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 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.

中文翻译：

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基于相关维数和分形分析的动态核PCA非线性动力过程故障检测与诊断

摘要 开发了一种新的动态核 PCA (DKPCA) 方法，用于非线性动态系统中的过程监控。经典的 DKPCA 方法仍然表现出模糊的线性假设来确定主成分的数量并构建动态结构。本文通过强大的非线性分形维数(FDim)理论构建了最优的静态PCA(SPCA)和动态PCA(DPCA)结构。虽然 DKPCA 提供了非线性动态系统的通用数据驱动建模，但分形相关维数提供了对非线性动态和混沌行为的数据复杂性计数的内在度量。提出的基于分形的 DKPCA（FDKPCA）整合了两种策略来克服 SPCA/DPCA/DKPCA 的缺点，FDim 允许验证拟合程度并确保最佳降维。使用具有真实异构数据的过程网络优化 (PRONTO) 基准测试通过七个应用程序验证了新颖的故障检测和诊断方法，与现代方法相比，FDKPCA 表现出卓越的性能。