Fault Detection and Isolation Using Principal Component Analaysis and a Least Squares Optimization Approach to PHMC
Calce Team: V. Sotiris and M. Pecht
Objective:
Develop an approach for anomaly detection and fault isolation in multivariate. Apply algorithm to computer data to analyze detection results and accuracy.
Abstract:
Principal Components Analysis is used in a wide array of applications to reduce a large data set to a smaller one while maintaining the majority of the variability present in the original data. It’s also very
useful in providing compact representation of temporal and spatial correlations in the fields of data being analyzed. PCA facilitates a multivariate statistical control to detect when abnormal processes exist and can isolate the source of the process abnormalities down to the component level. The results were obtained through principal component analysis (PCA) and least squares analysis (LS). Two statistical indices: the Hotelling squared T2 and the squared prediction error (SPE) are used in the PCA model.
The SPE statistic is related to the residuals of process variables that are not illustrated by the PCA model, and is a reliable indicator to a change in the correlation structure of the process variables. The SPE physically tests the fit of new data to the established PCA models and is efficient at identifying outliers from the PCA model. The Hotelling T2 score measures the Mahalanobis distance from the projected sample data point to the origin in the signal space defined by the PCA model.