State and parameter estimation in 1-D hyperbolic PDEs based on an adjoint method

International audienceAn optimal estimation method for state and distributed parameters in1-D hyperbolic system based on adjoint method is proposed in thispaper. A general form of the partial differential equations governingthe dynamics of system is first introduced. In this equation, theinitial condition or state variable as well as some empiricalparameters are supposed to be unknown and need to be estimated. TheLagrangian multiplier method is used to connect the dynamics of thesystem and the cost function defined as the least square error betweenthe simulation values and the measurements. The adjoint state method isapplied to the objective functional in order to get the adjoint systemand the gradients with respect to parameters and initial state. Theobjective functional is minimized by Broyden–Fletcher–Goldfarb–Shanno(BFGS) method. Due to the non-linearity of both direct and adjointsystem, the nonlinear explicit Lax–Wendroff scheme is used to solvethem numerically. The presented optimal estimation approach isvalidated by two illustrative examples, the first one about state andparameter estimation in a traffic flow, and the second one in anoverland flow system

Freeway Multisensor Data Fusion Approach Integrating Data from Cellphone Probes and Fixed Sensors

Freeway traffic state information from multiple sources provides sufficient support to the traffic surveillance but also brings challenges. This paper made an investigation into the fusion of a new data combination from cellular handoff probe system and microwave sensors. And a fusion method based on the neural network technique was proposed. To identify the factors influencing the accuracy of fusion results, we analyzed the sensitivity of those factors by changing the inputs of neural-network-based fusion model. The results showed that handoff link length and sample size were identified as the most influential parameters to the precision of fusion. Then, the effectiveness and capability of proposed fusion method under various traffic conditions were evaluated. And a comparative analysis between the proposed method and other fusion approaches was conducted. The results of simulation test and evaluation showed that the fusion method could complement the drawback of each collection method, improve the overall estimation accuracy, adapt to the variable traffic condition (free flow or incident state), suit the fusion of data from cellphone probes and fixed sensors, and outperform other fusion methods

Modeling, Control, and Impact Analysis of The Next Generation Transportation System

This dissertation aims to develop a systematic tool designated for connected and autonomous vehicles, integrating the simulation of traffic dynamics, traffic control strategies, and impact analysis at the network level. The first part of the dissertation is devoted to the traffic flow modeling of connected vehicles. This task is the foundation step for transportation planning, optimized network design, efficient traffic control strategies, etc, of the next generation transportation system. Chapter 2 proposes a cell-based simulation approach to model the proactive driving behavior of connected vehicles. Firstly, a state variable of connected vehicle is introduced to track the trajectory of connected vehicles. Then the exit flow of cells containing connected vehicles is adjusted to simulate the proactive driving behavior, such that the traffic light is green when the connected vehicle arrives at the signalized intersection. Extensive numerical simulation results consistently show that the presence of connected vehicles contributes significantly to the smoothing of traffic flow and vehicular emission reductions in the network. Chapter 3 proposes an optimal estimation approach to calibrate connected vehicles\u27 car-following behavior in a mixed traffic environment. Particularly, the state-space system dynamics is captured by the simplified car-following model with disturbances, where the trajectory of non-connected vehicles are considered as unknown states and the trajectory of connected vehicles are considered as measurements with errors. Objective of the reformulation is to obtain an optimal estimation of states and model parameters simultaneously. It is shown that the customized state-space model is identifiable with the mild assumption that the disturbance covariance of the state update process is diagonal. Then a modified Expectation-Maximization (EM) algorithm based on Kalman smoother is developed to solve the optimal estimation problem. The second part of the dissertation is on traffic control strategies. This task drives the next generation transportation system to a better performance state in terms of safety, mobility, travel time saving, vehicular emission reduction, etc. Chapter 4 develops a novel reinforcement learning algorithm for the challenging coordinated signal control problem. Traffic signals are modeled as intelligent agents interacting with the stochastic traffic environment. The model is built on the framework of coordinated reinforcement learning. The Junction Tree Algorithm based reinforcement learning is proposed to obtain an exact inference of the best joint actions for all the coordinated intersections. The algorithm is implemented and tested with a network containing 18 signalized intersections from a microscopic traffic simulator. Chapter 5 develops a novel linear programming formulation for autonomous intersection control (LPAIC) accounting for traffic dynamics within a connected vehicle environment. Firstly, a lane based bi-level optimization model is introduced to propagate traffic flows in the network. Then the bi-level optimization model is transformed to the linear programming formulation by relaxing the nonlinear constraints with a set of linear inequalities. One special feature of the LPAIC formulation is that the entries of the constraint matrix has only values in {-1, 0, 1}. Moreover, it is proved that the constraint matrix is totally unimodular, the optimal solution exists and contains only integer values. Further, it shows that traffic flows from different lanes pass through the conflict points of the intersection safely and there are no holding flows in the solution. Three numerical case studies are conducted to demonstrate the properties and effectiveness of the LPAIC formulation to solve autonomous intersection control. The third part of the dissertation moves on to the impact analysis of connected vehicles and autonomous vehicles at the network level. This task assesses the positive and negative impacts of the system and provides guidance on transportation planning, traffic control, transportation budget spending, etc. In this part, the impact of different penetration rates of connected vehicle and autonomous vehicles is revealed on the network efficiency of a transportation system. Chapter 6 sets out to model an efficient and fair transportation system accounting for both departure time choice and route choice of a general multi OD network within a dynamic traffic assignment environment. Firstly, a bi-level optimization formulation is introduced based on the link-based traffic flow model. The upper level of the formulation minimizes the total system travel time, whereas the lower level captures traffic flow propagation and the user equilibrium constraint. Then the bi-level formulation is relaxed to a linear programming formulation that produces a lower bound of an efficient and fair system state. An efficient iterative algorithm is proposed to obtain the exact solution. It is shown that the number of iterations is bounded, and the output traffic flow solution is efficient and fair. Finally, two numerical cases (including a single OD network and a multi-OD network) are conducted to demonstrate the performance of the algorithm. The results consistently show that the travel time of different departure rates of the same OD pair are identical and the algorithm converges within two iterations across all test scenarios

Filtering and Control of Traffic Volume on Arterial

This paper studies the filtering and control of traffic volume consistently from the system-theoretic viewpoint. Based on the statistical analysis of the traffic volumes observed by detector, the time-dependent characteristics of traffic volume are formulated by the linear time-varying discrete-time system. Moreover, the time-dependent characteristics of traffic congestion length are formulated by the linear time-varying discrete-time system based on the traffic volume balance at each signalized intersection. Next, the algorithms of the Kalman filter and the MIPA Kalman filter are derived as the state estimation method for the abovementioned dynamical system. The priority control method of the traffic congestion length with respect to the direction along the arterial is proposed by using the systematic control method of signal control parameters. Finally, the effectiveness of the MIPA Kalman filter and the priority control method of the traffic congestion length is confirmed by the simulation results of Route 2 national road in Fukuyama city

Integration of Real-time Traffic State Estimation and Dynamic Traffic Assignment with Applications to Advanced Traveller Information Systems

Accurate depiction of existing traffic states is essential to devise effective real-time traffic management strategies using Intelligent Transportation Systems (ITS). Existing applications of Dynamic Traffic Assignment (DTA) methods are mainly based on either the prediction from macroscopic traffic flow models or measurements from the sensors and do not take advantage of traffic state estimation techniques, which produce estimate of the traffic states with less uncertainty than the prediction or measurement alone. On the other hand, research studies highlighting estimation of real-time traffic state are focused only on traffic state estimation and have not utilized the estimated traffic state for DTA applications. This research introduces a framework which integrates real-time traffic state estimate with applications of DTA to optimize network performance during uncertain traffic conditions through traveller information system. The estimate of real-time traffic states is obtained by combining the prediction of traffic density using Cell Transmission Model (CTM) and the measurements from the traffic sensors in Extended Kalman Filter (EKF) recursive algorithm. The estimated traffic state is used for predicting travel times on available routes in a traffic network and the predicted travel times are communicated to the commuters by a variable message sign (VMS). In numerical experiments, the proposed estimation and information framework is applied to optimize network performance during traffic incident on a two route network. The proposed framework significantly improved the network performance and commuters’ travel time when compared with no-information scenario during the incident. The application of the formulated methodology is extended to model day-to-day dynamics of traffic flow and route choice with time-varying traffic demand. The day-to-day network performance is improved by providing accurate and reliable traveller information. The implementation of the proposed framework through numerical experiments shows a significant improvement in daily travel times and stability in day-to-day performance of the network when compared with no-information scenario. The use of model based real-time traffic state estimation in DTA models allows modelling and estimating behaviour parameters in DTA models which improves the accuracy of the modelling process. In this research, a framework is proposed to model commuters’ level of trust in the information provided which defines the weight given to the information by commuters while they update their perception about expected travel time. A methodology is formulated to model and estimate logit parameter for perception variation among commuters for expected travel time based on measurements from traffic sensors and estimated traffic state. The application of the proposed framework to a test network shows that the model accurately estimated the value of logit parameter when started with a different initial value of the parameter

Traffic-aware cell management for green ultra-dense small cell networks

To reduce the power consumption of fifth-generation ultradense small-cell networks, base stations can be switched to low-power sleep modes when local traffic levels are low. In this paper, a novel sleep mode control algorithm is proposed to control such sleep modes. The algorithm innovates a concept called traffic-aware cell management (TACM). It involves cell division, cell death, and cell migration to represent adaptations of networks, where the state transitions of base stations are controlled. Direction of arrival (DOA) is adopted for distributed decision making. The TACM algorithm aims at reducing the network power consumption while alleviating the impacts of applying sleep modes, such as mitigating system overheads and reducing user transmission power. The TACM algorithm is compared with a recent consolidated baseline scheme by simulation on networks with unbalanced traffic distributions and with base stations at random locations. In contrast, the TACM algorithm shows a significant improvement in mitigating system overheads due to the absence of load information exchange overhead and up to 72 times less switching frequency. Up to 81% network power consumption can be reduced compared with the baseline scheme if considering high energy consumption of switching transient states. In addition, at a low traffic level, average uplink transmission power is reduced by 79% comparatively. Furthermore, the impact of important performance-governing parameters of the TACM algorithm is analyzed. The insensitivity to the estimation accuracy of DOA is also demonstrated. The results show that the proposed TACM algorithm has a comprehensive advantage of power reduction and overhead mitigation over the baseline scheme

A Computationally Efficient Method for Online Identification of Traffic Control Intervention Measures

Adaptive traffic control systems such as SCOOT and SCATS are designed to respond to changes in traffic conditions and provide heuristically optimised traffic signal settings. However, these systems make gradual changes to signal settings in response to changing traffic conditions. In the EPSRC and TSB funded FREEFLOW project, a tool is being designed to rapidly identify severe traffic problems using traffic sensor data and recommend traffic signal plans and UTC parameters that have worked well in the past under similar traffic conditions for immediate implementation. This paper will present an overview of this tool, called the Intelligent Decision Support (IDS),that is designed to complement adaptive traffic control systems. The IDS is essentially a learning based system. It requires an historic database of traffic sensor data and traffic control intervention data for the application area as a knowledge base. The IDS, when deployed online, will monitor traffic sensor data to determine if the network is congested using traffic state estimation models. When IDS identifies congestion in the network, the historic database is queried for similar congestion events, where the similarity is based on both the severity and the spatial pattern of congestion. Traffic control interventions implemented during similar congestion events in the historic database are then evaluated for their effectiveness to mitigate co ngestion. The most effective traffic control interventions are recommended by IDS for implementation, along with an associated confidence indicator. The IDS is designed to work online against large historic datasets, and is based on traffic state estimation models developed at Imperial College London and pattern matching tools developed at the University of York. The IDS is tested offline using Inductive Loop Detector (ILD) data obtained from the ASTRID system and traffic control intervention data obtained from the UTC system at Transport for London (TfL) during its development. This paper presents the preliminary results using TfL data and outlines future research avenues in the development of ID