Machine Learning-Based Reduced Kernel PCA Model for Nonlinear Chemical Process Monitoring
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Machine Learning-Based Reduced Kernel PCA Model for Nonlinear Chemical Process Monitoring M.-F. Harkat1 · A. Kouadri2 · R. Fezai3 · M. Mansouri4
· H. Nounou4 · M. Nounou5
Received: 8 December 2019 / Revised: 14 March 2020 / Accepted: 21 April 2020 © Brazilian Society for Automatics–SBA 2020
Abstract Principal component analysis (PCA) is a popular tool for linear dimensionality reduction and fault detection. Kernel PCA (KPCA) is the nonlinear form of the PCA, which better exploits a complicated spatial structure of high-dimensional features, where a kernel function implicitly defines a nonlinear transformation into a feature space wherein standard PCA is performed. Despite its success and flexibility, conventional KPCA might not perform properly because the use of KPCA for a large-sized training dataset imposes a high computational load and a significant storage memory space since the required elements used for modelling have to be saved and used for monitoring, as well. To address this problem, a reduced KPCA (RKPCA) for fault detection of chemical processes is developed. RKPCA is a novel machine learning tool which merges dimensionality reduction, supervised learning as well as kernel selection. This novel method is used to reduce the size of recorded measurements while maintaining the most relevant data features. The removed observations, including redundant samples that are linearly correlated in the collected measurements, are described by only one sample. The obtained uncorrelated observations via PCA technique are then employed to identify the reduced KPCA model by which Hotelling T 2 and squared predictive error or Q statistics are extracted for detection purposes. Besides, their combination is also used as a detection index. The performance of the proposed process monitoring technique is illustrated through its application to Tennessee Eastman process. The obtained results demonstrate the effectiveness of the developed RKPCA technique in detecting various faults with remarkably reduced computation time and memory storage space. Keywords Fault detection (FD) · Principal component analysis (PCA) · Kernel PCA (KPCA) · Reduced KPCA · Tennessee Eastman (TE) process
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M. Mansouri [email protected] M.-F. Harkat [email protected] A. Kouadri [email protected] R. Fezai [email protected] H. Nounou [email protected] M. Nounou [email protected]
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LASMA, Badji Mokhtar - Annaba University, P.O. Box 12, 23000 Annaba, Algeria Signals and Systems Laboratory, Institute of Electrical and Electronics Engineering, University M Hamed Bougara of Boumerdes, 3500 Boumerdes, Algeria
Abbreviations and List of Symbols X Training data matrix x Measurement vector m Number of variables N Number of samples Covariance matrix of X Diagonal eigenvalue matrix σ Width of a Gaussian function φ Mapping function K Kernel matrix 3
Research Laboratory of Automation, Signal Processing and Image, National Engineering School of Monastir, 5019 Monastir, Tunisia
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Department of Ele
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