Fault detection & diagnosis, correlation dimension, fractal analysis dynamic kernel PCA

What is it about?

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 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.

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Why is it important?

•Fractal Analysis is investigated for Optimized Dimensionality Reduction in Nonlinear Dynamical Processes. •Nonlinear Correlation Dimension improves Statistical Models’ accuracy and prevents overfitting/underfitting. •It ensures Intrinsic number of principal components in static PCA and optimized dynamical PCA structure. •Accurate and robust extraction of Nonlinear Dynamical relations in Fractal-based Dynamic Kernel PCA. •FDKPCA outperforms contemporary methods to detect real faults in PRONTO heterogeneous benchmark.