(404b) Fault Detection and Diagnosis in the Statistics Pattern Analysis Framework
Statistics pattern analysis (SPA) is a new multivariate statistical monitoring framework proposed by the authors recently . It addresses some challenges that cannot be readily addressed by the commonly used multivariate statistical methods such as principal component analysis (PCA) in monitoring batch processes in the semiconductor industry. It was later extended to the monitoring of continuous processes using a moving window based approach .
The major difference between the PCA-based and SPA-based fault detection methods is that PCA monitors process variables while SPA monitors the statistics of the process variables (e.g. mean, variance, autocorrelation, cross-correlation, etc.). In other words, in PCA singular value decomposition (SVD) is applied to the original process variables to build a model for normal operation, and the new measurements of the process variables are projected onto the PCA model to perform fault detection; while in SPA, SVD is applied to the computed statistics pattern matrix (i.e. various statistics of the process variables) of normal operating data to build the model, and the statistics calculated using the new measurements are projected onto the model to perform fault detection. In this way, different statistics that capture the different characteristics of the process can be selected to build the model for normal process operation, and higher order statistics can be utilized explicitly to cope with non-linearity and non-Gaussianity.
In this work, we explore the potential of our recently proposed SPA framework in fault diagnosis for continuous process. Specifically, the variable contributions are derived based on the fault detection indices used in SPA to generate contribution plots  for fault diagnosis. We use the Tennessee Eastman process [4,5] to evaluate the performance of the developed fault detection and diagnosis method based on the SPA framework, and compare with PCA, dynamic PCA (DPCA), kernel PCA (KPCA) and independent component analysis (ICA). The case study shows that in general all methods work well in detecting and diagnosing most of faults. However, for some faults that are difficult to detect and/or diagnose by PCA and DPCA based methods, SPA based method provides superior performance. In addition, because the SPA-based method breaks down the contribution of a fault to different variable statistics, they provide extra information in addition to identifying the major fault-contributing variable(s). For example, the SPA-based contribution plots tell us whether the fault is due to a change in variable mean or variance. It also should be noted that in general SPA requires more training data to build a reliable model due to the computation of variable statistics. However, this is not a big issue because most modern processes are equipped with DCS systems and therefore are data rich.
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