MATLAB Implementation of KPCA with Fault Diagnosis Capabilities

This KPCA (Kernel Principal Component Analysis) implementation provides a robust foundation for fault detection and diagnosis applications. The code utilizes kernel methods to handle nonlinear data relationships by mapping input data to a high-dimensional feature space using Gaussian kernel functions. Key algorithmic steps include data normalization, kernel matrix computation, eigenvalue decomposition, and projection onto principal components. The implementation generates two essential diagnostic charts: 1. T2 (Hotelling's T-squared) chart: Monitors the variation within the principal component subspace by calculating Mahalanobis distance, where values exceeding control limits indicate abnormal process behavior 2. SPE (Squared Prediction Error) chart: Tracks residuals outside the principal component subspace, with threshold violations signaling model mismatch or novel fault conditions The code structure includes modular functions for kernel computation, center adjustment, and statistical limit calculation using kernel density estimation or empirical methods. Users can customize kernel parameters and control limits based on specific process requirements. This implementation supports batch processing of multivariate data and provides visualization tools for real-time monitoring applications, making it particularly valuable for industrial process control and mechanical system fault detection.