Determination of Observation Weight to Calibrate Freeway Traffic Fundamental Diagram Using Weighted Least Square Method (WLSM)

  • Chunbo Zhang School of Transportation, Southeast University
  • Xiucheng Guo School of Transportation, Southeast University
  • Zhenping Xi School of Transportation, Southeast University
Keywords: fundamental diagram, Weighted Least Square Method, observation weight, speed-density relationship,

Abstract

Due to unbalanced speed-density observations, the one-regime traffic fundamental diagram and speed-density relationship models using least square method (LSM) cannot reflect actual conditions under congested/jam traffic. In that case, it is inevitable to adopt the weighted least square method (WLSM). This paper used freeway Georgia State Route 400 observation data and proposed 5 weight determination methods except the LSM to analyse 5 wellknown one-regime speed-density models to determine the best calibrating models. The results indicated that different one-regime speed-density models have different best calibrating models, for Greenberg, it was possible to find a specific weight using LSM, which is similar for Underwood and Northwestern Models, but different for that one known as 3PL model. An interesting case is the Newell's Model which fits well with two distinct calibration weights. This paper can make contribution to calibrating a more precise traffic fundamental diagram.

Author Biographiesaaa replica rolex repwatches replica rolex watches for men replica iwc watch

Chunbo Zhang, School of Transportation, Southeast University
PhD Candidate of Transportation Engineering
Xiucheng Guo, School of Transportation, Southeast University
Professor of Transportation Engineering
Zhenping Xi, School of Transportation, Southeast University
Master of Transportation Planning and Management

References

Ambarwati L, Pel AJ, Verhaeghe R, van Arem B. Empirical analysis of heterogeneous traffic flow and calibration of porous flow model. Transp Res Part C: Emerg Technol. 2014;48:418-436. doi:10.1016/j.trc.2014.09.017

Antoniou C, Koutsopoulos HN, Yannis G. Dynamic data-driven local traffic state estimation and prediction. TranspRes Part C: Emerg Technol. 2013;34:89-107. doi:10.1016/j.trc.2013.05.012

Ngoduy D, Maher MJ. Calibration of second order traffic models using continuous cross entropy method. Transp Res Part C: Emerg Technol. 2012;24:102-121. doi:10.1016/j.trc.2012.02.007

Greenshields BD, Bibbins JR, Channing WS, Miller, HH.A study of traffic capacity. Highway Research Board. 1935;14:448-477.

Greenberg H. An analysis of traffic flow. Oper Res. 1959;7(1):79-85. doi: 10.1287/opre.7.1.79

Heydecker BG, Addison JD. Analysis and modelling of traffic flow under variable speed limits. Transp Res Part C: Emerg Technol. 2011;19(2):206-217. doi: 10.1016/j.trc.2010.05.008

Newell GF. Nonlinear effects in the dynamics of car following. Oper Res. 1961;9(2):209-229.

Wang H, Li H, Chen QY, Ni D. Logistic modeling of the equilibrium speed-density relationship. Transp Res Part A: Policy Pract. 2011;45(6):554-566. doi:10.1016/j.tra.2011.03.010

Edie LC. Car-following and steady-state theory for noncongested traffic. Oper Res. 1961;9:66-76.

Sun L, Zhou J. Development of multiregime speed–density relationship by cluster analysis. Transp Res Rec J Transp Res Board. 2005;193:64-71. doi: http://dx.doi.org/10.3141/1934-07

Qu X, Wang S, Zhang J. On the fundamental diagram for freeway traffic: A novel calibration approach for single-regime models. Transp Res Part B: Method. 2015;73:91-102. doi:10.1016/j.trb.2015.01.001

Veraart J, Sijbers J, Sunaert S, Leemans A, Jeurissen B. Weighted linear least squares estimation of diffusion MRI parameters: strengths, limitations, and pitfalls. Neuroimage. 2013;81:335-346. doi:10.1016/j.neuroimage.2013.05.028

Zhuang X, Zhu H, Augarde C. An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function. Comput Mech. 2014;53(2):343-357. doi: 10.1007/s00466-013-0912-1

Fang X. Weighted total least squares: necessary and sufficient conditions, fixed and random parameters. J Geodesy. 2013;87(8):733-749. doi: 10.1007/s00190-013-0643-2

Mahboub V, Sharifi MA. On weighted total leastsquares with linear and quadratic constraints. J Geodesy. 2013;87(3):279-286. doi:10.1007/s00190-012-0598-8

Ciucci F. Revisiting parameter identification in electrochemical impedance spectroscopy: Weighted least squares and optimal experimental design. Electrochim Acta. 2013;87:532-545. doi:10.1016/j.electacta.2012.09.073

Wang L, Xu L, Feng S, Meng MQH, Wang K. Multi-Gaussian fitting for pulse waveform using weighted least squares and multi-criteria decision making method. Comput Biol Med. 2013;43(11):1661-1672. doi:10.1016/j.compbiomed.2013.08.004

Khatibinia M, Fadaee MJ, Salajegheh J, Salajegheh E. Seismic reliability assessment of RC structures including soil–structure interaction using wavelet weighted least squares support vector machine. Reliab Eng Syst Safe. 2013;110:22-33. doi:10.1016/j.ress.2012.09.006

Parrish RM, Sherrill CD, Hohenstein EG, Kokkila SI, Martínez TJ. Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction. J Chem Phys. 2014;140(18). doi:10.1063/1.4876016

Stanley TD, Doucouliagos H. Neither fixed nor random: weighted least squares meta-analysis. Stat Med. 2015;34(13):2116-2127. doi:10.1002/sim.6481

Einemo M, So HC. Weighted least squares algorithm for target localization in distributed MIMO radar. Signal Processing. 2015;115:144-150. doi: 10.1016/j.sigpro.2015.04.004

Washington SP, Karlaftis MG, Mannering FL. Statistical and econometric methods for transportation data analysis. London: Chapman and Hall; 2013.

Published
2017-04-21
How to Cite
1.
Zhang C, Guo X, Xi Z. Determination of Observation Weight to Calibrate Freeway Traffic Fundamental Diagram Using Weighted Least Square Method (WLSM). Promet [Internet]. 2017Apr.21 [cited 2024Mar.28];29(2):203-12. Available from: http://traffic.fpz.hr/index.php/PROMTT/article/view/2088
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