Wavelet functional principal component analysis for batch process monitoring

Liu, Jingxiang; Chen, Junghui; Wang, Dan

doi:10.1016/j.chemolab.2019.103897

Cited by 27 publications

(17 citation statements)

References 35 publications

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“…Most of the functional data can not be observed directly so that the latent stochastic process of interest must be reconstructed from discrete observations of each sample curve on a fixed or random time grid, which can be dense or sparse and different for the sample individuals. One usual form of reconstructing the functional form of sample curves is by an expansion in terms of basis functions such as Fourier, B-splines or wavelets [10][11][12][13][14][15]. The equivalence between FPCA of basis expansion of functional data and certain multivariate PCA in terms of the basis coefficients data matrix was studied in [8].…”

Section: Introductionmentioning

confidence: 99%

New Modeling Approaches Based on Varimax Rotation of Functional Principal Components

2020

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Functional Principal Component Analysis (FPCA) is an important dimension reduction technique to interpret the main modes of functional data variation in terms of a small set of uncorrelated variables. The principal components can not always be simply interpreted and rotation is one of the main solutions to improve the interpretation. In this paper, two new functional Varimax rotation approaches are introduced. They are based on the equivalence between FPCA of basis expansion of the sample curves and Principal Component Analysis (PCA) of a transformation of the matrix of basis coefficients. The first approach consists of a rotation of the eigenvectors that preserves the orthogonality between the eigenfunctions but the rotated principal component scores are not uncorrelated. The second approach is based on rotation of the loadings of the standardized principal component scores that provides uncorrelated rotated scores but non-orthogonal eigenfunctions. A simulation study and an application with data from the curves of infections by COVID-19 pandemic in Spain are developed to study the performance of these methods by comparing the results with other existing approaches.

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Section: Introductionmentioning

confidence: 99%

New Modeling Approaches Based on Varimax Rotation of Functional Principal Components

2020

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“…In this work, DB4 wavelet is applied for illustration and application owing to its good properties of multi-scale, orthogonal and compact support. To get more delicate model and better modelling performance, an active learning strategy is recently proposed to determine the numbers and locations of wavelet basis functions [4] [20].…”

Section: B Active Strategy To Determine Wavelet Basis Functionsmentioning

confidence: 99%

“…Repeat the above steps until the approximation error meet the predefined threshold. More details about the active strategy can be found in [4] [20], which is thus omitted here.…”

Section: Figure 1 a Schematic Diagram About The Active Strategy To Cmentioning

confidence: 99%

“…Therefore, functional data analysis (FDA) methods can be applied to spectra data analysis [18]- [21]. Explanatorily, FDA deals with the analysis and the theory of data that are in the form of functions [19] [20]. By comparison, FDA methods are suitable for the irregular nonstationary time series analysis and emphasize the smoothness of the variable trajectories [22] [23].…”

Section: Introductionmentioning

confidence: 99%

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Functional Soft Sensor Based on Spectra Data for Predicting Multiple Quality Variables

et al. 2020

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In many complex chemical processes, such as ethanol fermentation process, prediction of the multivariate quality variables based on spectra data presents a great challenge because the dimensions of the spectra far exceed their sampling number. To address this problem, the dimension reduction of the predictors is necessary. It can be conducted either by regressing on components or by smoothing methods with basis functions. Based on the functional data analysis methods, this work introduces a novel wavelet functional partial least squares (WFPLS), which combines both of the foregoing dimension-reduction approaches. The high-dimensional spectra can be well fitted by fewer wavelet basis functions in the proposed method. Using the proposed WFPLS method does not require the measured data to be linear and to be sampled on a regular basis. It will be proved that the proposed WFPLS method can be finally transferred into the traditional PLS method in computation. By comparison with the existing prediction methods, the advantages of the proposed method are well demonstrated via a numerical case and an ethanol fermentation experiment. INDEX TERMS Wavelet functional partial least squares, soft sensor, functional data analysis, spectra data analysis, active learning.

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“…The use of PCA and PLS for process monitoring is well established, especially for continuous processes [13][14][15][16]. When it comes to the monitoring and troubleshooting of batch processes, methodologies and applications typically refer to individual units rather than to plant-wide systems [17][18][19][20][21][22][23][24][25]. That is not surprising, as the task of isolating the root cause of an observed product quality inconsistency may be relatively easy if the unit causing the inconsistency is known in advance, so that the task boils down to identifying what is going wrong with that particular unit.…”

Section: Introductionmentioning

confidence: 99%

Backstepping Methodology to Troubleshoot Plant-Wide Batch Processes in Data-Rich Industrial Environments

et al. 2021

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Troubleshooting batch processes at a plant-wide level requires first finding the unit causing the fault, and then understanding why the fault occurs in that unit. Whereas in the literature case studies discussing the latter issue abound, little attention has been given so far to the former, which is complex for several reasons: the processing units are often operated in a non-sequential way, with unusual series-parallel arrangements; holding vessels may be required to compensate for lack of production capacity, and reacting phenomena can occur in these vessels; and the evidence of batch abnormality may be available only from the end unit and at the end of the production cycle. We propose a structured methodology to assist the troubleshooting of plant-wide batch processes in data-rich environments where multivariate statistical techniques can be exploited. Namely, we first analyze the last unit wherein the fault manifests itself, and we then step back across the units through the process flow diagram (according to the manufacturing recipe) until the fault cannot be detected by the available field sensors any more. That enables us to isolate the unit wherefrom the fault originates. Interrogation of multivariate statistical models for that unit coupled to engineering judgement allow identifying the most likely root cause of the fault. We apply the proposed methodology to troubleshoot a complex industrial batch process that manufactures a specialty chemical, where productivity was originally limited by unexplained variability of the final product quality. Correction of the fault allowed for a significant increase in productivity.

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Wavelet functional principal component analysis for batch process monitoring

Cited by 27 publications

References 35 publications

New Modeling Approaches Based on Varimax Rotation of Functional Principal Components

New Modeling Approaches Based on Varimax Rotation of Functional Principal Components

Functional Soft Sensor Based on Spectra Data for Predicting Multiple Quality Variables

Backstepping Methodology to Troubleshoot Plant-Wide Batch Processes in Data-Rich Industrial Environments

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