Optimally robust redundancy relations for failure detection in uncertain systems

Abstract

A geometric interpretation of the concept of analytical redundancy leads to computationally simple procedures, involving singular value decompositions, Jor determining redundancy relations that are maximally insensitive to model uncertainties.Key Words--Failure detection; robustness; model reduction; least-squares approximation; linear systems.Al~traet--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 the problem of determining redundancy relations that are optimally robust is addressed 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. A procedure is given 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.

Direct Adaptive Control of Systems with Actuator Failures: State of the Art and Continuing Challenges

“…Reconfigurable flight control designs using neural networks [22][23][24][25][26] have been developed for aircraft systems with failures. Results on control of systems with failures also include those using: fault tolerant control designs [27][28][29][30] ; identification of multiplicative faults based on parameter estimation techniques [31][32][33][34] ; function approximations for control and adaptive law design 35 ; residual generation techniques for fault detection and diagnosis 21,[36][37][38][39][40][41] ; and other design and analysis techniques. [42][43][44][45] In addition, direct adaptive reconfigurable control of a tailless fighter aircraft was presented and successfully flight-tested, 26 and an adaptive controller for failure compensation in uncertain systems was presented.…”

Actuator Failure Detection Through Interaction Matrix Formulation

“…3 Hence, the first step for failure detection is to develop a mathematical algorithm that accentuates the residual signal when a fault has occurred in a system. So far, parity space (consistency checking 4,5 ) and observer-based methods 6,7 have been widely used for the residual generation. Once residual signals are detected, the next step is to separate the source of the failure, a so-called fault isolation.…”

Detection of abrupt changes in dynamic systems

“…However, we will focus for the most part on the first task of change detection, that is, the problem of producing signals which make subsequent detection as easy as possible. As discussed here and in more detail in [27][28][29], this is an exceedingly important perspective in the design of detection methods which are robust to uncertain details of the dynamic models on which they are based.…”

“…These efforts have been motivated by a wide variety of applications including the detection of sensor and actuator failures [1,2,4,19,[26][27][28][29][30][31][32][33][34][35] the tracking of maneuvering vehicles [20,21,23,25], and numerous signal analysis problems (electrocardiogram analysis [5,6], geophysical signal processing [7], edge detection in images [8,9], freeway monitoring [10,11],...).…”