Robust Residual Generation Using Optimal Parity Relations

Abstract

AbstractIn Chapters 3-6, robust observer-based residual generators have been discussed. This chapter focuses on the problem of robust residual generation via optimal parity relations. The parity relation is one of the most commonly accepted approaches for generating residuals. To achieve robustness for this approach, Chow and Willsky (1984) reformulated the design of parity relations for robust residual generation as a minmax optimization problem. The optimal objective they defined specifies robustness with respect to a particular operating point, thereby allowing the possibility of adaptively choosing the best parity relations. However, the main drawback of their method is that it leads to an extremely complex optimization problem for which there is no analytical solution. Lou et al. (1986) proposed an alternative method to find “optimally robust parity relations” for generating robust residuals. They used multiple models to describe the modeling uncertainty due to parameter variations so that the residual becomes minimally sensitive to system parameters variation. The introduction of the multiple model description in parity relation design and the provision of an analytical strategy for solving the optimization problem are the main contributions of Lou et al. (1986). However, the optimal objective they proposed seems inappropriate, because they only considered the minimization of effects of parameter variations. A residual designed to be insensitive to modeling uncertainty may also be insensitive to faults. An appropriate performance index for robust residual design should take account of both effects of modeling uncertainty and faults. Following this philosophy, Wünnenberg and Frank (Wünnenberg and Frank, 1988; Frank, 1990; Wünnenberg and Frank, 1990; Wünnenberg, 1990) studied the design of optimal parity relations by adopting a modified performance index which is the ratio of the modeling uncertainty response effect to that of the fault effect. However, the modeling uncertainty description they used was the unknown input (or disturbance) description which, as discussed Chapters 2-5, cannot be used to represent a wide range of uncertain situations without any modification and approximation. This disappointing feature was due to the lack of application study even in a simple academic exercise or simulation setting.KeywordsParity RelationPerformance IndexSingular Value DecompositionModeling UncertaintyMatrix PencilThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.