No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Total projection to latent structures for process monitoring
AIChE Journal
Abstract
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
... The partial least squares (PLS) and canonical correlation analysis (CCA) are the most commonly used quality related monitoring methods [10][11][12][13][14][15]. They extract latent variables from high-dimensional space using the covariance matrices of the process and quality variables. ...
... Trygg et al. put forward the orthogonal projection to latent structures, which removes systematic orthogonal variation of the quality variables from that of the process variables [10]. To improve the detection sensitivity of quality-related fault, Zhou et al. decomposed the process variables into four subspaces using total projection to latent structures (T-PLS), which are orthogonal or correlated to the quality variables [11]. Li et al. modified the T-PLS as dynamic T-PLS with the dynamic correlation between the process variables block and quality variables block [12]. ...
... Consider a quality-relevant monitoring model with the normalized process variables . Using NIPALS method, the process data and quality data can be projected to a low-dimensional space with latent variables [11]. Specifically, the PLS model can be formulated as follows ...
The causality between different variables can reveal the flows of material, energy, and information in the process system. It is beneficial to reflect the relationship between quality variables and process variables. In this study, a concurrent quality and process monitoring method is proposed with intrinsic causality analytics. The proposed method explores the causality between different variables using transfer entropy. Then, the directly related variables and their corresponding time lags are combined to extract convolutional features, which are used to generate feature matrices for process and quality variables. In this way, the quality related information is extracted from the process variables which are directly related to the quality variables. After that, monitoring models are established for each pair of feature matrices, and the monitoring results are integrated to provide a final monitoring result. Since the process disturbances usually smear to directly related variables, the fault signature can be amplified to improve the detection sensitivity when the directly related variables are combined. Finally, the operation status of the process system is identified through the designed monitoring policy, which combines the decisions of different statistics. It is noted that the proposed strategy can be readily generalized to many other existing quality related monitoring methods. Experiments on a real industrial condenser show that the proposed method can distinguish the quality related faults from the process related faults in the condenser. Besides, it has better detection sensitivity than some commonly used quality related monitoring methods.
... The multivariate statistical process monitoring methods are considered the most popular among data-driven techniques where they directly use the input-output measurements for process monitoring purposes. The basic multivariate statistical process monitoring methods including principal component analysis (PCA) [6,7], partial least squares (PLS) [8], total projection to latent structures (TPLS) [9], modified partial least squares (MPLS) [10], orthogonal projection to latent structures (O-PLS) [11], modified orthogonal projection to latent structures (MOPLS) [12], expectation-maximization partial robust M-regression (EMPRM) [13], and total principal component regression (TPCR) [14]. All these methods have been successfully applied to many large industrial processes, e.g., chemical plants, water treatment processes, power grids, and cyber-physical systems [15][16][17]. ...
... Moreover, residual subspace usually has quite large variations that are not proper to be monitored. [9] proposed the TPLS algorithm to treat the standard PLS model-associated problems. TPLS model works well for characterizing the observed X and is appropriate for monitoring various parts of X. ...
... More details about the TPLS model are given in the research work of [9]. It should be noted that both T 2 y and SPE r are used to detect the faults related to Y. On the contrary, T o and T r are used together to detect the faults that are not related to Y. ...
Fault detection plays a crucial role in ensuring the safety, availability, and reliability of modern industrial processes. This study focuses on data-driven fault detection methods, which have gained significant attention across various industrial sectors due to the rapid development of industrial automation technologies and the availability of extensive datasets. The objectives of this paper are to comprehensively review and present the theoretical foundations of widely used data-driven fault detection approaches. Specifically, these approaches are applied to fault detection in wind turbine systems, with performance evaluation conducted using multiple statistical measures. The data utilized in this study were collected from a simulated benchmark of a wind turbine system. The data-driven methods are tested under the assumption that the wind turbine operates in a steady-state region. Additionally, a comparative study is conducted to identify and discuss the primary challenges associated with the practical application of these methods in real-world scenarios. Simulation results show the effectiveness and efficacy of data-driven approaches concerning the sensitivity and robustness of wind turbine sensor faults as applied in practical industrial environments.
... MSPM methods generally extract features using generalized singular value decomposition (SVD), and the commonly used methods are principal component analysis (PCA) [10], partial least squares (PLS) [11], [12], canonical correlation analysis (CCA) [13], and so on. Among them, PCA is the most commonly used monitoring method, whose statistics are established based on the retained principal components and the corresponding reconstruction residuals [10]. ...
... Among them, PCA is the most commonly used monitoring method, whose statistics are established based on the retained principal components and the corresponding reconstruction residuals [10]. By taking the key performance indicator (KPI) into consideration, the PLS model is established to detect the abnormal conditions in KPI-related components with higher accuracy [11], [12]. In CCA model, both the input and output of the process system are considered to extract latent variables with maximum correlation between the input and output [13]. ...
... An optimization problem with two independent variables is formulated in the following. The equivalence between (11) and (12) can be demonstrated by partially optimizing problem (12) ...
Unsupervised fault detection and diagnosis methods generally have the following shortcomings in their projection vectors: 1) they may not be specially designed to differentiate between normal and abnormal samples; 2) they may remain unchanged for different abnormal conditions; and 3) the key variables for the process anomalies may have not been effectively selected. In this study, a fault detection and diagnosis scheme sparse distribution dissimilarity analytics (SDDA) is proposed with a lasso penalty and distribution dissimilarity to solve these issues. The proposed method is formulated through a nonconvex optimization problem with a lasso penalty, which aims to maximize the distribution dissimilarity between different data sets. Then, the nonconvex optimization problem is recast to an iterative convex optimization problem using the minorization–maximization algorithm. After that, the constraint conditions are removed using the Karush–Kuhn–Tucker conditions for further simplification. Finally, the unconstraint optimization problem is solved through the proposed feasible gradient direction method. Based on the obtained sparse projection vectors, a fault detection model with both static deviation and dynamic fluctuation is developed. Since the statistics are designed using distribution dissimilarity, some abnormal conditions with small fault magnitudes can also be accurately detected. Besides, a reconstruction-based contribution (RBC) method is proposed for the statistics, and its diagnosability has been strictly demonstrated in theory. The detection and diagnosis performance of the proposed SDDA method is validated using a simulated process and a real industrial process. Experimental results illustrate the superiority of the proposed method to some commonly used methods.
... By reference to the criteria established by Zhou et al. (2010), 15 disturbances (IDV (1-15)) can be classified into two categories, quality-relevant and quality-irrelevant disturbances. IDV (1-2, 5-8, 10, 12-13) are identified as qualityrelevant disturbances, while IDV (3-4, 9, 11, 14-15) are quality-irrelevant disturbances. ...
... As shown in Table 11, both cross-correlation part and auto-correlation part have higher MSEs than the overall MSE value of DALVR, which implies that the modelling performance with past process samples only or past quality samples only is not satisfactory. (Downs and Vogel 1993), and based on the criterion proposed in the work of Zhou et al. (2010), they can be classified into two categories: quality-relevant and quality-irrelevant disturbances. IDV (1, 2, 5-8, 10, 12, and 13) are identified as quality-relevant disturbances, while IDV (3, 4, 9, 11, 14, and 15) are quality-irrelevant disturbances. ...
... (2) PLS does not extract covariances between input and output variables in descending order, so the input residuals may contain large variations that are not suitable for monitoring using the statistic. Zhou [15] used the total projection to latent structures (TPLS) model in 2010. This method significantly improves the performance of quality-related fault diagnosis. ...
... Therefore, there is an urgent need to address this shortcoming of CPLS. Yin [15] proposed the modified-PLS (MPLS) model, which achieves an orthogonal decomposition of the process variable space, while the SVD method is used to solve the problem of a large number of iterations of the PLS method. Zhang [16] showed that MPLS may lead to the loss of relevant information. ...
Partial Least Squares (PLS) is a fault diagnosis model used in statistical process monitoring. PLS decomposes the data space into a quality correlated subspace and an uncorrelated subspace, and monitors the state of both subspaces by setting the appropriate statistics. However, post-processing methods such as modified-PLS (MPLS) and efficient projection to latent structures (EPLS) gradually lose their ability to detect faults when low-intensity faults that do not affect quality. In order to eliminate the drawbacks of post-processing methods and improve the stability of algorithms under different conditions, this paper introduces the competitive and adaptive reweighted sampling method (CARS) into the field of fault diagnosis and proposes a fault filtering method combining CARS and orthogonal signal correction algorithm (OSC). First, an initial screening of the variable space was completed using CARS method. OSC algorithm is then used to remove quality- uncorrelated components. Next, the variable space is completely decomposed into a quality-correlated and an irrelevant subspace using intensified partial least squares method (IPLS). Finally, the validity of the model was verified using the simulations.
... Quality-relevant fault monitoring is thus a significant advance to avoid nuisance process alarms that have no impact on product quality. Several improved PLS methods that decompose the quality-relevant variations and quality-irrelevant variations have been developed [32], [33], [34]. ...
Supervised latent variable regression methods such as partial least squares (PLS) and dynamic PLS have found wide applications in data analytics, quality prediction, and fault monitoring in various industries. In this article, we tackle the unbalanced data problem of sparse quality measurement and abundant process data in process control systems to make use of all data samples for modeling. A novel semi-supervised dynamic latent variable regression (SemiDLVR) method is proposed for quality prediction and quality-relevant fault monitoring. The proposed SemiDLVR method integrates Laplacian manifold regularization with dynamic regularized latent variable regression (DrLVR) to form a semi-supervised framework to efficiently model unlabeled data. A unified objective that combines DrLVR and the Laplacian matrix is proposed and the solution is provided. Statistical monitoring indices are, thereafter, defined for quality-relevant fault monitoring in the semi-supervised framework. Results from experimental studies on a numerical simulation, an industrial sulfur recovery unit (SRU), and the Tennessee Eastman (TE) process benchmark are presented to demonstrate the effectiveness of the proposed method.
... Vásquez Lizcano -Wagner Medina -Santacruz Castro, Saray Culma -Meneses Buitrago -Burbano Figueroa -Aja Eslava / Territorios Hidrosociales: una metodología para promover la seguridad hídrica ante el cambio climático a través de la gobernanza, visión y acción participativa hídrica, estos modelos serán revisados por expertos. En la construcción de este indicador, tanto actores como expertos participarán en la provisión de rangos de calificación para las variables usadas en las estimaciones de los indicadores de seguridad hídrica, esto facilitará la identificación de variables con mayor impacto (proyección a estructuras latentes (Zhou et al., 2010)), y aquellas que son mayor fuente de riesgo e incertidumbre (valor esperado de la información perfecta (Tuffaha, 2021)). ...
La gobernanza en territorios hidrosociales a partir de la participación ciudadana, el diálogo de saberes, y la confianza entre los actores territoriales es fundamental para garantizar una distribución justa y sostenible del agua. Este artículo presenta un enfoque metodológico para la promoción de la seguridad hídrica fundamentada en el fortalecimiento de la gobernanza del agua que permitan formalizar las aspiraciones de seguridad hídrica en la comunidad, la construcción de una visión y acciones estratégicas colectivas y concertadas. El enfoque integra conceptos pragmáticos y transdisciplinarios considerando sólo aquellos conceptos que proveen una explicación a partir de las perspectivas de actores independientemente de su disciplina, promueve la adaptación al cambio climático y la transformación hacia territorios sostenibles. La implementación de enfoques transdisciplinarios suele carecer de documentación, con este manuscrito se busca sistematizar como una oportunidad para promover la transparencia y la reproducibilidad de este tipo de iniciativas.
... Paper [11] developed a preprocessing method, called the orthogonal projections to latent structures (O-PLS), to remove orthogonal information to quality variables. To achieve further decomposition of the input subspace, the work of [12] proposed the total projection to latent structures (T-PLS). However, the above methods inherit the shortcoming that PLS encounters difficulties in dealing with complex data with large capacities and poor information. ...
... Five hundred samples were used in the training set and 960 samples were used in the test set. According to the research of Zhou et al. [25], only some faults can be regarded as quality related. In this article, fault types 1, 2, 6, 8, 12, and 13 were selected as comparison tests, and two other types of faults were selected, namely, faults 11 and 21. ...
Process monitoring is very important for the safety of industrial production processes. The traditional monitoring method based on independent component analysis has the disadvantages as follows. (1) The importance ordering problem of independent components has not been solved; (2) The dynamic problem is not considered. To address these issues, a fractal dimension-based dynamic kernel independent components regression (FD-KICR) method is proposed. The contributions of the proposed method are as follows: (1) The intrinsic dimension of the data is calculated through the improved fractal dimension, and then the number of selected nonlinear ICs (nICs) is determined; (2) The time lags are computed with fractal dimension to effectively describe the dynamic structure of data; (3) By correlating temperature with independent components selection and indirectly monitoring temperature changes through bands of independent components, this method can effectively monitor the safety of the production process. This proposed method is applied to the electrical fused magnesia furnace (EFMF). The experience results show the effectiveness of this method.
... With continued advancements of sensors and data storage equipment, a large amount of process data can be obtained more easily, and many data-driven assessment methods with respect to the process operating performance have been developed on the basis of multivariate statistics and data distribution description techniques. For linear industrial processes, i.e., the correlation between process variables is linear or nearly linear, some traditional multivariate statistical analysis methods were improved to accurately extract the features related to the performance index 7,8 and applied to the process operating performance assessment. 9,10 However, complex process mechanism and fluctuating external environment often lead to nonlinear correlation between process variables, making those linear assessment methods perform poorly, and some nonlinear assessment methods came into being. ...
The operating performance of a process may degenerate due to process interferences and operation errors, which cancel the benefits of technology design and economic production. Traditional operating performance assessment methods are either lack of real-time due to the post-analysis or difficult to distinguish performance grades for process data with weak differences and strong noise interferences based on shallow learning structures. In this paper, a new layer attention-based stacked performance-relevant denoising auto-encoder (LA-SPDAE) is proposed for the operating performance assessment of industrial processes. It overcomes the defect that the original SDAE ignores task-relevant information in training and only uses the feature of the last hidden layer to complete special tasks. In this study, the original SDAE is improved by optimizing the cross-entropy loss of the performance grade labels in the layer-wise pretraining, which is named stacked performance-relevant denoising auto-encoder (SPDAE), and the performance-relevant features can be extracted under supervision. Moreover, for making good use of performance-relevant features of each layer, they are fused by adaptive weights based on the layer attention mechanism. In the case study of cyanide leaching, the assessment accuracy of the proposed LA-SPDAE model is up to 99.85% under the corrupted proportion of 20%, and the advantage is still maintained as the proportion increases to 80%, which demonstrates the superiority of LA-SPDAE compared with conventional deep neural networks and shallow learning structures.
... If a fault occurs in the variable space Y, i.e., the fault affects the quality change, the fault must occur in the subspace S p ,.I If the fault does not affect the quality change, the fault must occur in the subspace S r . Usually, the T 2 indicator is used to detect faults in S p , and the Q indicator is used to detect faults occurring in S r [26]. ...
In this paper, a data-driven approach is used to process W-Beam Barrier monitoring data, expecting to achieve online estimation of the number of trucks and accurate identification of barrier impact events. By analyzing the data features, significant noise was found in the original data, hiding the useful information, so this paper proposes an improved wavelet thresholding algorithm to achieve data denoising. As there is no study of the same application, this paper compares three commonly used data fault diagnosis algorithms: Principal Component Analysis (PCA), Partial Least Squares (PLS) and Fisher Discrimination Analysis (FDA). By designing and conducting comparison experiments, the results show that the PCA model is more suitable for estimating the number of trucks and the FDA model is more suitable for identifying barrier impact events. The data processing results are shared with the highway operation management system as a trigger condition to enable the strategy of forbidden truck overtaking. Through long-term application, the results show that highway capacity is improved by 12.7% and the congestion index and emissions are slightly reduced after adopting this paper’s method.
... A relevant variation to the basic PCA and PLS methods is the Total Projection to Latent Structure (TPLS) approach proposed in [8] to handle the oblique decomposition problem of standard PLS and the concurrent projection to latent structures (CPLS) method [9]. The issue of system dynamics and temporal correlation in the data have been faced in variants such as the Dynamic PCA (D-PCA) [10], the dynamic PLS (DPLS) [11] and the Canonical Variate Analysis (CVA) approach [12]. ...
In this paper PCA and D-PCA techniques are applied for the design of a Data Driven diagnostic Fault Isolation (FI) and Fault Estimation (FE) scheme for 18 primary sensors of a semi-autonomous aircraft. Specifically, Contributions-based, and Reconstruction-based Contributions approaches have been considered. To improve FI performance an inference mechanism derived from evidence-based decision making theory has been proposed. A detailed FI and FE study is presented for the True Airspeed sensor based on experimental data. Evidence Based Filtering (EBF) showed to be very effective particularly in reducing false alarms.
... In this case, subsequent PCA modeling of the X residuals can be conducted, which is suggested in the total PLS algorithm. 32 ...
In this article, we explore the connection of partial least squares (PLS) to other regularized regression algorithms including the Lasso and ridge regression, and consider a steepest descent alternative to the PLS algorithm. First, the PLS latent variable analysis is emphasized and formulated as a standalone procedure. The PLS connections to the conjugate gradient, Krylov space, and the Cayley–Hamilton theorem for matrix pseudo‐inverse are explored based on known results in the literature. Comparison of PLS with the Lasso and ridge regression are given in terms of the different resolutions along the regularization paths, leading to an explanation of why PLS sometimes does not outperform the Lasso and ridge regression. As an attempt to increase resolutions along the regularization paths, a steepest descent PLS is formulated as a regularized regression alternative to PLS and is compared to other regularized algorithms via simulations and an industrial case study.
... Zhou et al. [133] proposed a PLS-based scheme, total projection to latent structure (TPLS), to deal with skew decomposition in standard PLS. However, TPLS does not clearly explain the reason that the principal component space of PLS contains the change independent of the fault in the practical application, and the principal component space does not need to be decomposed into four subspaces, which can be completely decomposed into the subspace related to the process fault and the subspace related to the input. ...
Process fault detection and diagnosis (FDD) is a predominant task to ensure product quality and process reliability in modern industrial systems. Those traditional FDD techniques are largely based on diagnostic experience. These methods have met significant challenges with immense expansion of plant scale and large numbers of process variables. Recently, deep learning has become the newest trends in process control. The upsurge of deep neural networks (DNNs) in leaning highly discriminative features from complicated process data has provided practitioners with effective process monitoring tools. This paper is to present a review and full developing route of deep learning-based FDD in complex process industries. Firstly, the nature of traditional data projection-based and machine learning-based FDD methods is discussed in process FDD. Secondly, the characteristics of deep learning and their applications in process FDD are illustrated. Thirdly, these typical deep learning techniques, e.g., transfer learning, generative adversarial network, capsule network, graph neural network, are presented for process FDD. These DNNs will effectively solve these problems of fault detection, fault classification, and fault isolation in process. Finally, the developing route of DNN-based process FDD techniques is highlighted for future work.
Partial least squares (PLS) is a widely used multivariate statistical technique, which can be used in neuroimaging, process monitoring, economics, etc. Because the standard PLS is trained by nonlinear iterative partial least squares (NIPALS) algorithm, which can only obtain the numerical solution rather than the analytical solution. Therefore, it is hard for the subsequent theoretical analysis in PLS and the iterative optimization process is computationally intensive. This paper proposes an analytical solution to take the place of NIPALS. This determination meaningfully contributes to future theoretical analysis of PLS. In addition, the analytical solution demonstrates that the selection of initial vector in NIPALS does not affect the PLS training results. Moreover, the analytical solution avoids the multiple iterative calculations, so the divergence of the calculation process will be avoided and the computation burden will be reduced significantly.
The issue of quality-related fault detection in the industrial process has attracted much attention in recent years. The partial least squares (PLS) is considered an efficient tool for predicting and monitoring. The modified partial least squares (MPLS) is an extended algorithm for solving the oblique decomposition of PLS, however, the study indicated that the loss of quality variable information may affect the prediction of quality information in the decomposition process of the MPLS algorithm. Furthermore, the detection rate of traditional statistics and static control limit is low, and the existing dynamic control limit has certain limitations. Therefore, a new PLS space-decomposition algorithm called advanced partial least squares (APLS) is proposed. APLS avoids the loss of quality information by orthogonal decomposition of process variables according to their relationship with quality. APLS has a more accurate prediction of quality when process variables contain more noise; the fault false alarm rates (FAR) of quality-related faults are reduced by using the new statistics and thresholds combined with local information increment technology in the process variable principal component subspace. Finally, the effectiveness of the proposed approach is verified by a numerical example and an industrial benchmark problem.
To solve the problem of incipient fault detection, a fault targeted gated recurrent unit-canonical correlation analysis (CCA) method is proposed. First, this article proposed fault targeted gated recurrent unit (FTGRU) to establish a temporal feature extraction model. The features extracted by FTGRU are more sensitive to the incipient faults, thus increasing the accuracy of the fault detection model. Then, a fault detection model is established by CCA method. In addition, in order to ensure the universality of the detection model, a multilayer fault detection strategy is proposed. At the first layer, the basic CCA model is used. When no fault is detected at this layer, the second layer fault detection method is enabled. In the second layer, the proposed FTGRU-CCA method is used. Finally, the proposed method and detection strategy are validated by two different industrial cases.
Compared with PLS and PCA, independent component analysis (ICA) uses higher-order statistical information (above third-order) of the signal, so as to extract the non-Gaussian characteristic. In recent years, ICA was commonly used as a fault diagnosis method in the field of non-Gaussian process monitoring.
The MSPC-based method is the main data-driven fault monitoring and diagnosis method, which takes principal component analysis (PCA)(Word et al. in Chemom Intell Lab Syst 2:37–52, 1987), partial least squares (PLS) (Burnham et al. in J Chemom 10:31–45, 1996;De in Chemom Intell Lab Syst 18:251–263, 1993;), Fisher discriminant analysis (FDA)( Chiang LH, Kotanchek ME, Kordon AK (2004) Fault diagnosis based on fisher discriminant analysis and support vector machines. Comput Chem Eng 28(8):1389–1401), independent component analysis (ICA) (Hyvärinen and Oja in Neural Netw 13:411–430, 2000), etc. as the core. This chapter will briefly introduce the main principle of the above-mentioned models and some MSPC-based process monitoring and diagnosis methods.
Data-driven process monitoring techniques (Ge in Chemom Intell Lab Syst 171:16–25, 2017; Ge and Song in Multivariate statistical process control: process monitoring methods and applications. Springer, 2013; Yin et al. in IEEE Trans Industr Electron 62:657–667, 2015; Ding in J Process Control 24:431–449, 2014) are very popular in industrial process safety detection due to their easy implementation and low requirements for the underlying model. The PCA (Jolliffe in Principal component analysis, Springer, New York, NY, USA, 1986) and PLS (Wold et al. in Pattern regression finding and using regularities in multivariate data, U. K., Applied Science, London, 1983) are two typical MSPC methods for monitoring process security by projecting measurements into a low-dimensional space and constructing Q statistics and T2 statistics (Qin in Annual Review of Control 36:220–234, 2012). When an abnormal variable occurs in an industrial process, there are two possible scenarios. One is that the fault directly affects the output variables, which needs to be alarmed in time.
PCA, ICA, PLS, etc., are popular MSPC approaches applied in industry process monitoring. In general, both PCA and ICA are employed in process monitoring to identify anomalous.
In complex industrial processes, the mixed characteristics of Gaussian/non-Gaussian and nonlinear data are a common phenomenon. This process is characterized by a nonlinear distribution among the different variables, while some variables are non-Gaussian.
Nonlinear process is a common phenomenon in industrial processes, which shows a nonlinear relationship between the variables. Generally, PLS and its modifications (Yin et al. in IEEE Trans Industr Electron 62:1651–1658, 2015; Zhou et al. in AIChE J 56:168–178, 2010; Qin and Zheng in AIChE J 59:496–504, 2013) have a high performance when dealing with linear variation among process variables. However, when applied to a nonlinear process, which generally means that there exists a nonlinear relationship between X and Y, or the process data distributed nonlinearly, or both, these methods cannot perform well.
Several complex process monitoring approaches introduced in previous chapters can be used to determine whether the system is abnormal. However, once a fault has been detected, it is important to diagnose the root cause and identify the fault type. Since it can extract information related to output variables and infer the quality variables from the input variables, PLS has been applied to the diagnosis of key performance indicators by analyzing process variables. In the chapter, input variables refer to the process variables measured online and output variables refer to some key performance indicators (KPI).
As a novel multivariable regression method, orthonormal subspace analysis (OSA) divides input data and key performance indicators (KPIs) data into three orthonormal subspaces, resulting in effective detection of KPI-related faults in industrial processes. However, the detection of incipient faults is still a challenging problem. To this end, a deep OSA model is established to extract incipient fault information and detect it in this article. First, the correlation matrix (CM), based on the KPI-related information and input-related information that are completely orthogonal to irrelevant information, is calculated to accurately describe the correlation between input and KPIs. Second, the deep singular value decomposition is performed on CM to divide KPI-related information into multiple subspaces, deeply separate KPI-related information and, not least, mine incipient features of data. Furthermore, the detection statistics of multiple subspaces, fault detectability, and complexity are presented. Finally, a numerical example and an actual thermal power plant are employed to confirm the validity of the proposed method. The results demonstrate that the proposed deep OSA achieves much better detectability for incipient KPI-related fault in theoretical and engineering application than some other existing methods.
Several data-driven methodologies for process monitoring and detection of faults or abnormalities have been developed for the safety of processing systems. The effectiveness of data-based models, however, is impacted by the volume and quality of training data. This work presents a robust neural network model for addressing the mislabeled and low-quality data in detecting faults and process abnormalities. The approach is based on harnessing data quality features along with supervisory labels in the network training. The data quality has been computed using the Mahalanobis distances and trusted centers of each class of data e.g., normal and faulty data. The method has been examined for detecting abnormalities in two case studies; a continuous stirred tank heater problem for detecting leaks and the Tennessee Eastman chemical process for detecting the step and sticking faults. The performance of the proposed robust ANN model is evaluated in terms of accuracy, fault detection rate, false alarm rate, and classification index at varying extents of mislabeling namely, 1%, 5%, and 10% mislabeled data. The proposed model demonstrates higher detection performance, especially at increased labels of mislabeled data where the performance of the conventional ANN is severely impacted. The proposed methodology can be advantageous in handling mislabeled and low-quality data issues which are crucial in the data-driven modeling of processing systems.
With the complexity and intelligence of the process, process monitoring plays a vital role in ensuring production safety and product quality, in which quality-related fault detection techniques have been extensively studied. The traditional monitoring strategies have the problem that the production process cannot be accurately monitored when the quality indicators are insufficient. It is difficult to extract accurate quality-related features with the guidance of limited quality labels. In addition, the model trained with limited quality indicators will get caught in overfitting problems. Motivated by the limitations, a novel semi-supervised relevance variable selection and hierarchical feature regularization variational auto-encoder (SS-RVS-HFRVAE) is proposed to monitoring the process with limited quality indicators. First, a hierarchical feature regularization variational auto-encoder is proposed to overcome the overfitting problem brought by limited quality labels. Secondly, a semi-supervised relevance variable selection strategy is proposed to extract the most quality-related features under semi-supervised process data set. Finally, the experiments on numerical case and Tennessee Eastman process describe the effectiveness of the proposed method in semi-supervised quality-related process monitoring.
Multivariate statistical analysis approaches are extensively employed in process monitoring because they can effectively detect abnormal conditions in industrial processes. However, both Gaussian and non-Gaussian variables are often present in industrial processes. A single multivariate statistical process monitoring method often has difficulty simultaneously dealing with variable information of mixed distribution characteristics. This paper proposes a multivariate quality-related process monitoring method based on a Bayesian classifier to address this issue. The proposed method separates the variables into Gaussian and non-Gaussian parts using a Jarque–Bera test. Then, Gaussian and non-Gaussian properties are extracted through modified kernel partial least squares and kernel independent component analysis. After feature extraction, a Bayesian-based classifier relevance vector machine is constructed to monitor quality-related information of the process, which avoids the construction of a threshold in conventional methods and offsets the drawbacks of insufficient single statistic information. A numerical simulation and the Tennessee-Eastman process verify the effectiveness of the method.
Quality‐related fault detection and diagnosis are crucial in the data‐driven process monitoring field. Most existing methods are based on principal component analysis (PCA) or partial least squares (PLS), which will miss high‐order statistical information when the industrial process does not satisfy a Gaussian distribution. Meanwhile, the traditional contribution plot is difficult to directly apply to nonlinear processes in some cases due to its limitation of convergence. As such, a modified kernel independent component regression (MKICR) model, which considers high‐order statistical information, is proposed for quality‐related fault detection and faulty variable identification. First, the relationship between the independent components and quality variables is established by kernel independent component regression, and the correlation matrix is obtained. Then, the kernel independent components can be suitably divided into quality‐related and quality‐unrelated parts. Finally, an analysis of the contribution of each variable to the statistics based on Lagrange's mean value theorem is presented. In addition, a numerical case and the Tennessee Eastman process (TEP) demonstrate the efficacy and superiority of the proposed method.
Quality-related process monitoring as a supervised technology has increasingly attracted attention in complex industries. Various approaches have been studied to cope with this issue. Nevertheless, these methods cannot reasonably decompose the process variable space, resulting in deficiencies in monitoring quality-related faults. To handle this issue, this paper presents an orthogonal kernel partial least squares improved kernel least squares with a preprocessing-modeling-postprocessing (PMP) structure to implement quality-related process monitoring with more proper decomposition and more straightforward monitoring logic. Compared with the previous approaches, a nonlinear preprocessing technology is presented to eliminate the quality-unrelated knowledge of process variables, enormously enhancing the interpretability of modeling and improving the monitoring efficiency. Then, a proper decomposition is presented to decompose the kernel matrix into two orthogonal parts, significantly improving the monitoring performance. The theoretical analysis of the proposed method is provided in this paper. Finally, two cases indicate the validity and superiority of the proposed method.
Partial least squares (PLS) is a widely used and effective method in the field of fault detection. However, due to the fact that the standard PLS decomposes the process variable space into two subspaces which are not completely orthogonal, it is insufficient in quality-related fault detection. To solve this problem, principal component regression (PCR) is used to decompose the quality variables of PLS model and realize the reconstruction of the process variable space. In this way, the process variable space is decomposed into highly correlated and highly irrelevant parts of quality variables, and the two are monitored by designing statistics respectively. Furthermore, an adaptive threshold based on the idea of exponential weighted moving average (EWMA) is introduced to reduce the false positives and missed positives caused by the traditional fixed threshold, and this method is named as improved regression partial least squares (RPLS). Finally, linear and nonlinear numerical examples and Tennessee Eastman (TE) processes are used to verify the effectiveness of the proposed method which named improved regression partial least squares (IRPLS). Finally, linear and nonlinear numerical cases and Tennessee Eastman (TE) processes are used to verify the effectiveness of IRPLS. The results show that the proposed method can effectively improve the fault detection rate and algorithm follow-through performance, and reduce false positives.KeywordsPLSPCREWMAIRPLSTE
Fluid catalytic cracking (FCC) is an important process in petroleum processing. Effective monitoring of the status and quality of FCC is vital. Accurate description of the relationship between process and quality variables is the basis of quality-driven monitoring. Many process variables affect the quality of FCC; some of these effects are linear, and others are nonlinear. We propose a combination method from the perspective of linearity and nonlinearity to improve the monitoring performance of FCC quality. Partial least squares (PLS) is initially used to extract linear features, and its residual space is saved as the input of the deep feedforward neural network (DFNN). DFNN is then used to extract nonlinear features for the further decomposition of subspaces. The PLS-DFNN method accurately describes processes involving linearity and nonlinearity. We construct three monitoring statistics to characterize the types of faults. The proposed method proves its excellent effect on a numerical simulation data set. It effectively distinguishes the types of faults on the Tennessee Eastman process data set, and the fault detection rate is superior to other related methods. Finally, we apply this method to the actual FCC and verify the superiority of this combination.
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.
The dynamic time-varying characteristic has brought great challenges to the plant-wide process monitoring. In this paper, a distributed adaptive principal component regression algorithm is proposed for the online indicator monitoring of large-scale dynamic process. Firstly, the distributed data subblocks are constructed according to the process operation units. In each subblock, an adaptive re-sampling method based on the subblock data and plant-wide data is presented to construct the modeling sample sets, which can extract the process local and global information simultaneously. Afterwards, the indicator-related feature is extracted, and the Bayesian method is used to integrate the subblock monitoring results. Through the collaborative monitoring of the process local and global feature spaces, a refined monitoring decision can be obtained. Finally, a numerical example and Tennessee Eastman process are used to illustrate the effectiveness of the proposed method.
Kernel partial least squares (KPLS) has poor robustness and cannot achieve effective monitoring for key performance indicators (KPI). This study investigates a new KPI-oriented robust KPLS approach to mitigate these drawbacks. In this methodology, the robust KPLS inspired by the gradient boosting principle incorporates a weighting matrix into the KPLS to mitigate the influence of outliers. Simultaneously, the associated coefficient matrix is derived in detail. Then, a decomposition approach is used to separate the process variable space into two orthogonal parts. Two strategies are discussed to obtain the unknown projection matrices based on the kernel principal component analysis and the elastic network frameworks. Finally, the performance of the proposed methods in terms of prediction, monitoring and robustness to outliers is evaluated by the Tennessee Eastman process and the three-phase flow facility. The results show that the proposed methods have good prediction accuracy and monitoring performance in the presence of outliers, demonstrating the effectiveness and advantages of the proposed approaches.
Projection to latent structure (PLS) is a well-known data-based approach widely used in industrial process monitoring. Kernel PLS (KPLS) was proposed in prior studies to apply the PLS in the nonlinear process. However, KPLS-based methods only consider the nonlinear variation of the input and ignore that of the input and output simultaneously. Once the nonlinearity lies in inputs and outputs, the KPLS-based methods cannot accurately describe the nonlinear feature, and result in missing alarms. To provide a common monitoring approach for various nonlinear cases, an input-output kernel PLS (IO-KPLS) model is proposed. The proposed IO-KPLS maps both the original input and output variables into a high-dimensional space. A new nonlinear objective function is then established to extract latent variables. In addition, a nonlinear regression is designed to construct the IO-KPLS model. By constructing statistics, a complete quality-related process monitoring strategy is designed. Driven by the proposed strategy, the nonlinear feature between input and output can be efficiently extracted, and a comprehensive monitoring performance is provided. A numerical example and two industrial benchmarks are performed to demonstrate the efficiency of the proposed method.
Key performance indicator-partial least squares (KPI-PLS) achieves linear indicator fault detection through the appropriate decomposition of variables into related and unrelated parts. This approach uses the projection matrix obtained by general singular value decomposition to decompose the residual space of PLS and thus achieves a more reasonable division of data space. However, KPI-PLS has limitations in handling nonlinear issues. Such problems can be effectively addressed by a local model, just-in-time learning (JITL). Therefore, in this study, an improved KPI-PLS method combined with JITL (JITL-KPI-PLS) is proposed to achieve nonlinear fault detection. The local model is built using hierarchical clustering to improve computational efficiency of JITL for searching relevant samples. By updating the model and control limit in real time, the current status of online samples can be better tracked. Finally, better fault detection performance of the proposed method is confirmed on the Tennessee Eastman benchmark and the Zhoushan thermal power plant.
State reconstruction approach is very useful for sensor fault isolation, reconstruction of faulty measurement and the determination of the number of components retained in the principal components analysis (PCA) model. An extension of this approach based on a Nonlinear PCA (NLPCA) model is described in this paper. The NLPCA model is obtained using five layer neural network. A simulation example is given to show the performances of the proposed approach. © 2007 Institute of Engineering Mechanics, China Earthquake Administration.
The hybrid fault diagnosis method based on a combination of the signed digraph and partial least-squares (PLS) has the advantage of improving the diagnosis resolution, accuracy, and reliability, compared to those of previous qualitative methods, and of enhancing the ability to diagnose multiple fault [Ind. Eng. Chem. Res. 2003, 42, 6145-6154]. In this study, the method is applied for the multiple fault diagnosis of the Tennessee Eastman challenge process. The target process is decomposed using the local qualitative relationships of each measured variable. Linear and quadratic models based on dynamic PLS are built to estimate each measured variable, which is then compared with the estimated value in order to diagnose the fault. Through case studies, the proposed method demonstrated a good diagnosis capability compared with previous statistical methods.
The appearance of this book is quite timely as it provides a much needed state-of-the-art exposition on fault detection and diagnosis, a topic of much interest to industrialists. The material included is well organized with logical and clearly identified parts; the list of references is quite comprehensive and will be of interest to readers who wish to explore a particular subject in depth.
The presentation of the subject material is clear and concise, and the contents are appropriate to postgraduate engineering students, researchers and industrialists alike. The end-of-chapter homework problems are a welcome feature as they provide opportunities for learners to reinforce what they learn by applying theory to problems, many of which are taken from realistic situations.
However, it is felt that the book would be more useful, especially to practitioners of fault detection and diagnosis, if a short chapter on background statistical techniques were provided.
Joe Au
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.
A well-defined variance of reconstruction error (VRE) is proposed to determine the number of principal components in a PCA model for best reconstruction. Unlike most other methods in the literature, this proposed VRE method has a guaranteed minimum over the number of PC's corresponding to the best reconstruction. Therefore, it avoids the arbitrariness of other methods with monotonic indices. The VRE can also be used to remove variables that are little correlated with others and cannot be reliably reconstructed from the correlation-based PCA model. The effectiveness of this method is demonstrated with a simulated process.
In this paper, we discuss a new fault detection and identification approach based on a multiblock partial least squares (MBPLS) method to monitor a complex chemical process and to model a key process quality variable simultaneously. In multivariate statistical process monitoring using MBPLS, four kinds of monitoring statistics are discussed. In particular, new definitions of the block and variable contributions to T2 and Q statistics are proposed and derived in order to identify faults. Also, the relative contribution, which is the ratio of the contribution to the corresponding upper control limit, is considered to find process variables or blocks responsible for faults. As an application study, a large wastewater treatment process in a steel mill plant is monitored and the effluent chemical oxygen demand, which indicates the current process performance, is modeled based on the proposed MBPLS-based fault detection and diagnosis method.
The problem of using time-varying trajectory data measured on many process variables over the finite duration of a batch process is considered. Multiway principal-component analysis is used to compress the information contained in the data trajectories into low-dimensional spaces that describe the operation of past batches. This approach facilitates the analysis of operational and quality-control problems in past batches and allows for the development of multivariate statistical process control charts for on-line monitoring of the progress of new batches. Control limits for the proposed charts are developed using information from the historical reference distribution of past successful batches. The method is applied to data collected from an industrial batch polymerization reactor.
The objective of this paper is to present new properties of the orthogonal projections to latent structures (O-PLS) method developed by Trygg and Wold (J. Chemometrics 2002; 16: 119–128). The original orthogonal signal correction (OSC) filter of Wold et al. (Chemometrics Intell. Lab. Syst. 1998; 44: 175–185) removes systematic variation from X that is unrelated to Y. O-PLS is a more restrictive OSC filter. O-PLS removes only systematic variation in X explained in each PLS component that is not correlated with Y. O-PLS is a slight modification of the NIPALS PLS algorithm, which should make O-PLS a generally applicable preprocessing and filtering method. The computation of the O-PLS components under the constraint of being correlated with one PLS component imposes particular properties on the space spanned by the O-PLS components. This paper is divided into two main sections. First we give an application of O-PLS on near-infrared reflectance spectra of soil samples, showing some graphical properties. Then we give the mathematical justifications of these properties. Copyright © 2004 John Wiley & Sons, Ltd.
In this paper a proof is given that only one of either the X- or the Y-matrix in PLS algorithms needs to be deflated during the sequential process of computing latent vectors. With the aid of this proof the original kernel algorithm developed by Lindgren et al. (J. Chemometrics, 7, 45 (1993)) is modified to provide two faster and more economical algorithms. The performances of these new algorithms are compared with that of De Jong and Ter Braak's (J. Chemometrics, 8, 169 (1994)) modified kernel algorithm in terms of speed and the new algorithms are shown to be much faster. A very fast kernel algorithm for updating PLS models in a recursive manner and for exponentially discounting past data is also presented. © 1997 John Wiley & Sons, Ltd.
This paper provides an overview and analysis of statistical process monitoring methods for fault detection, identification and reconstruction. Several fault detection indices in the literature are analyzed and unified. Fault reconstruction for both sensor and process faults is presented which extends the traditional missing value replacement method. Fault diagnosis methods that have appeared recently are reviewed. The reconstruction-based approach and the contribution-based approach are analyzed and compared with simulation and industrial examples. The complementary nature of the reconstruction- and contribution-based approaches is highlighted. An industrial example of polyester film process monitoring is given to demonstrate the power of the contribution- and reconstruction-based approaches in a hierarchical monitoring framework. Finally we demonstrate that the reconstruction-based framework provides a convenient way for fault analysis, including fault detectability, reconstructability and identifiability conditions, resolving many theoretical issues in process monitoring. Additional topics are summarized at the end of the paper for future investigation. Copyright © 2003 John Wiley & Sons, Ltd.
A novel multivariate statistical process monitoring (MSPM) method based on modified independent component analysis (ICA) is proposed. ICA is a multivariate statistical tool to extract statistically independent components from observed data, which has drawn considerable attention in research fields such as neural networks, signal processing, and blind source separation. In this article, some drawbacks of the original ICA algorithm are analyzed and a modified ICA algorithm is developed for the purpose of MSPM. The basic idea of the approach is to use the modified ICA to extract some dominant independent components from normal operating process data and to combine them with statistical process monitoring techniques. Variable contribution plots to the monitoring statistics (T2 and SPE) are also developed for fault diagnosis. The proposed monitoring method is applied to fault detection and diagnosis in a wastewater treatment process, the Tennessee Eastman process, and a semiconductor etch process and is compared with conventional PCA monitoring methods. The monitoring results clearly illustrate the superiority of the proposed method. © 2006 American Institute of Chemical Engineers AIChE J, 2006
Soft sensors are used widely to estimate a process variable which is difficult to measure online. One of the crucial difficulties of soft sensors is that predictive accuracy drops due to changes of state of chemical plants. To cope with this problem, a regression model can be updated. However, if the model is updated with an abnormal sample, the predictive ability can deteriorate. We have applied the independent component analysis (ICA) method to the soft sensor to increase fault detection ability. Then, we have tried to increase the predictive accuracy. By using the ICA-based fault detection and classification model, the objective variable can be predicted, updating the PLS model appropriately. We analyzed real industrial data as the application of the proposed method. The proposed method achieved higher predictive accuracy than the traditional one. Furthermore, the nonsteady state could be detected as abnormal correctly by the ICA model. © 2008 American Institute of Chemical Engineers AIChE J, 2009
Schemes for monitoring the operating performance of large continuous processes using multivariate statistical projection methods such as principal component analysis (PCA) and projection to latent structures (PLS) are extended to situations where the processes can be naturally blocked into subsections. The multiblock projection methods allow one to establish monitoring charts for the individual process subsections as well as for the entire process. When a special event or fault occurs in a subsection of the process, these multiblock methods can generally detect the event earlier and reveal the subsection within which the event has occurred. More detailed diagnostic methods based on interrogating the underlying PCA/PLS models are also developed. These methods show those process variables which are the main contributors to any deviations that have occurred, thereby allowing one to diagnose the cause of the event more easily. These ideas are demonstrated using detailed simulation studies on a multisection tubular reactor for the production of low-density polyethylene.
A generic preprocessing method for multivariate data, called orthogonal projections to latent structures (O-PLS), is described. O-PLS removes variation from X (descriptor variables) that is not correlated to Y (property variables, e.g. yield, cost or toxicity). In mathematical terms this is equivalent to removing systematic variation in X that is orthogonal to Y. In an earlier paper, Wold et al. (Chemometrics Intell. Lab. Syst. 1998; 44: 175–185) described orthogonal signal correction (OSC). In this paper a method with the same objective but with different means is described. The proposed O-PLS method analyzes the variation explained in each PLS component. The non-correlated systematic variation in X is removed, making interpretation of the resulting PLS model easier and with the additional benefit that the non-correlated variation itself can be analyzed further. As an example, near-infrared (NIR) reflectance spectra of wood chips were analyzed. Applying O-PLS resulted in reduced model complexity with preserved prediction ability, effective removal of non-correlated variation in X and, not least, improved interpretational ability of both correlated and non-correlated variation in the NIR spectra. Copyright © 2002 John Wiley & Sons, Ltd.
A novel soft-sensor model which incorporates PCA (principal component analysis), RBF (Radial Basis Function) networks, and
MSA (Multi-scale analysis), is proposed to infer the properties of manufactured products from real process variables. PCA
is carried out to select the most relevant process features and to eliminate the correlations of input variables; multi-scale
analysis is introduced to acquire much more information and to reduce uncertainty in the system; and RBF networks are used
to characterize the nonlinearity of the process. A prediction of the melt index (MI), or quality of polypropylene produced
in an actual industrial process, is taken as a case study. Research results show that the proposed method provides promising
prediction reliability and accuracy.
Principal component analysis (PCA) is the most commonly used dimensionality reduction technique for detecting and diagnosing faults in chemical processes. Although PCA contains certain optimality properties in terms of fault detection, and has been widely applied for fault diagnosis, it is not best suited for fault diagnosis. Discriminant partial least squares (DPLS) has been shown to improve fault diagnosis for small-scale classification problems as compared with PCA. Fisher's discriminant analysis (FDA) has advantages from a theoretical point of view. In this paper, we develop an information criterion that automatically determines the order of the dimensionality reduction for FDA and DPLS, and show that FDA and DPLS are more proficient than PCA for diagnosing faults, both theoretically and by applying these techniques to simulated data collected from the Tennessee Eastman chemical plant simulator.
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.
Virtual metrology (VM) is the prediction of metrology variables (either measurable or non-measurable) using process state and product information. In the past few years VM has been proposed as a method to augment existing metrology and has the potential to be used in control schemes for improved process control in terms of both accuracy and speed. In this paper, we propose a VM based approach for process control of semiconductor manufacturing processes on a wafer-to-wafer (W2W) basis. VM is realized by utilizing the pre-process metrology data and more importantly the process data from the underlying tools that is generally collected in real-time for fault detection (FD) purposes. The approach is developed for a multi-input multi-output (MIMO) process that may experience metrology delays, consistent process drifts, and sudden shifts in process drifts. The partial least squares (PLS) modeling technique is applied in a novel way to derive a linear regression model for the underlying process, suitable for VM purposes. A recursive moving-window approach is developed to update the VM module whenever metrology data is available. The VM data is then utilized to develop a W2W process control capability using a common run-to-run control technique. The proposed approach is applied to a simulated MIMO process and the results show considerable improvement in wafer quality as compared to other control solutions that only use lot-to-lot metrology information.
A very important problem in industrial applications of PCA and PLS models, such as process modelling or monitoring, is the estimation of scores when the observation vector has missing measurements. The alternative of suspending the application until all measurements are available is usually unacceptable. The problem treated in this work is that of estimating scores from an existing PCA or PLS model when new observation vectors are incomplete. Building the model with incomplete observations is not treated here, although the analysis given in this paper provides considerable insight into this problem. Several methods for estimating scores from data with missing measurements are presented, and analysed: a method, termed single component projection, derived from the NIPALS algorithm for model building with missing data; a method of projection to the model plane; and data replacement by the conditional mean. Expressions are developed for the error in the scores calculated by each method. The error analysis is illustrated using simulated data sets designed to highlight problem situations. A larger industrial data set is also used to compare the approaches. In general, all the methods perform reasonable well with moderate amounts of missing data (up to 20% of the measurements). However, in extreme cases where critical combinations of measurements are missing, the conditional mean replacement method is generally superior to the other approaches.
Near-infrared (NIR) spectra are often pre-processed in order to remove systematic noise such as base-line variation and multiplicative scatter effects. This is done by differentiating the spectra to first or second derivatives, by multiplicative signal correction (MSC), or by similar mathematical filtering methods. This pre-processing may, however, also remove information from the spectra regarding Y (the measured response variable in multivariate calibration applications). We here show how a variant of PLS can be used to achieve a signal correction that is as close to orthogonal as possible to a given Y-vector or Y-matrix. Thus, one ensures that the signal correction removes as little information as possible regarding Y. In the case when the number of X-variables (K) exceeds the number of observations (N), strict orthogonality is obtained. The approach is called orthogonal signal correction (OSC) and is here applied to four different data sets of multivariate calibration. The results are compared with those of traditional signal correction as well as with those of no pre-processing, and OSC is shown to give substantial improvements. Prediction sets of new data, not used in the model development, are used for the comparisons.
A new algorithm for orthogonal signal correction is presented, compared with existing algorithms, and illustrated on an example from near infrared spectroscopy. Given a matrix X of spectral or other high dimensional data and a vector or matrix Y of concentrations or other reference measurements on the same samples, orthogonal signal correction subtracts from X factors that account for as much as possible of the variance in X and are orthogonal to Y. The aim is to improve the performance of a subsequent partial least squares (PLS) regression of Y on X.
Chemometrics, the application of mathematical and statistical methods to the analysis of chemical data, is finding ever widening applications in the chemical process environment. This article reviews the chemometrics approach to chemical process monitoring and fault detection. These approaches rely on the formation of a mathematical/statistical model that is based on historical process data. New process data can then be compared with models of normal operation in order to detect a change in the system. Typical modelling approaches rely on principal components analysis, partial least squares and a variety of other chemometric methods. Applications where the ordered nature of the data is taken into account explicitly are also beginning to see use. This article reviews the state-of-the-art of process chemometrics and current trends in research and applications.
De Jong, S., 1993. SIMPLS: an alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 18: 251–263.A novel algorithm for partial least squares (PLS) regression, SIMPLS, is proposed which calculates the PLS factors directly as linear combinations of the original variables. The PLS factors are determined such as to maximize a covariance criterion, while obeying certain orthogonality and normalization restrictions. This approach follows that of other traditional multivariate methods. The construction of deflated data matrices as in the nonlinear iterative partial least squares (NIPALS)-PLS algorithm is avoided. For univariate y SIMPLS is equivalent to PLS1 and closely related to existing bidiagonalization algorithms. This follows from an analysis of PLS1 regression in terms of Krylov sequences. For multivariate Y there is a slight difference between the SIMPLS approach and NIPALS-PLS2. In practice the SIMPLS algorithm appears to be fast and easy to interpret as it does not involve a breakdown of the data sets.
This paper discusses contribution plots for both the D-statistic and the Q-statistic in multivariate statistical process control of batch processes. Contributions of process variables to the D-statistic are generalized to any type of latent variable model with or without orthogonality constraints. The calculation of contributions to the Q-statistic is discussed. Control limits for both types of contributions are introduced to show the relative importance of a contribution compared to the contributions of the corresponding process variables in the batches obtained under normal operating conditions. The contributions are introduced for off-line monitoring of batch processes, but can easily be extended to on-line monitoring and to continuous processes, as is shown in this paper.
This paper presents a new method to perform fault diagnosis for data-correlation based process monitoring. As an alternative to the traditional contribution plot method, a reconstruction-based contribution for fault diagnosis is proposed based on monitored indices, SPE, T2 and a combined index φ. Analysis of the diagnosability of the traditional contributions and the reconstruction-based contributions is performed. The lack of diagnosability of traditional contributions is analyzed for the case of single sensor faults with large fault magnitudes, whereas for the same case the proposed reconstruction-based contributions guarantee correct diagnosis. Monte Carlo simulation results are provided for the case of modest fault magnitudes by randomly assigning fault sensors and fault magnitudes.
This paper describes the application of multivariate regression
techniques to the Tennessee Eastman benchmark process. Two methods are
applied: linear partial least squares, and a nonlinear variant of this
procedure using a radial basis function inner relation. These methods
are used to create online inferential models of delayed process
measurement. The redundancy so obtained is then used to generate a fault
detection and isolation scheme for these sensors. The effectiveness of
this scheme is demonstrated on a number of test faults