有向网络中线性时不变系统的故障检测与隔离
Detection and Isolation of Failures in Directed Networks of LTI Systems
AI总结：
研究针对有向网络中多输入多输出LTI系统故障检测与隔离方法，基于输出导数的跳跃不连续性进行故障识别，并提出传感器布置算法及性能保证。
摘要：
我们提出了一种方法，用于检测和隔离有向网络中相同多输入多输出LTI系统中的链路故障，当仅部分节点的输出响应可用时。我们的方法基于输出导数中的跳跃不连续性，这可以明确与链路故障的发生相关联。导数阶数由$r(d+1)$给出，其中$r$是每个系统传递矩阵的相对阶数，$d$表示故障位置到观测点的距离。我们随后基于此关系提出检测和隔离策略。此外，我们提出了一种高效的传感器布置算法，用于使用少量传感器检测和隔离任何可能的链路故障。可用的子模函数理论结果提供了性能保证，将所选传感器集的大小限制在最小可行传感器集的对数因子内。这些结果通过详细的示例和计算机实验进行说明。
英文摘要：
We propose a methodology to detect and isolate link failures in a weighted and directed network of identical multi-input multi-output LTI systems when only the output responses of a subset of nodes are available. Our method is based on the observation of jump discontinuities in the output derivatives, which can be explicitly related to the occurrence of link failures. The order of the derivative at which the jump is observed is given by $r(d+1)$, where $r$ is the relative degree of each system's transfer matrix, and $d$ denotes the distance from the location of the failure to the observation point. We then propose detection and isolation strategies based on this relation. Furthermore, we propose an efficient algorithm for sensor placement to detect and isolate any possible link failure using a small number of sensors. Available results from the theory of sub-modular set functions provide us with performance guarantees that bound the size of the chosen sensor set within a logarithmic factor of the smallest feasible set of sensors. These results are illustrated through elaborative examples and supplemented by computer experiments.
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