SUMMARYThis paper presents a new data mining method that integrates adaptive B-spline regression and traffic flow theory to develop multi-regime traffic stream models (TSMs). Parameter estimation is implemented adaptively and optimally through a constrained bi-level programming method. The slave programming determines positions of knots and coefficients of the B-spline by minimizing the error of B-spline regression. The master programming model determines the number of knots through a regularized function, which balances model accuracy and model complexity. This bi-level programming method produces the best fitting to speed-density observations under specific order of splines and possesses great flexibility to accommodate the exhibited nonlinearity in speed-density relationships. Jam density can be estimated naturally using spline TSM, which is sometimes hardly obtainable in many other TSM. Derivative continuity up to one order lower than the highest spline degree can be preserved, a desirable property in some application. A five-regime B-spline model is found to exist for generalized speed-density relationships to accommodate five traffic operating conditions: free flow, transition, synchronized flow, stop and go traffic, and jam condition. A typical two-regime B-spline form is also explicitly given, depending only on free-flow speed, optimal speed, optimal density, and jam density.
In this paper, we developed a methodological framework to deal with traffic-stream modeling based on data mining, steepest-ascend algorithm, and genetic algorithm. The new method is adaptive in nature and has a greater flexibility and generality compared with existing methods. It provides an optimum overall fitting of the observed data. Specifically, the advantages of adaptive regression are that (1) knot positions and model parameters are estimated optimally and simultaneously using genetic algorithm, and presetting of knot positions can be performed in terms of either density or speed; (2) the method is automatic and data driven, and it will always find out the best fitting model to site-dependent actual traffic data; and (3) the user has a great flexibility to specify the degree-model continuity and to define and add new basis functions that are parsimonious and fit better into the traffic data in some regime of speed-density relation. The proposed method and developed computer software package MiningFlow will be beneficial to traffic operations and traffic simulation.
Résumé: Nous avons développé dans cet article un cadre méthodologique pour traiter de la modélisation du flot de circulation basée sur l'exploration des données, un algorithme de la plus grande pente et un algorithme génétique. La nouvelle méthode est adaptive de nature et présente une plus grande flexibilité et généralité que les méthodes existantes. Elle fournit un ajustement global optimal aux données observées. Plus spécifiquement, les avantages de la régression adaptative sont (1) la position des noeuds et les paramètres du modèle sont estimés de manière optimale et simultanée en utilisant un algorithme génétique et le préréglage des positions des noeuds peut être effectué en termes de densité ou de vitesse, (2) la mé-thode est automatique et dirigée par les données et trouvera toujours le modèle le mieux ajusté aux données réelles de circulation liées au site et (3) l'utilisateur possède une grande souplesse pour spécifier le niveau de continuité du modèle et définir et ajouter de nouvelles fonctions de base minimales et s'ajustant mieux aux données de circulation à certains ré-gimes de relation vitesse-densité dans la fonction de base réglée pour élargir le bassin de modèles candidats. La méthode proposée et le logiciel développé, MiningFlow, seront utiles à la pratique des opérations et de la simulation de la circulation.
Daily travel time is cast into a framework of nonstationary stochastic process. For a fixed value of departure time in a day, travel time given origin, destination, and route information, is treated as a random variable. For a specific date, travel time is treated as a deterministic function of departure time t. Under this framework, the expected travel time for a given departure time is defined as an ensemble mean travel time (EMTT) over a number of days. The method of moment is proposed to compute EMTT based on a hypothetical piecewise constant speed trajectory for travel time estimation. The advantage of the method of moment for EMTT estimation is that it only requires ensemble mean and ensemble variance of spot speed information at point detectors, which is much easier and cost-effective to get than obtaining collections of massive spot speed data per se. The result is compared against Monte Carlo simulation and direct sampling based simulation. The proposed method of moment approach provides accurate estimation of EMTT (e.g., the expected travel time estimation) under a wide range of traffic conditions (e.g., free flow and congestion).
An analytical solution of steady-state dynamic response of a multilayered viscoelastic medium to a moving distributed load is obtained using a novel approach that combines transfer matrix method with Sun’s convolution representation integrated over impulse response function of the layered medium. The layered media under consideration include elastic and viscoelastic media with four different viscoelastic constitutive models, while the moving load is allowed to have a circular spatial distribution, which is more realistic for mimicking tire footprint than a commonly used point load. Efficient numerical algorithms based on fast evaluation of various integral transformations and their inversions are developed and validated through numerical example.
A rigorous theoretical foundation for solving elastodynamic inverse problem of multilayered media under an impulse load is established in this paper. The inversion is built upon the forward dynamic analysis of multilayered elastic media using transfer matrix approach, with which displacement continuity is assumed at the interfaces of upper and lower adjacent layers. Formulations for inverse analysis are derived in both the time domain and the complex frequency domain. Least square estimates and nonlinear optimization algorithms are used to implement parameter identification. The proposed theory and formulae can be utilized to develop a computer software for nondestructive evaluation of laminated civil and aerospace structure (highway and airport pavements, bridge decks, soil foundations, aircraft wing, etc.), exploration and dynamic source detection and identification, and petroleum exploration in geophysics.
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