Nonlinear analysis of high accuracy and reliability in traffic flow prediction

AbstractFor quantitatively identifying the chaotic patterns in traffic flow prediction, certain types of Duffing systems can be used. The accuracy and reliability of numerical results of the system’s solution have significant influence on the traffic flow prediction. The nonlinear dynamic behavior of Duffing system used for the traffic flow prediction is investigated in this research. The solutions of the system are developed and solved numerically by using the P-T method. The regular and irregular responses of the system considered are graphically illustrated with the newly developed P-R method. Based on the results of the research, the frequency and amplitude of the external excitations applied on the system significantly affecting the nonlinear dynamic behavior therefore the traffic flow prediction in transferring the results by Wigner-Ville transform. Additionally, a comparison between the P-T and Runge-Kutta method is conducted in regarding the accuracy and reliability of the methods.

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Effect of temperature on the nonlinear dynamic behavior of two-lobe non-circular gas-lubricated micro-bearings

Proceedings of the Institution of Mechanical Engineers Part J Journal of Engineering Tribology ◽

10.1177/1350650121995689 ◽

2021 ◽

pp. 135065012199568

Author(s):

Azizmohammad Gharanjik ◽

Ardeshir Karami Mohammadi

Keyword(s):

Dynamic Behavior ◽

High Temperatures ◽

Nonlinear Dynamic ◽

Phase Portraits ◽

Effect Of Temperature ◽

Behavior Changes ◽

Runge Kutta Method ◽

Nonlinear Dynamic Behavior ◽

Effects Of Temperature ◽

Increasing Temperature

In this paper, the molecular gas lubrication model was used to analyze the nonlinear dynamic behavior of two-lobe non-circular gas-lubricated micro-bearings. The effects of temperature rise are taken into account. At high temperatures, in addition to gas rarefaction, its viscosity and friction will also change, and slip across boundaries will occur. The rarefaction of the lubricating gas film caused by the microscale effect at high temperatures was considered. The effects of temperature and rotation speed (with and without rarefaction effect) on the dynamic behavior of the non-circular micro gas bearing were studied. The nonlinear equation governing the gas behavior is discretized using the finite-element method and then solved simultaneously with the dynamic equations of rotor motion using the fourth-order Runge–Kutta method. Center orbit diagrams, phase portraits, Poincare maps, power spectrum, and bifurcation diagrams are used to investigate the dynamic behavior of two-lobe non-circular gas-lubricated micro-bearings. Some results show that with increasing temperature, the rotor behavior changes from T-periodic to quasi-periodic. It was also observed that at high temperatures, with increasing rotational speed, the behavior of the system changes from T-periodic to quasi-periodic, but if the gas is rarefied, this change occurs at a slower speed.

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