Evaluating covariance in prognostic and system health management applications. (June 2015) - Menon, Sandeep; Jin, Xiaohang; Chow, Tommy W.S.; Pecht, Michael
Abstract: Developing a diagnostic and prognostic health management system involves analyzing system parameters monitored during the lifetime of the system. This data analysis may involve multiple steps, including data reduction, feature extraction, clustering and classification, building control charts, identification of anomalies, and modeling and predicting parameter degradation in order to evaluate the state of health for the system under investigation. Evaluating the covariance between the monitored system parameters allows for better understanding of the trends in monitored system data, and therefore it is an integral part of the data analysis. Typically, a sample covariance matrix is used to evaluate the covariance between monitored system parameters. The monitored system data are often sensor data, which are inherently noisy. The noise in sensor data can lead to inaccurate evaluation of the covariance in data using a sample covariance matrix. This paper examines approaches to evaluate covariance, including the minimum volume ellipsoid, the minimum covariance determinant, and the nearest neighbor variance estimation. When the performance of these approaches was evaluated on datasets with increasing percentage of Gaussian noise, it was observed that the nearest neighbor variance estimation exhibited the most stable estimates of covariance. To improve the accuracy of covariance estimates using nearest neighbor-based methodology, a modified approach for the nearest neighbor variance estimation technique is developed in this paper. Case studies based on data analysis steps involved in prognostic solutions are developed in order to compare the performance of the covariance estimation methodologies discussed in the paper. Highlights: Simulated noisy data sets are used to compare the accuracy of four existing covariance estimation methodologies Among the discussed methodologies the NNVE algorithm provides the most accurate estimates of covariance. To further improve the accuracy of the covariance estimation, a new methodology based on a modification of the NNVE methodology is proposed. The proposed methodology is shown to exhibit improved performance in classification as well as anomaly detection applications.