Nonlinear Fault Detection of Batch Processes Using Functional Local Kernel Principal Component Analysis

Abstract

In order to guarantee and improve the product quality, the data-driven fault detection technique has been widely used in industry. For three-way datasets of batch process in industry process (i.e., batch × variable × time), a novel method named functional local kernel principal component analysis (FLKPCA) is proposed. Since the variables' trajectories often show functional nature and can be considered as smooth functions rather than just vectors. Firstly, the variables' trajectory is expressed as the combination of smooth basis functions using functional data analysis (FDA), which means that the datasets of batches process would be transformed from the three-ways array into two-ways function matrix. Then, kernel locality preserving projections (LKPCA) is used to perform dimensionality reduction on two-way function matrix directly. Different from kernel principal component analysis (KPCA). LKPCA aims at preserving the both local and global structure of the data in a new optimization objective. Consequently, FLKPCA could more effectively seek the potential information that hidden in the three-ways datasets. Lastly, the effectiveness of the proposed approach is illustrated by the benchmark of fed-batch penicillin fermentation process and the hot strip rolling process. INDEX TERMS Kernel functional local principal component analysis, process monitoring, fault detection, function data analysis.

Proceedings of The First SIMS EUROSIM Conference on Modelling and Simulation, SIMS EUROSIM 2021, and 62nd International Conference of Scandinavian Simulation Society, SIMS 2021, September 21-23, Virtual Conference, Finland

“…Functional data representation is used in a multivariate functional kernel principal component analysis in (H. Wang & Yao, 2015). The functional local kernel principal component analysis is also in (F. He & Zhang, 2020). For more information about the FDA's fundamentals, see Ramsay et al works on Functional Data Analysis (Ramsay & Silvermann, 1998).…”

“…The KPCA can accommodate underlying nonlinear characteristics and show itself to outperform the PCA when performing feature extraction and classification on datasets with nonlinear behavior. (Lee et al, 2004) Works on fault detection using KPCA can be further viewed in the works by Lee et al (2004), H. Want andYao (2015), and He and Zhang (2020). For a fundamental look into Kernel methods, the reader is referred to the work of Schölkopf et al (1997).…”

Specific Emitter Identification through Multi-Domain Mixed Kernel Canonical Correlation Analysis

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“…Tao et al have introduced a further dynamic‐weight principal component analysis (DWPCA) methodology for FDI and have applied their method for Tennessee Eastman (TE) process 11 . Functional Local Kernel Principal Component Analysis (FLKPCA) has been used for nonlinear fault detection and has been tested on the fed‐batch penicillin fermentation process in Reference 12. In Reference 13, a fault‐tolerant control method is presented for unknown cooperative quadrotors subject to nonlinearities.…”