Residual Generation for Fault Diagnosis in Linear

A residual generation method for fault diagnosis in determin- istic and stochastic linear time-varying systems is proposed in this note. Based on appropriate assumptions on the monitored faults and on some persistent excitation condition, it enables complete diagnosis of any number of faults, regardless of the number of output sensors. In order to generate residuals for fault diagnosis, part of the possible faults are estimated with a recently developed technique of adaptive observer. The sensitivity of the residuals to the monitored faults is rigorously analyzed, as well as their in- sensitivity to the faults to be ignored. Due to the increasing complexity of modern engineering systems, fault diagnosis, as part of the techniques for system supervision, is at- tracting the attention of more and more researchers. When a system is affected by faults, the purpose of fault diagnosis is to decide, among a set of possible faults, which ones are actually present. Typically, model-based methods for fault diagnosis rely on the design of resid- uals which are signals computed from available sensor measurements with the aid of a mathematical model of the monitored system. Each of the residuals is sensitive to a subset of the possible faults, and fault diagnosis is achieved by the evaluation of these residuals. In this note, residual generation for deterministic linear time-varying (LTV) state-space systems is first considered. Then the same problem for stochastic LTV system is considered to some extent. The considered deterministic system subject to faults is assumed to have the form