(183a) Review and Comparative Study of Nonlinear PCA Fault Detection Methods

In the process and manufacturing industries, safe operations and high quality product are assured by process monitoring systems (e.g., [1]). The frontline of any process monitoring system is fault detection, which is the detection of anomalous behavior. Most fault detection methods implemented in industrial systems are data-driven methods, that is, methods based on models constructed entirely or nearly entirely from process data. The data-driven fault detection methods most used in the early chemical industry were one-variable-at-a-time control charts, namely, Shewart, CUSUM, and EWMA charts. The past many decades have seen major growth in the application of multivariate statistical techniques, which can handle correlations between the data associated with different variables (aka “multivariable correlations”). The multivariate statistical technique most widely used in industry is principal component analysis (PCA), which handles high-dimensional, highly correlated, and noisy data [1].

Part of the success of PCA has been that (i) the sampling times used in many applications have been long, which minimizes temporal correlations within the data that would violate one of the assumptions underlying PCA, and (ii) most continuous processes have input-output relationships that are very close to linear, which is another assumption underlying PCA. Some industrial applications have been using sampling times that are fast enough that the data have significant temporal correlations. It is well known that the temporal correlations are well addressed by data-driven fault detection methods based on canonical variate analysis (e.g., [1]), and such methods have been applied in industrial practice for some years now.

This presentation considers the second limitation of PCA, which is that PCA can give poor fault detection performance for processes that have nonlinear input-output behavior. To overcome the linear restriction, different nonlinear extensions of PCA have been proposed, going back to early work by Thomas McAvoy, Jong Min Lee, and others (e.g., [2,3]). The literature on nonlinear PCA has grown substantially over the past twenty years, both within and outside of the chemical process systems community, and this presentation provides a thorough systematic review and comparative study. Our main interest is in the characteristics of nonlinear PCA methods relevant for their effective application for data-driven fault detection. The most widely studied nonlinear PCA methods for fault detection, including neural network PCA [2] and kernel PCA [3], are compared with PCA in several case studies that collectively illustrate significant limitations and strengths of various nonlinear PCA methods. The case studies are (1) a simple nonlinear example, (2) a realistic simulation of a full chemical plant commonly used in the literature, and (3) a realistic simulation of a highly nonlinear pharmaceutical manufacturing facility. In addition to pointing out some common misconceptions in the literature, the case studies are used to provide general guidelines on when to use nonlinear PCA, how to use nonlinear PCA effectively, and how to interpret the results for the purposes of fault detection of nonlinear systems.

[1] L.H. Chiang, E.L. Russell, and R.D. Braatz (2000) Fault Detection and Diagnosis in Industrial Systems. Springer Science & Business Media.

[2] D. Dong and T.J. McAvoy (1996) Nonlinear principal component analysis based on principal curves and neural networks. Computer and Chemical Engineering, 20(1), 65-78.

[3] J.M. Lee, C. Yoo, and S.W. Choi (2004) Nonlinear process monitoring using kernel principal component analysis. Chemical Engineering Science, 59(1), 223-234.