No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
A novel fault detection framework integrated with variable importance analysis for quality-related nonlinear process monitoring
... The conditions of a system are usually evaluated by analyzing a large number of process variables (Yang, Karimi and Pawelczyk, 2023). When the dimension of available data or features becomes extremely high, a critical issue known as the curse of dimensionality arises, leading to overfitting and huge computational costs (Yang, Wang et al., 2023). Besides, it is common that multiple sensors measure similar aspects of the process, bringing about the problem of multicollinearity. ...
Feature selection plays a vital role in improving the efficiency and accuracy of condition monitoring by constructing sparse but effective models. In this study, an advanced feature selection algorithm named the local regularization assisted split augmented Lagrangian shrinkage algorithm (LR-SALSA) is proposed. The feature selection is realized by solving a 1-norm optimization problem, which usually selects more sparse and representative features at less computational costs. The proposed algorithm operates in two stages, namely variable selection and coefficient estimation. In the stage of variable selection, the primal problem is converted into three subproblems which can be solved separately. Then individual penalty parameters are applied to every coefficient of the model when dealing with the first subproblem. Under the Bayesian evidence framework, an iterative algorithm is derived to optimize these hyperparameters. During the optimization process, redundant variables will be pruned to guarantee model sparsity and improve computational efficiency at the same time. In the second stage, the coefficients for the selected model terms are determined using the least squares technique. The superior performance and efficiency of the proposed LR-SALSA method are validated through two numerical examples and a real-world cutting tool wear prediction case study. Compared with the existing methods, the proposed method can generate a sparse model and ensure a good trade-off between estimation accuracy and computational efficiency.
Monitoring wastewater holds significant importance in minimizing pollution discharge and enhancing resource utilization. This study aims to develop a soft sensor for the prediction and optimization of critical wastewater treatment...
During the long operation of wastewater treatment systems, there is a risk of various failures due to aging equipment and environmental climate change. Hence, to ensure the stability of the...
It is of great importance to obtain accurate effluent quality indices in time for pulping and papermaking wastewater treatment processes. However, considering the complex characteristics of industrial wastewater treatment systems, conventional modeling methods such as partial least squares (PLS) and artificial neural networks (ANN) cannot achieve satisfactory prediction accuracy. As a supervised metric learning method, neighborhood component analysis (NCA) is able to significantly improve the prediction performance by training an appropriate model in metric space using the distance between samples for papermaking wastewater treatment processes. The results on two data sets show that NCA has a higher prediction accuracy compared with PLS and ANN. Specifically, NCA has the highest determination coefficient (R²) and the lowest root mean square error in a benchmark simulation data set. On the other hand, the results on the data from an industrial wastewater process indicate that NCA has better modeling accuracy and its R² increases by 32.80% and 29.08% compared with PLS and ANN, respectively. NCA provides a feasible way to realize online monitoring and automatic control in wastewater treatment processes.
Multiblock principal component analysis (MBPCA) methods are gaining increasing attentions in monitoring plant-wide processes. Generally, MBPCA assumes that some process knowledge is incorporated for block division; however, process knowledge is not always available. A new totally data-driven MBPCA method, which employs mutual information (MI) to divide the blocks automatically, has been proposed. By constructing sub-blocks using MI, the division not only considers linear correlations between variables, but also takes into account non-linear relations thereby involving more statistical information. The PCA models in sub-blocks reflect more local behaviors of process, and the results in all blocks are combined together by support vector data description. The proposed method is implemented on a numerical process and the Tennessee Eastman process. Monitoring results demonstrate the feasibility and efficiency.
The objective of this paper is to perform an uncertainty and sensitivity analysis of the predictions of the Benchmark Simulation Model (BSM) No. 1, when comparing four activated sludge control strategies. The Monte Carlo simulation technique is used to evaluate the uncertainty in the BSM1 predictions, considering the ASM1 bio-kinetic parameters and influent fractions as input uncertainties while the Effluent Quality Index (EQI) and the Operating Cost Index (OCI) are focused on as model outputs. The resulting Monte Carlo simulations are presented using descriptive statistics indicating the degree of uncertainty in the predicted EQI and OCI. Next, the Standard Regression Coefficients (SRC) method is used for sensitivity analysis to identify which input parameters influence the uncertainty in the EQI predictions the most. The results show that control strategies including an ammonium (S(NH)) controller reduce uncertainty in both overall pollution removal and effluent total Kjeldahl nitrogen. Also, control strategies with an external carbon source reduce the effluent nitrate (S(NO)) uncertainty increasing both their economical cost and variability as a trade-off. Finally, the maximum specific autotrophic growth rate (micro(A)) causes most of the variance in the effluent for all the evaluated control strategies. The influence of denitrification related parameters, e.g. eta(g) (anoxic growth rate correction factor) and eta(h) (anoxic hydrolysis rate correction factor), becomes less important when a S(NO) controller manipulating an external carbon source addition is implemented.
We present two classes of improved estimators for mutual information M(X,Y), from samples of random points distributed according to some joint probability density mu(x,y). In contrast to conventional estimators based on binnings, they are based on entropy estimates from k -nearest neighbor distances. This means that they are data efficient (with k=1 we resolve structures down to the smallest possible scales), adaptive (the resolution is higher where data are more numerous), and have minimal bias. Indeed, the bias of the underlying entropy estimates is mainly due to nonuniformity of the density at the smallest resolved scale, giving typically systematic errors which scale as functions of k/N for N points. Numerically, we find that both families become exact for independent distributions, i.e. the estimator M(X,Y) vanishes (up to statistical fluctuations) if mu(x,y)=mu(x)mu(y). This holds for all tested marginal distributions and for all dimensions of x and y. In addition, we give estimators for redundancies between more than two random variables. We compare our algorithms in detail with existing algorithms. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis (ICA), for improving ICA, and for estimating the reliability of blind source separation.
Given two time series X and Y , their mutual information, I (X,Y) = I (Y,X) , is the average number of bits of X that can be predicted by measuring Y and vice versa. In the analysis of observational data, calculation of mutual information occurs in three contexts: identification of nonlinear correlation, determination of an optimal sampling interval, particularly when embedding data, and in the investigation of causal relationships with directed mutual information. In this contribution a minimum description length argument is used to determine the optimal number of elements to use when characterizing the distributions of X and Y . However, even when using partitions of the X and Y axis indicated by minimum description length, mutual information calculations performed with a uniform partition of the XY plane can give misleading results. This motivated the construction of an algorithm for calculating mutual information that uses an adaptive partition. This algorithm also incorporates an explicit test of the statistical independence of X and Y in a calculation that returns an assessment of the corresponding null hypothesis. The previously published Fraser-Swinney algorithm for calculating mutual information includes a sophisticated procedure for local adaptive control of the partitioning process. When the Fraser and Swinney algorithm and the algorithm constructed here are compared, they give very similar numerical results (less than 4% difference in a typical application). Detailed comparisons are possible when X and Y are correlated jointly Gaussian distributed because an analytic expression for I (X,Y) can be derived for that case. Based on these tests, three conclusions can be drawn. First, the algorithm constructed here has an advantage over the Fraser-Swinney algorithm in providing an explicit calculation of the probability of the null hypothesis that X and Y are independent. Second, the Fraser-Swinney algorithm is marginally the more accurate of the two algorithms when large data sets are used. With smaller data sets, however, the Fraser-Swinney algorithm reports structures that disappear when more data are available. Third, the algorithm constructed here requires about 0.5% of the computation time required by the Fraser-Swinney algorithm.
For quality-related process monitoring, the current approaches, such as partial least square (PLS) and its variants, often misjudge quality-unrelated anomalies as quality-related anomalies, which brings confusion to quality control personnel. Hence it is important to achieve high detection rates while ensuring the quality-related/-unrelated anomalies can be exactly detected and distinguished. In this article, dynamic related component analysis (DRCA) in full space is proposed to exactly distinguish quality-related/-unrelated anomalies while decreasing the rate of misjudging quality-unrelated anomalies as quality-related anomalies in dynamic processes. The augmented sample covariance matrices with the time lag shift technique are used to conduct eigenvalue decomposition and data transformation. Dynamic related components (DRCs) containing quality-related dynamic information and dynamic unrelated components (DUCs) containing quality-unrelated dynamic information are obtained, and their statistics are used for process monitoring. Both orthogonal quality-related subspaces and orthogonal quality-unrelated subspaces are modeled. Case studies on Tennessee Eastman Process (TEP) and a practical thermal power plant demonstrate the anomaly detection performance of DRCA and its ability to determine whether anomalies affect quality correctly.
This work concerns the issue of quality-related fault detection and diagnosis (QrFDD) for nonlinear process monitoring. A kernel principal component analysis (KPCA) based canonical correlation analysis (CCA) model is proposed in this paper. First, KPCA is utilized to extract the kernel principal components (KPCs) of original variables data to eliminate nonlinear coupling among the variables. Then, the KPCs and output are used for CCA modeling, which not only avoids the complex decomposition of kernel CCA but also maintains high interpretability. Afterwards, under the premise of Gaussian kernel, a proportional relationship between process variables sample and kernel sample is introduced, on the basis of which, the linear regression model between process and quality variables is established. Based on the coefficient matrix of the regression model, a nonlinear QrFDD method is finally implemented which has both the data processing capability of nonlinear methods and the form of linear methods. Therefore, it significantly outperforms existing kernel-based CCA methods in terms of algorithmic complexity and interpretability, which demonstrated by the simulation results of the Tennessee-Eastman (TE) chemical process.
Quinoa flour is prone to economically motivated adulteration due to its high nutritional value and growing demand worldwide. In this study, portable near-infrared spectroscopy (NIRS) combined with multivariate analysis was used to detect adulteration in quinoa flour. The initial investigation was carried out using principal component analysis (PCA) and uniform manifold approximation and projection (UMAP) to identify the most potential adulterate in quinoa flour. Quinoa flour samples were then adulterated with identified adulterant in the range of 0–51% (w/w). The partial least squares regression (PLSR) model built with original spectral data had the best performance for detecting the level of adulteration, with a coefficient of determination (Rp²) of 0.94, root-mean-square error of prediction (RMSEP) of 3.04%, ratio of prediction to deviation (RPD) of 4.04, and range error ratio (RER) of 11.84. The variable importance in projection (VIP) resulting from the PLSR model was used to select 13 informative spectral bands. The new PLSR model led to an R²p of 0.98, RMSEP of 1.60%, RPD of 7.71, and RER of 22.56. The results demonstrated the potential of portable NIRS as a rapid, low cost and non-destructive analytical tool for adulteration detection in quinoa flour.
Process monitoring is critical to ensure process safety and maintain quality stabilization. Currently, a large-scale industrial process commonly consists of multiple operation units or manufacturing plants, and a huge number of variables that reflect operation conditions can be collected easily. The conventional monitoring methods usually utilize all process variables to model, which will submerge the correlation between the process and quality variables. In this paper, a new dynamic concurrent partial least squares (DCPLS) monitoring scheme based on variable importance in the projection (VIP) is proposed for large-scale processes. Firstly, process variables are firstly partitioned into quality-related and weakly quality-related space based on their VIP value. Then, DCPLS model is used to monitor abnormal events in these two spaces, respectively. Finally, fusing the statistics of these two spaces through support vector data description to provide an overall indication. The proposed distributed process monitoring scheme not only automatically realizes the division of variables but also characterizes the dynamic information of data. The monitoring results of the Tennessee Eastman process indicate that the proposed VIP-DCPLS method is more efficient than other monitoring methods.
Quality-relevant fault detection is a primary task to reveal the changes of quality variables in process monitoring. Current works mainly focus on learning quality-relevant features, however, how to distinguish quality-relevant and irrelevant information is responsible for the excellent monitoring performance. In this study, a novel quality-relevant fault detection method is proposed on the basis of adversarial learning and distinguished contribution of latent features to quality is originally introduced. First of all, we map the input variables into a gaussian manifold in adversarial and unsupervised manner. Then a fully connected neural network is trained to learn the relationship between latent and quality variables. To distinguish necessary information in such manifold, the Jacobi operator at the corresponding point is calculated to project the latent variables into quality-relevant and quality-irrelevant subspaces. Third, fault detection is implemented in these dynamic subspaces using the probabilities of latent variables. Finally, the proposed method is evaluated by numerical example, the Tennessee-Eastman process and wind turbine blade icing process.
In order to ensure the long-term stable operation of a large-scale industrial process, it is necessary to detect and solve the minor abnormal conditions in time. However, the large-scale industrial process contains a large number of complex related process variables, some of which are redundant for abnormal condition detection. To solve this problem, a new decentralized PCA modeling method based on relevance and redundancy variable selection (RRVS-DPCA) is presented. First, considering the complex dynamic relation of process variables, a variable selection strategy based on relevance and redundancy (RRVS) is designed to select variables that carried the most profitable information from different temporal dimensions for each key process variables, so the optimal variable sub-block for each individual key process variables can be obtained. Then, for each sub-block, a corresponding sub-PCA monitoring model is established. The sub-blocks’ monitoring results are combined to form a probability statistical indicator through a Bayesian inference. Finally, the weighed contribution plot method is proposed to find the root cause of a fault. The proposed method is compared with several state-of-the-art process monitoring methods on a numerical example and the Tennessee Eastman benchmark process. The comparison results illustrate the feasibility and effectiveness of the proposed monitoring scheme.
Environmental problems have attracted much attention in recent years, especially for papermaking wastewater discharge. To reduce the loss of effluence discharge violation, quality-related multivariate statistical methods have been successfully applied to achieve a robust wastewater treatment system. In this work, a new dynamic multiblock partial least squares (DMBPLS) is proposed to extract the time-varying information in a large-scale papermaking wastewater treatment process. By introducing augmented matrices to input and output data, the proposed method not only handles the dynamic characteristic of data and reduces the time delay of fault detection, but enhances the interpretability of model. In addition, the DMBPLS provides a capability of fault location, which has certain guiding significance for fault recovery. In comparison with other models, the DMBPLS has a superior fault detection result. Specifically, the maximum fault detection rate of the DMBPLS is improved by 35.93% and 12.5% for bias and drifting faults, respectively, in comparison with partial least squares (PLS).
In modern chemical processes, a large number of process variables are collected and these variables are usually intricately correlated, which makes it difficult to carry out plant-wide monitoring of a process. To handle this problem, multiblock based distributed monitoring methods have been proposed. However, how to reasonably categorize the process variables has not been well handled. In this paper, a hierarchical hybrid distributed PCA (HDPCA) modeling framework is proposed to address this issue. In HDPCA, process variables are divided twice into subblocks in a hierarchical two-layer manner. The first-layer blocks of variables are obtained based on an improved general knowledge-based strategy. Then, the process variables in each block are further divided into subblocks in the second layer based on an improved mutual information (MI)-spectral clustering. A two-layer Bayesian inference fusion strategy is used to obtain the distributed monitoring results by fusing statistics and control limits from the second layer backward to the entire process. The feasibility of HDPCA is demonstrated on a benchmark process and an industrial hydrocracking process, in which HDPCA outperforms the other compared methods.
Machine Learning (ML) is a branch of artificial intelligence that studies algorithms able to learn autonomously, directly from the input data. Over the last decade, ML techniques have made a huge leap forward, as demonstrated by Deep Learning (DL) algorithms implemented by autonomous driving cars, or by electronic strategy games. Hence, researchers have started to consider ML also for applications within the industrial field, and many works indicate ML as one the main enablers to evolve a traditional manufacturing system up to the Industry 4.0 level. Nonetheless, industrial applications are still few and limited to a small cluster of international companies. This paper deals with these topics, intending to clarify the real potentialities, as well as potential flaws, of ML algorithms applied to operation management. A comprehensive review is presented and organized in a way that should facilitate the orientation of practitioners in this field. To this aim, papers from 2000 to date are categorized in terms of the applied algorithm and application domain, and a keyword analysis is also performed, to details the most promising topics in the field. What emerges is a consistent upward trend in the number of publications, with a spike of interest for unsupervised and especially deep learning techniques, which recorded a very high number of publications in the last five years. Concerning trends, along with consolidated research areas, recent topics that are growing in popularity were also discovered. Among these, the main ones are production planning and control and defect analysis, thus suggesting that in the years to come ML will become pervasive in many fields of operation management.
Effective online modeling of papermaking wastewater treatment processes (WWTPs) is an important means to ensure wastewater recycling and harmless discharge. A composite model integrating variable importance in projection with dynamic Bayesian networks (VIP-DBN) is proposed to improve the modeling ability and reliability in WWTPs. First, a variable selection method is applied to simplify the network structure and reduce modeling costs. Then the augmented matrices technique is embedded into the Bayesian networks to cope with the dynamic characteristics, nonlinearity, and uncertainty simultaneously. The modeling performance of VIP-DBN is evaluated through two case studies, a simulated WWTP based on benchmark simulation model no. 1 (BSM1) and a real papermaking WWTPs, in which the VIP-DBN model shows better modeling performance than its rivals. Specifically, compared with partial least squares, artificial neural networks, and Bayesian networks, the determination coefficient value of VIP-DBN is increased by 34.36%, 20.55%, and 3.30%, respectively, for the prediction of effluent nitrate in BSM1. The VIP-DBN can be used to deal with complex WWTPs in industrial applications, which provides a better practical method for soft sensor modeling and a guarantee for the effective decision-making of wastewater treatment processes for papermaking enterprises.
This paper is concerned with data science and analytics as applied to data from dynamic systems for the purpose of monitoring, prediction, and inference. Collinearity is inevitable in industrial operation data. Therefore, we focus on latent variable methods that achieve dimension reduction and collinearity removal. We present a new dimension reduction expression of state space framework to unify dynamic latent variable analytics for process data, dynamic factor models for econometrics, subspace identification of multivariate dynamic systems, and machine learning algorithms for dynamic feature analysis. We unify or differentiate them in terms of model structure, objectives with constraints, and parsimony of parameterization. The Kalman filter theory in the latent space is used to give a system theory foundation to some empirical treatments in data analytics. We provide a unifying review of the connections among the dynamic latent variable methods, dynamic factor models, subspace identification methods, dynamic feature extractions, and their uses for prediction and process monitoring. Both unsupervised dynamic latent variable analytics and the supervised counterparts are reviewed. Illustrative examples are presented to show the similarities and differences among the analytics in extracting features for prediction and monitoring.
Data-driven modeling and applications in plant-wide processes have recently caught much attention in both academy and industry. This paper provides a systematic review on data-driven modeling and monitoring for plant-wide processes. First, methodologies of commonly used data processing and modeling procedures for the plant-wide process are presented. Detailed research statuses on various aspects for plant-wide process monitoring are reviewed since 2000. After that, extensions, opportunities, and challenges on data-driven modeling for plant-wide process monitoring are discussed and highlighted for future research.
Traditional process monitoring methods take all the measured variables into account, whereas it will be inappropriate for indicating quality relevant faults. Some measured variables are independent from the quality variables and these redundancy variables will no doubt degrade the prediction performance of quality variables. This paper proposes a novel quality relevant and independent two block monitoring scheme based on mutual information (MI) and kernel principal component analysis (KPCA). First, all the process variables are divided into two sub-blocks according to their MI value with quality variables. Then, KPCA monitors the quality relevant sub-block and quality independent sub-block, respectively. When a fault is detected, kernel principal component regression (KPCR) is further utilized to obtain the predicted state of quality variables. Either of the information, whether the current fault disturbs quality relevant variables or process quality, is necessary and important for engineers. The benefits of MI-KPCA are illustrated through a numerical simulation and the Tennessee Eastman Process, and the results reveal the superiority of the proposal compared with some other monitoring methods.
Projection to latent structures (PLS) and concurrent PLS are approaches for solving quality-relevant process monitoring. In this paper, a new approach called concurrent kernel PLS (CKPLS) is presented to detect faults comprehensively for nonlinear processes. The new model divides the nonlinear process and quality spaces into five subspaces: the co-varying, process-principal, process-residual, quality-principal, and quality-residual subspaces. The co-varying subspace reflects nonlinear relationship between quality variables and original process variables. The process-principal and process-residual subspaces reflect the principal variations and residuals, respectively, in the nonlinear process space. Further, the quality-principal and quality-residual subspaces reflect the principal variations and residuals, respectively, in the quality space. The proposed approach is demonstrated by a numerical simulation and an application of the Tennessee Eastman process.
Fault detection (FD) and diagnosis in industrial processes is essential to ensure process safety and maintain product quality. Partial least squares (PLS) has been used successfully in process monitoring because it can effectively deal with highly correlated process variables. However, the conventional PLS-based detection metrics, such as the Hotelling’s T2 and the Q statistics are ill suited to detect small faults because they only use information from the most recent observations. Other univariate statistical monitoring methods, such as the exponentially weighted moving average (EWMA) control scheme, has shown better abilities to detect small faults. However, EWMA can only be used to monitor single variables. Therefore, the main objective of this paper is to combine the advantages of the univariate EWMA and PLS methods to enhance their performances and widen their applicability in practice. The performance of the proposed PLS-based EWMA FD method was compared with that of the conventional PLS FD method through two simulated examples, one using synthetic data and the other using simulated distillation column data. The simulation results clearly show the effectiveness of the proposed method over the conventional PLS, especially in the presence of faults with small magnitudes.
Partial least squares (PLS) is an efficient tool widely used in multivariate statistical process monitoring. Since standard PLS performs oblique projection to input space $mathbf{X}$, it has limitations in distinguishing quality-related and quality-unrelated faults. Several postprocessing modifications of PLS, such as total projection to latent structures (T-PLS), have been proposed to solve this issue. Further studies have found that these modifications fail to reduce false alarm rates (FARs) of quality-unrelated faults when fault amplitude increases. To cope with this problem, this paper proposes an enhanced quality-related fault detection approach based on orthogonal signal correction (OSC) and modified-PLS (M-PLS). The proposed approach removes variation orthogonal to output space $mathbf{Y}$ from input space $mathbf{X}$ before PLS modeling, and further decomposes $mathbf{X}$ into two orthogonal subspaces in which quality-related and quality-unrelated statistical indicators are designed separately. Compared with T-PLS, the proposed approach has a more robust performance and a lower computational load. Two case studies, including a numerical example and the Tennessee Eastman (TE) process, show the effeteness of the proposed approach.
Increasing global competition is setting even higher demands for the safety, quality and operating efficiency of industrial processes. The traditional projection to latent structures (PLS) based methods for quality-relevant fault detection has appeared in several industrial applications, while total PLS that performs more completely has been used as a better tool for monitoring associated with the product quality. However, the running/operating states for the process variables are often non-stationary, time-varying. Thus, the static PLS or TPLS for these processes will reduce the efficiency of the monitoring, unreliable monitoring results will affect the engineers׳ decision-making. Under this background, an adaptive modification on total PLS model named as recursive TPLS will be proposed to adapt the monitoring model on line. The new recursive version is achieved via a far more computation-efficient manner and the operating cost is significantly lowered. The simulation on TE process illustrates the effectiveness of the new adaptive fault monitoring approach based on RTPLS.
For plant-wide process monitoring, most traditional multiblock methods are under the assumption that some process knowledge should be incorporated for dividing the process into several sub-blocks. However, the process knowledge is not always available in practice. In this case, the monitoring scheme should be implemented through an automatic way. This paper intends to develop a new sub-block principal component analysis (PCA) method for plant-wide process monitoring, which is named as distributed PCA model. By constructing sub-blocks through different directions of PCA principal components, the original feature space can be automatically divided into several subfeature spaces. The constructed distributed PCA models in different subspaces can not only reflect the local behavior of the process change but also enhance the monitoring performance through the combination of individual monitoring results. Both of the monitoring and fault diagnosis schemes are developed based on the distributed PCA model. Two simulation case studies are carried out, on the basis of which the effectiveness of the proposed method is confirmed.
The process monitoring based on concurrent partial least square (CPLS) performs well on the monitoring of input and quality variables through five monitoring statistics. However, in practice, the case of missing variable is very common and the incomplete measurements will make it difficult to implement this monitoring method. Considering the presence of missing measurements occurring in both input and quality variables, this paper analyzes the influence of missing measurements on monitoring performance based on the assumption that input and quality variables satisfy multivariate Gaussian distribution under normal operation. The proposed method estimates the conditional distributions of missing variables, scores and residuals given the observable variables, and denotes monitoring statistics with these conditional distributions. Then, the probabilistic uncertain ranges of monitoring statistics are derived by calculating the general quadratic formulations of Gaussian-distributed missing variables. To determine the process operation in the presence of missing variables, the proposed method employs these uncertain ranges as monitoring statistics. Simulation examples illustrate feasibility of this proposed method and demonstrate its effectiveness.
This paper proposes a new concurrent projection to latent structures is proposed in this paper for the monitoring of output-relevant faults that affect the quality and input-relevant process faults. The input and output data spaces are concurrently projected to five subspaces, a joint input-output subspace that captures covariations between input and output, an output-principal subspace, an output-residual subspace, an input-principal subspace, and an input-residual subspace. Fault detection indices are developed based on these subspaces for various fault detection alarms. The proposed monitoring method offers complete monitoring of faults that happen in the predictable output subspace and the unpredictable output residual subspace, as well as faults that affect the input spaces only. Numerical simulation examples and the Tennessee Eastman challenge problem are used to illustrate the effectiveness of the proposed method. © 2012 American Institute of Chemical Engineers AIChE J, 59: 496–504, 2013
In a typical large-scale chemical process, hundreds of variables are measured. Since statistical process monitoring techniques typically involve dimensionality reduction, all measured variables are often provided as input without weeding out variables. Here, we demonstrate that incorporating measured variables that do not provide any additional information about faults degrades monitoring performance. We propose a stochastic optimization-based method to identify an optimal subset of measured variables for process monitoring. The benefits of the reduced monitoring model in terms of improved false alarm rate, missed detection rate, and detection delay is demonstrated through PCA based monitoring of the benchmark Tennessee Eastman Challenge problem.
This paper provides a state-of-the-art review of the methods and applications of data-driven fault detection and diagnosis that have been developed over the last two decades. The scope of the problem is described with reference to the scale and complexity of industrial process operations, where multi-level hierarchical optimization and control are necessary for efficient operation, but are also prone to hard failure and soft operational faults that lead to economic losses. Commonly used multivariate statistical tools are introduced to characterize normal variations and detect abnormal changes. Further, diagnosis methods are surveyed and analyzed, with fault detectability and fault identifiability for rigorous analysis. Challenges, opportunities, and extensions are summarized with the intent to draw attention from the systems and control community and the process control community.
This paper describes a model of an industrial chemical process for the purpose of developing, studying and evaluating process control technology. This process is well suited for a wide variety of studies including both plant-wide control and multivariable control problems. It consists of a reactor/ separator/recycle arrangement involving two simultaneous gas—liquid exothermic reactions of the following form:A(g) + C(g) + D(g) → G(liq), Product 1,A(g) + C(g) + E(g) → H(liq), Product 2. Two additional byproduct reactions also occur. The process has 12 valves available for manipulation and 41 measurements available for monitoring or control.The process equipment, operating objectives, process control objectives and process disturbances are described. A set of FORTRAN subroutines which simulate the process are available upon request.The chemical process model presented here is a challenging problem for a wide variety of process control technology studies. Even though this process has only a few unit operations, it is much more complex than it appears on first examination. We hope that this problem will be useful in the development of the process control field. We are also interested in hearing about applications of the problem.
Partial least squares or projection to latent structures (PLS) has been used in multivariate statistical process monitoring similar to principal component analysis. Standard PLS often requires many components or latent variables (LVs), which contain variations orthogonal to Y and useless for predicting Y. Further, the X-residual of PLS usually has quite large variations, thus is not proper to monitor with the Q-statistic. To reduce false alarm and missing alarm rates of faults related to Y, a total projection to latent structures (T-PLS) algorithm is proposed in this article. The new structure divides the X-space into four parts instead of two parts in standard PLS. The properties of T-PLS are studied in detail, including its relationship to the orthogonal PLS. Further study shows the space decomposition on X-space induced by T-PLS. Fault detection policy is developed based on the T-PLS. Case studies on two simulation examples show the effectiveness of the T-PLS based fault detection methods. © 2009 American Institute of Chemical Engineers AIChE J, 2010
Projection to latent structures or partial least squares (PLS) produces output-supervised decomposition on input X, while principal component analysis (PCA) produces unsupervised decomposition of input X. In this paper, the effect of output Y on the X-space decomposition in PLS is analyzed and geometric properties of the PLS structure are revealed. Several PLS algorithms are compared in a geometric way for the purpose of process monitoring. A numerical example and a case study are given to illustrate the analysis results.
Variable selection is one of the important practical issues for many scientific engineers. Although the PLS (partial least squares) regression combined with the VIP (variable importance in the projection) scores is often used when the multicollinearity is present among variables, there are few guidelines about its uses as well as its performance. The purpose of this paper is to explore the nature of the VIP method and to compare with other methods through computer simulation experiments. We design 108 experiments where observations are generated from true models considering four factors–the proportion of the number of relevant predictors, the magnitude of correlations between predictors, the structure of regression coefficients, and the magnitude of signal to noise. Confusion matrix is adopted to evaluate the performance of PLS, the Lasso, and stepwise method. We also discuss the proper cutoff value of the VIP method to increase its performance. Some practical hints for the use of the VIP method are given as simulation results.
In this paper, a new nonlinear process monitoring technique based on kernel principal component analysis (KPCA) is developed. KPCA has emerged in recent years as a promising method for tackling nonlinear systems. KPCA can efficiently compute principal components in high-dimensional feature spaces by means of integral operators and nonlinear kernel functions. The basic idea of KPCA is to first map the input space into a feature space via nonlinear mapping and then to compute the principal components in that feature space. In comparison to other nonlinear principal component analysis (PCA) techniques, KPCA requires only the solution of an eigenvalue problem and does not entail any nonlinear optimization. In addition, the number of principal components need not be specified prior to modeling. In this paper, a simple approach to calculating the squared prediction error (SPE) in the feature space is also suggested. Based on T2 and SPE charts in the feature space, KPCA was applied to fault detection in two example systems: a simple multivariate process and the simulation benchmark of the biological wastewater treatment process. The proposed approach effectively captured the nonlinear relationship in the process variables and showed superior process monitoring performance compared to linear PCA.