Bayesian Reconstruction of Missing Observations

We focus on an interpolation method referred to Bayesian reconstruction in this paper. Whereas in standard interpolation methods missing data are interpolated deterministically, in Bayesian reconstruction, missing data are interpolated probabilistically using a Bayesian treatment. In this paper, we address the framework of Bayesian reconstruction and its application to the traffic data reconstruction problem in the field of traffic engineering. In the latter part of this paper, we describe the evaluation of the statistical performance of our Bayesian traffic reconstruction model using a statistical mechanical approach and clarify its statistical behavior

Reconstructing the Traffic State by Fusion of Heterogeneous Data

We present an advanced interpolation method for estimating smooth spatiotemporal profiles for local highway traffic variables such as flow, speed and density. The method is based on stationary detector data as typically collected by traffic control centres, and may be augmented by floating car data or other traffic information. The resulting profiles display transitions between free and congested traffic in great detail, as well as fine structures such as stop-and-go waves. We establish the accuracy and robustness of the method and demonstrate three potential applications: 1. compensation for gaps in data caused by detector failure; 2. separation of noise from dynamic traffic information; and 3. the fusion of floating car data with stationary detector data.Comment: For more information see http://www.mtreiber.de or http://www.akesting.d

Trajectory Reconstruction Techniques for Evaluation of ATC Systems

This paper is focused on trajectory reconstruction techniques for evaluating ATC systems, using real data of recorded opportunity traffic. We analyze different alternatives for this problem, from traditional interpolation approaches based on curve fitting to our proposed schemes based on modeling regular motion patterns with optimal smoothers. The extraction of trajectory features such as motion type (or mode of flight), maneuvers profile, geometric parameters, etc., allows a more accurate computation of the curve and the detailed evaluation of the data processors used in the ATC centre. Different alternatives will be compared with some performance results obtained with simulated and real data sets

Comparative model accuracy of a data-fitted generalized Aw-Rascle-Zhang model

The Aw-Rascle-Zhang (ARZ) model can be interpreted as a generalization of the Lighthill-Whitham-Richards (LWR) model, possessing a family of fundamental diagram curves, each of which represents a class of drivers with a different empty road velocity. A weakness of this approach is that different drivers possess vastly different densities at which traffic flow stagnates. This drawback can be overcome by modifying the pressure relation in the ARZ model, leading to the generalized Aw-Rascle-Zhang (GARZ) model. We present an approach to determine the parameter functions of the GARZ model from fundamental diagram measurement data. The predictive accuracy of the resulting data-fitted GARZ model is compared to other traffic models by means of a three-detector test setup, employing two types of data: vehicle trajectory data, and sensor data. This work also considers the extension of the ARZ and the GARZ models to models with a relaxation term, and conducts an investigation of the optimal relaxation time.Comment: 30 pages, 10 figures, 3 table

Use of Kriging Technique to Study Roundabout Performance

Road intersections are dangerous places because of the many conflicting points between motorized and nonmotorized vehicles. In the case of defined traffic volume, several research groups have proved that roundabouts reduced the number of injuries and fatal accident cases. In recent years, many countries have adopted roundabouts as a standard design solution for both urban and rural roads. Several recent studies have investigated the performance of roundabouts, including some with models that calculated the entering flow (Q sub e) as a function of the circulating flow (Q sub c). Most existing models have been constructed with the use of linear or exponential statistical regression. The interpolative techniques in classical statistics are based on the use of canonical forms (linear or polynomial) that completely ignore the correlation law between collected data. As such, the determined interpolation stems from the assumption that the data represent a random sample. In the research reported in this paper, a geostatistical approach was considered: the relationship Q sub e versus Q sub c is supposed to be a regionalized phenomenon. According to that supposition, collected data do not represent a random sample of values but are supposed to be related to each other with a defined law. This recognition allows the realization of interpolation on the basis of the real law of the phenomenon. This paper discusses the fundamental theories, the applied operating procedures, and the first results obtained in modeling the Q sub e versus Q sub c relationship with the application of geostatistics

Bridge damage detection based on vibration data: past and new developments

Overtime, bridge condition declines due to a number of degradation processes such as creep, corrosion, and cyclic loading, among others. Traditionally, vibration-based damage detection techniques in bridges have focused on monitoring changes to modal parameters. These techniques can often suffer to their sensitivity to changes in environmental and operational conditions, mistaking them as structural damage. Recent research has seen the emergence of more advanced computational techniques that not only allow the assessment of noisier and more complex data but also allow research to veer away from monitoring changes in modal parameters alone. This paper presents a review of the current state-of-the-art developments in vibration-based damage detection in small to medium span bridges with particular focus on the utilization of advanced computational methods that avoid traditional damage detection pitfalls. A case study based on the S101 bridge is also presented to test the damage sensitivity to a chosen methodology.Peer ReviewedPostprint (published version

Characterization of Vehicle Behavior with Information Theory

This work proposes the use of Information Theory for the characterization of vehicles behavior through their velocities. Three public data sets were used: i.Mobile Century data set collected on Highway I-880, near Union City, California; ii.Borl\"ange GPS data set collected in the Swedish city of Borl\"ange; and iii.Beijing taxicabs data set collected in Beijing, China, where each vehicle speed is stored as a time series. The Bandt-Pompe methodology combined with the Complexity-Entropy plane were used to identify different regimes and behaviors. The global velocity is compatible with a correlated noise with f^{-k} Power Spectrum with k >= 0. With this we identify traffic behaviors as, for instance, random velocities (k aprox. 0) when there is congestion, and more correlated velocities (k aprox. 3) in the presence of free traffic flow

A rarefaction-tracking method for hyperbolic conservation laws

We present a numerical method for scalar conservation laws in one space dimension. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compression waves. The solution is represented by particles that carry function values and move according to the method of characteristics. Between two neighboring particles, an interpolation is defined by an analytical similarity solution of the conservation law. An interaction of particles represents a collision of characteristics. The resulting shock is resolved by merging particles so that the total area under the function is conserved. The method is variation diminishing, nevertheless, it has no numerical dissipation away from shocks. Although shocks are not explicitly tracked, they can be located accurately. We present numerical examples, and outline specific applications and extensions of the approach.Comment: 21 pages, 7 figures. Similarity 2008 conference proceeding