Wavelet functional principal component analysis for batch process monitoring

Abstract To facilitate the understanding and analysis of process conditions, a novel wavelet functional principal component analysis is proposed for monitoring batch processes from the functional perspective. In the proposed method, the variables’ trajectories are taken as smooth functions instead of discrete vectors. To this end, the original discrete variables are transferred into continuous functions using wavelet basis functions in an active way. This can not only highlight the subtle shape differences between the normal and faulty variables trajectories but also easily address the uneven-length issue in practical batch processes. Additionally, without unfolding the operation, the 3D matrix is transferred into the functional matrix directly. The functional principal component analysis method is then performed on the functional space to establish monitoring models. Thanks to the compact-support characteristics of the wavelet functions, the proposed method can be directly applied to within-batch detection without data pre-treatment. A numerical case, a case of the simulated penicillin fermentation process, and a case of the laboratorial injection molding process are given to demonstrate the effectiveness of the proposed method.

[1]  Weiwei Dong,et al.  Phase Analysis and Identification Method for Multiphase Batch Processes with Partitioning Multi-way Principal Component Analysis (MPCA) Model , 2012 .

[2]  Si-Zhao Joe Qin,et al.  Survey on data-driven industrial process monitoring and diagnosis , 2012, Annu. Rev. Control..

[3]  Julian Morris,et al.  Progressive multi-block modelling for enhanced fault isolation in batch processes , 2014 .

[4]  Jie Zhang,et al.  Window-Based Stepwise Sequential Phase Partition for Nonlinear Batch Process Monitoring , 2016 .

[5]  M. Reuss,et al.  A mechanistic model for penicillin production , 2007 .

[6]  Jesús Picó,et al.  On-line monitoring of batch processes based on PCA: does the modelling structure matter? [corrected]. , 2009, Analytica chimica acta.

[7]  Chunhui Zhao,et al.  Subspace decomposition and critical phase selection based cumulative quality analysis for multiphase batch processes , 2017 .

[8]  J. Ramsay,et al.  Some Tools for Functional Data Analysis , 1991 .

[9]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[10]  Junghui Chen,et al.  Application of wavelet analysis and decision tree in UTDR data for diagnosis of membrane filtration , 2012 .

[11]  Junghui Chen,et al.  Derivation of function space analysis based PCA control charts for batch process monitoring , 2001 .

[12]  Furong Gao,et al.  A survey on multistage/multiphase statistical modeling methods for batch processes , 2009, Annu. Rev. Control..

[13]  Ali Cinar,et al.  Statistical monitoring of multistage, multiphase batch processes , 2002 .

[14]  Yi Yang.  Injection molding control : from process to quality , 2004 .

[15]  John F. MacGregor,et al.  Multi-way partial least squares in monitoring batch processes , 1995 .

[16]  Frans van den Berg,et al.  Correlation optimized warping and dynamic time warping as preprocessing methods for chromatographic data , 2004 .

[17]  J. Ramsay.  When the data are functions , 1982 .

[18]  A. Cuevas.  A partial overview of the theory of statistics with functional data , 2014 .

[19]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Furong Gao,et al.  Review of Recent Research on Data-Based Process Monitoring , 2013 .

[21]  B. Bakshi.  Multiscale PCA with application to multivariate statistical process monitoring , 1998 .

[22]  P. Vieu,et al.  Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics) , 2006 .

[23]  Yi Hu,et al.  Enhanced batch process monitoring using just-in-time-learning based kernel partial least squares , 2013 .

[24]  Krist V. Gernaey,et al.  Functional unfold principal component regression methodology for analysis of industrial batch process data , 2016 .

[25]  Junghui Chen,et al.  Sequential local-based Gaussian mixture model for monitoring multiphase batch processes , 2018 .

[26]  P. A. Taylor,et al.  Synchronization of batch trajectories using dynamic time warping , 1998 .

[27]  J. Macgregor,et al.  Monitoring batch processes using multiway principal component analysis , 1994 .

[28]  Chee Peng Lim,et al.  A hybrid neural network model for rule generation and its application to process fault detection and diagnosis , 2007, Eng. Appl. Artif. Intell..

[29]  Bhavik R. Bakshi,et al.  Wave‐net: a multiresolution, hierarchical neural network with localized learning , 1993 .

[30]  Jun Chen,et al.  A data-driven wavelet-based approach for generating jumping loads , 2018, Mechanical Systems and Signal Processing.

[31]  Alberto Ferrer,et al.  Real-time synchronization of batch trajectories for on-line multivariate statistical process control using Dynamic Time Warping , 2011 .

[32]  Jie Zhang,et al.  Fault Localization in Batch Processes through Progressive Principal Component Analysis Modeling , 2011 .

[33]  ChangKyoo Yoo,et al.  Fault detection of batch processes using multiway kernel principal component analysis , 2004, Comput. Chem. Eng..

[34]  T. McAvoy,et al.  Nonlinear principal component analysis—Based on principal curves and neural networks , 1996 .

[35]  Gülnur Birol,et al.  A modular simulation package for fed-batch fermentation: penicillin production , 2002 .

[36]  J. O. Ramsay,et al.  Functional Data Analysis (Springer Series in Statistics) , 1997 .

[37]  Ma Yao,et al.  Fault detection of batch processes based on multivariate functional kernel principal component analysis , 2015 .

[38]  Junghui Chen,et al.  On-line batch process monitoring using MHMT-based MPCA , 2006 .