This paper addresses the state estimation problem for new operation modes when there is insufficient measurement data available to learn model parameters. The proposed method, called the transfer state estimator, is formulated using variable-structure multiple model estimation, which enables one to improve estimation performance by transferring model knowledge from different source modes to the target mode. Specifically, first, to track system parameter changes, this work utilizes residuals, which represent the deviations between the actual state and the predicted state. These residuals play a crucial role in determining which knowledge needs to be updated. The transfer state estimator is then derived by integrating knowledge from source models. Through this fusion process, the estimator leverages the existing knowledge to handle the new mode in the target domain. Finally, we provide numerical examples and practical simulations to show the efficacy of the proposed method. The results illustrate that the proposed state estimator is a competitive alternative to various existing state estimation methods when dealing with state estimation in the presence of a new mode.

This paper presents a reinforcement learning-based model predictive control (RL-MPC) output regulation approach for uncertain constrained linear systems. The proposed approach addresses key challenges in trajectory tracking under unknown parameters, state-input constraints, and external disturbances. By transforming the original system dynamics and constraint sets via regulator equations, the output regulation problem (ORP) is reformulated as a constrained stabilization for the tracking error dynamics. An MPC scheme is then constructed based on the uncertain transformed model, providing constraint-satisfying control policies applied to the actual system. Meanwhile, RL employs the parameterized MPC as a function approximator, recursively updating both regulator and MPC parameters online to enable adaptive policy optimization via continuous state feedback. A safety validation mechanism is integrated into the parameter learning to ensure recursive feasibility and closed-loop stability. The effectiveness of the proposed scheme is verified by a speed regulation simulation of a permanent magnet synchronous motor (PMSM) system.

This work aims at developing a novel direct design and analysis method of learning control protocol toward consensus performance of multiagent systems (MASs) without using any model. A nonlinear autoregressive moving average (NARMA) function is designed at first to formulate the inherent consensus dynamics with respect to the consensus error and the control protocols. Then, a consensus performance-related iterative linear data model (CPiLDM) is constructed for equivalently reformulating the NARMA consensus system's iterative dynamics in a data-driven framework. The CPiLDM does not rely on a model no matter through first-principle modeling or system identification methods. Next, a direct distributed iterative learning control (DirDILC) method is developed through an optimization technique subject to the CPiLDM. The convergence is proved directly for the virtual NARMA consensus system, without relying on the dynamics of the agent itself, and thus simplifies the analysis consequently. Since the presented DirDILC is purely data-driven without relying on an explicit model, it constitutes a significant step forward from the existing consensus control theory.

Effective state estimation is crucial for ensuring operational safety, environmental compliance, and efficient resource utilization in high-dimensional wastewater treatment plants (WWTPs). This study proposes a purely data-driven methodology based on dynamic mode decomposition (DMD) to construct a linear dynamic model capable of globally capturing the inherent nonlinearity and complexity of wastewater treatment processes. Moreover, DMD can generate system representations in both full-dimension and reduced-dimension forms and offers flexibility in modeling complex dynamics. Then, the Kalman filter and ensemble Kalman filter (EnKF) are implemented using the derived models for state estimation. A detailed analysis of estimation accuracy and computational cost is also provided. Furthermore, the performance of the proposed DMD-based method is comparatively evaluated against a traditional linearization-based approach, in which the process is linearized at a nominal operating point. Results from the high-dimensional WWTP demonstrate the effectiveness and superiority of the proposed method.

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.

Considering the four challenges of non-identical initial states, non-repetitive uncertainties, different batch lengths, and unavailable mathematical model of a rubber mixing process (RMP), this article proposes a data-driven iterative learning temperature control (DDILTC) for the RMP. Specifically, an iterative linear data model (iLDM) is developed to formulate the iterative dynamics of RMP and is further used as a one-step iterative linear predictive model to estimate the RMP’s temperature that is unavailable when the current batch length is shorter than the desired one. The unknown parameters of the iLDM are estimated iteratively by designing an iterative adaption law. Further, an iterative learning based observer is designed to estimate the non-repetitive uncertainties and non-identical initial states as an extended state. The proposed DDILTC is a data-driven method and the iLDM is only used to formulate the iterative relationship of the input-output between two batches instead of a mathematical model of the RMP with physical meanings. Simulation study verifies the results. Note to Practitioners—The mixing temperature of a rubber mixing process (RMP) is a critical variable, ensuring the desired plasticity and viscosity of the rubber compounds. Indeed, RMP is a typical batch process performing repetitively over the finite time interval. However, no ILC results about the RMP temperature control have been reported even though ILC can learn the control experience from the past batches to improve control performance. The main reason lies in that the practical environments of RMP make it impossible to satisfy the strictly repetitive conditions, i.e., the initial states, disturbances, and batch lengths are all iteration-varying. Furthermore, it is difficult to establish a mathematical model of the RMP due to its large production scale and complex dynamics along both time and iteration directions. Therefore, the main motivation of this paper is to study the iterative learning temperature control problem of RMP by considering the nonrepetitive uncertainties of initial states, disturbances, and batch lengths, bypassing the use of any model information. An iterative linear data model (iLDM) is established to equivalently reformulate the unavailable two-dimensional dynamic behavior of RMP and to facilitate the controller design and analysis. The gradient uncertainty of RMP is reformulated as the unknown parameters in the iLDM and can be iteratively estimated by designing an iterative adaptation algorithm. The non-repetitive initial states and disturbances can be estimated by designing an iterative observer. Moreover, the unavailable mixing temperatures at the unreachable operation points are estimated by using the iLDM as the iterative predictive model. To summarize, the proposed method is simple in computation and easy in implementation since only the I/O data is used, and thus it is of great practical significance.

Precise control of roasting temperature is paramount for optimizing production efficiency in the zinc smelting process. However, existing research mainly focuses on average temperature control, and there is little research on temperature distribution control. To achieve this, a roasting temperature distribution model is first established based on the principles of heat transfer. Second, accounting for modeling errors and environmental disturbances, a discrete sliding mode control with disturbance compensation is proposed. Besides, continuous reaching law is implemented to address issues related to chattering, so as to ensure stable roasting temperature. Finally, the quasi-sliding-mode domain of the proposed method is obtained by boundary analysis. The simulation results of roasting temperature distribution control substantiate the efficacy of the proposed approach.Note to Practitioners—Roasting temperature is the most critical temperature that directly determines product quality and stable production during the roasting process. Currently popular schemes all use average temperature as the control target. However, the average temperature does not represent the actual temperature inside the roaster. This paper aims to achieve the temperature distribution of the roaster, thereby ultimately improving product quality and ensuring safe production. This paper proposes a roasting temperature control scheme based on discrete sliding mode control. During the implementation of this method, the current temperature error distribution is used as input to adjust the zinc concentrate feeding rate in real time. Experimental simulations verified the feasibility of this method, but it has not yet been applied in actual production.

The primary separation cell (PSC) plays a key role in bitumen recovery during oil sands extraction. Controlling the froth-middling interface level in PSC is vital for optimal bitumen recovery. Existing sensors for the interface level measurement can be either costly or less reliable. This paper introduces an image restoration algorithm to enhance degraded images of PSC sight glasses followed by an image segmentation technique, which can serve as an alternative for interface level estimation. The restoration algorithm uses a regular state-space model with a skew-t distribution for measurement noise to account for image contamination. States and parameters are estimated using an expectation-maximization (EM) algorithm along with a robust Kalman filter (KF). The restored images are segmented using a Gaussian mixture model (GMM) with Markov random fields (MRF) for interface detection. Experimental results on a lab-scale PSC demonstrate the method’s effectiveness in improving interface level estimation compared to the existing models.

Process uncertainty, which is usually caused by various factors, is generally subject to unknown complex distribution. However, many existing monitoring methods are established with a single distribution, and thus they may not accurately reflect the uncertainty within process systems. In this study, a probabilistic quality- relevant monitoring (PQM-GMM) is proposed with the Gaussian mixture model to address the aforementioned issue. Different from conventional monitoring methods, the proposed method measures the process uncertainty using multiple Gaussian distributions, which can be used to approximate any unknown complex distribution. Then, the optimization problem of the proposed PQM-GMM model is solved using the expectation maximization (EM) algorithm, which includes an augmented Lagrange multiplier in the M-step for model parameter estimation. Using the obtained results, a quality-relevant monitoring model is established with three statistics. It is noted that the proposed model can also be extended to many existing methods since they share a similar structure. Besides, the detailed information such as initial value selection, missing data problem, computation complexity is discussed. The effectiveness and superiority of the proposed method are tested using a numerical simulation example and a real low-pressure heater application. In comparison with some commonly used quality-relevant methods, the proposed model can be robustly established in the presence of corrupted data, and has a better detection sensitivity for the process anomalies in both process and quality variables. Note to Practitioners—A quality-relevant monitoring method is proposed in this study with Gaussian mixture model (GMM) for detecting the abnormal conditions of industrial processes under harsh environment. Since GMM can be used to approximate any unknown complex distribution, the process uncertainty within the collected data can be meticulously measured using the proposed PQM-GMM model. Besides, the quality-independent faults and quality-related faults can also be effectively distinguished using the designed monitoring statistics.

Considering the three critical factors of data quantization, channel fading, and denial of service (DoS) attack introduced by the networked control systems (NCSs) simultaneously, we propose a novel compensatory data-driven networked iterative learning control (COMP-DDNILC) method for nonlinear repetitive NCSs under a model-free design and analysis framework. By reformulating the iterative input-and-output (I/O) dynamics of the nonlinear NCS as an iterative linear data model (iLDM), an iterative linear predictive data model (iLPDM) is developed to predict the missing data arisen from DoS attacks. Then, a relationship is built to describe the coupling effects of the three critical factors, based on which the COMP-DDNILC is designed by involving the compensatory mechanism of DoS attacks and the fading coefficient inversion to improve the control performance. The COMP-DDNILC also involves an iterative adaption mechanism to update the iLPDM to enhance the robustness against uncertainties. The data-driven nature of COMP-DDNILC makes it applicable to practical NCSs without model information available. The simulation study verifies the results.

In industrial automation and intelligence, fault tolerance mechanisms have always been an attractive topic. To develop soft sensors with fault tolerance for different types of faults and unforeseen new faults, this article proposes a two-dimensional group distributionally robust optimization (2D-GDRO) framework for fault-tolerant soft sensor modeling. We propose to describe the potential distributions of new fault conditions with an uncertainty set and optimize the soft sensor model by minimizing the worst-case risk over the uncertainty set. Considering the restricted representation range of the uncertainty set constructed directly from a mixture distribution of a limited number of existing fault conditions in the training set, a two-dimensional uncertainty set is designed at the group dimension and the sample dimension. To efficiently train a fault-tolerant soft sensor within the 2D-GDRO framework, we introduce a triple-interleaved optimization algorithm. This algorithm integrates mini-batch stochastic gradient descent, exponentiated gradient ascent, and group-wise SoftMax techniques. Finally, the fault tolerance of the 2D-GDRO framework based soft sensor is verified using the Tennessee-Eastman process and the real three-phase flow facility. The experimental results show that 2D-GDRO outperforms other training frameworks in average soft sensing accuracy under new fault conditions.

Effective fault diagnosis is crucial for maintaining the reliability and safety of industrial systems. Incremental learning, which enables models to continuously update and adapt to new data or emerging fault classes without complete retraining, has recently gained attention as a promising solution for addressing nonstationary data streams in fault diagnosis applications. Nevertheless, most existing review articles on fault diagnosis adopt a broad perspective, primarily discussing general techniques such as deep learning and transfer learning, without providing a dedicated focus on incremental learning strategies. To the best of our knowledge, it is the first review focusing specifically on incremental learning-enabled fault diagnosis methods. In this work, state-of-the-art incremental learning-enabled fault diagnosis are systematically reviewed. These methods are categorized into distinct groups based on their incremental learning strategies and application contexts. In addition, major challenges associated with applying incremental learning to fault diagnosis, including concept drift and catastrophic forgetting, are discussed, along with emerging solutions proposed to address these issues. A novel taxonomy and perspective on incremental learning-enabled fault diagnosis approaches is presented, providing a timely and comprehensive reference for researchers and practitioners in this evolving field.

Process variables may exhibit both temporal trends and periodic responses, with their fault propagation pathways manifesting in time-domain and frequency-domain causalities, respectively. However, the differing causal perspectives of time-domain and frequency-domain methods can lead to distinct causalities, posing the causal heterogeneity challenge for root cause diagnosis (RCD). Thereupon, we reveal the mechanism of source consistency in Granger causality (GC), that is, the root cause variable provides the most significant predictive information in both time and frequency domains. Accordingly, we propose a causal source consistency analytics (CSCA) framework that achieves time-frequency synergy. First, we design a nonlinear enhancement module to extract temporal features for causal inference. Second, to extract time-domain and frequency-domain GC, we develop a parallel causality learning module, where a differentiable frequency-domain expansion operator is designed along with a temporal prediction submodule. Meanwhile, a time-frequency entropy constraint is constructed to ensure causal significance by inducing sparsity. Finally, a root cause alignment module is proposed to ensure source consistency. A predictive information quantification algorithm, formulated as an eigenvalue decomposition problem, is designed to locate the root cause. We develop an approximate exponential transformation to convert the eigenvalue decomposition into a differentiable source alignment loss. Thus, source consistency can be ensured during end-to-end inference. The validity of CSCA is illustrated through the Tennessee Eastman process and a gas turbine application. CSCA identified the root causes in both examples correctly. Furthermore, ablation studies validate that CSCA enables the time-domain and frequency-domain models to identify consistent root causes, thereby overcoming causal heterogeneity.

This article presents a novel data-driven approach to nonlinear system control using a behavioral systems framework. A dynamic latent variable autoencoder (DLVAE) is proposed to project the nonlinear physical variable space onto a linear latent variable space. A data-predictive control approach is developed to control the physical process variables through the latent variables. Based on the behavioral systems theory, the proposed data-driven control framework does not require knowledge of the causality of the latent variables. The stability of the controlled system is ensured by utilizing the concept of trajectory-based dissipativity. The robustness of this control approach is achieved by incorporating the Lipschitz bounds between the latent and physical variables under dissipativity conditions.

The historical data collected from industrial processes are generally disturbed by ambient noise and outliers. Hence, accurate estimation of process uncertainty is essential in order to correctly determine the status of the process systems. In this study, a robust probabilistic quality-relevant monitoring model with a Laplace distribution is proposed for industrial process monitoring under noisy environment. Because of the heavy tailed characteristic of Laplace distribution, the proposed model is more robust than models with Gaussian distribution. The solution of the proposed probabilistic model is provided through variational Bayesian inference and maximum likelihood estimation after recasting Laplace distribution as Gaussian scale mixtures. Based on the obtained model parameters and estimated latent variables, a quality-relevant monitoring model can be established and four statistics are designed. According to the calculated statistics, the proposed method can effectively detect and differentiate quality-relevant from quality-independent faults. The performance of the proposed method is illustrated using a numerical simulation and a condenser application, which are disturbed by ambient noise and outliers. Experimental results demonstrate that Laplace distribution can better reveal the process uncertainty to effectively alleviate their negative effect. As a result, the proposed method performs better than some commonly used quality-relevant monitoring strategies.

This article investigates loosely coupled inertial navigation system/global positioning system (INS/GPS) integration for land vehicle navigation. To achieve navigation with higher accuracy and lower computational complexity, we present an integration solution using factor graph optimization (FGO) based on the graphical state-space model (GSSM). This solution is referred to as GSSM-FGO. Compared with traditional methods, the unique specialty of our work lies in both modeling and problem-solving aspects under the assumption of calibration parameter invariance. Specifically, we suggest that the time-series state-space model is not always suitable for widely existing constant calibration parameters. Thus, we propose GSSM as a more flexible and accurate state description by extracting the constant states as singular nodes. The FGO is adopted to manage this novel graphical model, while traditional filter-based algorithms fail when faced with the cyclic model structure. The universality of our approach is validated through a real-world land vehicle navigation dataset, featuring four distinct-grade inertial measurement units. Compared to the methods based on extended Kalman filter and FGO with the traditional state-space model, our approach demonstrates a substantial enhancement in estimation accuracy and computational speed.

Causal discovery in multi-rate time series encounters greater challenges compared to regular time series. This stems from a potential problem that has not been noticed and explored in existing studies:information granularity heterogeneity, which refers to the natural difference in information granularity between fast sampling rate data (high information granularity) and slow sampling rate data (low information granularity). Such an imbalance in information granularity can hinder forecasting relationships modeling and induce biased causal learning. Therefore, we propose aMutual Information-iNspired causalDiscovery framework (MIND), aiming to derive rate-agnostic features with consistent information granularity to alleviate information granularity heterogeneity problem. Technically, MIND comprises Stage 1 (pre-training) and Stage 2 (fine-tuning and causal discovery). In Stage 1, empowered by pseudo-slow sampling rate data (generated through the interleaved down sampling strategy) and mutual information, we can eliminate the influence of sampling rates and drive rate-aware encoders (RAEs) to sense key information (i.e., rate-agnostic) that remains unchanged across varying sampling rates. In Stage 2, the well-trained RAEs can extract rate-agnostic features from real multi-rate time series, thus facilitating effective forecasting relationships modeling and yield accurate causal discovery. Empirically, MIND realizes superior performance on various multi-rate scenarios, including four simulation datasets and one real-world dataset.

The series includes two parts, articulating the two novel avenues of research on intelligent fault diagnosis (FD) for nonlinear feedback control systems. In Part I of the series, we design a novel FD paradigm by elaborating an invertible neural network (INN) for feedback control systems. With the aid of a left manifold, the core idea behind the INN-based FD scheme is as follows: 1) formulation of residual generator used for FD as a projection of system data onto the null space that has the same dimension as system outputs; 2) in a topological space, elaboration of a homeomorphism that delivers an invertible relationship between system outputs and residual signals when the system input is given; and 3) skillful introduction of both the master and slave objective functions to achieve system/parameter identification with information loseless property. Comparing with the existing FD approaches, the three superior strengths of the proposed FD scheme deserving mentation are as follows: 1) it specializes in nonlinear feedback control systems; 2) it can effectively avoid the overfitting problem when approximating or learning nonlinear system dynamics; and 3) control theory guides the whole design, ensuring the interpretability of the learning process. Finally, two studies on nonlinear systems demonstrate the feasibility of the invertible left manifold (ILM)-based FD strategy. Part I would contribute to the future development of machine learning (ML)-based system identification and explainable FD approaches, and also benefits the right manifold-based FD designs in Part II.

Due to sensor malfunctions and data transmission corruptions, the industrial process data collected commonly contain missing values. It poses a significant challenge for data-driven approaches in aggregating temporal-spatial correlations that reflect dependencies across both variables and times, which makes it difficult to directly carry out downstream industrial operational applications. In this study, a self-supervised representation learning model is proposed to extract probabilistic temporal-spatial latent variables (LVs) from sequential data under missing value interference. The extracted LVs can be utilized for typical industrial operational applications through a unified framework. First, a novel deep dynamic probabilistic latent variable model, named Markov dynamic variational autoencoder (MD-VAE), is proposed to explicitly model the temporal-spatial dependencies between LVs. The latent posteriors are Bayesian smoothed by global sequence information for effective variational inference (VI). Second, a self-supervised learning approach, termed masked MD-VAE (M2D-VAE), is proposed to address the challenge of directly extracting temporal-spatial LVs under missing value interference. Controllable constraints with practical interpretations are introduced to balance the latent bottleneck capacity with reconstruction accuracy during model optimization. A unified framework is proposed to utilize the latent representations for typical industrial downstream tasks. Case studies conducted on a real-world multiphase flow process demonstrate the superiority of M2D-VAE in unsupervised industrial operational applications including missing value imputation and dynamic process monitoring under missing value interference.

A novel data-driven internal model learning control (DIMLC) strategy is developed for a nonlinear nonaffine system subject to unknown nonrepetitive uncertainties. At first, an iterative dynamic linearization (IDL) approach is employed for reformulating the nonlinear plant to an iterative linear data model (iLDM). Then, the nominal form of the IDL-based iLDM is used as an internal model of the nonlinear plant whose parameters are estimated by an iterative adaptive updating mechanism using only input-output (I/O) data. The equivalent feedback-principle-based internal model inversion is further applied to the subsequent controller design and analysis. The proposed DIMLC contains two parts. One is a nominal controller designed by the inversion of the internal model which achieves a perfect tracking of the target output; the other is a compensatory controller which offsets the uncertainties. The novel DIMLC is data-driven and does not require an explicit model. It can deal with model-plant mismatch and disturbances, enhancing the robustness against uncertainties. The theoretical results are verified by simulation study.

Aiming to solve issues of limited resources in topology network communication, unavailability of the mathematical models, direct controller design without considering system dynamical formulation, and lack of efficient use of learning ability from repetitive operations, an event-triggered direct data driven iterative learning control (ET-DirDDILC) is developed for a multiagent system (MAS). Since the control protocol directly affects control performance, there is definitely a close relationship between the consensus performance of the agents and the control protocols. To this end, a nonaffine nonlinear relationship of consensus error regarding the control protocol is established. Then, to deal with the unknown nonlinearity, a dynamic linear input–output relationship between two triggered batches is established by an event-triggering linearly parametric data model (ET-LPDM) where a triggering mechanism is designed along the iteration axis. Furthermore, both the event-triggered control law and the event-triggered parameter estimation law are derived from two objective functions, respectively, by using the ET-LPDM, where the values at nontriggering iteration remain unchanged from the latest triggering iteration to reduce the consumption of system resources. The proposed ET-DirDDILC does not rely on the MAS dynamical formulation. The convergence is proved and simulation study verifies the effectiveness of the presented ET-DirDDILC for MASs with both fixed and switching topologies.

Due to various reasons, outliers, ambient noise and missing data inevitably exist in the industrial processes, and thus the robustness is important when establishing monitoring models. In this study, a robust dissimilarity analytics model (RDAM) is established with Laplace distribution to detect process anomalies in noisy environment. Because of the heavy-tailed characteristic of Laplace distribution, the proposed RDAM method is more robust to ambient noise and outliers when compared to Gaussian distribution-based models. Besides, the missing data problem is also considered and solved in the model development procedure. Using the variational Bayesian inference, the model parameters and latent variables of the RDAM model can be estimated. After that, a monitoring strategy is designed based on the obtained results with both static and dynamic statistics. By this means, both the static deviation of the current sample and the temporal correlation within the process data can be effectively revealed. A simulated example and a real low-pressure heater process are adopted to illustrate the performance of the proposed RDAM method. Specifically, the proposed RDAM method is robust to the ambient noise and missing values, and it has better detection sensitivity for the process anomalies than the selected comparison methods.

This work aims at presenting a new sampled-data model-free adaptive control (SDMFAC) for continuous-time systems with the explicit use of sampling period and past input and output (I/O) data to enhance control performance. A sampled-data-based dynamical linearization model (SDDLM) is established to address the unknown nonlinearities and nonaffine structure of the continuous-time system, which all the complex uncertainties are compressed into a parameter gradient vector that is further estimated by designing a parameter updating law. By virtue of the SDDLM, we propose a new SDMFAC that not only can use both additional control information and sampling period information to improve control performance but also can restrain uncertainties by including a parameter adaptation mechanism. The proposed SDMFAC is data-driven and thus overcomes the problems caused by model-dependence as in the traditional control design methods. The simulation study is performed to demonstrate the validity of the results.

In this work, a data-driven indirect iterative learning control (DD-iILC) is presented for a repetitive nonlinear system by taking a proportional-integral-derivative (PID) feedback control in the inner loop. A linear parametric iterative tuning algorithm for the set-point is developed from an ideal nonlinear learning function that exists in theory by utilizing an iterative dynamic linearization (IDL) technique. Then, an adaptive iterative updating strategy of the parameter in the linear parametric set-point iterative tuning law is presented by optimizing an objective function for the controlled system. Since the system considered is nonlinear and nonaffine with no available model information, the IDL technique is also used along with a strategy similar to the parameter adaptive iterative learning law. Finally, the entire DD-iILC scheme is completed by incorporating the local PID controller. The convergence is proved by applying contraction mapping and mathematical induction. The theoretical results are verified by simulations on a numerical example and a permanent magnet linear motor example.

A data-driven dynamic internal model control (D3IMC) scheme is proposed for unknown nonlinear nonaffine systems bypassing modeling steps. Different from the traditional internal model constructed by either a first-principle or an identified model, a dynamic internal model (DIM) is developed in this work using I/O data where a compact form dynamic linearization approach is introduced for addressing the nonlinearity and nonaffine structure. Then, the D3IMC is proposed with both a nominal control algorithm and an uncertainty compensation control algorithm. The former can quickly respond to the feedback errors and the latter can compensate the model-plant mismatch and external disturbances. Meanwhile, the adaptive parameter updating law in the proposed D3IMC method inherits the robustness against uncertainties. A nominal D3IMC is also designed without including the compensator when there is no exogenous disturbance since the adaptive mechanism can handle system uncertainty. Further, the results are extended and a full-form dynamic linearization-based D3IMC is developed to address control of nonlinear systems with more complex dynamics. All the proposed D3IMC methods are data-driven without need of an explicit model, and thus they are significant extensions from the traditional model-based IMC. Simulation study verifies the results.

This work considers three main problems related to fast finite-iteration convergence (FIC), nonrepetitive uncertainty, and data-driven design. A data-driven robust finite-iteration learning control (DDRFILC) is proposed for a multiple-input-multiple-output (MIMO) nonrepetitive uncertain system. The proposed learning control has a tunable learning gain computed through the solution of a set of linear matrix inequalities (LMIs). It warrants a bounded convergence within the predesignated finite iterations. In the proposed DDRFILC, not only can the tracking error bound be determined in advance but also the convergence iteration number can be designated beforehand. To deal with nonrepetitive uncertainty, the MIMO uncertain system is reformulated as an iterative incremental linear model by defining a pseudo partitioned Jacobian matrix (PPJM), which is estimated iteratively by using a projection algorithm. Further, both the PPJM estimation and its estimation error bound are included in the LMIs to restrain their effects on the control performance. The proposed DDRFILC can guarantee both the iterative asymptotic convergence with increasing iterations and the FIC within the prespecified iteration number. Simulation results verify the proposed algorithm.

The industry is undergoing a transformation toward smart manufacturing, fostering intelligent operations, sustainability, and digitalization. However, the current state of the process industry falls short of this future vision. Key areas, such as hybrid modeling, autonomous control, dynamic scheduling, intelligent decision making, security and safety control, and predictive maintenance, still require significant development. Given that the industrial metaverse enables the virtualization and digitization of industrial processes using technologies, such as artificial intelligence, blockchain, cloud computing, and digital twins, it is promising to establish the industrial metaverse for manufacturing, encompassing the entire lifecycle based on the industrial Internet and other modern information technologies.

Due to the high-stakes nature of industrial processes, there is an immediate and pressing need on soft sensors for stability and interpretability. In this regard, causality-inspired modeling aims to learn causal features corresponding to the direct causes of quality variables, exhibiting great potential in terms of both stability and interpretability. However, most existing causality-inspired methods overlook temporal modeling and domain knowledge integration, which hinders their real-world application in industrial soft sensing. To this end, this article proposes a novel causality-inspired stable long short-term memory (Stable-LSTM), which leverages Bayesian-based causal structure inference and incorporates domain knowledge as a prior to enhance the performance stability and physical interpretability of soft sensors. After extracting temporal features via long short-term memory (LSTM), a Bayesian-based causal structure inference approach is developed by leveraging variational inference to learn the underlying hidden causal structure within the industrial processes. Through a hidden explanation of domain knowledge, a prior distribution is placed on the hidden causal structure, which will greatly enhance the physical interpretability and facilitate the exploration for true causality. Moreover, we also introduce a global sample reweighting strategy to remove spurious correlations and reveal causal effects between time series hidden features and quality variables. Finally, the performance stability and physical interpretability of the proposed Stable-LSTM are verified using a three-phase flow facility and a m-phenylenediamine distillation process. The results show that the Stable-LSTM achieves the highest soft sensing accuracy under distribution shift, and the inferred causal structure exhibits the greatest consistency with the domain knowledge, when compared with the seven existing methods.

Process control can become challenging when the measurements are affected by irregular noise. Classical approaches utilize Gaussian methods to alleviate the sensory noise. However, many industries involve skewed noise in their processes. While the closed skew-normal (CSN) distribution generalizes a Gaussian distribution with additional parameters, its dimension increases during recursive estimation, making it impractical. Even though there are some techniques for the solution, they are typically too complicated or inaccurate for higher-dimensional problems. This study proposes a novel online optimization scheme to reduce the dimensionality of a CSN distribution while considering the properties of the complete empirical distribution. Since the objective function used during the optimization step considers the geometry of the metric space, the proposed scheme achieves higher accuracy without sacrificing computational efficiency. The proposed filter is applied to two pilot-scale experiments. The results indicate that it is beneficial for recursive state estimation in the presence of skewed noise.

Slow feature analysis aims to linearly transform measured data into uncorrelated signals that vary from slow to fast. While earlier extensions successfully extracted slow features from nonlinear sequential data, they lacked a modeling preference for nonstationary and oscillating features due to constraints on the prior distribution. To address this limitation, a semisupervised encoder-decoder architecture is proposed in this article, integrating a statistical preference for such characteristics. This regularization is achieved by introducing a first-order autoregressive Gaussian prior within a regular variational auto-encoder framework, as opposed to the standard Gaussian distribution. The evidence lower bound associated with the proposed model is derived using the variational Bayesian inference, and the model parameters are estimated iteratively. The effectiveness of the proposed approach is evaluated on both simulated and real industrial processes.

In industrial processes, quality variables are typically sampled at a considerably lower frequency than system inputs due to technical or cost constraints. Dynamic soft sensors utilize temporal prediction to bridge these sampling gaps, thus enabling real-time closed-loop control. However, existing approaches primarily focus on one-step prediction accuracy, potentially leading to significant deviations in long-term predictions. In addition, these methods are incapable of evaluating the reliability of prediction results, subsequently increasing the potential risk of closed-loop systems. To tackle these challenges, this study presents a novel regression modeling approach based on the conditional variational autoencoder (CVAE) framework. In contrast to traditional regression approaches, this method focuses on modeling the transition probability distribution of the system, allowing the model to produce a range of credible quality variable predictions via Monte Carlo (MC) sampling. Based on the CVAEs, the sequential MC method is further employed to simulate diverse potential system state trajectories, thereby achieving multistep soft measurement prediction. Compared with traditional soft measurement techniques, the proposed method demonstrates lower prediction biases and the capacity to assess the credibility of prediction results from a probabilistic standpoint. When online quality variables are assessed by the laboratory, this method can update predictions utilizing the resampling scheme. Two case studies are offered to validate the effectiveness of the proposed scheme.

The increased complexity and intelligence of automation systems require the development of intelligent fault diagnosis (IFD) methodologies. By relying on the concept of a suspected space, this study develops explainable data-driven IFD approaches for nonlinear dynamic systems. More specifically, we parameterize nonlinear systems through a generalized kernel representation for system modeling and the associated fault diagnosis. An important result obtained is a unified form of kernel representations, applicable to both unsupervised and supervised learning. More importantly, through a rigorous theoretical analysis, we discover the existence of a bridge (i.e., a bijective mapping) between some supervised and unsupervised learning-based entities. Notably, the designed IFD approaches achieve the same performance with the use of this bridge. In order to have a better understanding of the results obtained, both unsupervised and supervised neural networks are chosen as the learning tools to identify the generalized kernel representations and design the IFD schemes; an invertible neural network is then employed to build the bridge between them. This article is a perspective article, whose contribution lies in proposing and formalizing the fundamental concepts for explainable intelligent learning methods, contributing to system modeling and data-driven IFD designs for nonlinear dynamic systems.

Over the last decade, transfer learning has attracted a great deal of attention as a new learning paradigm, based on which fault diagnosis (FD) approaches have been intensively developed to improve the safety and reliability of modern automation systems. Because of inevitable factors such as the varying work environment, performance degradation of components, and heterogeneity among similar automation systems, the FD method having long-term applicabilities becomes attractive. Motivated by these facts, transfer learning has been an indispensable tool that endows the FD methods with self-learning and adaptive abilities. On the presentation of basic knowledge in this field, a comprehensive review of transfer learning-motivated FD methods, whose two subclasses are developed based on knowledge calibration and knowledge compromise, is carried out in this survey article. Finally, some open problems, potential research directions, and conclusions are highlighted. Different from the existing reviews of transfer learning, this survey focuses on how to utilize previous knowledge specifically for the FD tasks, based on which three principles and a new classification strategy of transfer learning-motivated FD techniques are also presented. We hope that this work will constitute a timely contribution to transfer learning-motivated techniques regarding the FD topic.

Typically, industrial processes possess both temporal and spatial dependencies due to intravariable dynamics and intervariable couplings. The two dependencies have different manifestations, indicating diverse process characteristics. However, the existing methods fail to separate temporal and spatial information well, leading to inappropriate representation and inaccurate fault detection and isolation results. This study proposes an explicit representation and customized fault isolation framework to tackle temporal and spatial characteristics, so as to identify and locate anomalies affecting different dependencies. First, we design a double-level separation method for temporal and spatial information. In the first level, we construct two independent auto-encoding modules to extract temporal correlation and spatial graph structure in parallel. In the second level, we propose an information aliasing loss function to guild the two modules to distinguish between temporal and spatial characteristics, further facilitating information separation. By monitoring the explicit temporal and spatial statistics obtained by the two modules, spatiotemporal dependencies of anomalies can be determined for subsequent isolation. Furthermore, we propose a customized isolation strategy for anomalies in temporal and spatial characteristics. By quantifying changes in intravariable temporal dynamics and intervariable spatial graph structure individually, temporal impact and spatial propagation of faults can be finely characterized and isolated. Three examples are adopted to verify the performance of the proposed framework, including a numerical example, a real condensing system of the thermal power plant process, and the Tennessee Eastman benchmark process.

This article develops a novel data-driven finite-iteration learning control (DDFILC) for the nonlinear repetitive systems that are stable for the finite operation length. Both the error range and the finite-iteration number can be designated beforehand by considering the efficiency and economy of the industrial processes. As a result, not only can the proposed DDFILC guarantee the desired product quality but also can reduce the operation cost. First, a linear data model (LDM) is constructed to reformulate the system dynamics that satisfies the Lipschitz continuity condition. Then, an iterative updating law of the DDFILC is developed for estimating the unknown parameter of the LDM. The proportional-differential type learning law used in the DDFILC has two iteration-time-varying learning gains, both of which are updated according to the linear matrix inequality conditions. Not only the finite-iteration convergence but also the iteratively asymptotic convergence can be shown mathematically by using the two-dimensional (2-D) system theory. The proposed DDFILC approach does not require an exact model and is robust to uncertainties. The simulation study verifies the results.

This work aims at improving the control performance of the iterative learning control through set-point learning along iteration direction. A double-layered learning control mechanism is designed for both the control input and the set-point, respectively. The learning control of the input is regarded as a local controller in the inner layer, and the learning control of the set-point is designed as an auxiliary controller in the outer layer whose design is a main challenge since no any priori knowledge is available to describe the relationship between the set-point and the control performance. To solve this issue, an ideal nonlinear nonaffine set-point learning optimization (SPLO) algorithm is designed by taking the set-point and the tracking error as the arguments. Then, an iterative dynamic linearization (iDL) is introduced to formulate the ideal SPLO algorithm as a linear parametric one whose unknown parameter is estimated by designing a parameter updating algorithm. Further, since a strongly nonlinear and nonaffine system is considered without any model information available, the iDL is also used to derive its equivalent linear data model which is then updated by the input and output data to make the linear parametric SPLO realizable. Finally, a double-layered iterative learning control (DLILC) is proposed under the data-driven framework for tracking an iteration-varying trajectory. Convergence analysis and extensive simulations are included to demonstrate the effectiveness of the presented DLILC.

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.

This article presents a robust variational Bayesian (VB) algorithm for identifying piecewise autoregressive exogenous (PWARX) systems with time-varying time-delays. To alleviate the adverse effects caused by outliers, the probability distribution of noise is taken to follow a t -distribution. Meanwhile, a solution strategy for more accurately classifying undecidable data points is proposed, and the hyperplanes used to split data are determined by a support vector machine (SVM). In addition, maximum-likelihood estimation (MLE) is adopted to re-estimate the unknown parameters through the classification results. The time-delay is regarded as a hidden variable and identified through the VB algorithm. The effectiveness of the proposed algorithm is illustrated by two simulation examples.

This article is concerned with data-driven realization of fault detection (FD) for nonlinear dynamic systems. In order to identify and parameterize nonlinear Hammerstein models using dynamic input and output data, a stacked neural network-aided canonical variate analysis (SNNCVA) method is proposed, based on which a data-driven residual generator is formed. Then, the threshold used for FD purposes is obtained via quantiles-based learning, where both estimation errors and approximation errors are considered. Compared with the existing work, the main novelties of this study include: 1) SNNCVA provides a new parameterization strategy for nonlinear Hammerstein systems by utilizing input and output data only; 2) the associated residual generator can ensure FD performance where both the system model and its nonlinearity are unknown; and 3) with consideration of modeling-induced errors, the quantiles are invoked and used to provide a reliable FD threshold in situations where only limited samples are available. Studies on a nonlinear hot rolling mill process demonstrate the effectiveness of the proposed method.

Due to the frequent changes in operating conditions, time-varying behaviors, including slow-varying dynamics and switching modes, commonly exist in industrial processes, resulting in different degrees of shifting in the process data distribution. When the data distribution shifts in a relatively wide range, conventional adaptive methods become ineffective since they are unable to distinguish normal shifts from real faults, leading to false alarms. In this study, an incremental variational Bayesian Gaussian mixture model (IncVBGMM) is proposed for developing a fine-scale adaptive monitoring scheme to efficiently accommodate the shifting data distribution caused by different degrees of time-varying behaviors. First, IncVBGMM with decremental optimization is proposed to adapt to the changing data distribution via the automatic complement of local models while reducing redundancy to optimize the mixture model. Then, a fine-scale adaptive monitoring scheme is built with physical interpretations to discern between normal shifts and real faults by joint analysis of the static and dynamic information. In addition, a novel monitoring statistic called the expectation of variational Bayesian inference distance (EVBID) is proposed, which can quantify the distance from samples to the variational monitoring model and indicate the fault effects. Case studies involving a real-world three-phase flow facility reveal that the proposed method can accurately differentiate various types of faults from normal shifts and effectively adapt to the time-varying dynamics.

In this article, a higher order indirect adaptive iterative learning control (HO-iAILC) scheme is developed for nonlinear nonaffine systems. The inner loop adopts a P -type controller whose set-point is updated iteratively by learning from the iterations. To this end, an ideal nonlinear learning control law is designed in the outer loop. It is then transferred to a linear parametric-learning controller with a corresponding parameter estimation law by introducing an iterative dynamic linearization (IDL) method. This IDL method is also used to gain an iterative linear data model of the nonlinear system. A parameter iterative updating algorithm is utilized for estimating the unknown parameters of the obtained linear data model. Finally, the HO-iAILC is presented that utilizes additional error information to improve the control performance and employs two iterative adaptive mechanisms to deal with uncertainties. The convergence of the proposed HO-iAILC scheme is proved by using two basic mathematical tools, namely: 1) contraction mapping and 2) mathematical induction. Simulation studies are conducted for the verification of the theoretical results.

Probabilistic principal component analysis (PPCA) is a feature extraction method that has been widely used in the field of process monitoring. However, PPCA assumes that training and testing data are drawn from the same input feature space with the same distributions. This assumption is not valid for complex processes that exhibit multiple operating modes and generate data with different distributions. In this article, we propose a novel transfer learning approach to monitoring processes with data from multiple distributions. To this end, we introduce a novel extension of PPCA, which is we refer to as the domain adversarial probabilistic principal component analysis (DAPPCA). DAPPCA algorithm automatically learns feature representations that are relevant across different operational modes. The algorithm extracts the most informative shared fault features and improves the accuracy of the fault detection model in a new operating mode using the knowledge transferred from previously known modes. The parameters of DAPPCA are estimated using a variational inference approach, and the monitoring statistics are calculated using the proposed model. We demonstrate the efficacy and real-time applicability of the proposed method with simulated and industrial examples.

Inferential modeling has been of significance for modern manufacturing in estimating the quality-related process variables. As an effective inferential model, probabilistic slow feature analysis (PSFA) has gained attention in regression tasks to interpret dynamic properties with a slowness preference. However, PSFA is often challenged by the nonlinear sequential data due to its linear state-space structure. In this article, a new nonlinear extension of PSFA is proposed under the deep learning framework to enhance the dynamic feature extraction with limited labels, incorporating variational inference and Monte Carlo inference to derive the objective function. The proposed model considers the relevance of inputs with outputs as the input weights to upgrade prediction performance. The proposed model is verified through an industrial hydrocracking process to predict diesel yield with missing labels ranged from 0% to 50%, and the root mean squared error is reduced by at least 8.78% compared to PSFA.

As a significant ingredient regarding health status, data-driven state of health (SOH) estimation has become dominant for lithium-ion batteries. To handle data discrepancy across batteries, current SOH estimation models engage in transfer learning (TL), which reserves a priori knowledge gained through reusing partial structures of the offline trained model. However, multiple degradation patterns of a complete life cycle of a battery make it challenging to pursue TL. The concept of the stage is introduced to describe the collection of continuous cycles that present a similar degradation pattern. A transferable multistage SOH estimation model is proposed to perform TL across batteries in the same stage, consisting of four steps. First, with identified stage information, raw cycling data from the source battery are reconstructed into the phase space with high dimensions, exploring hidden dynamics with limited sensors. Next, domain invariant representation across cycles in each stage is proposed through cycling discrepancy subspace with reconstructed data. Third, considering the unbalanced discharge cycles among different stages, a switching estimation strategy composed of a lightweight model with the long short-term memory network and a powerful model with the proposed temporal capsule network is proposed to boost estimation accuracy. Finally, an updating scheme compensates for estimation errors when the cycling consistency of target batteries drifts. The proposed method outperforms its competitive algorithms in various transfer tasks for a run-to-failure benchmark with three batteries. Especially through transferring the estimation model from batteries B7 to B6, the proposed method improves the estimation accuracy by as high as 42.6% in the third stage in terms of the root mean square error, compared to the other state-of-the-art approaches. In addition, similar conclusions can be drawn from other contributed experiments.

In this article, an approach for identification of an errors-in-variable system whose output is contaminated by heteroscedastic noise is developed. A Markov chain is applied to depict the correlation of the switching of heteroscedastic noise model. The estimation of model parameters adopts a variational Bayesian algorithm. The advantage of the Bayesian approach is the full probability description of the estimates while the classical expectation-maximization algorithm only provides point estimation. A simulated numerical example and an experimental study on a polyester fiber process are provided to demonstrate the effectiveness of the proposed method. Three performance indexes, normalized mean-absolute error, mean-relative error and root-mean-squared error, are used to evaluate the performance of the proposed algorithm. Meanwhile, Monte Carlo cross validations are performed to demonstrate the effectiveness and superiority of the proposed algorithm.

Heterogeneous dynamics, strongly nonlinear and nonaffine structures, and cooperation-antagonism networks are considered together in this work, which have been considered as challenging problems in the output consensus of multiagent systems. A heterogeneous linear data model (LDM) is presented to accommodate the nonlinear nonaffine structure of the heterogeneous agent. It also builds an I/O dynamic relationship of the agents along the iteration-dimensional direction to make it possible to learn control experience from previous iterations to improve the transient consensus performance. Then, an adaptive update algorithm is developed for the estimation of the uncertain parameters of the LDM to compensate for the unknown heterogeneous dynamics and model structures. To address the problem of cooperation and antagonism, an adaptive learning consensus protocol is proposed considering two signed graphs, which are structurally balanced and unbalanced, respectively. The learning gain can be regulated using the proposed adaptive updating law to enhance the adaptability to the uncertainties. With rigorous analysis, the bipartite consensus is proven in the case that the graph is structurally balanced, and the convergence of the agent output to zero is also proven in the case that the graph is unbalanced in its structure. The presented bipartite consensus method is data-based without the use of any explicit model information. The theoretical results are demonstrated through simulations.

This article aims at solving the problems of data-driven control design in the presence of strong uncertainties, hard nonlinearities, and model dependency by using a dynamic linearization (DL) method and an extended state observer (ESO). An unknown nonlinear nonaffine system is considered, whose input–output dynamics is then equivalently reformulated into a modified linear data model (mLDM) in which both a linear parametric increment description that is affine to the control input and the unmodeled uncertainties along with disturbances are included without omission or approximation. The uncertain parameter of the mLDM is estimated in real time by designing an adaptive mechanism, and the unmodeled uncertainties and disturbances are considered as a total extended state which is further estimated by developing a linear ESO. Subsequently, a modified DL-and-ESO-based data-driven adaptive control (mDLESO-DDAC) is proposed by using knowledge from previous control input to improve the control performance. The theoretical results are mathematically proved and then verified by simulations.

In this work, a data-driven virtual reference setting learning (DDVRSL) method is proposed to enhance the proportional-derivative (PD) feedback controller of the repetitive nonlinear system. First, an ideal nonlinear virtual reference setting learning law is presented in the outer loop of the control system to tune the reference setting. Such an ideal nonlinear learning law exists theoretically and is transferred to a linear parametric DDVRSL via iterative dynamic linearization (IDL). Next, an iterative adaptation law is proposed for the estimation of the parameters in the DDVRSL law subject to the nonlinear system which is also transferred into a linear form by using the IDL method. The iterative adaptation algorithm tunes the learning gains of DDVRSL law using input and output measurements, therefore improving the robust ability against uncertainties. The proposed DDVRSL-based PD control method does not require any exact mechanistic model knowledge. The convergence is proved via the contraction mapping principle, mathematical induction, and time-weighted norm. Further, the theoretical results are verified through simulations.

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.

Unsupervised cross-domain fault diagnosis has been actively researched in recent years. It learns transferable features that reduce distribution inconsistency between source and target domains without target supervision. Most of the existing cross-domain fault diagnosis approaches are developed based on the consistency assumption of the source and target fault category sets. This assumption, however, is generally challenged in practice, as different working conditions can have different fault category sets. To solve the fault diagnosis problem under both domain and category inconsistencies, a multisource-refined transfer network is proposed in this article. First, a multisource-domain-refined adversarial adaptation strategy is designed to reduce the refined categorywise distribution inconsistency within each source-target domain pair. It avoids the negative transfer trap caused by conventional global-domainwise-forced alignments. Then, a multiple classifier complementation module is developed by complementing and transferring the source classifiers to the target domain to leverage different diagnostic knowledge existing in various sources. Different classifiers are complemented by the similarity scores produced by the adaptation module, and the complemented smooth predictions are used to guide the refined adaptation. Thus, the refined adversarial adaptation and the classifier complementation can benefit from each other in the training stage, yielding target-faults-discriminative and domain-refined-indistinguishable feature representations. Extensive experiments on two cases demonstrate the superiority of the proposed method when domain and category inconsistencies coexist.

Deep-learning-based soft sensors have been extensively developed for predicting key quality or performance variables in industrial processes. However, most approaches assume that data are uniformly sampled while the multiple variables are often acquired at different rates in practical processes. This article designed a progressive transfer strategy, based on which a variational progressive-transfer network (VPTN) method is proposed for the soft sensor development of industrial multirate processes. In VPTN, the multirate data are first separated into multiple data chunks where the variables within each chunk are acquired at a uniform rate. Then, a variational multichunk data modeling framework is developed to model the multiple chunks in a unified fashion through deep variational structures. The base models, including the unsupervised ones with only partial process variables and the supervised soft sensor model share a similar network structure, such that the subsequent transfer strategy can be readily implemented. Finally, a progressive transfer learning strategy is designed to transfer the model parameters from the fastest sampled data chunk to the slowest one in a progressive manner. Thus, the knowledge from various data chunks can be sequentially explored and transferred to enhance the performance of the terminal soft sensor model. Case studies on both a debutanizer column dataset and a real coal mill dataset in a thermal power plant validate the performance of the proposed method.

Recently, canonical correlation analysis (CCA) has been explored to address the fault detection (FD) problem for industrial systems. However, most of the CCA-based FD methods assume both Gaussianity of measurement signals and linear relationships among variables. These assumptions may be improper in some practical scenarios so that direct applications of these CCA-based FD strategies are arguably not optimal. With the aid of neural networks, this work proposes a new nonlinear counterpart called a single-side CCA (SsCCA) to enhance FD performance. The contributions of this work are four-fold: 1) an objective function for the nonlinear CCA is first reformulated, based on which a generalized solution is presented; 2) for the practical implementation, a particular solution of SsCCA is developed; 3) an SsCCA-based FD algorithm is designed for nonlinear systems, whose optimal FD ability is illustrated via theoretical analysis; and 4) based on the difference in FD results between two test statistics, fault diagnosis can be directly achieved. The studies on a nonlinear three-tank system are carried out to verify the effectiveness of the proposed SsCCA method.

This article addresses an important problem of how to improve the learnability of an intelligent agent in a strongly connected multiagent network. A novel spatial-dimensional linear dynamic relationship (SLDR) is developed to formulate the spatial dynamic relationship of an agent with respect to all the related agents. The obtained SLDR virtually exists in the computer to describe the input-output (I/O) relationship in the spatial domain and an iterative adaptation mechanism is developed to update the SLDR using I/O information to show real-time dynamical behavior of multiagent systems with nonrepetitive initial states. Subsequently, an SLDR-based adaptive iterative learning control (SLDR-AILC) is presented with rigorous analysis for iteration-variant formation control targets. Not only the 3-D dynamic behavior of the multiagent network but also the control protocols of the communicated agents are incorporated in the learning mechanism and thus strong learnability of the proposed SLDR-AILC is achieved to improve control performance. The proposed SLDR-AILC is a data-driven scheme where no explicit model structure is needed. Simulations with strongly connected topologies verify the theoretical results.

This article reconsiders the data quantization problem in iterative learning control (ILC) for nonlinear nonaffine systems from four aspects: 1) use of available additional control knowledge; 2) different tracking tasks; 3) adaptation to uncertainties; and 4) data-driven design and analysis framework. An iterative linear data model (iLDM) is established first to represent the nonlinear nonaffine system for subsequent control algorithm design and analysis under a data-driven framework. A quantitative data-driven adaptive ILC (QDDAILC) is then developed using quantized tracking errors based on the nonlifted iLDM and, thus, additional available input information from previous time instants can be utilized to improve control performance. The parameter estimation derived from an adaptive updating law makes the learning gain of the QDDAILC adjustable, therefore improving the robustness to uncertainties. Due to the coupled dynamics among inputs and tracking errors, a new double-dynamics analysis method is introduced besides the contraction mapping principle to show error convergence. A quantized data-driven adaptive point-to-point ILC (QDDAPTPILC) is further presented using partial quantized measurements at the specified instants for multi-intermediate-point tracking. Simulation examples verify theoretical results and illustrate that the QDDAPTPILC outperforms the QDDAILC for multi-intermediate-point tracking tasks because it removes the unnecessary constraints.

In this article, the optimal consensus problem at specified data points is considered for heterogeneous networked agents with iteration-switching topologies. A point-to-point linear data model (PTP-LDM) is proposed for heterogeneous agents to establish an iterative input-output relationship of the agents at the specified data points between two consecutive iterations. The proposed PTP-LDM is only used to facilitate the subsequent controller design and analysis. In the sequel, an iterative identification algorithm is presented to estimate the unknown parameters in the PTP-LDM. Next, an event-triggered point-to-point iterative learning control (ET-PTPILC) is proposed to achieve an optimal consensus of heterogeneous networked agents with switching topology. A Lyapunov function is designed to attain the event-triggering condition where only the control information at the specified data points is available. The controller is updated in a batch wise only when the event-triggering condition is satisfied, thus saving significant communication resources and reducing the number of the actuator updates. The convergence is proved mathematically. In addition, the results are also extended from linear discrete-time systems to nonlinear nonaffine discrete-time systems. The validity of the presented ET-PTPILC method is demonstrated through simulation studies.

Modern industrial plants generally consist of multiple manufacturing units, and the local correlation within each unit can be used to effectively alleviate the effect of spurious correlation and meticulously reflect the operation status of the process system. Therefore, the local correlation, which is called spatial information here, should also be taken into consideration when developing the monitoring model. In this study, a cascaded monitoring network (MoniNet) method is proposed to develop the monitoring model with concurrent analytics of temporal and spatial information. By implementing convolutional operation to each variable, the temporal information that reveals dynamic correlation of process data and spatial information that reflects local characteristics within individual operation unit can be extracted simultaneously. For each convolutional feature, a submodel is developed and then all the submodels are integrated to generate a final monitoring model. Based on the developed model, the operation status of the newly collected sample can be identified by comparing the calculated statistics with their corresponding control limits. Similar to the convolutional neural network (CNN), the MoniNet can also expand its receptive field and capture deeper information by adding more convolutional layers. Besides, the filter selection and submodel development in MoniNet can be replaced to generalize the proposed network to many existing monitoring strategies. The performance of the proposed method is validated using two real industrial processes. The illustration results show that the proposed method can effectively detect process anomalies by concurrent analytics of temporal and spatial information.

In this article, a new sensor fault estimation algorithm is proposed for industrial processes described by linear discrete-time systems, where the fault dynamics are modeled as a stochastic process. By performing the variational Bayesian inference, the potential sensor fault, as well as the system states, is estimated simultaneously in a probabilistic framework. It is shown that the target fault signal can be satisfactorily estimated through the proposed method, without knowing the statistics of measurement noise and fault coefficient matrix. The efficiency and superiority of the proposed method are demonstrated through numerical simulations and experimental tests performed on a hybrid tank system.

Data-driven soft sensors have been widely used in industrial processes for over two decades. Industrial processes often exhibit nonlinear and time-varying behavior due to complex physical and chemical mechanisms, feedback control, and dynamic noise. Lately, variational autoencoder (VAE) has arisen as one of the most prevalent methods for unsupervised learning of intricate distributions. Despite being successful in deep feature extraction and uncertain data modeling, it still suffers from instability and reconstruction error due to random sampling in the latent subspace representation of original input space. In this article, to deal with those limitations, constrained VAE (CVAE) is proposed by utilizing input sample information. Enthused by parallel interaction mechanism between the ventral and dorsal stream of the human brain in object recognition, parallel interaction spatial-temporal CVAE (PIST-CVAE) is proposed to extract spatial and temporal features from input samples. Lower dimensional nonlinear features extracted from PIST-CVAE are used to build the soft sensor. The effectiveness of CVAE and PIST-CVAE is demonstrated in an industrial case study, a polyester polymerization process. The obtained results demonstrate that CVAE is able to reconstruct inputs with higher accuracy and the proposed PIST-CVAE-based soft sensor yields more accurate estimations for the melt viscosity index of the polymerization process.

Recently, to ensure the reliability and safety of high-speed trains, detection and diagnosis of faults (FDD) in traction systems have become an active issue in the transportation area over the past two decades. Among these FDD methods, data-driven designs, that can be directly implemented without a logical or mathematical description of traction systems, have received special attention because of their overwhelming advantages. Based on the existing data-driven FDD methods for traction systems in high-speed trains, the first objective of this paper is to systematically review and categorize most of the mainstream methods. By analyzing the characteristic of observations from sensors equipped in traction systems, great challenges which may prevent successful FDD implementations on practical high-speed trains are then summarized in detail. Benefiting from theoretical developments of data-driven FDD strategies, instructive perspectives on this topic are further elaborately conceived by the integration of model-based FDD issues, system identification techniques, and new machine learning tools, which provide several promising solutions to FDD strategies for traction systems in high-speed trains.

Data-driven methods have been extensively utilized in establishing predictive models from historical data for process monitoring and prediction of quality variables. However, most data-driven approaches assume that training data and testing data come from steady-state operating regions and follow the same distribution, which may not be the case when it comes to complex industrial processes. To avoid these restrictive assumptions and account for practical implementation, a novel online transfer learning technique is proposed to dynamically learn cross-domain features based on the variational Bayesian inference in this work. Stemming from the probabilistic slow feature analysis, a transfer slow feature analysis (TSFA) technique is presented to transfer dynamic models learned from different source processes to enhance prediction performance in the target process. In particular, two weighting functions associated with transition and emission equations are introduced and updated dynamically to quantify the transferability from source domains to the target domain at each time instant. Instead of point estimation, a variational Bayesian inference scheme is designed to learn the parameters under probability distributions accounting for corresponding uncertainties. The effectiveness of the proposed technique with applications to soft sensor modelling is demonstrated by a simulation example, a public dataset and an industrial case study.

Soft sensors have been extensively developed and applied in the process industry. One of the main challenges of the data-driven soft sensors is the lack of labeled data and the need to absorb the knowledge from a related source operating condition to enhance the soft sensing performance on the target application. This article introduces deep transfer learning to soft sensor modeling and proposes a deep probabilistic transfer regression (DPTR) framework. In DPTR, a deep generative regression model is first developed to learn Gaussian latent feature representations and model the regression relationship under the stochastic gradient variational Bayes framework. Then, a probabilistic latent space transfer strategy is designed to reduce the discrepancy between the source and target latent features such that the knowledge from the source data can be explored and transferred to enhance the target soft sensor performance. Besides, considering the missing values in the process data in the target operating condition, the DPTR is further extended to handle the missing data problem utilizing the strong generation and reconstruction capability of the deep generative model. The effectiveness of the proposed method is validated through an industrial multiphase flow process.

With the aid of neural networks, this article develops two data-driven designs of fault detection (FD) for dynamic systems. The first neural network is constructed for generating residual signals in the so-called finite impulse response (FIR) filter-based form, and the second one is designed for recursively generating residual signals. By theoretical analysis, we show that two proposed neural networks via self-organizing learning can find their optimal architectures, respectively, corresponding to FIR filter and recursive observer for FD purposes. Additional contributions of this study lie in that we establish bridges that link model- and neural-network-based methods for detecting faults in dynamic systems. An experiment on a three-tank system is adopted to illustrate the effectiveness of two proposed neural network-aided FD algorithms.

The problem of consensus learning from network topologies is studied for strongly connected nonlinear nonaffine multiagent systems (MASs). A linear spatial dynamic relationship (LSDR) is built at first to formulate the dynamic I/O relationship between an agent and all the other agents that are communicated through the networked topology. The LSDR consists of a linear parametric uncertain term and a residual nonlinear uncertain term. Utilizing the LSDR, a data-driven adaptive learning consensus protocol (DDALCP) is proposed to learn from both time dynamics of agent itself and spatial dynamics of the whole MAS. The parametric uncertainty and nonlinear uncertainty are estimated through an estimator and an observer respectively to improve robustness. The proposed DDALCP has a strong learning ability to improve the consensus performance because time dynamics and network topology information are both considered. The proposed consensus learning method is data-driven and has no dependence on the system model. The theoretical results are demonstrated by simulations.

Aiming to addressing the nonrepetitive uncertainties of multiagent systems, this work proposes a discrete-time-distributed adaptive iterative learning control (DDAILC) scheme for an output consensus problem, where two fundamental requirements in the traditional distributed iterative learning control (ILC) methods, i.e., the identical initial states and the repetitive desired trajectories, are removed. Furthermore, the algorithm design and analysis are directly aimed at discrete-time nonlinear multiagent systems, rather than continuous-time ones, to meet the needs of practical implementations. The iteration-varying trajectory of the virtual leader is included in the learning control protocol for a compensation. The adaptive parameter-updating law works along the iteration dimension by using a general consensus error that contains the output data of adjacent agents. To ensure the estimation of the control gain to be nonzero, a semisaturator is utilized in the parameter-updating law. The convergence of the output consensus is shown rigorously. Both numerical and practical examples are used to test the theoretical results. Moreover, the DDAILC efficiently improves performance of the building heating, ventilation, and air conditioning (HVAC) system by utilizing both the distributed topology and the repetitive dynamic characteristic.

In this article, an event-triggered distributed state estimation mechanism is proposed for general linear systems that comprise several subsystems. Two distributed moving horizon estimation (MHE) algorithms that can handle constraints on disturbances and noise are proposed. An event scheduler is exploited to govern the evaluation of the estimators and networked information exchange between the plant and the estimators, such that good estimates can be provided while both the usage of processors and networked communication frequency can be reduced. The estimation error provided by the event-triggered estimation mechanism is proven to be convergent and bounded. A numerical example and a chemical process example are used to verify the effectiveness and applicability of the proposed method.

For 2-D causal systems, the variables depend both on time, and on spatial coordinates. This article develops two identification algorithms for two-dimensional causal systems. First, a maximum likelihood estimation algorithm is developed for two-dimensional causal systems when there is no missing data. Second, an expectation-maximization based auxiliary model algorithm, and an expectation-maximization based modified Kalman filtering and smoothing algorithm are derived for 2-D causal systems with missing outputs. It is demonstrated that the modified Kalman filtering, and smoothing algorithm is more effective for systems with missing outputs. The effectiveness of these two algorithms is verified by a simulation example.

An event-triggered nonlinear iterative learning control (ET-NILC) method is presented for repetitive nonaffine and nonlinear systems that have 2-D dynamic behavior along both time and iteration directions. Based on the virtual linear data model, the ET-NILC method is proposed by designing an event triggering condition based on the Lyapunov-like stability analysis conducted along the iteration direction. The learning gain function of ET-NILC is nonlinear and updated by designing an iterative learning parameter estimation law to enhance the robustness. From the perspective of the time dynamics, the proposed ET-NILC is a feedforward control and the event-triggering condition can be verified offline using tracking errors, event triggering errors, and the estimated parameters together. Moreover, the proposed ET-NILC is a data-driven scheme since it merely uses I/O data for the design. The results are also extended to repetitive multiple-input-multiple-output (MIMO) nonaffine nonlinear systems using the property of input-to-state stability as the basic mathematical tool. The convergence of the proposed ET-NILC methods is proved. Several simulations illustrate the effectiveness of the proposed methods.

In this paper, an extended state observer-based data-driven iterative learning control [extended state observer (ESO)-based DDILC] is developed for a permanent magnet linear motor (PMLM). The PMLM is formulated mathematically by using a general nonlinear discrete-time system with consideration of exogenous disturbances. Then, a new iterative dynamic linearization (IDL) is proposed to equivalently reformulate the nonlinear PMLM system with a linear input-output incremental form involving iteration-varying initial states and disturbances. The concept of ESO is introduced into iteration direction to iteratively estimate the random initial states and disturbances as well as their corresponding partial derivatives by considering all of them as a whole extended state. The proposed ESO-based DDILC scheme contains a learning control algorithm and a gradient parameter updating algorithm obtained from two distinct objective functions, respectively. Moreover, the proposed method is data-driven and no explicit model is involved. Theoretical analysis shows the robustness of the proposed method in the presence of iteration-varying initial shifts and disturbances. The simulation on PMLM is conducted to confirm the validity and applicability of the ESO-based DDILC.

A sampled-data model-free adaptive control (SMFAC) strategy is proposed for continuous-time nonlinear nonaffine systems with input rate constraints. By using differential and integral mean value theorems as two basic mathematic tools, a sampled-data local dynamic linearization method is proposed at first to transform the continuous-time nonlinear nonaffine model into a sampled-data nonlinear affine I/O model, including a linear parametric term affined to the control input and a nonlinear uncertainty term. On this basis, we consequently propose an observer-based SMFAC (ObSMFAC) scheme, including a sampled-data parameter estimator to estimate the unknown partial derivatives and a sampled-data observer to estimate the residual nonlinear uncertainty, respectively. Note that the sampling period is incorporated explicitly in the proposed ObSMFAC which enhances the control performance by reducing its negative influence on the system stability. The constraint on the input rate is also considered in the control law as the transition condition of the input updating algorithms. The convergence of the proposed ObSMFAC is proved by using the contraction mapping principle. The simulation study demonstrates the theoretical results.

This paper investigates an event-triggered model-free adaptive control for nonaffined nonlinear systems under a data-driven design framework. By introducing a compact form dynamic linearization (CFDL) scheme, a linear data model of the nonlinear nonaffine system is derived. Then, a parameter estimation algorithm is developed to offline identify the linear data model. On the basis of the identified linear data model, a CFDL-based event-triggered model-free adaptive control (CFDL-ET-MFAC) is developed by designing an event-triggering condition to guarantee the Lyapunov stability. The control action is active only when the event-triggering condition is satisfied. Otherwise, the input signal remains the same as that at the previous triggering instant. In addition, the parameter estimation algorithm is developed for the proposed CFDL-ET-MFAC to identify the CFDL model in real time for improving the robustness to the uncertainties. Meanwhile, both a partial form dynamic linearization-based event-triggered MFAC and a full form dynamic linearization-based event-triggered MFAC are proposed to further improve the control performance by using additional parameters to capture the more complicated behavior of complex nonlinear systems. The proposed ET-MFAC methods only rely on the linear data models directly obtained from data without using any other mechanistic model information. The validity of the three ET-MFAC methods is confirmed through both theoretical analysis and simulation studies.

This paper reconsiders the iterative learning control (ILC) problem for variable trial lengths via compensating output data by using an auxiliary predictive model when the controlled process does not reach the desired trial length. Moreover, this paper aims to propose a general and data-driven ILC method without requiring any explicit mechanistic model information. Specifically, an iterative difference with state transition expression is performed at first over the desired trial length in iteration domain to build an auxiliary predictive model for the iterative input-output dynamics of the linear discrete-time system. Then, an auxiliary predictive compensation-based ILC (APC-ILC) method is presented by defining an expanded output variable in which the predictive output is incorporated to compensate the unavailable output data due to the shorter operation length. The learning gain is iteration-time-varying and is updated using real-time data to adapt to system changes. Furthermore, the proposed learning control law contains additional input information to further improve the control performance. Theoretical analysis and simulations further verify the effectiveness of the proposed APC-ILC.

State estimation is an important component for advance control and fault detection. This paper addresses the problem of smoother design for state estimation based on a finite number of measurements collected in a finite estimation horizon. Three different finite impulse response (FIR) smoothing algorithms are proposed using the maximum likelihood FIR estimation, which is robust against uncertain noise statistics and model parameters, and also independent of the initial states of each finite horizon. Moreover, we provide equivalent but iterative Kalman-like structures of these algorithms for practical implementation. The applications of the proposed smoothing algorithms to an object tracking and image processing examples are demonstrated, and it shows that they have better robustness against model uncertainties than traditional smoothing approaches.

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.

The dynamical relationship of the multiple agents' behavior in a networked system is explored and utilized to enhance the control performance of the multiagent formation in this paper. An adjacent-agent dynamic linearization is first presented for nonlinear and nonaffine multiagent systems (MASs) and a virtual linear difference model is built between two adjacent agents communicating with each other. Considering causality, the agents are assigned as parent and child, respectively. Communication is from parent to child. Taking the advantage of the repetitive characteristics of a large class of MASs, an adjacent-agent dynamic linearization-based iterative learning formation control (ADL-ILFC) is proposed for the child agent using 3-D control knowledge from iterations, time instants, and the parent agent. The ADL-ILFC is a data-driven method and does not depend on a first-principle physical model but the virtual linear difference model. The validity of the proposed approach is demonstrated through rigorous analysis and extensive simulations.

The papers in this special section examine smart process manufacturing that is driven by artificial intelligence (AI). As a fundamental industry, process industry mainly involves elementary raw material industries, such as petroleum, chemical, steel, nonferrous metal, and building. However, there are a series of problems existing in process industry such as inaccurate perception of industrial data, low production efficiency, high materials consumption and limitations in safety and environment protection. In order to solve these restriction problems, we must pursue the goal of efficient, green, and smart processes in manufacturing and marketing. On the other hand, artificial intelligence (AI) has powerful strengths in perception, knowledge representation, learning, reasoning and planning, so that it has been successfully utilized in diverse areas, such as autonomous vehicles and so on. It is promising to have deep and tight integration between artificial intelligence and process industry, to achieve “smart process industry”.

Autoencoder (AE) is a deep neural network that has been widely utilized in process industry owing to its superior abilities of feature extraction and data reconstruction. Recently, assuming the latent variables to be random variables, a probabilistic variant of it called variational autoencoder (VAE) has achieved a major success in different applications. In this article, we develop two novel submodels based on deep VAEs (DVAE), which are further utilized to establish a soft sensor framework. By the use of our first submodel known as supervised DVAE (SDVAE), the distribution information of latent features can be obtained. This is used as a prior of the second submodel known as the modified unsupervised DVAE (MUDVAE). Then, a new soft sensor framework can be constructed by combing the encoder of SDVAE with the decoder of MUDVAE. Since our designed VAE has superior ability in data reconstruction, it also works well under the missing data situation which is common in process industries due to sensor failures. Thus, we extend the proposed soft sensor framework to handle the missing data situation. The effectiveness of our proposed soft sensor frameworks is finally demonstrated via an industrial polymerization dataset.

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.

This paper explores the formation control problem of repetitive nonlinear homogeneous and asynchronous multiagent networks, where the early starting agent is designated as the parent, and the later starting agent with a small delayed time is designated as the child. Moreover, the desired formation reference is allowed to be different from iteration to iteration. A space-dimensional dynamic linearization method is presented to build the linear dynamic relationship between two parent-child agents in a networked system. Then, a 3-D learning-enhanced adaptive iterative learning control (3D-AILC) is proposed by utilizing the additional control information from previous time instants, iterative operations, and parent agents. In other words, the proposed method processes 3-D dynamics to strengthen its learnability, i.e., time dimension, iteration dimension, and space dimension. The desired formation signal is incorporated into the learning control law to compensate its iterative variation to achieve a fast and precise tracking performance. The proposed 3D-AILC is data based and does not use an explicit mechanistic model. The validity of the proposed approach is proven theoretically and tested through simulations as well. Moreover, the proposed method also works well with time-iteration-varying topologies and nonrepetitive uncertainties.

The identification of the multiple model-based Hammerstein parameter varying systems is studied in this paper. The parameters of the considered systems vary as the systems perform on different operating conditions. For each local model, the input nonlinear output-error structure is introduced to describe the dynamical property. Allocating an exponential weighting function to each local model, the nonlinear dynamics of the global system is approximated by combining all local models. The variational Bayesian (VB) approach is adopted to find the solution to the problem of parameter estimation. For the parameter uncertainties, instead of the point estimation, the posterior distribution of each model parameters is obtained under the framework of the VB approach. Two numerical simulation examples and an experiment carried on a multitank system have been employed to demonstrate that the proposed approach can work effectively.

In this paper, a hybrid model is proposed to simultaneously mine causal connections and features responsible for contemporaneous correlations in a multivariate process. The model is developed by combining the vector auto-regressive exogenous model and the factor analysis model. The parameters of the resulting model are regularized using the hierarchical prior distributions for pruning insignificant/irrelevant ones from the model. It is then estimated under the variational Bayesian expectation maximization framework. The estimation is initiated with a complex model which is then systematically reduced to a simpler model that retains only the parameters corresponding to significant causal connections and contemporaneous correlations. Model reduction is carried out through a series of deterministic jumps from complex models to simpler models using a relevance criterion. The approach is illustrated with a number of simulated examples and an industrial case study.

Feature extraction has become an essential prerequisite of developing data-based models, control and monitoring tools from massive industrial data. When the temporal correlation is significant, the latent feature is commonly described by a dynamic model, such as the state-space model. Industrial processes are widely subject to certain boundary constraints. However, most of the existing feature extraction methods have not considered the boundary constraints on the latent features. This study develops a learning approach with consideration of boundary constrained latent features. To retain dynamic behavior with a compact probability description, a novel state transition model is developed by using the Beta distribution for the constrained state. To learn the constrained dynamic feature from regularly observed data, a nonlinear observation function is incorporated, and the variational Bayesian inference is adopted for solving the problem. The effectiveness of the proposed method is demonstrated through numerical simulations along with industrial data sets.

Closed-loop control is commonly used in industrial processes to track setpoints or regulate process disturbances. Process dynamics resulting from closed-loop control are reflected in data mainly in two aspects, namely serial correlation and variation of response speed. Concurrent analysis of both aspects from data has not been fully investigated in the literature. In this work, a combined strategy of canonical variate analysis and slow feature analysis is proposed to monitor process dynamics resulting from closed-loop control by exploring both serial correlations and variation speed of process data. First, the canonical subspaces reflecting serial correlation are modeled by maximizing correlation between the past and future values of the process data. Then, both the serially correlated canonical subspace and its residual subspace are further explored to extract the slow features, which are representations of process variation speed. The proposed method provides a meaningful physical interpretation and in-depth process analysis with considerations of process dynamics under closed-loop control. Besides, it provides a concurrent monitoring of both process faults and operating condition deviations, resulting in fine-scale identification of different operation statuses. To demonstrate the feasibility and effectiveness, the proposed strategy is tested in a simulated typical chemical process under closed-loop control, namely the three-phase flow process.

The outlier is a common issue in the design of state estimators for an industrial process. In this paper, a robust finite impulse response (FIR) filter is proposed for time-invariant state-space models with its noise following the Student's t distributions. A batch solution is first derived by maximizing the likelihood, and then, an equivalent iterative realization is given to provide a clearer insight into the FIR structure. It shows that the essence of the proposed approach is the convergence of the maximum likelihood estimates in horizon scale through iterations, and the state estimate at each sampling instant is independent of the degree-of-freedom (DOF) parameter of the Student's t distribution. Based on this, a modified algorithm that updates the DOF parameter in each iteration is further proposed. Applications to a moving target tracking example and a 3-DOF helicopter system demonstrate that the proposed methods can exhibit good immunity against outliers during the filtering.

In this paper, an improved data-driven point-to-point iterative learning control is proposed for nonlinear repetitive systems where only the system outputs at the multiple intermediate prespecified points are considered. The entire finite time interval is divided into multiple time-subintervals according to the prespecified points. Then a new objective function is designed to generate optimal control inputs over a time-subinterval piecewisely. As a result, the control inputs are updated in a time-subinterval wise using additional input signals from the previous time-subintervals of the same iteration to help improving control performance. By removing the constraints on the unimportant intermediate points, the control system can be designed with additional freedom to achieve a better performance in tracking points of interest. Meanwhile, the proposed approach is data-driven and no process model is required for the control system design and analysis. Both a simulation with nonlinear batch reactor and an experiment with a permanent magnet linear motor servomechanism are provided to demonstrate the effectiveness of the proposed method.

The demand of indoor localization has recently grown quickly in industries. In general, a localization system is required to be reliable, fast, and have high accuracy. In this paper, the ultrawideband (UWB) technique is combined with the inertial navigation sensor (INS) to form a coupled UWB/INS localization framework, which inherits the advantages from both components. A minimum variance unbiased finite impulse response (MVU FIR) method is then applied to obtain accurate position and velocity estimations from noisy measurements. Two experiments and several simulations are conducted. Compared with the traditional Kalman filter (KF) and particle filter, the MVU FIR filter exhibits better immunity to the errors about a priori knowledge of noise variances. It can handle the kidnapped problem, and recover from some extreme failures satisfactorily. Moreover, the MVU FIR filtering algorithm is fast and easily implementable. Its online computational time is even lower than that of the KF, which is favorable in localization applications.

This paper is concerned with robust identification of processes with time-varying time delays. In reality, the delay values do not simply change randomly, but there is a correlation between consecutive delays. In this paper, the correlation of time delay is modeled by the transition probability of a Markov chain. Furthermore, the measured data are often contaminated by outliers, and therefore, -distribution is adopted to model the measurement noise. The variational Bayesian (VB) approach is applied to estimate the model parameters along with time delays. Compared with the classical expectation-maximization algorithm, VB approach has the advantage of capturing the uncertainty of the estimated parameter and time delays by providing their full probabilities. The effectiveness of the proposed method is demonstrated by both a numerical example and a pilot-scale hybrid-tank experiment.

This paper deals with the design of a distributed adaptive high-gain extended Kalman filtering (AHGEKF) approach based on triggering communication for nonlinear systems being composed of several interconnected subsystems. For each subsystem, a local AHGEKF is designed, which receives local measurements, communicates with other filters, and computes local state estimates. In order to reduce the information transmission frequency among the distributed estimators, a communication trigger is designed for each filter. Each filter transmits its current state estimate when its corresponding triggering criterion is satisfied. Sufficient conditions are provided under which the convergence and ultimate boundedness of the estimation error is guaranteed. A simulated chemical process is used to demonstrate the applicability and performance of the proposed approach.

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.

Based on a nonlifted iterative dynamic linearization formulation, a novel data-driven higher order optimal iterative learning control (DDHOILC) is proposed for a class of nonlinear repetitive discrete-time systems. By using the historical data, additional tracking errors and control inputs in previous iterations are used to enhance the online control performance. From the online data, additional control inputs of previous time instants within the current iteration are utilized to improve transient response. The data-driven property of the proposed method implies that no model information except for the I/O data is utilized. The computational complexity is reduced by avoiding matrix inverse operation in the proposed DDHOILC approach due to the nonlifted linear formulation of the original model. The asymptotic convergence is proved rigorously. Furthermore, the convergence property is analyzed and evaluated via three performance indexes. By elaborately selecting the higher order factors, the higher order learning control law outperforms the lower order one in terms of convergence performance. Simulation results verify the effectiveness of the proposed approach.

This paper proposes an augmented model approach for identification of nonlinear errors-in-variables (EIVs) systems. An EIV model accounts for uncertainties in the observations of both inputs and outputs. As the direct identification of nonlinear functions is difficult, we propose to approximate the nonlinear EIV model using multiple ARX models. To estimate the noise-free input signal, we use a collection of particle filters which run in parallel corresponding to each of the multiple ARX models. The parameters of local models are estimated by applying expectation maximization algorithm, under a maximum likelihood framework, using the input-output data of the nonlinear EIV system. Simulated numerical examples and an experiment study on a multitank system are used to illustrate the efficacy of the proposed approach.

In this paper, control performance assessment (CPA) is studied for batch processes controlled by iterative learning control (ILC). A 2-D linear quadratic Gaussian (LQG) benchmark is proposed to assess the performance of ILC in a 2-D framework. Based on the 2-D theory, an ILC-controlled batch process is first converted into a 2-D Roesser model. Subsequently, in order to assess the control performance of the converted 2-D system, the conventional LQG tradeoff curve is upgraded to the LQG performance assessment tradeoff surface. However, the complete knowledge of the system model is required to obtain the LQG tradeoff surface. For system without accurate model knowledge, a novel data-driven CPA method is further proposed. In this case, a novel 2-D closed-loop subspace identification method is proposed to identify the converted 2-D Roesser system. Based on the identified model, the LQG tradeoff surface can be obtained and utilized to assess the control performance. Overall, several simulation examples verified the feasibility and effectiveness of the proposed method.

This paper is concerned with control of processes with uncertain delays for disturbance rejection. The effect of the uncertain delays on the stability is studied. First, the method to compute the maximum uncertain delay that a given controller can tolerate is described. Second, in the case of PI/PID controller, all of the admissible controller parameters stabilizing a system with uncertain but bounded delays are determined. Meanwhile, we propose a simple method to construct the parameter space satisfying a given robustness index for the nominal model. In the admissible regions satisfying various objectives, the global optimum controller is achieved for disturbance rejection in the presence of uncertain delay. As a result, the MIGO ( Ms-constrained Integral Gain Optimization) method is revisited in the case of uncertain delay, and the rule of selecting the value of maximum sensitivity function is proposed in terms of the bound on the uncertain delay. Two simulation examples and an experiment are given to demonstrate the effectiveness and advantage of the proposed method.

Major impediments in developing models based on the input-output data of an industrial process are the outliers in the output and uncertainties in the inputs. To address this problem, this article proposes a robust identification approach for nonlinear errors-in-variables systems. The t- distribution is employed to model the process data to account for the outliers through the adjustable degrees of freedom. Furthermore, we propose to approximate the nonlinear dynamics of the process using multiple local ARX models and combine them using a softmax function based weighting approach. To deal with parameter uncertainties, the identification problem is casted in the Bayesian framework and posterior distributions of the model parameters are estimated using the variational Bayesian approach, instead of point estimations. A numerical example of continuous fermenter as well as an experiment study on the multitank system is employed to demonstrate potential of the proposed method.

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.

Higher-order cumulants analysis (HCA) is an up-to-date method that utilizes higher-order cumulants rather than lower-order statistics (e.g., variances) to achieve the state monitoring purpose. Although HCA has a strong capability for state monitoring, it still exhibits many inadequacies for monitoring dynamic processes. Currently, there are various approaches (e.g., dynamic principle component analysis and dynamic independent component analysis) that are applicable to dynamic features. However, the key step of dynamic state monitoring methods is determination of the time lags or the lag structure. Almost all the reported dynamic methods select a single number of time lags for all variables. This simple selection method may not be appropriate since it is generally not possible that all variables have the same lag structure. In order to address this issue, a new lag selection method for each individual variable is proposed in this study. Hence, two dynamic higher-order cumulants analysis (DHCA) approaches are proposed for state monitoring, among which one is based on the conventional lag selection method and another is based on the new lag selection method proposed in this study. The two kinds of DHCA approaches are tested on the Tennessee Eastman process, and are demonstrated to be superior to all the compared methods.

A variational Bayesian approach to robust identification of switched auto-regressive exogenous models is developed in this paper. By formulating the problem of interest under a full Bayesian identification framework, the number of local-models can be determined automatically, while accounting for the uncertainty of parameter estimates in the overall identification procedure. A set of significance coefficients is used to assign proper importance weights to local-models. By maximizing the marginal likelihood of the identification data, insignificant local-models will be suppressed and the optimal number of local-models can be determined. Considering the fact that the identification data may be contaminated with outliers, t distributions with adjustable tails are utilized to model the contaminating noise so that the proposed identification algorithm is robust. The effectiveness of the proposed Bayesian approach is demonstrated through a simulated example as well as a detailed industrial application.

Sampled-data control which is capable of stabilizing general nonlinear systems is of great current interest. In this paper, the Takagi-Sugeno (TS) fuzzy model is used to represent the nonlinear plant. The paper is primarily concerned with designing digital controllers for the TS fuzzy continuous-time model to stabilize the closed-loop system. In the problem formulation, we only assume that the sampled values at a sampling rate of (1/T/sub s/) are available for control. Within the sampling intervals, the fuzzy controller uses the sampled data at the sampling instants to fire a fuzzy rule and generate a digital control action series. This digital control action is then fed into the nonlinear system through a zero-order-holder. In this paper, two kinds of digital controllers are designed: Multirate and single-rate digital controllers. Within a sampling interval, the single-rate controller is static, while the multirate controller is periodically time-varying, i.e., the control action is switched at a small switching period T. Clearly, for the single-rate case, this switching period T is equal to the sampling period T/sub s/. This paper presents a design procedure for the multirate fuzzy controller with the single-rate control as a special case. The results are formulated as linear matrix inequalities. Numerical example shows the effectiveness of the proposed design procedures.