279056 Comprehensive Investigation of Fault Detection Based On the Statistics Pattern Analysis Framework
The increasing demand for safer and more reliable systems in modern process operation leads to the rapid development of process monitoring techniques. With large number of variables measured and stored automatically by distributed control systems (DCS), multivariate statistical process monitoring approaches have been developed and successfully applied to monitor various industrial processes. Currently, Principal Component Analysis (PCA) based process monitoring methods have gained wide application in chemical and petrochemical industries [1-2]. PCA-based monitoring methods can easily handle high dimensional, noisy and highly correlated data generated from industrial processes [3-5], and provide superior performance compared to univariate methods such as Shewhart, CUSUM and EWMA charts. However, there are cases where PCA do not perform well due to the following reasons. First, PCA only considers the mean and variance-covariance of the process data, and lacks the capability of providing higher-order representation for non-Gaussian data. Second, the control limits of Hotelling’s T2 and the squared prediction error (SPE) charts are developed based on the assumption that the latent variables follow a multivariate Gaussian distribution. When the latent variables are non-Gaussian distributed due to the process nonlinearity or other reasons, using Hotelling’s T2 and SPE may be misleading.
In our previous work [6-9], a new multivariate statistical monitoring framework termed statistics pattern analysis (SPA) was developed. SPA addresses some challenges that cannot be readily handled by the commonly used multivariate statistical methods such as multiway-PCA for batch processes . In addition, the SPA framework has also shown better monitoring performance in continuous processes compared to other linear and nonlinear monitoring methods using a moving window approach .
The major difference between the traditional multivariate monitoring methods such as PCA and SPA-based fault detection methods is that SPA monitors the statistics of the process variables (e.g. mean, variance, autocorrelation, cross-correlation, etc.) rather than the process variables themselves. 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, the key different aspects of fault detection for continuous processes, such as detection rate and false alarms rates are studied in detail using a simple benchmark simulation case study and a more complicated nonlinear quadruple-tank case study. Different faults with different characteristics are used to make a thorough analysis of the fundamental reasons of the performance improvement of SPA compared to other monitoring methods including PCA, dynamic PCA (DPCA), kernel PCA (KPCA), independent component analysis (ICA). In addition, since the application of SPA to monitor continuous processes is based on a window approach, detection delay may be a concern. However, our previous results [8-9] indicate that the detection delay associated with SPA is not significant compared with other linear and nonlinear monitoring methods. In this work, a comprehensive analysis of the insignificant detection delay associated with SPA is performed. Both simulated case studies with different types of faults are used to assess and comprehensively compare the different aspects associated with an accurate and prompt detection of faults using different monitoring methods including PCA, DPCA, KPCA, ICA and SPA.
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