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

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