PCA-based Detection for TE Data Including SPE Statistic Calculation

In this article, we provide a comprehensive discussion on implementing Principal Component Analysis (PCA) algorithms in MATLAB for TE data detection. The detection process requires calculating SPE (Squared Prediction Error) statistics through matrix operations involving residual computations between original and reconstructed data. Additionally, we demonstrate control limit calculations for both SPE and T-squared statistics using statistical distribution functions (such as chi-square distributions for T-squared and approximate distributions for SPE limits). These steps are critical as they enable rapid and accurate anomaly detection through threshold-based monitoring. Furthermore, we explore MATLAB visualization techniques including score plots and residual charts to better understand data distribution patterns. The implementation utilizes key MATLAB functions like pca() for dimensionality reduction and eig() for covariance matrix decomposition. Finally, we provide practical tips for parameter tuning and handling real-world data challenges, helping readers effectively apply these techniques to practical industrial scenarios.