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Many chemical and industrial processes are complex, and the dynamics of such processes cannot be explained using a partial differential equation (PDE) or a system of PDEs with constant coefficients. Parametric PDEs, that is, PDEs with their coefficients varying across time or space, are utilized for this purpose. The non‐availability of data at all spatial locations and partially available process knowledge add to the complexity of modelling such processes. This paper proposes a framework to discover parametric PDEs using data‐driven and hybrid modelling approaches with the temperature dynamics of steam‐assisted gravity drainage (SAGD) process in an oil reservoir as the system under study. We utilize an ensemble of 200 realizations of the temperature dynamics generated using the variogram for the PDE discovery. Permeability, which is one of the oil reservoir's petrophysical properties, is used to develop the hybrid models. We infer that utilizing partial process knowledge aids in improving the model's accuracy. [ABSTRACT FROM AUTHOR]

The dynamic control of the heat exchanger network is important for developing energy‐efficient and safe industrial processes. In such a system, the control is achieved through the bypass stream around the heat exchanger. This work aims to track the setpoint temperature of the mixed stream by manipulating the bypass fraction of the cold stream around the heat exchanger. The implemented control is in a non‐linear model predictive control (NMPC) framework. The first‐principles model of a shell and a tube heat exchanger is used. The orthogonal collocation technique is used to discretize the first‐principles model into the system of algebraic equations. In this work, uncertainty is also considered in the inlet temperature of the hot stream. The uncertain optimal control problem is dealt with by using a scenario tree‐based approximation along with the affine policy‐based method. The results show that, under different scenarios of uncertainty, the controlled variable efficiently tracks the setpoint. In comparison, considering the same scenarios of uncertainty used, the deterministic optimization approach shows significant deviation in the controlled variable from the setpoint as time passes. [ABSTRACT FROM AUTHOR]

Sensors provide insights into the industrial processes, while misleading sensor outputs may result in inappropriate decisions or even catastrophic accidents. In this article, the Bayesian estimation algorithms are developed to estimate unforeseen signals in sensor outputs without tuning. The optimal Bayesian estimation method is first derived by incorporating a Gaussian distribution specifying potential unmodeled dynamics into the measurement equation. Since its performance depends on tuning parameters, an iterative Bayesian estimation algorithm is developed using the variational inference technique. Specifically, an inverse Wishart distribution is introduced to describe the predicted covariance of abnormal signals. We then estimate it together with the other independent Gaussian distributions to conditionally approximate the joint posterior distribution, by which the effects of tuning parameters can be replaced adaptively. Testing the proposed algorithms through a simulated electromechanical brake model and a real experimental system shows that the proposed algorithm can satisfactorily estimate additive sensor faults online and services as a sensor monitor that simultaneously provides the locations and magnitudes of faulty signals without tuning. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this article, an online estimator for faulty sensor signal is proposed for industrial processes described by nonlinear state-space models. The potential sensor fault is modeled as an unknown additive Gaussian signal, whose distribution is estimated together with the probability density function (pdf) of the state by using the variational Bayesian inference. To solve the problem that transition dynamics of faults are unavailable, a heuristic model with probabilistic features is discussed together with other commonly-used descriptions. For the computation issue caused by nonlinearities, a set of weighted particles is employed to estimate the pdf of state empirically, while the counterpart of the faulty signal is still calculated analytically. The effectiveness of the proposed algorithm is verified by a robot localization example and an experiment conducted on a flexible rotary joint. It shows that the proposed algorithm yields improvements over the existing algorithms, including the Bayesian estimator and the modified multiple-model-based method, and can satisfactorily estimate the magnitude of fault as well as its location in an online manner. [ABSTRACT FROM AUTHOR]

Multivariate statistical process monitoring (MSPM) methods provide sensitive indicators of process conditions by harnessing the value of massive process data. Large-scale industrial processes are subject to wide-range time-varying operating conditions such that some variables inevitably exhibit nonstationary behavior, which poses significant challenges for the design of MSPM schemes. In this brief, a novel nonstationary probabilistic slow feature analysis algorithm is developed to comprehensively describe both nonstationary and stationary variations that underlie process measurements during routine operations. For efficient parameter estimation, the expectation–maximization algorithm is employed. By modeling nonstationarity and stationarity as the random walk and stable autoregressive processes, interpretable monitoring statistics are constructed to detect abnormality in nonstationary dynamics, stationary dynamics, and stationary steady conditions. This forms a holistic and pragmatic monitoring framework for industrial processes, which is beneficial for reducing false alarms and providing meaningful operational information for industrial practitioners. The efficacy of the proposed monitoring framework is validated via two case studies. [ABSTRACT FROM AUTHOR]

Data-driven soft sensors, estimating the pivotal quality variables, have been widely employed in industrial process. This paper proposes a novel soft sensor modeling approach based on a two-stream ${\rm{\lambda }}$ gated recurrent unit ($TS - {\rm{\lambda }}$ GRU) network. First, factors ${{\rm{\lambda }}_1}$ and ${{\rm{\lambda }}_2}$ are implemented to alter the linear constraint existing in the original GRU unit, enriching the information passing through. Then, a two-stream network structure is designed, equipped with some advanced network parameter adjustment techniques, such as batch normalization and dropout rate, to learn diverse features of the various process data. Finally, the learned features from the two streams are fused and a supervised learning regression layer is employed to decrease the error between the output and label. The application in melt viscosity index estimation for a real polymerization industrial process has demonstrated that the proposed $TS - {\rm{\lambda }}$ GRUs algorithm for soft sensor modeling is more accurate and promising than other existing methods. [ABSTRACT FROM AUTHOR]

Salvadori discovered a new variety of rent, called singular rent, when requirements are functions of income distribution. This note makes a simple generalization of the singular rent model by introducing many agricultural processes. Hence the problem of choice of technique arises. With respect to singular rent alone, it is shown that there may exist more than one cost-minimizing technique even though joint production is set aside, and there may be no cost-minimizing technique even though all techniques are feasible. However, in the latter case, at least one system determining intensive rent is feasible and cost-minimizing. [ABSTRACT FROM AUTHOR]

In this paper, we consider an important practical industrial process identification problem where the time delay can change at every sampling instant. We model the time-varying discrete time-delay mechanism by a Markov chain model and estimate the Markov chain parameters along with the time-delay sequence simultaneously. Besides time-varying delay, processes with both time-invariant and time-variant model parameters are also considered. The former is solved by an expectation-maximization (EM) algorithm, while the latter is solved by a recursive version of the EM algorithm. The advantages of the proposed identification methods are demonstrated by numerical simulation examples and an evaluation on pilot-scale experiments. [ABSTRACT FROM AUTHOR]

Root cause diagnosis can locate abnormalities of industrial processes, ensuring production safety and manufacturing efficiency. However, existing root cause diagnosis models only consider pairwise direct causality and ignore the multi-level fault propagation, which may lead to incomplete root cause descriptions and ambiguous root cause candidates. To address the above issue, a novel framework, named multi-level predictive graph extraction (MPGE) and RootRank scoring, is proposed and applied to the root cause diagnosis for industrial processes. In this framework, both direct and indirect Granger causalities are characterized by multi-level predictive relationships to provide a sufficient characterization of root cause variables. First, a predictive graph structure with a sparse constrained adjacency matrix is constructed to describe the information transmission between variables. The information of variables is deeply fused according to the adjacency matrix to consider multi-level fault propagation. Then, a hierarchical adjacency pruning (HAP) mechanism is designed to automatically capture vital predictive relationships through adjacency redistribution. In this way, the multi-level causalities between variables are extracted to fully describe both direct and indirect fault propagation and highlight the root cause. Further, a RootRank scoring algorithm is proposed to analyze the predictive graph and quantify the fault propagation contribution of each variable, thereby giving definite root cause identification results. Three examples are adopted to verify the diagnostic performance of the proposed framework, including a numerical example, the Tennessee Eastman benchmark process, and a real cut-made process of cigarette. Both theoretical analysis and experimental verification show the high interpretability and reliability of the proposed framework. • Distinctions between root cause diagnosis and causal inference are analyzed. • Both direct and indirect causalities are characterized to highlight root causes. • Critical multi-level fault propagation paths can be automatically identified. • RootRank can convert complex causal structures into definitive root cause scores. [ABSTRACT FROM AUTHOR]

Abstract: Automatic oscillation detection for univariate time series is the very first step in detection and compensation of oscillations in process industries. This paper is motivated by our industrial experience of applying the discrete cosine transform (DCT)-based method for oscillation detection. An improved DCT-based method is proposed with three main modifications, namely, a revised hypothesis test based on the confidence interval of coefficient of variation, a fitness index to determine a dominant oscillation component, and a hypothesis test on the regularity of oscillation magnitudes. These modifications are also applicable to other oscillation detection methods in the literature. Moreover, an online oscillation detection method is proposed, with a mechanism by which the size of a supervision time window is adaptive to frequency variation of process variables. Industrial examples are provided to demonstrate the effectiveness of the two proposed methods. [Copyright &y& Elsevier]

Dynamic information plays an important role in developing monitoring models for industrial processes, and thus accurate evaluation of the dynamic behaviors within multiple consecutive process samples is of great significant. In this study, a geometrical analysis method is introduced to establish monitoring model for reflecting the operation status of the process system. By maximizing the volume of the obtained simplex, the source signals with least joint correlation are extracted from the archived process data. Based on the obtained signals, an offline model is developed with three monitoring statistics. Among them, two statistics are adopted to evaluate the static deviations of current sample, and the other one is used to reveal the dynamic behavior of the process system. After that, an online monitoring policy is designed for identifying the operation status of the industrial process based on the decisions of both static and dynamic statistics. Using the volume of simplex constructed by several consecutive samples, the dynamic behaviors of the process system can be better described and thus the detection sensitivity can be further improved. Besides, the normal shifts of operation conditions can also be distinguished from real process anomalies, so that the false alarms of the established model can be effectively reduced. Process data collected from a simulated process and a real industrial application is adopted to test the performance of the proposed method. Experimental results illustrate that the proposed method has better detection sensitivity for the faulty samples and can accurately identify varying operation condition. • Using the simplex volume of several consecutive samples, the dynamic relationship existed in the process data can be meticulously reflected. • By combining the decisions of both static and dynamic statistics, the normal shift of operation conditions can be identified to reduce the false alarm. • Experimental results have sufficiently illustrated that the proposed method can accurately reflect the operation status of the process system. [ABSTRACT FROM AUTHOR]

In industrial processes, the availability of a large amount of process variables provides flexibility for process monitoring; however, too many process variables with possible redundant information can also contribute to high false positives. In order to make good use of the relevant information included in the process variables, a novel two-stage hidden conditional random field (HCRF) algorithm is developed in this paper to perform real-time process operating mode diagnosis. In the first-stage HCRF, the max-margin training strategy is employed to discriminate multiple operating modes, and by recursively eliminating the fault-irrelevant variables, the most relevant variables can be selected during the first-stage training process. On the basis of the first-stage HCRF outputs, the second-stage HCRF is proposed to adapt the dynamic changes of the process with time-varying model structure. Therefore, switchings among process operating modes can be captured to make timely diagnosis. To demonstrate the performance of the proposed algorithm, two case studies are conducted with comparisons to the conventional algorithms. Superior performance is observed through the examples. • A novel two-stage time-varying hidden conditional random field (HCRF) approach is proposed for real-time process monitoring. • This approach can perform automatic relevant variable selection and online adaption to the process operating mode changes. • In first-stage modeling, HCRF structure is employed with specifically designed latent layer to reduce model parameters. • In second-stage modeling, linear-chain CRF model is extended to a time-varying version for self-adaption to process changes. • In online implementation, an integrated two-stage time-varying HCRF model is proposed for better monitoring performance. [ABSTRACT FROM AUTHOR]

Predicting quality-relevant process variables is of paramount importance in optimizing and controlling chemical processes. Probabilistic Slow Feature Analysis (PSFA), a potent data-driven technique, plays a pivotal role in deducing quality indices by abstracting gradual variations in processes distinctly characterized by pronounced inertia. Nevertheless, PSFA's predictive efficacy encounters a substantial bottleneck due to the assumption of a single operating condition, compromising its accuracy, particularly in industries represented by switching operating conditions. To surmount this limitation, this study proposes an innovative approach that enriches PSFA with multi-operating condition process data and limited labels within a Bayesian framework, effectively combining continuous and discrete first-order Markov chains to capture the processes' inertia and dynamic shifts. The proposed method updates latent posterior distributions and model parameters iteratively via the Expectation–Maximization algorithm. The effectiveness of the proposed methodology is verified through a numerical case and industrial hydrocracking process data. • A novel switching probabilistic slow feature analysis model is introduced. • The computational complexity is mitigated by applying the finite Gaussian mixtures. • The proposed method effectively handles random missing labels. [ABSTRACT FROM AUTHOR]

• A Slow feature network (SFNet) method is proposed for dynamics extraction and parallel linear and nonlinear monitoring. • A slow constraint is added to the autoencoder to extract both variability and velocity characteristics concurrently. • The linear and nonlinear characteristics are captured in parallel by the SFNet method. • A monitoring strategy based on SFNet is established to indicate the operating statuses with meaningful interpretation. In a typical industrial process, there may exist both linear and nonlinear relationships among process variables. Besides, the existence of process dynamics poses challenges to process monitoring. Some monitoring methods have been developed for dynamic processes. However, purely linear or nonlinear methods can hardly tackle the hybrid linear and nonlinear relationships among process variables. In this work, a novel unsupervised neural network model, named slow feature network (SFNet), is proposed to monitor dynamic processes. In SFNet, a linear mapping module and a transform gate structure are constructed to realize the parallel extraction of linear and nonlinear characteristics. Moreover, slow constraints on features are designed to capture the velocity characteristics while retaining variability information so that the process dynamic behavior can be directly observed. Various statistics are developed to monitor the process status from both variability and velocity as well as both linear and nonlinear perspectives. Thus, monitoring results corresponding to different statistical information reflect different process behavior and fault characteristics with meaningful interpretations. One numerical example and two real industrial examples are adopted to validate the proposed method. For these experimental examples, the proposed SFNet method achieves an average false alarm rate of 5.17% (min 0.8%, max 8.08%), an average detection accuracy of 87.5% (min 50.2%, max 100%), and an average precision of 98.6% (min 96.3%, max 100%), outperforming counterpart methods in the literature. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach called physics-informed probabilistic slow feature analysis. The probabilistic slow feature analysis method has been employed to extract slowly varying latent patterns from high-dimensional measured data. The extracted slow features have proven effective in industrial applications such as soft sensing and process monitoring. However, industrial processes come with various physical constraints that must be taken into account, such as energy requirements, equipment limitations, and safety considerations. The conventional black-box nature of the slow feature model often leads to physically inconsistent or unacceptable results. To address this issue, we propose integrating physics principles into the probabilistic slow feature model, ensuring that the extracted features adhere to physics laws. Our formulation incorporates two types of physical constraints: linear algebraic equality and inequality constraints. Through an industrial case study, we demonstrate the effectiveness of our methodology, showcasing the advantages of incorporating physics in feature extraction. These advantages include improved interpretability, reduced data dimensionality, and enhanced generalization performance. [ABSTRACT FROM AUTHOR]

Considering industrial process with high-dimensional, intrinsic nonlinearities and possibly abnormal observations, a robust deep learning soft sensor model is developed under the just-in-time learning framework. As an unsupervised deep learning approach, Variational Autoencoder (VAE) has been successfully applied to soft sensing problems owing to its ability to describe the latent representations by probability distributions. In this work, to construct high performance soft sensor model, mutual information (MI) is first introduced for input variable selection. By further incorporating MI as weights on variable of the traditional VAE model, a MI-based output-relevant VAE is developed. For each new sample that arrives, by utilizing Symmetric Kullback-Leibler (SKL) divergence, its relevance with historical samples is determined. Based on the SKL divergence, the input samples that are most relevant to the query sample can be collected. The selected historical input samples and corresponding output samples are employed to build a Gaussian process regression (GPR) local model. Expectation maximation (EM) algorithm is utilized to deal with the nonlinearity and abnormal output observations in GPR local model simultaneously for robustness of the soft sensors. Numerical simulations and a benchmark process are employed to validate the effectiveness of the proposed soft sensor, which demonstrates its superior performance over traditional approaches. • A MI-based output-relevant VAE is presented by incorporating MI as weights on variable of the traditional VAE model. • The selected historical samples through SKL divergence are employed to build a GPR local model. • The abnormal output observations in GPR local model for robustness of the soft sensors is dealt with the EM algorithm. • Numerical simulations and a benchmark process are employed to validate the effectiveness of the proposed soft sensor. [ABSTRACT FROM AUTHOR]

Over the past few decades, both academic and industrial communities have shown increasing interest in the use of data-driven models for process monitoring applications. There exist numerous data-driven techniques in the literature for process monitoring based on the models borrowed from fields such as chemometrics, statistics and different areas of machine learning. This paper reviews a class of probabilistic models, conjugate exponential family graphical models (CEFGMs) for process monitoring applications and also serves as a tutorial for two popular estimation algorithms for the CEFGMs, the expectation maximization (EM) and variational Bayesian expectation maximization (VBEM) algorithms. • Conjugate exponential family graphical models (CEFGMs) are an important family of probabilistic models. • CEFGMs can be used to derive data-driven models for the industrial processes. • This article provides a general introduction to probabilistic modelling, Bayesian networks and CEFGMs. • We have aimed to provide a tutorial review of use of CEFGMs for process monitoring. • This article includes tutorials for the estimation of CEFMGs and control charts development from CEFGMs. [ABSTRACT FROM AUTHOR]

In industrial processes, soft sensor techniques are used to predict the hard-to-measure quality variables under the classic supervised learning paradigm. However, the data challenges, i. e., the widespread noises and inadequate labeled samples, usually make the data-driven sensors weak for application. In this paper, a simple but effective regularization method termed as adversarial smoothing regularization (ASR) is proposed, which measures the local smoothness of prediction around each input sample. By minimizing the divergence between the predictions for noisy and clean inputs, the proposed ASR regulates the learning model to be robust against local perturbation in a semi-supervised manner. Theoretical analysis explains the smoothing capability of ASR, and shows that it is helpful for the improvement of generalization performance. We also design a tri-regression framework to further use the information of unlabeled samples with pseudo labels and present the adversarial smoothing tri-regression (ASTR) model for soft sensor. Based on two industrial processes, comprehensive soft sensor experiments and noise tests are performed to show the robust semi-supervised learning capability of the proposed ASR and ASTR. • A new adversarial regularization is designed to measure the local smoothness around sample for robust modeling. • An adversarial tri-regression model is developed for soft sensor, which performs a semisupervised modeling. • The proposed technique could reduce the prediction variance and balance the prediction bias. • Experimental results on both simulated process and realistic process are provided. [ABSTRACT FROM AUTHOR]

For efficient process control and monitoring, accurate real-time information of quality variables is essential. To predict these quality (or slow-rate) variables at a fast-rate, in the industry, inferential/soft sensors are often used. However, most of the conventional methods for soft sensors do not utilize prior process knowledge even if it is available. The prediction accuracy of these inferential sensors depends mainly on the quality of available data, which can be affected by significant noise and possible sensor failures. To address these issues, in this work, a generic Gaussian Bayesian network based soft-sensor framework is developed, which can account multiple hidden states and multirate/missing data. In the proposed framework, due to the presence of hidden variables and missing data, posterior probability of these variables in E-step of the EM algorithm is evaluated using Bayesian inference. Compared to the existing soft-sensors, the proposed approach will allow users to integrate prior knowledge into the BN structure. Moreover, due to the probabilistic nature of BNs, variances of measurement noises and disturbances between hidden states are simultaneously estimated. The proposed framework is generic and can be used for any multi-layered structure. Its performance is demonstrated for two different structures, two-layer and multilayered structures, on a benchmark flow-network problem and an industrial process. It is observed that the proposed Gaussian Bayesian network based soft sensors are able to give significantly better and more reliable estimates compared to the conventional approaches. • A new framework for soft sensor development through Bayesian networks. • Incorporates prior process knowledge and accounts for uncertainties in the data. • Proposed framework is extended to handle missing/multi-rate data. • Performance is demonstrated on simulation and an industrial process. [ABSTRACT FROM AUTHOR]

Conventional adaptive monitoring strategies detect anomalies in time-varying process by frequently updating models, which requires high computation complexity and may falsely include abnormal samples. Cointegration analysis (CA) based monitoring strategies can be implemented with less model updating since they are developed based on the extracted long-term equilibrium relationship. However, once the cointegration relationship changes, the previous CA model cannot accurately reflect the operation status of future nonstationary process. In this study, an adaptive monitoring scheme based on recursive CA is proposed to address the aforementioned issues for nonstationary processes. First, a recursive strategy is developed for CA to effectively update the monitoring model. After that, three monitoring statistics are developed to reflect the operation status of the industrial process with representation of both static deviation and dynamic fluctuation. Finally, an adaptive monitoring strategy is constructed based on the proposed recursive CA using the aforementioned monitoring statistics. Experimental results of two real industrial processes show that the adaptive monitoring strategy based on recursive CA can effectively adapt to normal process changes without frequent model updating. • In comparison with conventional adaptive methods, the proposed method can detect anomalies in time-varying processes with less model updating. • With representation of both static deviation and dynamic fluctuation, the false alarms can be effectively reduced and the monitoring model can be correctly updated to adapt to new cointegration relationship. • The performance of the proposed method is illustrated using two real industrial processes, and the experimental results show that it can effectively adapt to normal process changes without frequent model updating. [ABSTRACT FROM AUTHOR]

Main challenges for developing data-based models lie in the existence of high-dimensional and possibly missing observations that exist in stored data from industry process. Variational autoencoder (VAE) as one of the deep learning methods has been applied for extracting useful information or features from high-dimensional dataset. Considering that existing VAE is unsupervised, an output-relevant VAE is proposed for extracting output-relevant features in this work. By using correlation between process variables, different weight is correspondingly assigned to each input variable. With symmetric Kullback–Leibler (SKL) divergence, the similarity is evaluated between the stored samples and a query sample. According to the values of the SKL divergence, data relevant for modeling are selected. Subsequently, Gaussian process regression (GPR) is utilized to establish a model between the input and the corresponding output at the query sample. In addition, owing to the common existence of missing data in output data set, the parameters and missing data in the GPR are estimated simultaneously. A practical debutanizer industrial process is utilized to illustrate the effectiveness of the proposed method. • An output-relevant VAE is proposed for extracting output-relevant features by using correlation between process variables. • With symmetric Kullback–Leibler divergence, the similarity is evaluated between the stored samples and a query sample. According to the values of the SKL divergence, data relevant for modeling are selected. • Owing to the common existence of missing data in output data set, the parameters and missing data in the GPR are estimated simultaneously. • A practical debutanizer industrial process is utilized to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a robust multi-mode dynamic data-driven model to identify complex industrial processes and study its application in detecting incipient faults. To model the process dynamics, a robust multi-mode probabilistic slow feature analysis (RMPSFA) is developed. A multiple switching conditional random field (MSCRF) is utilized to handle the multi-modality in the process. In order to make the model robust to the presence of outliers, a Laplace distribution is utilized to describe noise characteristics. To apply it in fault detection, several informative indices are defined. Then, the practical applicability of the proposed method is studied through an experiment on a hybrid tank pilot plant setup. Moreover, the real-life performance of the proposed model is tested on an industrial example. • A more general robust multimode modeling is designed for application in fault detection. • The model is an extension of robust probabilistic slow feature analysis. • The problem is solved using the Expectation–Maximization algorithm. • The proposed model is validated by an experimental and an industrial case studies. [ABSTRACT FROM AUTHOR]

Data-driven soft sensors have been extensively applied in the process industry for quality variable estimation. It is challenging to build reliable soft sensors for complex industrial processes under new operating conditions where available data are limited. To overcome this issue, we leverage samples from source domains, formulate the sample selection and soft sensor problem of the target domain as a Markov decision process, and solve this cross-domain soft sensor problem by proposing a reinforcement learning framework. Specifically, we propose an asynchronous advantage selector-actor-critic method for cross-domain sample selection and soft sensor design. The transferability of source-domain samples to the target domain is determined by the proposed method. The correlation and estimation error metrics are incorporated into the reward function for the performance-driven design. An extension to feature data selection is also proposed. The applicability of the proposed methods is demonstrated via a simulation study and an industrial case study. • A reinforcement learning frame for autonomous cross-domain soft sensing is proposed. • A Markov decision process formulation is developed. • Asynchronous advantage selector-actor-critic methods are proposed. • A novel reward is defined by combining the correlation and prediction error metrics. • A numerical simulation and an industrial case study verify the proposed methods. [ABSTRACT FROM AUTHOR]

Principal component regression (PCR) has been widely used as a multivariate method for data-based soft sensor design. In order to take advantage of probabilistic features, it has been extended to probabilistic PCR (PPCR). Commonly, industrial processes operate in multiple operating modes. Moreover, in most cases, outputs are measured at a slower rate than inputs, and for each sample of input variable, its corresponding output may not always exist. These two issues have been solved by developing the mixture semi-supervised PPCR (MSPPCR) method. In this paper, we extend this developed model to the case of simultaneous missing data in both input and output. Missing data in multidimensional input space constitutes a significantly more challenging problem. Missing input data occurs frequently in industrial plants because of sensor failure and other problems. We develop and solve the MSPPCR model by using the expectation-maximization (EM) algorithm to deal with missing inputs, in addition to missing outputs and multi-mode conditions. Finally, we present two case studies to demonstrate its performance. [ABSTRACT FROM AUTHOR]

• A new formulation of probabilistic slow feature analysis is proposed that can extract slow oscillating patterns from data. • Update expressions of all the parameters are obtained to obtain optimal parameter estimates in an iterative manner. • The article presents an algorithm for the root-cause analysis of the plant-wide oscillations using the proposed formulation. • Two industrial case studies are demonstrated to showcase the efficiency of the algorithm in root-cause analysis. Today, in modern industrial processes, thousands of correlated process variables are measured and stored. Dimension reduction techniques are often employed to construct informative features by discarding redundant information. Slow feature analysis is one such technique that extracts the slowly varying patterns from measured data. Oscillatory behaviour is prevalent in process data due to inadequate control loop tuning and external disturbances such as diurnal temperature variation. Extracting these oscillatory patterns is vital in applications such as control loop monitoring, fault diagnosis. Slow feature analysis may not extract oscillating patterns when the signal to noise ratio is low in process data. This paper proposes the complex probabilistic formulation that extracts slow oscillatory features. We also present the Expectation-Maximization algorithm to obtain the optimal parameter estimates. Finally, three case studies are presented to illustrate the efficacy of the proposed formulation in soft sensing and fault detection applications. [ABSTRACT FROM AUTHOR]

Industrial processes often operate in multiple operating modes. In most cases, the outputs are measured at a slower rate than the inputs due to various reasons, such as the unavailability of real-time sensors. In some cases, measurements of inputs are also not available and/or there are outliers in the measurements due to sensor failures. Furthermore, there can exist different properties of outliers in different variables. Not all of the aforementioned challenges have been considered or considered simultaneously while modeling a probabilistic principal component regression model in the existing literature. In the current paper, a mixture robust semi-supervised probabilistic principal component regression model with missing input data is developed, which can handle all the aforementioned challenges effectively when utilized for online predictions of process variables. The proposed approach is solved using the Expectation-Maximization algorithm, and the performance is demonstrated by a numerical example. An experimental case study of the hybrid tanks system is also utilized to demonstrate the practical applicability of the proposed method. • A mixture robust semi-supervised PPCR model for soft sensor design is proposed. • The proposed model is an extension of the semi-supervised MPPCR with missing input data. • The proposed model can handle outliers of different variances in different variables. • The problem is solved using the Expectation Maximization algorithm. • Robustness and performance are demonstrated by a numerical and an experimental case study. [ABSTRACT FROM AUTHOR]

In modern industrial processes, multimodality is a common characteristic and process monitoring tools should be capable of detecting the occurrence of abnormalities in the presence of process mode changes. Although Gaussian mixture model (GMM) is often used to depict the multimodal characteristics of processes, the conventional monitoring schemes rely on identifying the process mode and applying the unimodal statistical methods to each Gaussian component. However, the process mode of any given observation is typically unknown and it may belong to any process mode. Thus, multimodal process cannot be well modeled by unimodal models. In this paper, a multimodal process monitoring method using variational Bayesian principal component analysis (VBPCA) and Kullback-Leibler (KL) divergence between mixture models is proposed. GMM-VBPCA is used to capture multimodal process information. KL divergence between mixture Gaussians is used as statistics of both latent and noise variables to measure the dissimilarity between the reference mixture model and the monitored mixture model with respect to each process mode. Then, Bayesian inference is employed to fuse the statistics and control limits, and the final monitoring result is obtained by considering both latent and noise statistics. Finally, the proposed method and three other representative methods are evaluated through a simulated Continuous Stirred Tank Reactor (CSTR) and an industrial hydrocracking process. • Propose a KL divergence-based method for multimodal process monitoring. • Multimodality of observations is described by using Gaussian mixture models. • KL divergence between two Gaussian mixture distributions is derived and used as monitoring statistics. • Tested on a simulated CSTR process and a real hydrocracking process. [ABSTRACT FROM AUTHOR]

This paper presents a variational autoencoder-based just-in-time (JIT) learning framework for soft sensor modeling. Just-in-Time learning is often applied for soft sensor modeling in industrial processes. However, traditional just-in-time learning methods measure the similarity based on Euclidean distance, which has not taken into consideration the uncertainty in variables. To improve traditional just-in-time learning methods, in the proposed approach, the variational autoencoder is employed to extract features from input data set containing noise. Each feature variable is expressed by a Gaussian distribution. Then, by using the distribution of each feature variable, Kullback-Leibler divergence is employed to evaluate the similarity between the historical samples and a query sample. Furthermore, historical samples that are most similar to the query samples based on the values of the Kullback-Leibler divergence are selected for modeling. Finally, Gaussian process regression as a nonlinear regression model, is used to model the relationship between the selected input samples and the corresponding output samples, and then make a prediction. A numerical example as well as application on a practical debutanizer industrial process demonstrates the effectiveness of the proposed method. • Variational autoencoder is employed to extract the distribution of each feature variable. • Kullback-Leibler divergence is employed to evaluate the similarity between the historical samples and a query sample. • Gaussian process regression is used to build model based on the selected samples, and then make a prediction. • The effectiveness of the proposed method is demonstrated through a numerical example and an industrial process. [ABSTRACT FROM AUTHOR]

Apart from strong nonlinearity and time-varying behaviors in industrial processes, the hidden time-delay information, which is unfortunately overlooked in most existing modeling methods, should also be taken into account in soft sensor modeling. In view of this, a novel soft sensor, referred to as local time-delay reconstruction based moving window time difference Gaussian process regression (LTR-MWTDGPR), is proposed in this paper. To deal with the time-delay, a fuzzy curve analysis based local time-delay parameter extraction procedure is performed along with a strategy of a moving window, which simultaneously captures the process time-varying feature. Then the local window training dataset and new query sample are reconstructed according to the time-delay parameter set at the next sampling instant. Afterwards, the time difference Gaussian process regression is employed to handle the drifting feature of local reconstructed dataset. The effectiveness and accuracy of the proposed LTR-MWTDGPR approach in predicting quality variables are verified through a real sulfur recovery unit and an industrial debutanizer column. [ABSTRACT FROM AUTHOR]

• Reinforcement Learning for autonomous PID tuning. • Constrained learning for safe operation, improved safety by weight coefficient adjustment. • Simulated and experimental studies together with industrial standard distributed control system implementation. • Comparison of commonly used techniques. • Quantitative analysis by means of sensitivity analysis. Many industrial processes utilize proportional-integral-derivative (PID) controllers due to their practicality and often satisfactory performance. The proper controller parameters depend highly on the operational conditions and process uncertainties. This study combines the recent developments in computer sciences and control theory to address the tuning problem. It formulates the PID tuning problem as a reinforcement learning task with constraints. The proposed scheme identifies an initial approximate step-response model and lets the agent learn dynamics off-line from the model with minimal effort. After achieving a satisfactory training performance on the model, the agent is fine-tuned on-line on the actual process to adapt to the real dynamics, thereby minimizing the training time on the real process and avoiding unnecessary wear, which can be beneficial for industrial applications. This sample efficient method is tested and demonstrated through a pilot-scale multi-modal tank system. The performance of the method is verified through setpoint tracking and disturbance regulatory experiments. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the issues associated with the development of data-driven models as well as model update strategy for soft sensor applications. A practical yet effective solution is proposed. Key process variables that are difficult to measure are commonly encountered in practice due to limitations of measurement techniques. Even with appropriate instruments, some measurements are only available through off-line laboratory analysis with typical sampling intervals of several hours. Soft sensors are inferential models that can provide continuous on-line prediction of hidden variables; such models are capable of combining real-time measurements with off-line lab data. Due to the prevalence of plant-model mismatch, it is important to update the model using the latest reference data. In this paper, parameters of data-driven models are estimated using particle filters under the framework of expectation–maximization (EM) algorithms. A Bayesian methodology for model calibration strategy is formulated. The proposed framework for soft sensor development is applied to an industrial process to provide on-line prediction of a quality variable. [Copyright &y& Elsevier]