Fault isolation in nonlinear systems with structured partial principal component analysis and clustering analysis

Abstract

0 n-line monitoring of chemical processes is extremely important for plant safety and good product quality. Multivariate statistical methods have found many applications in monitoring complex chemical processes (Kresta et al., 1991; Piovoso et al ., 1992). A detailed procedure for multivariate monitoring, where principal component analysis (PCA) is used to model normal process data, is proposed by Kresta et al. (1991). In PCA monitoring, an implicit statistical model is built using data obtained when the process is operating well and under control. Unusual events are detected by referencing the measured process behaviour against the model. The PCA method can compress high dimensional and correlated process measurements into much lower dimensions while keeping important information.Though modern multivariate approaches are very effective a t detecting process faults, one important issue they do not specifically address is fault isolation. When a faulty condition is detected, one needs to determine the root cause of this problem. Contribution charts (MacCregor et al., 1994) and multi-block approaches (Chen and McAvoy, 1997) have been proposed to help solve this problem, but neither of them provides a complete solution.Analytical redundancy (AR) methods have well developed fault isolation capabilities utilizing a structured or directional design of the residual set (Certler and Singer, 1990; Massoumnia et al., 1989;Certler, 1998). Parity relations belong to the AR methods. Certler and McAvoy (1997) showed that there is a close duality between PCA and parity relations, and proposed a partial PCA method embedding the fault isolation properties of the structured parity relations into PCA. Certler et al. (1 998) gave a strict proof of the duality, and proposed a direct algebraic method of generating a set of partial PCA models from the full PCA model. A potential problem for the partial PCA approach i s that PCA is a linear method and most processes are nonlinear.Efforts have been made to introduce nonlinearity into PCA. Cnanadesikan (1 977) proposed a generalized PCA (CPCA) in which the normal data set is extended to include nonlinear functions of its elements, and PCA is performed on the extended data set. Etezadi-Amoli and McDonald (1 983) used I dimensional polynomials to approximate m dimensional data with / < rn latent factors. The coefficients of the polynomials in the reduced I dimensional space are computed by the linear least squares method. Kramer (1 992) proposed a nonlinear PCA (NPCA) method based on a five-layered neural network, but such a network is very difficult to train. The NPCA approach proposed by Dong and McAvoy (1 996) uses a similar neural network structure, but employs the *Author to whom correspondence may be addressed. E-mail address: mcavoy@ glue.umd.edu Partial principal component analysis (PCA) and parity relations are proven to be useful methods in fault isolation. To overcome the limitation of applying partial PCA to nonlinear problems, a new approach utilizing clustering analysis is p...

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Sensor fault detection and isolation of an autonomous underwater vehicle using partial kernel PCA

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