Fault detection using multiscale PCA-based moving window GLRT

The presence of measurement errors (noise) in the data and mode l uncertainties degrade the performance quality of fault detection (FD) techniques. Therefore, an objective of this paper is to enhance the quality of FD by suppressing the effect of these errors using wavelet-based multiscale representation of data, which is a powerful feature extraction tool. Multiscale representation of data has been used to improve the FD abilities of principal component analysis. Thus, combining the advantages of multiscale representation with those of hypothesis testing should provide further improvements in FD. To do that, a moving window generalized likelihood ratio test (MW-GLRT) method based on multiscale principal component analysis (MSPCA) is proposed for FD. The dynamical multiscale representation is proposed to extract the deterministic features and decorrelate autocorrelated measurements. An extension of the popular hypothesis testing GLRT method is applied on the residuals from the MSPCA model, in order to further enhance the fault detection performance. In the proposed MW-GLRT method, the detection statistic equals the norm of the residuals in that window, which is equivalent to applying a mean filter on the squares of the residuals. This means that a proper moving window length needs to be selected, which is similar to estimating the mean filter length in data filtering. The fault detection performance of the MSPCA-based MW-GLRT chart is illustrated through two examples, one using synthetic data, and the other using simulated Tennessee Eastman Process (TEP) data. The results demonstrate the effectiveness of the MSPCA-based MW-GLRT method over the conventional PCA-based and MSPCA-based GLRT methods, and both of them provide better performance results when compared with the conventional PCA and MSPCA methods, through their respective charts T² and Q charts.