Monitoring batch processes using multiway principal component analysis

Nomikos, Paul; MacGregor, John F.

doi:10.1002/aic.690400809

Cited by 1,379 publications

(940 citation statements)

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“…Since the first applications of PCA [21], this technique has found its way into a wide range of different application areas, for example signal processing [75], factor analysis [29,44], system identification [77], chemometrics [20,66] and more recently, general data mining [11,70,58] including image processing [17,72] and pattern recognition [47,10], as well as process monitoring and quality control [1,82] including multiway [48], multiblock [52] and multiscale [3] extensions. This success is mainly related to the ability of PCA to describe significant information/variation within the recorded data typically by the first few score variables, which simplifies data analysis tasks accordingly.…”

Section: Introductionmentioning

confidence: 99%

Developments and Applications of Nonlinear Principal Component Analysis – a Review

Krüger

Zhang

Xie

2008

Lecture Notes in Computational Science and Enginee

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Summary.Although linear principal component analysis (PCA) originates from the work of Sylvester [67] and Pearson [51], the development of nonlinear counterparts has only received attention from the 1980s. Work on nonlinear PCA, or NLPCA, can be divided into the utilization of autoassociative neural networks, principal curves and manifolds, kernel approaches or the combination of these approaches. This article reviews existing algorithmic work, shows how a given data set can be examined to determine whether a conceptually more demanding NLPCA model is required and lists developments of NLPCA algorithms. Finally, the paper outlines problem areas and challenges that require future work to mature the NLPCA research field. IntroductionPCA is a data analysis technique that relies on a simple transformation of recorded observation, stored in a vector z ∈ R N , to produce statistically independent score variables, stored in t ∈ R n , n ≤ N :(1.1)Here, P is a transformation matrix, constructed from orthonormal column vectors. Since the first applications of PCA [21], this technique has found its way into a wide range of different application areas, for example signal processing [75], factor analysis [29,44], system identification [77], chemometrics [20,66] and more recently, general data mining [11,70,58] including image processing [17,72] and pattern recognition [47,10], as well as process 2 U. Kruger, J. Zhang, and L. Xie monitoring and quality control [1,82] including multiway [48], multiblock [52] and multiscale [3] extensions. This success is mainly related to the ability of PCA to describe significant information/variation within the recorded data typically by the first few score variables, which simplifies data analysis tasks accordingly. Sylvester [67] formulated the idea behind PCA, in his work the removal of redundancy in bilinear quantics, that are polynomial expressions where the sum of the exponents are of an order greater than 2, and Pearson [51] laid the conceptual basis for PCA by defining lines and planes in a multivariable space that present the closest fit to a given set of points. Hotelling [28] then refined this formulation to that used today. Numerically, PCA is closely related to an eigenvector-eigenvalue decomposition of a data covariance, or correlation matrix and numerical algorithms to obtain this decomposition include the iterative NIPALS algorithm [78], which was defined similarly by Fisher and MacKenzie earlier on [80], and the singular value decomposition. Good overviews concerning PCA are given in Mardia et al. [45], Joliffe [32], Wold et al. [80] and Jackson [30].The aim of this article is to review and examine nonlinear extensions of PCA that have been proposed over the past two decades. This is an important research field, as the application of linear PCA to nonlinear data may be inadequate [49]. The first attempts to present nonlinear PCA extensions include a generalization, utilizing a nonmetric scaling, that produces a nonlinear optimization problem [42] and constructing a curves...

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Section: Introductionmentioning

confidence: 99%

Developments and Applications of Nonlinear Principal Component Analysis – a Review

Krüger

Zhang

Xie

2008

Lecture Notes in Computational Science and Enginee

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“…1). Multiway PCA is equivalent to unfolding the three-dimensional data matrix, X, into a large two-dimensional matrix, X, and then performing a regular PCA (Nomikos and MacGregor, 1994). In case of monitoring batch processes, it is important to determine differences between batches and to project new batches on the model.…”

Section: Multiway Principal Component Analysismentioning

confidence: 99%

“…Therefore, the most basic method of conventional PCA is not directly applicable to batch processes. Nomikos and MacGregor (1994) presented the MPCA approach for monitoring batch processes. MPCA is an extension of PCA for three-dimensional batch data (batch number × variables × time).…”

Section: Introductionmentioning

confidence: 99%

Monitoring of a sequencing batch reactor using adaptive multiblock principal component analysis

Lee

Vanrolleghem²

2003

Biotech & Bioengineering

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Abstract:Multiway principal component analysis (MPCA) for the analysis and monitoring of batch processes has recently been proposed. Although MPCA has found wide applications in batch process monitoring, it assumes that future batches behave in the same way as those used for model identification. In this study, a new monitoring algorithm, adaptive multiblock MPCA, is developed. The method overcomes the problem of changing process conditions by updating the covariance structure recursively. A historical set of operational data of a multiphase batch process was divided into local blocks in such a way that the variables from one phase of a batch run could be blocked in the corresponding blocks. This approach has significant benefits because the latent variable structure can change for each phase during the batch operation. The adaptive multiblock model also allows for easier fault detection and isolation by looking at the relationship between blocks and at smaller meaningful block models, and it therefore helps in the diagnosis of the disturbance. The proposed adaptive multiblock monitoring method is successfully applied to a sequencing batch reactor for biological wastewater treatment.

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“…The T 2 statistic measures the variation of principal components, and the Q statistic measures the variation of nonprincipal components. Later on, many improvements have been studied, such as the multiway PCA for batch processes (Nomikos and MacGregor, 1994), dynamic PCA introducing dynamic behavior into the PCA model (Ku et al, 1995), multiscale PCA based on wavelet analysis (Bakshi, 1998), recursive PCA (Li et al, 2000), dynamic PCA for batch monitoring with time-lagged windows (Chen and Liu, 2002), kernel PCA for nonlinear process monitoring (Cho et al, 2005;Lee et al, 2004;Schölkopf et al, 1998), and Robust multiscale PCA (Wang and Romagnoli, 2005). Qin (2003) reviewed several fault detection indices associated with T 2 statistic and Q statistic and compared the reconstruction-based approach and the contribution-based approach with simulation and industrial examples.…”

Section: Introductionmentioning

confidence: 99%

Fault Detection in Chemical Processes Using Discriminant Analysis and Control Chart

Pei

Yamashita

Yoshida

et al. 2008

J. Chem. Eng. Japan

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This paper presents a fault detection methodology based on the Fisher discriminant analysis (FDA) and individuals control charts (XmR control charts). As the first step, FDA is used to find the optimal discriminant direction between the normal operation data and the fault data. In the next step, XmR control charts on the discriminant direction are used to monitor the process. To reduce the amount of false alarms, we also used a variable selection technique based on the contribution plot of FDA. The performance of the proposed technique is demonstrated through application to the monitoring of the Tennessee Eastman challenge process.

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Monitoring batch processes using multiway principal component analysis

Cited by 1,379 publications

References 53 publications

Developments and Applications of Nonlinear Principal Component Analysis – a Review

Developments and Applications of Nonlinear Principal Component Analysis – a Review

Monitoring of a sequencing batch reactor using adaptive multiblock principal component analysis

Fault Detection in Chemical Processes Using Discriminant Analysis and Control Chart

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