(268d) A Quality Relevant Non-Gaussian Latent Subspace Projection Method for Chemical Process Monitoring and Fault Detection

Multivariate statistical process monitoring (MSPM) techniques have been developed for fault detection and diagnosis of complex processes by extracting useful information from large number of highly correlated process variables and historical data sets [1]. Partial least squares or projection to latent structure (PLS) method has been widely used in MSPM field [2]. The goal of traditional PLS method is to build the statistical model within the low dimensional subspace of measurement variables that retains most of the covariance with product quality variables. PLS essentially relies on the second-order statistic of covariance, which may effectively capture the Gaussian process features only. However, the Gaussian assumption on process data usually is not fulfilled in practice [3]. Meanwhile, independent component analysis (ICA) approach has recently been developed for non-Gaussian process monitoring and fault diagnosis [4]. The basic idea of ICA is to find the independent components (ICs) that are assumed to be non-Gaussian and mutually independent by means of maximizing the higher-order statistics such as negentropy instead of the second-order statistics including variance and covariance. Nevertheless, ICA model only includes process measurement variables but ignores product quality variables. Thus ICA may not be well suited for identifying the abnormal operating events that have the most significant influence on product quality variables [5]. 

In this study, a novel quality relevant non-Gaussian latent subspace projection (QNGLSP) method is proposed to monitor complex processes and detect abnormal operating events with significant influence on product quality. In order to characterize the non-Gaussian relationships between process measurement and product quality variables, the higher-order statistic of mutual information is adopted. Mutual information is a quantitative measure of statistical dependency between two random variables and can be estimated from information entropy. Compared to covariance, it can effectively extract the non-Gaussian process features due to the underlying higher-order statistics. The proposed algorithm is to first search for the optimal latent directions within process measurement and quality spaces concurrently so that the maximized mutual information between latent scores of measurement and quality variables is obtained. Then, a numerical optimization method termed as Nelder-Mead algorithm and multi-start optimization procedure are integrated to identify the optimal latent directions iteratively with nonlinear multi-peak function handling capability. Furthermore, a series of I² and SPE indices are developed to detect process faults within non-Gaussian latent variables and residual subspaces. Different from PCA or ICA based monitoring techniques, the presented QNGLSP method has the inherent model structure of combining process measurement and product quality variables. Meanwhile, this new approach relies on mutual information based objective function and thus can effectively identify the non-Gaussian features in latent subspaces, which cannot be achieved in the PLS based monitoring method. 

The presented QNGLSP method and the conventional PLS approach are applied to the Tennessee Eastman Chemical process for performance comparison. The monitoring results demonstrate that the QNGLSP based I² and SPE indices are superior to the PLS based T² and SPE indices in terms of maximized fault detection rates while minimized false alarm rates. 

Reference

[1] Nomikos, P. and MacGregor, J.F. (1995). Multivariate SPC charts for monitoring batch processes. Technometrics, 37, 41-59.

[2] Zhang, H. and Lennox, B. (2004). Integrated condition monitoring and control of fed-batch fermentation processes. J. Proc. Cont., 11(1), 41-50.

[3] Yu, J. and Qin, S.J. (2008). Multimode process monitoring with Bayesian inference-based finite Gaussian mixture models. AIChE J., 54, 1811-1829.

[4] Kaneko, H., Arakawa, M. and Funatsu, K. (2009). Development of a new soft sensor method using independent component analysis and partial least squares. AIChE J., 55, 87-98.

[5] Yu, J. (2012). A nonlinear kernel Gaussian mixture model based inferential monitoring approach for fault detection and diagnosis of chemical processes. Chem. Eng. Sci., 68, 506-519.