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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.

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., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

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.

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.

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 order to promote the acceptance of cell-based toxicity testings, the accuracy of cytotoxicity test must be determined when compared to in vivo results. Traditional methods of cytotoxicity analysis, such as LC[Formula: see text] (concentration where 50% of the cells are killed) can be problematic since they have been found to vary with time. Technological advances in cytotoxicity testing make it easy to record the dynamic data on changes in cell proliferation, morphology, and damage. To effectively and reasonably analyze the dynamic data, we present a new in vitro toxicity assessed method using the discrete-time Fourier transform (DTFT) which maps the measured cell index from the time domain to the frequency domain. The direct current (DC) component of the DTFT is extracted as a feature which reflects the intensity of cytotoxicity. The smaller the value, the higher the cytotoxicity. Then, a novel toxicity index, as expressed in terms of DC[Formula: see text], is calculated. Results generated with selected test chemicals are compared favorably with data obtained from The Interagency Coordinating Committee on the Validation of Alternative Method (ICCVAM) report concerning the prediction of acute systemic toxicity in rodents. The method can be applied with the standard and high throughput to estimate acute rodent oral toxicity which reduces the number of animals required in subsequent pharmacological/toxicological studies.

Objectives: To obtain perfusion as well as diffusion information in normal breast tissues and breast lesions from intravoxel incoherent motion (IVIM) imaging with biexponential analysis of multiple b-value diffusion-weighted imaging (DWI) and compare these parameters to apparent diffusion coefficient (ADC) obtained with monoexponential analysis in their ability to discriminate benign lesions and malignant tumors., Materials and Methods: In this prospective study, informed consent was acquired from all patients. Eighty-four patients with 40 malignant tumors, 41 benign lesions, 30 simple cysts and 39 normal breast tissues were imaged at 1.5 T utilizing contrast-enhanced magnetic resonance imaging (MRI) and DWI using 12 b values (range: 0-1000 s/mm(2)). Tissue diffusivity (D), perfusion fraction (f) and pseudo-diffusion coefficient (D*) were calculated using segmented biexponential analysis. ADC (b = 0 and 1000 s/mm(2)) was calculated with monoexponential fitting of the DWI data. D, f, D* and ADC values were obtained for normal breast tissues, simple cysts, benign lesions and malignant tumors. Receiver operating characteristic analysis was performed for all DWI parameters., Results: There was good interobserver agreement on the measurements between the 2 observers. D values were significantly different among malignant tumors, benign lesions, simple cysts and normal breast tissues (P = 0.000) and it was the same result for f, D* and ADC values. Further comparisons of these 4 parameters between every single pair were as the following. D and ADC values of malignant tumors were significantly smaller than those of benign lesions, simple cysts and normal tissues (P = 0.000, respectively). The f value of malignant tumors was significantly higher than that of benign lesions, simple cysts and normal breast tissues (P = 0.001, P = 0.000, and P = 0.000). D and ADC values demonstrated higher sensitivity and specificity in differentiating benign lesions and malignant tumors, with area under the curve (AUC) of 0.952 and 0.945, respectively, while f and D* with the lower AUC of 0.723 and 0.630, respectively. Combining f and D values had a sensitivity up to 98.75%., Conclusion: DWI response curves in malignant tumors, benign lesions and normal fibroglandular tissues are found to be biexponential fit in comparison with the monoexponential fit for simple cysts. IVIM provides separate quantitative measurement of D for cellularity and f and D* for vascularity and is helpful for differentiation between benign and malignant breast lesions., (Copyright © 2013. Published by Elsevier Ireland Ltd.)

The paper presents a constrained H2 approximation method for multiple input-output delay systems by using a genetic algorithm. The H2 error between the original and the approximate models is minimized subject to constraints on the H(infinity) error between them and the matching of their steady-state under step inputs. In particular, the H2 error is used as the objective (fitness) function for minimization with the best parameters of the approximate model obtained by repeating the genetic operations on the population incorporated a parameter search space expansion scheme. The effectiveness of the proposed method is demonstrated by numerical examples. It is shown that the approximate models obtained by this approach have better approximation performance in both the H2 and H(infinity) norms, as well as the steady-state response, than those obtained by a previous gradient-based minimization approach.

The primary objective of fault detection is to detect abrupt undesirable changes in a process at an early stage. This early detection has a potential of preventing loss of production and equipment damage due to these undesirable changes, thus reducing process downtime. This paper details the implementation of some parametric fault detection techniques for sensor decalibration monitoring. A parametric fault detection approach that is handled in depth in this paper is the local approach. This approach developed by Benveniste, Basseville, and Moustakides [Benveniste, A., Basseville, M., and Moustakides, G., The asymptotic local approach to change detection and model validation. IEEE Trans. Autom. Control AC-32 (7), 583-592 (1987)] offers a computationally inexpensive way to attain the objective of monitoring changes in model parameters. However, the algorithm in its original formulation is not applicable to certain processes such as sensors. Therefore, the local approach is coupled with other estimation algorithms such as the input independent Kalman filter to derive a robust sensor decalibration monitoring algorithm. The proposed fault detection algorithm is applied to a pilot scale process for evaluation of its performance.

Physics informed neural network (PINN) has become a promising method for solving partial differential equations (PDEs). The loss function of PINN is a weighted sum of multiple items. This makes it easy to fall into local optima, especially the gradient pathologies when solving high frequency problems. The value of penalty coefficients has a crucial impact on the prediction results. Therefore, a new PINN with adaptive penalty coefficients iteratively optimized by biased multiobjective coevolutionary algorithm (BC-PINN) is presented. In BC-PINN, a two-stage optimization mechanism is used to search for parameters of neural network and penalty coefficients respectively. This method involves constructing the fitness function of penalty coefficients based on the biased dominance ranking by data item and regularization item. Compared with the previous works of others, the accuracy of fitting the initial conditions and boundary conditions is considered to be given priority, which is more conducive to PINN converging to the particular solution of PDE. In addition, the set of penalty coefficients is divided into multiple populations to improve the optimization efficiency through coevolutionary algorithm. The empirical results show that: (1) Our method can improve the gradient pathologies and effectively capture the high-frequency features. (2) Compared to the original PINN, it reduces the MSE by 1–6 orders of magnitude in our benchmark functions. [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]

In certain non-stationary processes, the non-stationary dynamics is caused by degradation or wearing of certain process components. Such dynamics can be characterized by a latent monotonic signal. Meanwhile, there also exist stationary dynamics characterizing the regular process variables. It hence becomes pertinent to distinguish these two sets of latent variables for the monitoring of the process from both the stationary and non-stationary aspects. In this regard, we propose a methodology to achieve such a goal by modeling the latent monotonic trend as a closed skew-normal random walk model. The other stationary relations are characterized by a state-space model with Gaussian noises. The problem is solved as a simultaneous state and parameter estimation problem using the expectation–maximization algorithm. As a result of the closed skew-normal random walk model for the monotonic trend, the state estimation problem becomes a skew-normal filtering and smoothing problem. The effectiveness of the proposed method is verified through a numerical simulation, and the algorithm is applied to solve a Hot Lime Softener fouling predictive monitoring problem. • Separation of the stationary and non-stationary sources of a deteriorating process. • The non-stationary source is modeled as a monotonic random walk model. • The monotonic latent variable is modeled as a closed skew-normal random walk model. • The proposed model leads to a simultaneous state and parameter estimation problem. • The problem is solved using the expectation-maximization (EM) algorithm. • Analytical derivation of the smoothing equations for a CSN state-space model. • Application of the proposed method on an industrial hot lime softener process. [ABSTRACT FROM AUTHOR]

Measurements in the process industry can arrive with fast or slow sampling rates. Fast measurements, such as flowrate and temperature, are sampled frequently and are obtained instantly after sampling. The slow measurements, which are usually related to chemical quality variables such as product composition, are sampled infrequently and have some delay due to laboratory analysis. Moreover, sample collection for laboratory analysis may extend over a significant time interval, and the slow measurements are actually functions of all the states during the sampling period. Our objective is to develop a multirate state estimation method for this situation. We propose two methods to solve the problem: the exact Bayesian approach and the augmented state approach. In the exact Bayesian approach, the algorithm is developed by implementing the Bayes rule. In the augmented state approach, the system is reformulated by augmenting the current state with past information required for fusing the slow measurements and then applying general state estimation procedures. The performance of the proposed methods for state estimation is demonstrated through simulation and experimental studies and by comparison with methods that only use the fast measurements. [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]

We present an approach for parameter estimation with multirate measurements, with the slow measurements having variable time delays due to laboratory analysis, and also being functions of all the states during the sample collection. We formulate a particle filter‐based approach under the framework of the expectation maximization algorithm to develop the estimates. The effectiveness and applicability of the proposed method are demonstrated though a simulation example, a hybrid tank experiment and an industrial case study; in each case, the slow and fast measurements are for the same variable. We show that this approach results in improved parameter estimation when the information from the delayed measurements is fused with the fast measurement information. [ABSTRACT FROM AUTHOR]

The development of advanced closed‐loop irrigation systems requires accurate soil moisture information. In this work, we address the problem of soil moisture estimation for the agro‐hydrological systems in a robust and reliable manner. A nonlinear state‐space model is established based on the discretization of the Richards equation to describe the dynamics of the agro‐hydrological systems. We consider that model parameters are unknown and need to be estimated together with the states simultaneously. We propose a consensus‐based estimation mechanism, which comprises two main parts: (a) a distributed extended Kalman filtering algorithm used to estimate several model parameters; and (b) a distributed moving horizon estimation algorithm used to estimate the state variables and one remaining model parameter. Extensive simulations are conducted, and comparisons with existing methods are made to demonstrate the effectiveness and superiority of the proposed approach. In particular, the proposed approach can provide accurate soil moisture estimate even when poor initial guesses of the parameters and the states are used, which can be challenging to be handled using existing algorithms. [ABSTRACT FROM AUTHOR]

The problem of attack detection for Stuxnet in the industrial control system is discussed in this article. Different operating modes (normal and hazard modes) may occur in the nominal process. In this article, we consider that the transition between different modes follows a Markov chain model with a certain transition probability. However, when the Stuxnet attack is launched, the attack signals with random multitude and frequency will be injected to trigger more hazard modes, and finally, hasten fatigue of control devices. Under this unpredictable attack, the transition between operating modes will not follow the regular transition probabilities. Therefore, a hidden Markov model with time-varying transition probabilities is utilized to describe the Stuxnet attack. The transition probabilities are estimated based on the measurements. By recognizing operating modes and predicting the number of the occurrence of hazard modes, the Stuxnet attack can be detected earlier if the predicted value exceeds the threshold. In the operating mode recognition, the expectation maximization algorithm is used to estimate the parameters considering random packet dropouts caused by the unreliable network. A simulation is conducted to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: The problem of robust attack detection and prediction for networked control systems in the presence of outliers is discussed in this article. The conventional hidden Markov model (HMM) is trained to learn the system behavior (ie, transitions between different operating modes) in the nominal process. The HMM with time‐varying transition probabilities is used to track the attack behavior in which the adversary triggers more hazard modes to hasten fatigue of control devices by injecting attack signals with random magnitude and frequency. For different operating modes, the observations are assumed to follow different multivariate Student's t distributions instead of Gaussian distributions and thus address the robust estimation problem. The expectation maximization algorithm is used to estimate parameters. Finally, simulations are conducted to verify the effectiveness of the proposed method. [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]

Purpose: Computed tomography (CT) perfusion (CTP) source images contain both brain perfusion and cerebrovascular information, and may allow a dynamic assessment of collaterals. The purpose of the study was to compare the image quality and the collaterals identified on multiphase CT angiography (CTA) derived from CTP datasets (hereafter called CTPA) reconstructed with iterative model reconstruction (IMR) algorithm in patients with middle cerebral artery (MCA) steno-occlusion with those of routine CTA. Methods: Consecutive patients with a unilateral MCA steno-occlusion underwent non-contrast CT (NCCT), CTP, and CTA. CTPA images were reconstructed from CTP datasets. The vascular attenuation, image noise, signal-to-noise ratio (SNR), and contrast-to-noise ratio (CNR) of routine CTA and CTPA were measured and analyzed by Student's t test. Subjective image quality and collaterals were scored and compared using the Wilcoxon signed-rank test. Results: Fifty-eight patients (mean age 61.7 years, 78% males, median National Institutes of Health Stroke Scale score = 12) were included. The effective radiation dose of CTP was 1.28 mSv. The vascular attenuation, SNR, CNR, and the image quality of CTPA were considerably higher than that of CTA (all, p < 0.001). Collaterals were rated higher on CTPA compared with CTA (1.79 ± 0.64 vs. 1.22 ± 0.84, p < 0.001). Fifty-three percent of patients with poor collaterals assessed on single-phase CTA had good collaterals on CTPA. Conclusion: CTPA derived from CTP datasets reconstructed with IMR algorithm offers image quality comparable to routine CTA and provides time-resolved evaluation of collaterals in patients with MCA ischemic disease. [ABSTRACT FROM AUTHOR]

Abstract Considering that temperature makes a difference to near-infrared spectrum, a probabilistic principle component regression (PPCR) based temperature compensation modeling strategy is investigated under the framework of maximum likelihood estimation. First, a PPCR model is established to extract the dynamic information of the spectra at designated experimental temperature. Then, by decomposing the temperature-induced spectral variation into the shift in horizontal direction and the drift in vertical direction, the quantitative expression between spectral variation and temperature change is derived. Based on the decomposition, the estimation of new latent variables that vary with temperature is derived according to the spectral data set collected at certain temperatures. Finally, for performance evaluation, applications of the theoretical results to bisphenol-A and gasoline-ethanol mixture illustrate the effectiveness and advantages of the developed techniques. Highlights • Considering the fact that the collected NIR spectra contain random noises. • Traditional NIR model is established under the probabilistic framework. • The first attempt to establish a probabilistic NIR model with EM algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a novel high-order optimal terminal iterative learning control (high-order OTILC) is proposed via a data-driven approach for nonlinear discrete-time systems with unknown orders in the input and output. The objective is to track the desired values at the endpoint of the operation cycle. The terminal tracking errors over more than one previous iterations are used to enhance the high-order OTILC's performance with faster convergence. From rigor of the analysis, the monotonic convergence of the terminal tracking error is proved along the iteration direction. More importantly, the condition for a high-order OTILC to outperform the low-order ones is first established by this work. The learning gain is not fixed but iteratively updated by using the input and output (I/O) data, which enhances the flexibility of the proposed controller for modifications and expansions. The proposed method is data-driven in which no explicit models are used except for the input and output data. The applications to a highly nonlinear continuous stirred tank reactor and a highly nonlinear fed-batch fermentater demonstrate the effectiveness of the proposed high-order OTILC design. [ABSTRACT FROM AUTHOR]

State estimation for a system with irregular rate and delayed measurements is studied using fusion Kalman filter. Lab data in process plants is usually more accurate compared to other measurements. However, it is often slow rate and subject to variable delay and irregularity in sampling time. Fast rate state estimation can be conducted using fast rate measurement, while the slow rate lab data can be used to improve the accuracy of estimation whenever it is available. For this purpose, two Kalman filters are used to estimate the states based on each type of measurement. The estimates are fused in the next step by considering the correlation between them. An iterative algorithm to obtain the cross-covariance matrix between the estimation errors of the two Kalman filters is presented and employed in the fusion process. The improvement on the accuracy of estimation and comparison with other optimal fusion state estimation techniques are discussed through a simulation example, a pilot-scale experiment and an industrial case study. [ABSTRACT FROM AUTHOR]

Chance constraint is widely used for modeling solution reliability in optimization problems with uncertainty. Due to the difficulties in checking the feasibility of the probabilistic constraint and the non-convexity of the feasible region, chance constrained problems are generally solved through approximations. Joint chance constrained problem enforces that several constraints are satisfied simultaneously and it is more complicated than individual chance constrained problem. This work investigates the tractable robust optimization approximation framework for solving the joint chance constrained problem. Various robust counterpart optimization formulations are derived based on different types of uncertainty set. To improve the quality of robust optimization approximation, a two-layer algorithm is proposed. The inner layer optimizes over the size of the uncertainty set, and the outer layer optimizes over the parameter t which is used for the indicator function upper bounding. Numerical studies demonstrate that the proposed method can lead to solutions close to the true solution of a joint chance constrained problem. [ABSTRACT FROM AUTHOR]

Gaussian process (GP) regression is a fully probabilistic method for performing non-linear regression. In a Bayesian framework, regression models can be made robust by using heavy-tailed distributions instead of using normal distribution for modeling noise. This work focuses on estimation of parameters for robust GP regression. In literature, these are learned by maximizing the approximate marginal likelihood of data. However, gradient-based optimization algorithms which are used for this purpose can be unstable or may require tuning. In this work, an EM algorithm based approach is derived and implemented to infer the parameters. The pros and cons of the two approaches are analyzed. The advantage of EM algorithm lies in its ease of implementation and theoretical guarantees of numerical stability and convergence while its prediction performance is still comparable to gradient-based approaches. In some cases EM algorithm may be slow to converge. To circumvent this issue a faster EM based approach known as Expectation Conjugate Gradient (ECG) is implemented on robust GP regression. Finally, the proposed EM approach to robust GP regression is validated using an industrial data set. [ABSTRACT FROM AUTHOR]

Multivariate statistical process monitoring involves dimension reduction and latent feature extraction in large-scale processes and typically incorporates all measured variables. However, involving variables without beneficial information may degrade monitoring performance. This study analyzes the effect of variable selection on principal component analysis (PCA) monitoring performance. Then, it proposes a fault-relevant variable selection and Bayesian inference-based distributed method for efficient fault detection and isolation. First, the optimal subset of variables is identified for each fault using an optimization algorithm. Second, a sub-PCA model is established in each subset. Finally, the monitoring results of all of the subsets are combined through Bayesian inference. The proposed method reduces redundancy and complexity, explores numerous local behaviors, and provides accurate description of faults, thus improving monitoring performance significantly. Case studies on a numerical example, the Tennessee Eastman benchmark process, and an industrial-scale plant demonstrate the efficiency. [ABSTRACT FROM AUTHOR]

This paper considers parameter estimation for linear parameter varying (LPV) systems with randomly missing output data. The multi-model LPV model is adopted and the identification problem is formulated under the scheme of the generalized expectation–maximization (GEM) algorithm. In order to deal with the missing output data, the local models are firstly taken to have the finite impulse response (FIR) model structure. To alleviate potential overparameterization problem, a prior on FIR model coefficients is imposed and the GEM algorithm is modified to derive the maximum a posterior (MAP) estimates of the multi-mode LPV FIR model parameters. Since the FIR model is not suitable for general control applications, a multi-mode LPV output error (OE) model is then identified by applying the GEM algorithm to the same identification data set with parameters initialized based on the estimated FIR models. One simulation example and two experiments are presented to demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

A new approach for modeling and monitoring of the multivariate processes in presence of faulty and missing observations is introduced. It is assumed that operating modes of the process can transit to each other following a Markov chain model. Transition probabilities of the Markov chain are time varying as a function of the scheduling variable. Therefore, the transition probabilities will be able to vary adaptively according to different operating modes. In order to handle the problem of missing observations and unknown operating regimes, the expectation maximization algorithm is used to estimate the parameters. The proposed method is tested on two simulations and one industrial case studies. The industrial case study is the abnormal operating condition diagnosis in the primary separation vessel of oil-sand processes. In comparison to the conventional methods, the proposed method shows superior performance in detection of different operating conditions of the process. © 2014 American Institute of Chemical Engineers AIChE J, 61: 477-493, 2015 [ABSTRACT FROM AUTHOR]

Compared with daily recorded process variables that can be easily obtained through the distributed control system, acquirements of key quality variables are much more difficult. As a result, for soft sensor development, we may only have a small number of output data samples and have much more input data samples. In this case, it is important to incorporate more input data samples to improve the modeling performance of the soft sensor. On the basis of the semisupervised modeling method, this paper aims to extend the linear semisupervised soft sensor to the nonlinear one, with incorporation of the kernel learning algorithm. Under the probabilistic modeling framework, a mixture form of the nonlinear semisupervised soft sensor is developed in the present work. To evaluate the performance of the developed nonlinear semisupervised soft sensor, an industrial case study is provided. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper discusses the development of model predictive control algorithm which accounts for the input and state constraints applied to the parabolic partial differential equations (PDEs) system describing the axial dispersion chemical reactor. Spatially varying terms arising from the nonlinear PDEs model are accounted for in model development. Finite-dimensional modal representation capturing the dominant dynamics of the PDEs system is derived for controller design through Galerkin's method and modal decomposition technique. Tustin's discretization and Cayley transform are used to obtain infinite-dimensional discrete-time dynamic modal representations which are used in subsequent constrained controller design. The proposed discrete-time constrained model predictive control synthesis is constructed in a way that the objective function is only based on the low-order modal representation of the PDEs system, while higher-order modes are utilized only in the constraints of the PDEs state. Finally, the MPC formulations are successfully applied, via simulation results, to the PDEs system with input and state constraints. [ABSTRACT FROM AUTHOR]

Abstract: On-line estimation plays an important role in process control and monitoring. Obtaining a theoretical solution to the simultaneous state-parameter estimation problem for non-linear stochastic systems involves solving complex multi-dimensional integrals that are not amenable to analytical solution. While basic sequential Monte-Carlo (SMC) or particle filtering (PF) algorithms for simultaneous estimation exist, it is well recognized that there is a need for making these on-line algorithms non-degenerate, fast and applicable to processes with missing measurements. To overcome the deficiencies in traditional algorithms, this work proposes a Bayesian approach to on-line state and parameter estimation. Its extension to handle missing data in real-time is also provided. The simultaneous estimation is performed by filtering an extended vector of states and parameters using an adaptive sequential-importance-resampling (SIR) filter with a kernel density estimation method. The approach uses an on-line optimization algorithm based on Kullback–Leibler (KL) divergence to allow adaptation of the SIR filter for combined state-parameter estimation. An optimal tuning rule to control the width of the kernel and the variance of the artificial noise added to the parameters is also proposed. The approach is illustrated through numerical examples. [Copyright &y& Elsevier]

Abstract: Control-loop performance assessment methods have been evolving over the past two decades, with many different monitor algorithms being used to single out specific problems and determine the operating mode. However, a change in operating mode may affect multiple monitors, resulting in the possibility of conflicting assessments. Data-driven Bayesian methods were previously proposed which use multiple monitors to yield probabilistic assessments; however, training data for Bayesian methods requires complete knowledge of underlying operational modes. This paper proposes an approach based on proportionality parameters θ to address the problem of incomplete mode information in the training data; values in θ can be used to fill in missing information, and by varying θ one can determine the boundaries on a probabilistic diagnosis. Two diagnostic approaches are considered: the first type is direct probability approach, which can only be applied when historical data on the operation mode is sufficient and representative. The second type is the likelihood approach which can be applied to more general cases, including when the historical data is too limited to adequately represent mode frequency. In order to represent mode frequency, the likelihood approach takes into account prior probabilities of operating modes. The proposed methods are evaluated in two simulated chemical processes. [Copyright &y& Elsevier]

Abstract: This paper is concerned with model validation and detection of parameter changes under closed-loop conditions. Two closed-loop model validation algorithms are developed based on the two-model divergence method. The algorithms are only sensitive to the plant changes that affect closed-loop performance. The first algorithm is sensitive to changes in both plant and disturbance dynamics. A novel feature of the second algorithm is that it is only sensitive to the changes in plant dynamics, regardless of changes in disturbance dynamics. Under certain conditions, the proposed algorithms can also be applied for fault detection, e.g. detection of actuator or sensor fault, etc. The developed algorithms are evaluated by simulations as well as experimental applications on a pilot scale process. [Copyright &y& Elsevier]

Abstract: To investigate the features of the gastric interdigestive pressure activity under normal physiological conditions, we have developed the wireless radiotelemetry capsule based on a telemetry technique. Twelve healthy volunteers participated in this study. Pressure activity data which are an important index of gastric motility can be obtained from the wireless radiotelemetry capsule. But the capsule only records single-dimensional pressure time series which may contain a few interdependent components simultaneously. Automated embedding phase space reconstruction algorithm is employed to reconstruct multi-dimensional phase space. Then the dominant and separated component of the gastric contractions is identified using FastICA algorithm. Finally the use of Hilbert Huang transform method for analyzing the characters of gastric motility is investigated. The results show that the proposed method is an effective approach for the analysis of the gastric pressure series. [Copyright &y& Elsevier]

Abstract: This article is a continuation of an earlier work by Huang [2000. Multivariate model validation in the presence of timevariant disturbance dynamics. Chemical Engineering Science 55, 4583–4595] for validation of discrete time models. We present validation method for continuous-time transfer models with time delay. The proposed procedure is based on the local approach for change detection of model parameters. Both single input single output (SISO) and multiple input multiple output (MIMO) models are considered. The special feature of the proposed algorithm is its ability to detect and isolate changes in the time delay as well as in other parameters. The performance of the proposed method is demonstrated using Monte-Carlo simulations and by application to experimental data from a laboratory scale process. [Copyright &y& Elsevier]

Abstract: This paper is concerned with economic performance assessment of industrial model predictive control (MPC) applications for processes with constraints. The interest of this paper is to find sensitive process variables, which are the most contributive to the economic performance of MPC. Optimization algorithms for sensitivity analysis are presented for both constraint and variability tuning of industrial MPC applications. Several new problems related to sensitivity properties of process variables, which arise in the actual MPC economic performance assessment, are addressed. Industrial case studies are included to demonstrate how the proposed sensitivity analysis can be used to provide practical and selective tuning guidelines in industry. [Copyright &y& Elsevier]

Abstract: There exist many algorithms for control performance monitoring. There are also many algorithms available for process monitoring. There are, however, few methods available for synthesis of various monitoring techniques to form a diagnosing system for optimal decision making. This paper is concerned with establishing and demonstrating a novel probabilistic diagnostic framework for control loop monitoring. The new framework possesses a number of desired properties, including, for example, quantitative probabilistic diagnosis, flexibility in synthesizing different monitoring techniques, robustness in the presence of missing data or missing variables, ease of expanding or shrinking the diagnosing system, ability to incorporate a priori process knowledge, and capability for decision making. As the backbone of the proposed framework, the emerging Bayesian methods are introduced and shown to be the appropriate tools for solving the problem of concern. Several representative control loop diagnostic problems are formulated under the Bayesian framework and their solutions are demonstrated through examples. The experiences and challenges learned from industrial applications of Bayesian methods are summarized and some of future research directions are discussed. [Copyright &y& Elsevier]

Abstract: Over the last few years there have been some interesting developments in system identification from step and step-like responses. New methods have been proposed to simultaneously estimate model parameters and the delay from step responses that require the process to be at steady state when the step is applied. To deal with transient initial conditions, methods based on pulse responses and the so called piece-wise step tests and iterative algorithm based on a single step response have also been proposed. In this article we propose a new method to estimate model parameters and the delay from a single step response in the presence of transient initial conditions, which does not require iteration. The performance of the proposed procedure is demonstrated through simulations as well as applications on experimental data from a continuous heating tank process and a mixing process. [Copyright &y& Elsevier]

Abstract: Methods to estimate process model parameters from both open loop and closed loop step responses are proposed. The distinctive feature of the proposed methods is that the model parameters are estimated from a single step test even if the step input is applied when the process is not at a steady state. More importantly, the estimation equations are developed in terms of raw values of variables as opposed to their deviational values. This facilitates direct use of industrial data without preprocessing. The performance of the proposed algorithms is demonstrated via simulations as well as experimental applications. [Copyright &y& Elsevier]

Abstract: This paper is concerned with performance assessment of univariate control loops subject to time varying disturbance dynamics. The problem is motivated by the observation that most industrial controllers are linear time invariant (LTI) but the process, particularly the disturbance dynamics, is time varying. The time varying behavior of disturbance dynamics is modelled by piecewise constant parameters of linear disturbance models, namely linear time varying (LTV) dynamics. Thus, during a period of process operation, the process may be affected by several disturbances in terms of different disturbance dynamics or models. This problem has been previously solved by minimizing the variance of a most representative disturbance while satisfying a structured regulatory performance requirement for one of other disturbances, typically the transient but most significant disturbance. This leaves performance in regulating the remaining disturbances unspecified. In this paper, we formulate the problem as minimization of the sum of the weighted variances of all but one major disturbance that is considered under the structured regulatory performance requirement. Furthermore, the problem is solved from the following two perspectives: (1) Models of LTV disturbances are given, the limit of the achievable structured closed-loop performance of any LTI controller for the LTV disturbances is calculated, and the optimal LTI control law is derived if the process model is also known; (2) no complete models about the process or the disturbances are available except for the time delay of the process, an algorithm is developed to assess the performance of the existing LTI controller in the presence of LTV disturbances. Simulation and industrial examples are used to illustrate the proposed algorithms. [Copyright &y& Elsevier]

Abstract: Performance assessment of multi-variate control with minimum variance control as the benchmark requires an interactor matrix to filter the closed-loop output. This is to transfer the coordinate of the original variables into a new one in order to identify the control invariant disturbance dynamics from the first few terms of the closed-loop output Markov parameters. There has been a great deal of interest to simplify this approach, in particular, to find methods that do not need the interactor matrix. With this motivation, this paper explores alternative solutions to multi-variate control performance assessment problems. In particular, we will consider two practical scenarios: (1) known time delays between each pair of inputs and outputs, (2) no a priori knowledge about the process model or time delays at all. Solutions to these two scenarios are proposed. Two data-driven algorithms based on subspace approach are derived for the calculation of performance measures. Several examples illustrate the feasibility of the proposed approaches. [Copyright &y& Elsevier]

This paper presents a novel reduced-order algorithm for identifying rational models. From the Arnoldi process, an orthonormal basis of the Krylov subspace is constructed. Based on the Krylov subspace, a high-order cost function is transformed into a low-order one, thereby significantly reducing the computational efforts. This algorithm can be considered as a reduced-order least squares (LS) algorithm or an extension of the traditional gradient iterative (GI) algorithm for different Krylov subspaces, and it presents several advantages over the traditional LS and GI algorithms. The simulated numerical results/figures are consistent with the analytically derived results in terms of the feasibility and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

As a recursive state estimation algorithm, the Kalman filter (KF) assumes initial state distribution is known a priori , while in practice the initial distribution is commonly treated as design parameters. In this paper, we will answer three questions concerning initialization: (1) At each time step, how does the KF respond to measurements, control signals, and more importantly, initial states? (2) What is the price (in terms of accuracy) one has to pay if inaccurate initial states are used? and (3) Can we find a better strategy rather than through guessing to improve the performance of KF in the initial estimation phase when the initial condition is unknown? To these ends, the classical recursive KF is first transformed into an equivalent but batch form, from which the responses of the KF to measurements, control signal, and initial state can be clearly separated and observed. Based on this, we isolate the initial distribution by dividing the original state into two parts and reconstructing a new state-space model. An initialization algorithm is then proposed by employing the Bayesian inference technique to estimate all the unknown variables simultaneously. By analyzing its performance, an improved version is further developed. Two simulation examples demonstrate that the proposed initialization approaches can be considered as competitive alternatives of various existing initialization methods when initial condition is unknown. [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]

Minimum variance (MV) benchmark is a quantification that is widely applied to compare actual performance of a control loop against its optimal performance. For linear systems, MV benchmark has been well studied, and several well-practiced techniques have been proposed to evaluate the performance of the systems. However, these techniques may not provide satisfactory performance in some situations. For instance, the operational data sampled from a multi-model system does not satisfy stationary conditions that are required for conventional methods. As a result, linear MV benchmark techniques cannot be applied. One possible approach to design MV controller for a multi-model system is to segregate, and label the data using a dynamic clustering method. Then, the MV benchmark can be determined by the multi-model MV control. In this paper, a support vector regression based method is proposed in which all three steps of dynamic clustering, model identification and MV controller design are performed simultaneously through a data driven approach. In addition, a new support vector-based clustering method is proposed by which the data are clustered in residual space of the process model. The optimality and convergence of the proposed algorithm are studied. The proposed multi-model MV controller design technique is demonstrated through a simulated continuous stirred-tank reactor (CSTR) example, which is operated in varying conditions. • SVR based minimum variance controller is proposed. • Three steps of clustering, identification and controller design are performed simultaneously. • Multi-mode MV controller is designed. • Data driven approach is proposed. • The optimality and convergence are studied. [ABSTRACT FROM AUTHOR]

Purpose: To evaluate the value of intra- and peritumoral deep learning (DL) features based on multi-parametric magnetic resonance imaging (MRI) for identifying telomerase reverse transcriptase (TERT) promoter mutation in glioblastoma (GBM). Methods: In this study, we included 229 patients with GBM who underwent preoperative MRI in two hospitals between November 2016 and September 2022. We used four 2D Convolutional Neural Networks (GoogLeNet, DenseNet121, VGG16, and MobileNetV3-Large) to extract intra- and peritumoral DL features. The Mann–Whitney U test, Pearson correlation analysis, least absolute shrinkage and selection operator, and logistic regression analysis were used for feature selection and construction of DL radiomics (DLR) signatures in different regions. These multi-parametric and multi-region signatures were combined to identify TERT promoter mutation. The area under the receiver operating characteristic curve (AUC) was used to evaluate the effects of the signatures. Results: The signatures based on the DL features from the peritumoral regions with expansion distances of 2 mm, 8 mm, and 10 mm using the GoogLeNet architecture correlated with the optimal AUC values (test set:.823,.753, and.768) in the T2-weighted, T1-weighted contrast-enhanced, and T1-weighted images. Using the stacking fusion method, DLR with multi-parameter and multi-region fusion achieved the best discrimination with AUC values of.948 and.902 in the training and test sets, respectively. Conclusions: The radiomics model based on the fusion of multi-parameter MRI intra- and peritumoral DLR signatures may help to identify TERT promoter mutation in patients with GBM. [ABSTRACT FROM AUTHOR]

Highlights • A soft-sensor method is proposed by concurrently consideration of slowness and quality interpretation. • Critical quality-relevant slow features are identified for regression modelling. • The influences of slow features on quality prediction are explored. • The efficacy of the proposed method is verified through two chemical processes. Abstract Slowly varying process variations represented by slow features, which reflect the inherent dynamics of chemical processes, are revealed to be advantageous for quality prediction. However, if slow features are extracted from process variables as predictors without the supervision of quality indices, some obvious disadvantages are observed: (1) low quality interpretation and redundant slow features since quality information is not considered for feature extraction; (2) a lack of analysis to investigate the relationship between slow features and quality interpretation, especially for different types of quality indices. To solve the above-mentioned problems, a new soft-sensor algorithm, quality-relevant slow feature regression (QSFR), is proposed in the present work. It defines a new objective function by concurrent consideration of slowness and quality interpretation, yielding more meaningful features as predictors to interpret quality index. On the basis of this, a critical feature selection strategy is proposed based on quality interpretation to determine the retained features for regression. Moreover, an in-depth analysis of the properties of retained features is provided to reveal the hidden mechanism and how the slow time-varying process variations influence the quality interpretation. This algorithm can extract more powerful features as predictors and enhance understanding of inherent nature of slow features. Finally, the feasibility and performance of the proposed method are well illustrated for a well-known benchmark process and a real chemical process. The developed QSFR algorithm performs better than traditional slow feature regression method, in which the values of RMSE of three specific quality indices have been reduced by 8.87%, 16.60%, and 3.40%, respectively. [ABSTRACT FROM AUTHOR]

Abstract The Expectation Maximization (EM) algorithm has been widely used for parameter estimation in data-driven process identification. EM is an algorithm for maximum likelihood estimation of parameters and ensures convergence of the likelihood function. In presence of missing variables and in ill conditioned problems, EM algorithm greatly assists the design of more robust identification algorithms. Such situations frequently occur in industrial environments. Missing observations due to sensor malfunctions, multiple process operating conditions and unknown time delay information are some of the examples that can resort to the EM algorithm. In this article, a review on applications of the EM algorithm to address such issues is provided. Future applications of EM algorithm as well as some open problems are also provided. [ABSTRACT FROM AUTHOR]