Network sensor health problem

Many existing studies on the sensor health problem determine an individual sensor's health status based on the statistical characteristics of collected data by the sensor. In this research, we study the sensor health problem at the network level, which is referred to as the network sensor health problem. First, based on the conservation principle of daily flows in a network, we separate all links into base links and non-base links, such that the flows on the latter can be calculated from those on the former. In reality, the network flow conservation principle can be violated due to the existence of unhealthy sensors. Then we define the least inconsistent base set of links as those that minimize the sum of squares of the differences between observed and calculated flows on non-base links. But such least inconsistent base sets may not be unique in a general road network. Finally we define the health index of an individual sensor as the frequency that it appears in all of the least inconsistent base sets. Intuitively, a lower health index suggests that the corresponding sensor is more likely to be unhealthy. We present the brute force method to find all least inconsistent base sets and calculate the health indices. We also propose a greedy search algorithm to calculate the approximate health indices more efficiently. We solve the network sensor health problem for a real-world example with 16 nodes and 30 links, among which 18 links are monitored with loop detectors. Using daily traffic count data from the Caltrans Performance Measurement System (PeMS) database, we use both the brute-force and greedy search methods to calculate the health indices for all the sensors. We find that all the four sensors flagged as unhealthy (high value) by PeMS have the lowest health indices. This confirms that a sensor with a lower health index is more likely to be unhealthy. Therefore, we can use such health indices to determine the relative reliability of different sensors' data and prioritize the maintenance of sensors.