Fault detection and diagnosis of nonlinear dynamical processes through correlation dimension and fractal analysis based dynamic kernel PCA

A novel Dynamic Kernel PCA (DKPCA) method is developed for process monitoring in nonlinear dynam-ical systems. Classical DKPCA approaches still exhibit vague linearity assumptions to determine the number of principal components and to construct the dynamical structure. The optimal Static PCA (SPCA) and Dynamic PCA (DPCA) structures are constructed herein through the powerful theory of the nonlinear Fractal Dimension (FDim). While DKPCA offers a generic data-driven modelling of nonlinear dynamical systems, the fractal correlation dimension provides an intrinsic measure of the data complexity counting for the nonlinear dynamics and the chaotic behaviour. The proposed Fractal-based DKPCA (FDKPCA) integrates the two strategies to overcome SPCA/DPCA/DKPCA shortcomings, FDim allows verifying the degree of fitting and ensures optimal dimensionality reduction. The novel fault detection and diagnosis method is validated through seven applications using the Process Network Optimization (PRONTO) benchmark with real heterogeneous data, FDKPCA showed superior performance compared to contemporary approaches. (c) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This study introduces a novel Dynamic Kernel PCA method for process monitoring in nonlinear dynamical systems, using the powerful theory of the nonlinear Fractal Dimension. The Fractal-based DKPCA integrates the two strategies to overcome the shortcomings of traditional methods and showed superior performance in fault detection and diagnosis compared to contemporary approaches.