Efficient Fault Detection in Nonlinear Industrial Processes: A Reduced Kernel PCA-Based Spectral Clustering Approach

Abstract

Kernel Principal Component Analysis (KPCA) is a powerful tool for nonlinear process monitoring, yet its quadratic computational complexity (O( N2 )) and high memory demands limit its applicability to large-scale industrial systems. This paper proposes a novel Reduced Kernel Principal Component Analysis based on Spectral Clustering (RKPCASpC) paradigm to efficiently address these limitations. For comprehensive comparison and to demonstrate the general efficacy of data reduction, an RKPCAKmeans variant is also developed and evaluated. The proposed and comparative methods are rigorously assessed through extensive case studies on two complex industrial processes: the Tennessee Eastman Process (TEP) and the Ain El Kebira Cement Rotary Kiln Process. Performance is assessed using key metrics, including false alarm rate (FAR), missed detection rate (MDR), detection time delay (DTD), and computation time (CT). Furthermore, gained execution time (GET), gained storage space (GSP), and a composite loss function (J) are considered, providing a comprehensive assessment of the developed paradigms' effectiveness and efficiency. Experimental results clearly demonstrate that both RKPCA approaches achieve substantial computational gains, reducing execution time by over 66% (up to 74.41%) and storage space by over 38% (up to 60.93%) compared to conventional KPCA. The novel RKPCASpC method consistently delivers a superior balance between accuracy and computational efficiency, frequently outperforming RKPCAKmeans and conventional KPCA. The findings confirm that RKPCASpC offers a practical, scalable, and robust solution for real-time nonlinear process monitoring in computationally constrained industrial environments.

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