Statistical χ2 Testing Based Fault Detection for Linear Discrete Time-delay Systems

This paper is concerned with statistical χ² testing based fault detection (FD) for a class of linear discrete time-varying (LDTV) stochastic systems with delayed state. Different from the traditional residual based FD, we propose to construct the evaluation function by directly using measurement observations. Then an equivalent solution can be given in terms of Riccati recursion by utilizing projection and innovation analysis technique. Moreover, the fault free case evaluation function is with central χ² distribution and the heavy computational burden is reduced. Furthermore, strategies of χ² statistic testing on evaluation function are also discussed. Finally, a numerical example is given to illustrate the proposed method.