基于X2统计检验的线性离散时滞系统故障检测

基于X2统计检验，研究了一类含状态时滞线性离散时变系统的故障检测问题. 与基于残差的传统故障检测方法不同, 本文直接应用测量输出构造残差评价函数, 并通过投影与新息分析, 得到了残差评价函数的Riccati递推解. 分析表明, 该方法有效降低了残差评价函数的计算量, 并且在无故障发生情况下服从X2分布. 进一步, 通过X2统计检验可以判断系统是否有故障发生. 最后，通过一算例验证了提出方法的有效性.

Statistical X2 Testing Based Fault Detection for Linear Discrete Time-delay Systems

This paper is concerned with statistical X² 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 X² distribution and the heavy computational burden is reduced. Furthermore, strategies of X² statistic testing on evaluation function are also discussed. Finally, a numerical example is given to illustrate the proposed method.