Five PCA-Based Fault Diagnosis Routines (Including KPCA) with Implementation Examples

This document presents five PCA-based fault diagnosis routines, including KPCA implementation, designed for industrial system monitoring. The routines employ either Principal Component Analysis (PCA) or Kernel PCA (KPCA) methodologies for fault detection in industrial processes. Each routine contains comprehensive code annotations explaining the algorithm workflow, key mathematical operations, and implementation specifics. The PCA routines typically involve data standardization, covariance matrix computation, eigenvalue decomposition, and principal component selection using functions like 'zscore' and 'eig'. KPCA implementations extend this with kernel functions (such as Gaussian RBF) for nonlinear feature extraction through kernel matrix computation and eigenvector analysis. Notably, these open-source routines allow users to freely modify and customize the codebase to meet specific application requirements. The implementations include: - Data preprocessing and normalization steps - Principal component calculation and dimension reduction - Statistical monitoring indices (T² and SPE/Q statistics) - Fault detection thresholds calculation - Kernel parameter optimization for KPCA variants - Visualization tools for fault diagnosis results All routines maintain industrial applicability with practical examples demonstrating fault detection sensitivity and false alarm rate control mechanisms.