Robust Diagnosis of Intermittent Faults for Linear Stochastic Systems Subject to Time-varying Perturbations
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摘要: 间歇故障（Intermittent faults, IFs）具有随机性，其检测要求在本次间歇故障消失之前检测出间歇故障的发生，在下一次间歇故障发生之前检测出间歇故障的消失.本文针对一类存在未知时变参数摄动的离散线性随机动态系统，研究了其鲁棒间歇故障检测与分离问题.基于降维未知输入观测器，通过引入滑动时间窗口，本文设计了一组与未知时变摄动解耦的结构化截断残差，并提出其存在的一个充分条件.与传统残差相比，截断残差信号更为显著地反映了间歇故障的发生和消失.为满足间歇故障的检测要求，本文提出两个假设检验分别用于检测间歇故障的发生时刻和消失时刻，并给出了一个详细算法.最后，在沿参考轨道运行的卫星模型上对所述方法进行了仿真实验，结果表明该方法能够有效检测出间歇故障的所有发生时刻和消失时刻，并准确实现故障分离.Abstract: Since intermittent faults (IFs) have an intermittency property, the detection of IFs requires: the current appearing time of an IF must be detected before its disappearing time; the current disappearing time of an IF must be detected before the subsequent appearing time. In this paper, the robust detection problem of IFs for a class of linear discrete-time stochastic systems subject to unknown time-varying perturbations is investigated. Based on reduced-order unknown input observers (UIOs), a novel set of structured truncated residuals is designed to detect and isolate IFs by introducing sliding-time windows, and a sufficient condition is proposed for the existence of the residual generators. Compared to traditional residuals, the novel truncated residuals, which get decoupled from time-varying perturbations, are more sensitive to the IFs. Based on the analysis of these novel residuals, two hypothesis tests are proposed to detect all the appearing times and the disappearing times of an IF. In addition, a detailed algorithm is provided to perform the given scheme. Finally, simulation results on a model of a satellite moving in a circular reference orbit are presented to illustrate the effectiveness of the proposed method.
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图 1 间歇故障与滑动时间窗口的相对位置关系
Fig. 1 Relative positions between the intermittent fault and the sliding-time windo
图 4 初始残差信号 $r_1(k)$ 和新残差信号 $r_1(k, \Delta k_1)$
Fig. 4 Comparing $r_1(k, \Delta k_1)$ with $r_1(k)$
图 5 初始残差信号 $r_2(k)$ 和新残差信号 $r_2(k, \Delta k_2) $
Fig. 5 Comparing $r_2(k, \Delta k_2)$ with $r_2(k)$
图 6 初始残差信号 $r_3(k)$ 和新残差信号 $r_3(k, \Delta k_3) $
Fig. 6 Comparing $r_3(k, \Delta k_3)$ with $r_3(k)$
表 1 间歇故障发生(消失)时刻及其实际检测值
Table 1 The detection result of $m_3(k)$ by using the proposed method
q $\mu_{3, q}$ $\mu_{3, q}^{\text{dec}}$ $\nu_{3, q}$ $\nu_{3, q}^{\text{dec}}$ 1 5.00 5.03 5.57 5.62 2 6.02 6.03 6.59 6.67 3 7.14 7.15 7.75 7.77 4 8.32 8.34 8.83 8.87 5 9.26 9.28 9.76 9.87 
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