE-ILVM) is developed for PM. Based on Taylor expansions, two propositions are proposed to guide the design of appropriate activation functions for VAE-ILVM, allowing nondisappearing fault impact terms contained in the generated monitoring metrics (MMs). During threshold learning, the sequence of counting that test statistics exceed the threshold is considered a martingale, a representative of weakly dependent stochastic processes. A de la Peña inequality is then adopted to learn a suitable threshold. Finally, two chemical examples verify the effectiveness of the proposed method. The use of de la Peña inequality significantly reduces the minimum required sample size for modeling.

The occurrence of abnormal operating conditions in industrial flotation processes adversely influences flotation concentrate yields and quality. It is imperative to prioritize the maintenance of normal operating conditions within the flotation process for process optimization. Considering the influence of the operation variable adjustment of different flotation cells on the final production indicators and the difficulty of establishing an adequate mathematical model, an intelligent collaborative decision-making plan based on multiple flotation cells is proposed in this study. First, multimodal data from industrial flotation sites are collected to emulate the comprehensive perceptual capabilities exhibited by human operators. Then, based on the concept of collaborative optimization, an intelligent collaborative decision-making plan for adjusting operating parameters is proposed. Finally, a series of experiments are conducted using actual industrial data. The results demonstrate the efficacy of the proposed intelligent collaborative decision-making plan in enhancing abnormal operation conditions, thereby establishing its promising potential for practical implementation in the industrial flotation process.

Multiple modes are ubiquitous in current industrial processes, and the amount of historical data contained in different modes may vary considerably. Insufficient data can easily lead to cold start problems when building a fault detection model for a particular mode. To solve this problem, while considering the similarity and differences between multiple modes, a deep model using domain adaptation based on feature separation is proposed for nonlinear process monitoring with few samples. The model extracts common features from modes and the data deficiency is compensated by transferring the domain knowledge from the source to the common features. On the other hand, to avoid missing useful information by focusing only on common features, the model also extracts the specific features of the target domain. Thus, monitoring performance is improved with the help of domain adaptation while taking into account the specific characteristics of the target domain. Furthermore, three detection indices are designed to monitor the common feature subspace, the specific feature subspace, and the residual subspace, respectively. The benefit of this is allowing more diagnostic information to be obtained when a fault occurs. The proposed method was tested with a numerical example and a real industrial hydrocracking process to verify the detection effectiveness.

The primary goal of multimodal process monitoring is to detect abnormalities or occurrence of faults. However, the profound challenge in the multimodal monitoring problem is that it is difficult to quickly distinguish the fault occurrence on a process mode from other operating modes. In this work, a Gaussian mixture model based variational Bayesian principal component analysis (GMM-VBPCA) is proposed. GMM is used to capture the global multimodal information where each Gaussian component of GMM represents a corresponding normal operating mode. VBPCA is employed to construct a probabilistic model for each operating mode. Using the weights of posterior probabilities from global GMM, local VBPCA models can then be fused to characterize the normal multimodal processes. In order to detect the occurrence of faults, Kullback-Leibler (KL) divergence of latents and model residuals of the multimodal process are used as the monitoring statistics that measure the deviation from the normal multimodal distribution. Owing to the variational local model, the posterior distribution of latents and model residuals of the GMM-VBPCA can characterize the process behavior for every test sample. Finally, GMM-VBPCA based monitoring statistics are compared with existing process monitoring methods through a simulated numerical example and an industrial hydrocracking process. Note to Practitioners—In this paper, a novel process monitoring statistics has been proposed that can aid the practitioners in accurately identifying the process faults in near real-time with minimal false alarm. Also, the sensitivity to small bias faults is higher that the traditional methods, thus enabling higher fault detection rate. Based on the proposed statistics, an online monitoring scheme has been proposed. Hence, it is useful for practitioners in quickly taking preventive measures to avoid catastrophe, and also taking corrective measures to bring the plant to normal operating range or scheduling maintenance in case of early detection of sensor or equipment failures.

Missing values are ubiquitous in industrial data sets because of multisampling rates, sensor faults, and transmission failures. The incomplete data obstruct the effective use of data and degrade the performance of data-driven models. Numerous imputation algorithms have been proposed to deal with missing values, primarily based on supervised learning, that is, imputing the missing values by constructing a prediction model with the remaining complete data. They have limited performance when the amount of incomplete data is overwhelming. Moreover, many methods have not considered the autocorrelation of time-series data. Thus, an adaptive-learned median-filled deep autoencoder (AM-DAE) is proposed in this study, aiming to impute missing values of industrial time-series data in an unsupervised manner. It continuously replaces the missing values by the median of the input data and its reconstruction, which allows the imputation information to be transmitted with the training process. In addition, an adaptive learning strategy is adopted to guide the AM-DAE paying more attention to the reconstruction learning of nonmissing values or missing values in different iteration periods. Finally, two industrial examples are used to verify the superior performance of the proposed method compared with other advanced techniques.

Accurate prediction of quality variables that are difficult to measure is crucial for industrial process control and optimization. However, the fluctuations in raw material quality and production conditions may cause industrial process data to be distributed in multiple working conditions. The data under the same working condition show similar characteristics, which are often defined as one data mode. Hence, the overall process data exhibit multimode characteristics, which brings great challenges in developing a uniform prediction model. Besides, the noninterpretability of the existing data-driven prediction models brings great resistance to their practical application. To address these issues, this article proposes a novel data mode related interpretable transformer network (DMRI-Former) for predictive modeling and key sample analysis in industrial processes. In DMRI-Former, a novel data mode related interpretable self-attention mechanism is designed to enhance the homomode perceptual ability of each individual mode while also capturing cross-mode features of different modes. Moreover, the key samples under different modes can be discovered using DMRI-Former, which further improves the interpretability of the modeling process. Finally, the superiority of the proposed DMRI-Former is verified in two real-world industrial processes compared to other state-of-the-art methods.

Data modeling and online monitoring are two critical stages for data-driven anomaly detection. Regarding data modeling, deep neural networks (DNNs) can learn good decision boundaries to separate the anomaly and normal regions, due to their flexible model structures and excellent fitting ability. However, DNNs, using nonlinear activations with specific boundaries, may indirectly cause a limited anomaly detection margin, especially when there are samples far from centroids. Moreover, an anomaly detection model with a narrow detection margin is deemed insensitive to general faults. An anomaly detection model with a tight detection margin will suffer a severe performance degradation. To mitigate the intrinsic drawbacks of DNNs, we develop a new regularizer based on the maximum likelihood of complete data (i.e., observations and latent variables). The regularizer is neuronwise and mathematically acts as compressing neurons, dragging the marginal points into the centroids. Combining the regularizer with the encoding–decoding structure networks, we perform an industrial case study to verify the superiority of the proposed method.

Since the change of operation condition is common in industrial processes, it could cause historical process data multimodal characteristics. When the working conditions are switched, the new mode will suffer small sample problem in the initial stage of the working mode switching, which brings difficulties to the monitoring of the new mode. Different from traditional modeling method which only considers the new mode data, this paper proposes a novel multi-source transfer learning method that considers both the historical multimode and new mode data. First, the common features of historical multimode data are extracted. Then, the extracted features are transformed into the model of new mode data. In order to alleviate the problem of insufficient samples of the current working mode, the common subspace of the new mode is obtained by combining the common features of the historical multimode with the new mode data. Finally, a numerical case and a real industrial hydrocracking process are used to validate the effectiveness of the proposed method.

Due to the existence of complex disturbances and frequent switching of operational conditions characteristics in the real industrial processes, the process data under different operational conditions subject to different distributions, which means there exist different manifold structures under broad operations. Globally, the entire process data are distributed in a multimanifold structure. Nevertheless, the existing data-driven quality prediction methods do not consider the relationships among different manifolds of data and just treats the process data as a single manifold. How to extract effective multimanifold structure feature representation from complex process data and enhance online prediction ability are still challenging in the field of real industrial processes. To this end, in this article, a novel stacked multimanifold autoencoder (S-MMAE) is proposed for feature extraction and quality prediction. Especially, by introducing a new multimanifold regularization into the original loss function of stacked autoencoder at each layer, the intrinsic multimanifold structure information of data is utilized to guide the feature learning procedure. In this way, the learned features can offer a more comprehensive representation of original data and help enhance the prediction performance. At last, the application results in a practical hydrocracking process demonstrate that the proposed S-MMAE can achieve excellent prediction accuracy, which outperforms other state-of-the-art methods.

Process complexities are characterized by strong nonlinearities, dynamics, and uncertainties. Monitoring such a complex process requires a high-quality model describing the corresponding nonlinear dynamic behavior. The proposed model is constructed using deep neural networks (DNNs) to represent the state transition and observation generation, both of which constitute a stochastic nonlinear state-space model. A new bidirectional recurrent neural network (RNN), creating a connection of the hidden layer between a forward RNN and a backward RNN, is proposed to generate the filtering estimation and the smoothing estimation of process states which further generate observations with DNN-based process models. The smoothing estimator and the process model are first learned offline with all collected samples. Then the filtering estimator is fine-tuned by the learned smoother and process models to achieve real-time monitoring since the filter state is estimated based on the past and the current observations. Two indices are designed based on the learned model for monitoring the process anomaly. The proposed process monitoring model can deal with complex nonlinearities, process dynamics, and process uncertainties, all of which can be very challenging for the existing methods, such as kernel mapping and stacked auto-encoder. Two case studies validate that the effectiveness of the proposed method outperforms the other comparative methods by at least 10% when using the averaged fault detection rate in the industrial experimental data.

Multimodal data are common in industrial processes because of switched operating conditions, varying feedstocks and changed product designs and so on. To guarantee process safety and improving process performance, a variable-wise weighted parallel stacked auto-encoder model is proposed for nonlinear multimode process monitoring. Considering the similarity and difference between multiple operating modes with complex process nonlinearities, mode-common and mode-specific deep features are parallelly extracted with the proposed new model. Since each variable distinctly contributes to the mode-common features, variable-wise weights are designed with an optimal transport distance between modes when the mode-common features are learned. Moreover, different from designing a unified monitoring index for all modes, three asymmetric indices are designed to not only trigger an alarm for an anomaly, but also indicate whether the anomaly is caused by mode-common factors, mode-specific factors or others. Thus, the real-time monitoring results, together with some diagnosis information are simultaneously presented. A numerical example and a real industry application are used to validate the monitoring efficacy of the proposed model.

Population-based intelligent optimization algorithms are popular due to their global optimality. However, it will be time-consuming if they are directly applied to nonlinear dynamical systems. In this article, an efficient computational cost reduction strategy is presented for the population-based intelligent optimization algorithms when they are employed to search for the global optimum of nonlinear systems in dynamic equilibrium. Specifically, a novel constrained optimization problem is formulated according to the demand of dynamic equilibrium in industry, and the reason why population-based methods take much more computing time is analyzed from the perspective of solving nonlinear equations. Since the computational complexity of solving nonlinear equations is sensitive to their initial values, a sensitivity transfer condition is provided to explain the significance of candidate testing order. Finally, an optimal evaluation sequence, which minimizes the Euclidean distance of adjacent candidates, is designed for the population-based intelligent optimization algorithms. Simulations show the effectiveness.

In industrial processes, inferential sensors have been extensively applied for prediction of quality variables that are difficult to measure online directly by hard sensors. Deep learning is a recently developed technique for feature representation of complex data, which has great potentials in soft sensor modeling. However, it often needs a large number of representative data to train and obtain a good deep network. Moreover, layer-wise pretraining often causes information loss and generalization degradation of high hidden layers. This greatly limits the implementation and application of deep learning networks in industrial processes. In this article, a layer-wise data augmentation (LWDA) strategy is proposed for the pretraining of deep learning networks and soft sensor modeling. In particular, the LWDA-based stacked autoencoder (LWDA-SAE) is developed in detail. Finally, the proposed LWDA-SAE model is applied to predict the 10% and 50% boiling points of the aviation kerosene in an industrial hydrocracking process. The results show that the LWDA-SAE-based soft sensor is superior to multilayer perceptron, traditional SAE, and the SAE with data augmentation only for its input layer (IDA-SAE). Moreover, LWDA-SAE can converge at a faster speed with a lower learning error than the other methods.

Soft sensor has been extensively utilized in industrial processes for prediction of key quality variables. To build an accurate virtual sensor model, it is very significant to model the dynamic and nonlinear behaviors of process sequential data properly. Recently, a long short-term memory (LSTM) network has shown great modeling ability on various time series, in which basic LSTM units can handle data nonlinearities and dynamics with a dynamic latent variable structure. However, the hidden variables in the basic LSTM unit mainly focus on describing the dynamics of input variables, which lack representation for the quality data. In this paper, a supervised LSTM (SLSTM) network is proposed to learn quality-relevant hidden dynamics for soft sensor application, which is composed of basic SLSTM unit at each sampling instant. In the basic SLSTM unit, the quality and input variables are simultaneously utilized to learn the dynamic hidden states, which are more relevant and useful for quality prediction. The effectiveness of the proposed SLSTM network is demonstrated on a penicillin fermentation process and an industrial debutanizer column.

Deep learning is a recently developed feature representation technique for data with complicated structures, which has great potential for soft sensing of industrial processes. However, most deep networks mainly focus on hierarchical feature learning for the raw observed input data. For soft sensor applications, it is important to reduce irrelevant information and extract quality-relevant features from the raw input data for quality prediction. To deal with this problem, a novel deep learning network is proposed for quality-relevant feature representation in this article, which is based on stacked quality-driven autoencoder (SQAE). First, a quality-driven autoencoder (QAE) is designed by exploiting the quality data to guide feature extraction with the constraint that the potential features should largely reconstruct the input layer data and the quality data at the output layer. In this way, quality-relevant features can be captured by QAE. Then, by stacking multiple QAEs to construct the deep SQAE network, SQAE can gradually reduce irrelevant features and learn hierarchical quality-relevant features. Finally, the high-level quality-relevant features can be directly applied for soft sensing of the quality variables. The effectiveness and flexibility of the proposed deep learning model are validated on an industrial debutanizer column process.

Deep learning has been recently introduced for soft sensors in industrial processes. However, most of the existing deep networks, such as stacked autoencoder, are pretrained in a layerwise unsupervised way to learn feature representations for the raw input data itself. For soft sensors, it is necessary to extract quality-relevant features for quality prediction. Thus, a deep layerwise supervised pretraining framework is proposed for quality-relevant feature extraction and soft sensor modeling in this article, which is based on stacked supervised encoder-decoder (SSED). In SSED, hierarchical quality-relevant features are successively learned by a number of supervised encoder-decoder (SED) models. For each SED, the features from the previous hidden layer are served as new inputs to generate the high-level features that are learned with the constraint of predicting the quality data as good as possible at the output layer of this SED. With this new structure, the SED can learn quality-relevant features that can largely improve the prediction performance. By stacking multiple SEDs, hierarchical quality-relevant features can be progressively learned, and irrelevant information is gradually reduced by deep SSED network. The effectiveness of the proposed model is demonstrated on a numerical example and an industrial process of the debutanizer column.

Nowadays, data-driven soft sensors have been developed to estimate the quality variables which are difficult-to-measure in industrial processes. Feature representation plays a significant role in constructing accurate soft sensors. Recently, deep learning has been introduced for feature representation in process data modeling. However, traditional deep networks cannot capture quality-related features for output prediction. To handle this problem, a nonlinear variable-wise weighted stacked autoencoder (NVW-SAE) is proposed to learn deep quality-related features in this paper. By measuring the nonlinear Kendall correlations of input or feature variables with the quality variable in each autoencoder, a corresponding weighted reconstruction objective function is designed to learn quality-related features layer by layer in NVW-SAE. Finally, the proposed NVW-SAE based soft sensor method is applied to a debutanizer column to estimate the concentration of butane, which shows its effectiveness and superiority.

In modern industrial processes, soft sensors have played an important role for effective process control, optimization, and monitoring. Feature representation is one of the core factors to construct accurate soft sensors. Recently, deep learning techniques have been developed for high-level abstract feature extraction in pattern recognition areas, which also have great potential for soft sensing applications. Hence, deep stacked autoencoder (SAE) is introduced for soft sensor in this paper. As for output prediction purpose, traditional deep learning algorithms cannot extract high-level output-related features. Thus, a novel variable-wise weighted stacked autoencoder (VW-SAE) is proposed for hierarchical output-related feature representation layer by layer. By correlation analysis with the output variable, important variables are identified from other ones in the input layer of each autoencoder. The variables are assigned with different weights accordingly. Then, variable-wise weighted autoencoders are designed and stacked to form deep networks. An industrial application shows that the proposed VW-SAE can give better prediction performance than the traditional multilayer neural networks and SAE.

Just-in-time learning (JITL) is a commonly used technique for industrial soft sensing of nonlinear processes. However, traditional JITL approaches mainly focus on equal sample sizes between process (input) variables and quality (output) variables, which may not be practical in industrial processes since quality variables are usually much harder to obtain than other process variables. In order to handle unequal length dataset with only a few labeled data, a novel semisupervised JITL framework is proposed for soft sensor modeling for nonlinear processes, which is based on semisupervised weighted probabilistic principal component regression (SWPPCR). In the new semisupervised JITL framework, traditional Mahalanobis distance and a new proposed scaled Mahalanobis distance are used for similarity measurement and weight assignment. By selecting the most relevant labeled and unlabeled samples and assigning them with the corresponding weights, a local SWPPCR can be built to estimate the output variables of the query sample. Case studies are carried out to evaluate the prediction performance of the proposed semisupervised JITL framework on a numerical example and an industrial process. The effectiveness and flexibility of the proposed method are demonstrated by the prediction results.