Sensor placement considering the observability of traffic dynamics: On the algebraic and graphical perspectives
提出一种新传感器布设模型，通过代数和图论方法最大化动态交通网络中路段密度的可观测性，并利用流量守恒推导出识别部分可观测系统中可观测组件的简单解析结果。
In this paper, we present a new sensor location model that aims to maximize observability of link densities in a dynamic traffic network described using a piecewise linear system of ordinary differential equations. We develop an algebraic approach based on the eigenstructure to determine the sensor location for achieving full observability with a minimal number of sensors. Additionally, a graphical approach based on the concept of structural observability is developed. By exploiting the special property of flow conservation in traffic networks, we derive a simple analytical result that can be used to identify observable components in a partially observable system, which is the main contribution of this paper. The graphical and algebraic properties of observability are then integrated into a sensor location optimization model considering a wide range of traffic conditions. Through numerical experiments, we demonstrate the good performance of our sensor deployment strategies in terms of the average observability and estimation errors. • We establish new observability theories for linear time-invariant dynamic traffic systems. • The average number of observable components is maximized under various traffic modes. • Complex systems understanding is advanced in traffic setting by using domain knowledge. • Numerical experiments demonstrate the applicability of our methods.