线性随机系统的微小传感器故障检测

Incipient sensor fault detection for linear stochastic systems

针对一类线性随机系统,研究了其微小传感器故障检测问题.基于Kalman滤波算法构造状态估计器,利用移动加权平均方法设计残差与评价函数.根据非中心卡方分布的性质,分析了故障幅值、窗口长度、误报率和漏报率之间的关系.采用不等式技术,得到了确保在统计意义下微小故障可检测性的最优权值和最小窗口长度.最后,通过一个仿真实例验证了所提方法的有效性.

In this paper,the problem of incipient sensor fault detection is investigated for linear stochastic systems.The state estimator is constructed by using the Kalman filtering algorithm.Then,the residual and the evaluation function are designed by means of the weighted moving average method.According to the property of the non-centralχ~2 distribution,the relationships among the fault amplitude,the window length,the false alarm rate and the missed detection rate are analyzed.By using the inequality technique,the optimal weights and the minimum window length,which ensure the detectability of incipient faults in a probabilistic sense,are derived.Finally,an illustrative example is provided to verify the effectiveness of the proposed method.