Optimal Placement of Sensors in Traffic Networks Using Global Search Optimization Techniques Oriented towards Traffic Flow Estimation and Pollutant Emission Evaluation

Abstract

The relationship between estimating traffic flow and evaluating pollutant emissions lies in understanding how vehicular traffic patterns affect air quality. Traffic flow estimation is a complex field that involves a variety of analytical techniques to understand, predict, and manage the flow of vehicles on road networks. Different types of analyses commonly employed in this area are statistical analysis (e.g., descriptive statistics, inferential statistics, time series analysis), mathematical modeling (macroscopic models, microscopic models, mesoscopic models), computational methods (e.g., simulation modeling, machine learning, and AI techniques), geospatial analysis (e.g., geographic information systems (GISs), spatial data analysis), network analysis (e.g., graph theory and network flow models). In sensor network setups, the strategic placement of sensors is crucial, primarily due to the challenges posed by limited energy supplies, restricted storage capabilities, and the demands on processing and communication, all of which significantly impact maintenance costs and hardware limitations. To mitigate the burden on processing and communication, it is essential to deploy a limited number of sensors strategically. In practical applications, achieving an optimal layout of physical sensors (i.e., placing sensors within the network in such a way as to meet a specific optimality criterion, such as identifying the minimum number of sensors required to ensure the ability to design reliable state observers capable of reconstructing the network’s state based on the available data) is essential for the accurate monitoring of large-scale systems, including traffic flow or the distribution networks of water and gas. In the context of traffic systems, addressing the challenge of full link flow observability, that is, the ability to accurately monitor and assess the flow of entities (i.e., vehicles) across all the links or pathways within a network, entails selecting the smallest number of traffic sensors from a larger set to install. The goal is to choose a subset of p sensors, which may include redundancies, from a pool of n>>p potential sensors. This is conducted to maintain the structural observability of the entire traffic network. This concept pertains to deducing the complete internal state (traffic volume on each road link in the network) from external outputs and inputs (measurements from sensors). The traditional concept of system observability serves as a criterion for sensor placement. This article presents the development of a simulated annealing heuristic to address the selection problem. The selected sensors are then applied to construct a Luenberger observer, a mathematical construct used in control theory to accurately estimate the internal state of a dynamic system based on its inputs and outputs. Numerical simulations are carried out to demonstrate the effectiveness of this method, and a performance analysis using a digital twin of a transport network, designed using the Aimsun Next software, are also carried out to assess traffic flow and associated pollutant emissions. In particular, we examine a traffic network comprising 21 roads. We address the sensor selection problem by identifying an optimal set of six sensors, which facilitates the design of a Luenberger observer. This observer enables the reconstruction of traffic flow across the network with minimal estimation error. Furthermore, by integrating this observer with data from the Aimsun Next software, we assess the pollutant emissions related to traffic flow. The results indicate a high accuracy in estimating pollutant levels.