一类随机不确定线性系统鲁棒故障检测问题研究

Fault detection for a class of linear systems with stochastic uncertainties

将一类受乘性随机噪声影响线性系统的基于观测器的残差产生器设计归结为随机意义下的H∞-滤波问题,应用线性矩阵不等式技术,推导问题可解的充分条件,给出观测器增益矩阵的求解方法.另外,根据给定的残差评价函数和阈值,判断故障的发生并估计故障的误报率;或给定残差评价函数和容许故障误报率,通过适当的选取阈值把实际的故障误报率限定在容许的范围内.仿真算例验证了所给算法的有效性.

The residual generation is formulated into a problem of observer-based H∞-filtering in the sense of stochastic. By using linear matrix inequality technique, a sufficient condition for the existence of the fault deteetion filter is derived and a suitable observer gain matrix can be obtained. With the given residual evaluation function and threshold, the occurrence of fault can be detected and the false alarm rate estimated. Or with the given residual evaluation function, an available false alarm rate can also be guaranteed by suitably choosing threshold. A numerical example illustrates the effectiveness of the proposed method.