An improved weighted recursive PCA algorithm for adaptive fault detection

A novel weighted adaptive recursive fault detection technique based on Principal Component Analysis (PCA) is proposed to address the issue of the increment in false alarm rate in process monitoring schemes due to the natural, slow and normal process changes (aging), which often occurs in real processes. It has been named as weighted adaptive recursive PCA (WARP).The aforementioned problem is addressed recursively by updating the eigenstructure (eigenvalues and eigenvectors) of the statistical detection model when the false alarm rate increases given the awareness of non-faulty condition. The update is carried out by incorporating the new available information within a specific online process dataset, instead of keeping a fixed statistical model such as conventional PCA does. To achieve this recursive updating, equations for means, standard deviations, covariance matrix, eigenvalues and eigenvectors are developed. The statistical thresholds and the number of principal components are updated as well.A comparison between the proposed algorithm and other recursive PCA-based algorithms is carried out in terms of false alarm rate, misdetection rate, detection delay and its computational complexity. WARP features a significant reduction of the computational complexity while maintaining a similar performance on false alarm rate, misdetection rate and detection delay compared to that of the other existing PCA-based recursive algorithms. The computational complexity is assessed in terms of the Floating Operation Points (FLOPs) needed to carry out the update.