MATLAB Implementation of Principal Component Analysis for Fault Detection in TE Process Data

In this document, we will implement Principal Component Analysis (PCA) for fault detection using fault data (Fault Type 1) generated by the Tennessee Eastman (TE) process model. PCA is a statistical technique that transforms original correlated variables into a set of linearly uncorrelated variables called principal components. These principal components capture the maximum variance in the dataset and help identify underlying patterns and anomalies. Our implementation involves several key MATLAB functions: using pca() to compute principal components, calculating Hotelling's T² and Q statistics for monitoring, and establishing control limits through statistical distributions. The algorithm workflow includes data normalization, covariance matrix computation, eigenvalue decomposition, and score transformation. For Fault Type 1 detection, we will evaluate deviations from normal operation by analyzing principal component scores and residuals, enhancing detection accuracy through multivariate statistical process control techniques. This PCA-based approach provides deeper insights into process data variability and improves fault detection reliability by reducing false alarms and missed detections.