Optimally Robust Redundancy Relations for Failure Detection in Uncertain Systems

Abstract

All failure detection methods are based, either explicitly or implicitly, on the use of redundancy, i.e. on (possibly dynamic) relations among the measured variables. The robustness of the failure detection process consequently depends to a great degree on the reliability of the redundancy relations, which in turn is affected by the inevitable presence of model uncertainties.In this paper we address the problem of determining redundancy relations that are optimally robust, in a sense that includes several major issues .of importance in practical failure detection, and that provides a significant amount of intuition concerning the geometry of robust failure detection. We also give a procedure, involving the construction of a single matrix and its singular value decomposition, for the determination of a complete sequence of redundancy relations, ordered in terms of their level of robustness. This procedure also provides the basis for comparing levels of robustness in redundancy provided by different sets of sensors.

Analysis of order of redundancy relation for robust actuator fault detection

“…In Halder and Sarkar (2005) it is pointed out that an increase in the order of redundancy relation increases the robustness of the nonlinear residuals. This result is compatible with its linear counter part as given in Lou et al (1986). Experimental results using a PUMA 560 robotic arm are presented to demonstrate the usefulness of the theorem.…”

“…To address the robustness issue, Chow and Willsky (1984) have proposed an optimization method to select a parity vector from the parity space. This work was later extended by various researchers in Lou, Willsky, and Verghese (1986). Most recently in Han, Li, and Shah (2005) and Kwan and Xu (2004) the authors designed optimal primary residual that considered both the model-plant-mismatch (MPM) and process disturbances for linear systems.…”

“…It was pointed out in Lou et al (1986) that the selection of the order of redundancy relation has an influence on the optimization performance. In fact, it is proved in Ding, Guo, and Jeinsch (1999) that increasing the order of redundancy relation leads to an increase in the dimension of the parity space, which in turn provides greater flexibility in residual generation as well as improves robustness.…”

Fault detection and isolation in the presence of process uncertainties

“…Disturbances decoupling FDI methods include the works done by Frank (1994), and Chen (1992, 2000). On the other hand, a number of FDI schemes with robustness against the modelling errors have been proposed including the work by Lou, Willsky, and Verghese (1986), Ding (1994, 1997), Gertler and Kunwer (1995), Chen, Patton, and Zhang (1996), Shen and Hsu (1998), Hamelin and Sauter (2000), Qin and Li (2001), and Li and Shah (2002), in both the time and frequency domains. However, to the best of our knowledge, very few FDI schemes have the capability of simultaneously working in the presence of disturbances plus MPM, unless some restrictive assumptions on the MPM are assumed (Zhong, Ding, Lam, & Wang, 2003;Chen & Patton, 1999).…”

Parity relation based fault estimation for nonlinear systems: An LMI approach

“…Over the last three decades various fault detection and isolation (FDI) techniques have been developed [1−3] . The parity relation approach or analytical redundancy relation (ARR) is one of the most commonly used techniques in FDI, see [3][4][5][6][7][8][9][10]. This technique is first proposed in [5] to detect sensor faults in a flight control system.…”