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Moving window kernel PCA for adaptive monitoring of nonlinear processes

CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2009年第2期96卷 132-143页

作者： Liu, Xueqin Kruger, Uwe Littler, Tim Xie, Lei Wang, Shuqing Petr Inst Dept Elect Engn Abu Dhabi U Arab Emirates Queens Univ Belfast Sch Elect Elect Engn & Comp Sci Belfast BT9 5AH Antrim North Ireland Zhejiang Univ Inst Cyber Syst & Control State Key Lab Ind Control Technol Hangzhou 310027 Peoples R China

This paper discusses the monitoring of complex nonlinear and time-varying processes. Kernel principal component analysis (KPCA) has gained significant attention as a monitoring tool for nonlinear systems in recent years but relies on a fixed model that cannot be employed for time-varying systems. The contribution of this article is the development of a numerically efficient and memory saving moving window KPCA (MWKPCA) monitoring approach. The proposed technique incorporates an up- and downdating procedure to adapt (i) the data mean and covariance matrix in the feature space and (ii) approximates the eigenvalues and eigenvectors of the Gram matrix. The article shows that the proposed MWKPCA algorithm has a Computation complexity of O(N-2), whilst batch techniques, e.g. the Lanczos method, are of O(N-3). Including the adaptation of the number of retained components and an I-step ahead application of the MWKPCA monitoring model, the paper finally demonstrates the utility of the proposed technique using a simulated nonlinear time-varying system and recorded data from an industrial distillation column. (c) 2009 Elsevier B.V. All rights reserved.

关键词： Nonlinear process Kernel PCA Moving window multivariate statistical process control Adaptive Numerically efficient

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An adaptive thresholding-based process variability monitoring

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JOURNAL OF QUALITY TECHNOLOGY 2019年第3期51卷 242-256页

作者： Abdella, Galal M. Kim, Jinho Kim, Sangahn Al-Khalifa, Khalifa N. Jeong, Myong K. (MK) Hamouda, Abdel Magid Elsayed, Elsayed A. Qatar Univ Dept Mech & Ind Engn Doha Qatar Siena Coll Dept Business Analyt & Actuarial Sci Loudonville NY USA Rutgers State Univ Dept Ind & Syst Engn Piscataway NJ 08854 USA

In high-dimensional processes, monitoring process variability is considerably difficult due to the large number of variables and the limited number of samples. Monitoring changes in the covariance matrix of a multivariate process is often used for monitoring process variability under the assumption that only a few elements in the covariance matrix are changed simultaneously from the in-control values. The existing LASSO-based covariance monitoring charts in the high-dimensional settings provide good performance in detecting some shift patterns depending on the prespecified tuning parameter. In practice, control charts that perform reasonably well over various shift patterns are desired when shift patterns are unknown. In this article, we propose a control chart based on an adaptive LASSO-thresholding for monitoring changes in the covariance matrix. The performance of the proposed chart, which is called the ALT-norm chart, is evaluated for various shift patterns and compared with the existing penalized likelihood-based methods. The results show the effectiveness of the proposed chart. Finally, we illustrate the advantages of the ALT-norm chart through simulated and real data from both the semiconductor industry and a high-dimensional milling process.

关键词： adaptive thresholding estimation monitoring covariance matrix multivariate statistical process control

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A multivariate Robust control Chart for Individual Observations

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JOURNAL OF QUALITY TECHNOLOGY 2009年第3期41卷 259-271页

作者： Chenouri, Shoja'eddin Steiner, Stefan H. Variyath, Asokan Mulayath Univ Waterloo Dept Stat & Actuarial Sci Waterloo ON N2L 3G1 Canada Mem Univ Newfoundland Dept Math & Stat St John NF A1C 5S7 Canada

To monitor a multivariate process, a classical Hotelling's T-2 control chart is often used. However, it is well known that such control charts are very sensitive to the presence of outlying observations in the historical Phase I data used to set the control limit. In this paper, we propose a robust Hotelling's T-2-type control chart for individual observations based on highly robust and efficient estimators of the mean vector and covariance matrix known. as reweighted minimum covariance determinant (RMCD) estimators. We illustrate how to set the control limit for the proposed control chart, study its performance using simulations, and illustrate implementation in a real-world example.

关键词： Hotelling's T-2 multivariate Robust Estimation of Location and Scatter multivariate statistical process control Outliers Reweighted Minimum Covariance Determinant Estimators

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A Variable-Selection-Based multivariate EWMA Chart for process Monitoring and Diagnosis

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JOURNAL OF QUALITY TECHNOLOGY 2012年第3期44卷 209-230页

作者： Jiang, Wei Wang, Kaibo Tsung, Fugee Shanghai Jiao Tong Univ Antai Coll Econ & Management Shanghai 200052 Peoples R China Tsinghua Univ Dept Ind Engn Beijing 100084 Peoples R China Hong Kong Univ Sci & Technol Dept Ind Engn & Logist Management Hong Kong Hong Kong Peoples R China

Fault detection and root cause identification are both important tasks in multivariate statistical process control (MSPC) for improving process and product quality. Most traditional control charts, including Hotelling's T-2 chart and the multivariate Exponential Weighted Moving Average (MEWMA) chart, separate the two tasks into independent and successive procedures by signaling the existence of process faults followed by auxiliary methods to locate root causes. This paper proposes an integrated procedure, a Variable-Selection-based MEWMA (VS-MEWMA) chart, for multivariate process monitoring and fault diagnosis by utilizing dimensionality reduction techniques. The VS-MEWMA chart first locates potentially out-of-control variables via variable selection and then deploys such information in the monitoring statistics with the reduction in dimensionality providing increased sensitivity to out-of-control conditions. When a signal is given, the algorithm also identifies the suspected variables for further root cause diagnosis. Both numerical simulations and real examples are presented to illustrate the performance of the proposed chart, as well as design guidelines.

关键词： Average Run Length Fault Diagnosis Forward Selection MEWMA multivariate statistical process control

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A large-scale statistical process control approach for the monitoring of electronic devices assemblage

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COMPUTERS & CHEMICAL ENGINEERING 2012年 39卷 163-169页

作者： Reis, Marco S. Delgado, Pedro Univ Coimbra Dept Chem Engn CIEPQPF P-3030790 Coimbra Portugal

In this paper, we present a new procedure for monitoring the assembly process of electronic devices. Monitoring the status of this operation is a challenge, as the number of quality features under monitoring is very large (order of thousands) and the number of samples available quite low (order of dozens). We propose an efficient approach for the on-line and at-line monitoring of such a process, by addressing two, hierarchically related. problems: (i) detection of faulty units (printed circuits boards with abnormal deposits): (ii) given a faulty unit, find a candidate set of solder deposits responsible for the anomaly. Our methodology is based on a latent variable framework using PCA for effectively extracting the normal behavior of the process. Both the variability in the PCA plane and around it (residuals) are considered. We have tested the proposed approach with real industrial data, and the results achieved illustrate its good discrimination ability. (c) 2011 Elsevier Ltd. All rights reserved.

关键词： Printed circuits boards Principal components analysis multivariate statistical process control Receiver operating characteristic

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Fault detection in the Tennessee Eastman benchmark process using dynamic principal components analysis based on decorrelated residuals (DPCA-DR)

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2013年 125卷 101-108页

作者： Rato, Tiago J. Reis, Marco S. Univ Coimbra CIEPQPF Dept Chem Engn P-3030790 Coimbra Portugal

Current multivariate control charts for monitoring large scale industrial processes are typically based on latent variable models, such as principal component analysis (PCA) or its dynamic counterpart when variables present auto-correlation (DPCA). In fact, it is usually considered that, under such conditions, DPCA is capable to effectively deal with both the cross- and auto-correlated nature of data. However, it can easily be verified that the resulting monitoring statistics (T-2 and Q, also referred by SPE) still present significant auto-correlation. To handle this issue, a set of multivariate statistics based on DPCA and on the generation of decorrelated residuals were developed, that present low auto-correlation levels, and therefore are better positioned to implement SPC in a more consistent and stable way (DPCA-DR). The monitoring performance of these statistics was compared with that from other alternative methodologies for the well-known Tennessee Eastman process benchmark. From this study, we conclude that the proposed statistics had the highest detection rates on 19 out of the 21 faults, and are statistically superior to their PCA and DPCA counterparts. DPCA-DR statistics also presented lower auto-correlation, which simplifies their implementation and improves their reliability. (C) 2013 Elsevier B.V. All rights reserved.

关键词： multivariate statistical process control Principal component analysis Dynamic principal component analysis Missing data imputation Tennessee Eastman benchmark process

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Monitoring multivariate process variability via eigenvalues

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COMPUTERS & INDUSTRIAL ENGINEERING 2017年 113卷 269-281页

作者： Fan, Jinyu Shu, Lianjie Zhao, Honghao Yeung, Hangfai Univ Macau Fac Business Adm Zhuhai Guangdong Peoples R China Macau Univ Sci & Technol Sch Business Macau Peoples R China

Various methods have been proposed to monitor changes in a process covariance matrix. In view that a covariance matrix can be fully defined by its eigenvalues and eigenvectors, this paper suggests monitoring the covariance matrix based on eigenvalues as another alternative. Although there are some recent discussions about the use of eigenvalues for hypothesis testing in multivariate analysis, the use of them for monitoring covariance matrix changes has been less studied in multivariate quality control. The simulation results show that the proposed method performs especially well under simultaneous shifts in both variance and correlation elements and competitively under shifts in variance or correlation elements only, compared to the existing approaches. This demonstrates a good property of the proposed method being able to provide a robust detection performance under a wide variety of scenarios. A real example is also provided to illustrate the implementation of the proposed method.

关键词： multivariate statistical process control Variability Sparsity Covariance matrix Eigenvalues

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A nonparametric fault isolation approach through one-class classification algorithms

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IIE TRANSACTIONS 2011年第7期43卷 505-517页

作者： Kim, Seoung Bum Sukchotrat, Thuntee Park, Sun-Kyoung Korea Univ Sch Ind Management Engn Seoul South Korea Hanyang Cyber Univ Sch Business Adm Seoul South Korea Hanyang Cyber Univ Sch Business Adm Seoul 13379 South Korea Korea Univ Sch Ind Management Engn Seoul South Korea

multivariate control charts provide control limits for the monitoring of processes and detection of abnormal events so that processes can be improved. However, these multivariate control charts provide limited information about the contribution of any specific variable to the out-of-control alarm. Although many fault isolation methods have been developed to address this deficiency, most of these methods require a parametric distributional assumption that restricts their applicability to specific problems of process control and thus limits their broader usefulness. This study proposes a nonparametric fault isolation method based on a one-class classification algorithm that overcomes the limitation posed by the parametric assumption in existing fault isolation methods. The proposed approach decomposes the monitoring statistics obtained from a one-class classification algorithm into components that reflect the contribution of each variable to the out-of-control signal. A bootstrap approach is used to determine the significance of each variable. A simulation study is presented that examines the performance of the proposed method under various scenarios and to results are compared with those obtained using the T2 decomposition method. The simulation results reveal that the proposed method outperforms the T2 decomposition method in non-normal distribution cases.

关键词： Decomposition fault isolation multivariate statistical process control nonparametric one-class classification algorithm

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One class classifiers for process monitoring illustrated by the application to online HPLC of a continuous process

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JOURNAL OF CHEMOMETRICS 2010年第3-4期24卷 96-110页

作者： Kittiwachana, Sila Ferreira, Diana L. S. Lloyd, Gavin R. Fido, Louise A. Thompson, Duncan R. Escott, Richard E. A. Brereton, Richard G. Univ Bristol Sch Chem Ctr Chemometr Bristol BS8 1TS Avon England GlaxoSmithKline Stevenage SG1 2NY Herts England GlaxoSmithKline Old Powder Mills Tonbridge TN11 9AN Kent England

In process monitoring, a representative out-of-control class of samples cannot be generated. Here, it is assumed that it is possible to obtain a representative subset of samples from a single 'in-control class' and one class classifiers namely Q and D statistics (respectively the residual distance to the disjoint PC model and the Mahalanobis distance to the centre of the QDA model in the projected PC space), as well as support vector domain description (SVDD) are applied to disjoint PC models of the normal operating conditions (NOC) region, to categorise whether the process is in-control or out-of-control. To define the NOC region, the cumulative relative standard deviation (CRSD) and a test of multivariate normality are described and used as joint criteria. These calculations were based on the application of window principal components analysis (WPCA) which can be used to define a NOC region. The D and Q statistics and SVDD models were calculated for the NOC region and percentage predictive ability (%PA), percentage model stability (%MS) and percentage correctly classified (%CC) obtained to determine the quality of models from 100 training/test set splits. Q, D and SVDD control charts were obtained, and 90% confidence limits set up based on multivariate normality (D and Q) or SVDD D value (which does not require assumptions of normality). We introduce a method for finding an optimal radial basis function for the SVDD model and two new indices of percentage classification index (%CI) and percentage predictive index (%PI) for non-NOC samples are also defined. The methods in this paper are exemplified by a continuous process studied over 105.11 h using online HPLC. Copyright (C) 2010 John Wiley & Sons, Ltd.

关键词： control charts multivariate statistical process control one class classifiers quadratic discriminant analysis support vectors

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Blind Identification of Manufacturing Variation Patterns by Combining Source Separation Criteria

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TECHNOMETRICS 2008年第3期50卷 332-343页

作者： Shan, Xuemei Apley, Daniel W. Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA

Blind source separation recently has been investigated for blindly identifying variation patterns in multivariate manufacturing data, to aid in tracking down and eliminating root causes of manufacturing variation. Many different criteria can be used in blind separation algorithm, the performance and applicability of which depend on conditions that generally are not known a priori. We present a method for automatically combining the different criteria so as to directly minimize the mean squared estimation error. The resulting algorithm is more effective and more robust than counterparts that use other means of combining the criteria.

关键词： Blind source separation Factor rotation Manufacturing variation reduction multivariate statistical process control Principal components analysis

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