Statistical modeling and sensor fault diagnosis using PCA

Principal Components Analysis (PCA) is used to reduce the dimensionality of the data matrix and capture the underlying variation and latent relationship among the variables. In recent years, PCA has become a popular toot for identifying linear models of processes from historical data. This technique has been used for process monitoring and fault diagnosis. Fault detection is usually carried out using SPE/T2 statistics while contribution plots are used to identify the variables that are the primary causes of the fault. The success of fault-diagnosis methods depends upon: (1) the accuracy of the process models we can get from the identification; (2) the sensitivity of fault-detection techniques; (3) the resolution quality of fault-isolation strategies. (4) Robustness to model mis-match or non-linearity of the system.;Given the error covariance plus the assumption of normality, the linear model identification may be easily performed by a MLE approach. Unfortunately, the error covariance is usually unknown. A technique known as iterative PCA (IPCA) has recently been proposed by Narasimhan and Shah (2004) for simultaneous estimation of both the model and error covariance matrix.;First, this thesis demonstrates through simulation, the significant advantages of IPCA over PCA in providing accurate estimates of both the model and error covariance matrix. Second, this thesis shows that the estimated model and error covariance matrix can be combined with the well established techniques of Data Reconciliation (DR) and Gross Error Detection (GED) for more accurate state estimation and sensor fault diagnosis. In particular, it is shown through simulation that significanlt improvement in sensor fault diagnosis can be obtained by using the generalized likelihood ratio (GLR) test approach as compared to the use of SPE/T2 tests and contribution plots which are conventionally used with PCA based techniques. Furthermore, both the IPCA method as well as the GLR approach possess the characteristic of being invariant to scaling of the data. The following two important perspectives are obtained through this thesis. (1) PCA and IPCA should be regarded as tools for model identification and not be bundled together with contribution plots for fault diagnosis. Significant improvement in diagnostic resolution can be obtained by using these models with well established statistical techniques such as likelihood ratio tests. (2) The IPCA method and DR/GED techniques are shown to be complementary approaches for steady state processes. While IPCA is concerned with identifying a model and error covariance matrix from data, DR and GED are concerned with state estimation and fault diagnosis assuming the availability of the process model and error covariance matrix.;It is well known that the model obtained using PCA is optimal under the assumption that the measurement errors are identically, independently and normally distributed (lid normal), and the error covariance matrix Sigma e = sigma2I. However, this is seldom true in practice, as different sensors cannot be expected to have the same level of measurement noise. To circumvent this assumption but without guarantee, classical PCA typically applies auto-scaling to the process data to get unit-variance. A significant disadvantage of PCA, and also fault diagnosis using contribution plots, is that they both depend on the choice of data scaling.