On‐line monitoring of batch processes using a PARAFAC representation

Meng, Xianqiu; Morris, A.J.; Martin, E.B.

doi:10.1002/cem.776

Cited by 59 publications

(29 citation statements)

References 18 publications

(22 reference statements)

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“…It is easy to see that the distribution in Equation (20) could be derived from Equation (17), if each component had the same variance. However, in contrast to the SD, the OD consists of non-normalized variables each of them having its own variance being equal to l a I À1 .…”

Section: The Orthogonal Distance (Od)mentioning

confidence: 98%

“…Often this value is divided by K-A [14,23], or by J-A [24], and then the square root is extracted [14,23,24]. However, following [9,20] we keep value (16) as it is.…”

Section: The Orthogonal Distance (Od)mentioning

confidence: 98%

“…Such an approach is used in reference [19]. In papers [8,9,20] the authors suggest to use another SD distribution…”

Section: Principal Component Analysismentioning

confidence: 98%

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Acceptance areas for multivariate classification derived by projection methods

Pomerantsev

2008

Journal of Chemometrics

120

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In the projection methods (PCA, PLS) two distance measures are of importance. They are the score distance (SD, a.k.a. leverage) and the orthogonal distance (OD, a.k.a. the residual variance). This paper shows that both distance measures can be modeled by the x 2 -distribution. Each model includes a scaling factor that can be described by an explicit equation. Moreover, the models depend on an unknown number of degrees of freedom, which have to be estimated using a training dataset. Such modeling is further applied to classification within the SIMCA framework, and various acceptance areas are built for a given significance level. A triangular area, constructed using the sum of the normalized SD and OD, is deemed to be the most practical. This theoretical notion is supported by three examples. The first is based on a simulated dataset, while the other two employ real world data.

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Section: The Orthogonal Distance (Od)mentioning

confidence: 98%

“…Often this value is divided by K-A [14,23], or by J-A [24], and then the square root is extracted [14,23,24]. However, following [9,20] we keep value (16) as it is.…”

Section: The Orthogonal Distance (Od)mentioning

confidence: 98%

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Acceptance areas for multivariate classification derived by projection methods

Pomerantsev

2008

Journal of Chemometrics

120

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“…There are two main approaches to unfolding the three-way matrix (Dong and McAvoy, 1996;Kosanovich et al, 1996;Albert and Kinley, 2001), which give rise to distinct two-way matrices: • Approach A: Variables × time for each specific batch • Approach B: Batches × times for each specific variable Approach A allows one to analyze the variability among the batches by summarizing the information in the data with respect to both the measured variables and their time variation; in contrast, approach B can be used to obtain information on the variability among the batch variables. Approach B focuses on the local behavior of the process, whilst approach A aims to monitor the final behavior of the batch (Meng et al, 2003). Figure 1 shows schematic diagrams of the unfolding procedures used in approaches A and B.…”

Section: Mpcamentioning

confidence: 99%

On-line Batch Process Monitoring Using Different Unfolding Method and Independent Component Analysis.

Lee

2003

J. Chem. Eng. Japan

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In many industries, the effective monitoring and control of batch processes is crucial to the production of high-quality materials. Several techniques using multivariate statistical analysis have been developed for monitoring and fault detection of batch processes. Multiway principal component analysis (MPCA) has shown a powerful monitoring performance in many industrial batch processes. However, it has shortcomings that all batch lengths should be equalized and future values of batches should be estimated for on-line monitoring. In order to overcome these drawbacks and obtain better monitoring performance, we propose a new statistical method for on-line batch process monitoring that uses different unfolding method and independent component analysis (ICA). If the measured data set contains non-Gaussian latent variables, the ICA solution can extract the original source signal to a much greater extent than the PCA solution since ICA involves higher-order statistics and is not based on the assumption that the latent variables follow a multivariate Gaussian distribution. The proposed monitoring method was applied to fault detection and identification in the simulation benchmark of the fed-batch penicillin production, which is characterized by some fault sources with non-Gaussian characteristics. The simulation results clearly show the power and advantages of the proposed method in comparison to MPCA.

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“…Afterwards, other multiway methods were proposed to build empirical models for its subsequent application in monitoring batch process, such as Tucker models [4] and Parallel Factor Analysis (PARAFAC) [5]. One of the strong assumptions of most of these models is that all batch trajectories have Some authors emphasize the importance of using the warping information that comes out of the synchronization.…”

Section: Introductionmentioning

confidence: 99%

Real-time synchronization of batch trajectories for on-line multivariate statistical process control using Dynamic Time Warping

González-Martínez

Ferrer

Westerhuis

2011

Chemometrics and Intelligent Laboratory Systems

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This paper addresses the real-time monitoring of batch processes with multiple different local time trajectories of variables measured during the process run. For Unfold Principal Component Analysis (U-PCA)-or Unfold Partial Least Squares (U-PLS)-based on-line monitoring of batch processes, batch runs need to be synchronized, not only to have the same time length, but also such that key events happen at the same time. An adaptation from Kassidas et al.'s approach [1] will be introduced to achieve the on-line synchronization of batch trajectories using the Dynamic Time Warping (DTW) algorithm. In the proposed adaptation, a new boundaries definition is presented for accurate on-line synchronization of an ongoing batch, together with a way to adapt mapping boundaries to batch length. A relaxed greedy strategy is introduced to avoid assessing the optimal path each time a new sample is available. The key advantages of the proposed strategy are its computational speed and accuracy for the batch process context. Data from realistic simulations of a fermentation process of the Saccharomyces cerevisae cultivation are used to illustrate the performance of the proposed strategy.

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On‐line monitoring of batch processes using a PARAFAC representation

Cited by 59 publications

References 18 publications

Acceptance areas for multivariate classification derived by projection methods

Acceptance areas for multivariate classification derived by projection methods

On-line Batch Process Monitoring Using Different Unfolding Method and Independent Component Analysis.

Real-time synchronization of batch trajectories for on-line multivariate statistical process control using Dynamic Time Warping

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