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Optimal Structured Residuals for Multidimensional Fault Isolation Based on Multivariate Principal Component Models

Weilu Lin, Process Control and Optimization, Weyerhaeuser Company, PO BOX 275, Springfield, OR 97477 and S. Joe Qin, Chemical Engineering, The University of Texas at Austin, 1 University Station C0400, Austin, TX 78712.

Fault detection and isolation (FDI) in engineering systems are of great practical significance. The systems concerned encompass a broad of human made machinery, including industrial production facilities and household appliances. The early detection and diagnosis of faults are critical in avoiding product deterioration, performance degradation and major damage to the equipment. The traditional approaches to fault detection and diagnosis involve the limit checking of some key variables or the application of redundant sensors (physical redundancy). Over the last two decades, fault detection and diagnosis have gained increasing consideration world-wide. This development was mainly stimulated by the trend of automation towards more complexity and the growing demand for higher security of control systems.

Fault isolation using analytical redundancy can be traced to aerospace applications [1], which utilizes information embodied in the mathematical model of the process for fault detection and isolation. An important related activity is due Gertler and coworkers [2], who try to diagnose faults by designing structured residuals that are insensitive to a particular subset of faults. Qin and Li [3] proposed an optimal structured residual approach with maximized sensitivity (SRAMS) which makes one structured residual insensitive to one subset faults while with maximized sensitivity to other faults. In our recent work [4], we analyze the SRAMS approach in detail and propose a new optimal structured residuals (OSR) approach for enhanced fault isolation.

In this work, we extend the OSR approach to multidimensional fault isolation in dynamic systems based on dynamic principal component models. To maximize fault isolation ability, a matrix of optimal structured residuals are designed. Each of them is insensitive to one subset of faults while being most sensitive to one of remaining ones. The maximum of all structured residuals in each row of the structured residual matrix is then selected as the optimal one for fault isolation. Through this approach, optimal structured residual directions with maximum fault isolation ability are obtained. The multidimensional fault isolabilty condition for deterministic and stochastic faults is investigated as well in this work. Simulation studies using data from a MIMO dynamic system and an industrial reactor are given to demonstrate the efficiency of the proposed algorithm.


1. Chow, E. Y., and Willsky, A. S. Analytical redundancy and the design of robust failure detection systems. IEEE Trans. Auto. Cont. 29 (1984)

2. Gertler, J., and Singer, D. A new structural framework for parity equation based failure detection and isolation. Automatica 26 (1990)

3. Qin, S. J., and Li, W. Detection, identification, and reconstruction of faulty sensors with maximized sensitivity. AIChE J. 45 (1999).

4. Lin, W., and Qin, S. J. Optimal structured residual approach for improved faulty sensor diagnosis. Ind. Eng. Chem. Res. 44 (2005).