Traffic chaos and its prediction based on a nonlinear car-following model

This paper discusses the dynamic behavior and its predictions for a simulated traffic flow based on the nonlinear response of a vehicle to the leading car＇s movement in a single lane. Traffic chaos is a promising field, and chaos theory has been applied to identify and predict its chaotic movement. A simulated traffic flow is generated using a car-following model（ GM model）, and the distance between two cars is investigated for its dynamic properties. A positive Lyapunov exponent confirms the existence of chaotic behavior in the GM model. A new algorithm using a RBF NN （radial basis function neural network） is proposed to predict this traffic chaos. The experiment shows that the chaotic degree and predictable degree are determined by the first Lyapunov exponent. The algorithm proposed in this paper can be generalized to recognize and predict the chaos of short-time traffic flow series

Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses:discrete and continuum models

The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.

Comparison of nonlinear modeling methods for the composite rubber clamp

The cubic stiffness force model(CSFM)and Bouc-Wen model(BWM)are introduced and compared innovatively.The unknown coefficients of the nonlinear models are identified by the genetic algorithm combined with experiments.By fitting the identified nonlinear coefficients under different excitation amplitudes,the nonlinear vibration responses of the system are predicted.The results show that the accuracy of the BWM is higher than that of the CSFM,especially in the non-resonant region.However,the optimization time of the BWM is longer than that of the CSFM.

Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

Atlantic blocking events in a simplified nonlinear baroclinic model for local finite-amplitude wave activity

为研究北大西洋阻高的形成机制,本文在局部有限振幅波活动(LWA)框架下进行了一系列数值实验.采用的数值模型能显式地描绘出两种重要的大气内部动力过程,即非线性纬向位涡通量和Rossby波包传播.模拟结果显示,这两种动力学过程均是形成大西洋阻高的重要机理.具体地,非线性纬向位涡通量和Rossby波包传播,分别是大西洋阻高南部和北部LWA形成的主导因子.因此,本研究综合了前人关于大西洋阻高的研究成果,为其形成机理提供了新的认识.

Nonlinear free vibration of piezoelectric semiconductor doubly-curved shells based on nonlinear drift-diffusion model

In this paper, the nonlinear free vibration behaviors of the piezoelectric semiconductor(PS) doubly-curved shell resting on the Pasternak foundation are studied within the framework of the nonlinear drift-diffusion(NLDD) model and the first-order shear deformation theory. The nonlinear constitutive relations are presented, and the strain energy, kinetic energy, and virtual work of the PS doubly-curved shell are derived.Based on Hamilton's principle as well as the condition of charge continuity, the nonlinear governing equations are achieved, and then these equations are solved by means of an efficient iteration method. Several numerical examples are given to show the effect of the nonlinear drift current, elastic foundation parameters as well as geometric parameters on the nonlinear vibration frequency, and the damping characteristic of the PS doublycurved shell. The main innovations of the manuscript are that the difference between the linearized drift-diffusion(LDD) model and the NLDD model is revealed, and an effective method is proposed to select a proper initial electron concentration for the LDD model.

Remaining useful life prediction based on nonlinear random coefficient regression model with fusing failure time data

Remaining useful life(RUL) prediction is one of the most crucial elements in prognostics and health management(PHM). Aiming at the imperfect prior information, this paper proposes an RUL prediction method based on a nonlinear random coefficient regression(RCR) model with fusing failure time data.Firstly, some interesting natures of parameters estimation based on the nonlinear RCR model are given. Based on these natures,the failure time data can be fused as the prior information reasonably. Specifically, the fixed parameters are calculated by the field degradation data of the evaluated equipment and the prior information of random coefficient is estimated with fusing the failure time data of congeneric equipment. Then, the prior information of the random coefficient is updated online under the Bayesian framework, the probability density function(PDF) of the RUL with considering the limitation of the failure threshold is performed. Finally, two case studies are used for experimental verification. Compared with the traditional Bayesian method, the proposed method can effectively reduce the influence of imperfect prior information and improve the accuracy of RUL prediction.

A velocity-difference-separation model for car-following theory

We introduce a velocity-difference-separation model that modifies the previous models in the literature. The improvement of this new model over the previous ones lies in that it not only theoretically retains many strong points of the previous ones, but also performs more realistically than others in the dynamical evolution of congestion. Furthermore, the proposed model is investigated with analytic and numerical methods, with the finding that it can demonstrate some complex physical features observed in real traffic such as the existence of three phases： free flow, synchronized flow, and wide moving jam; sudden flow drop in flow-density plane; and traffic hysteresis in transition between the free and the synchronized flow.

Feedback control scheme of traffic jams based on the coupled map car-following model

Based on the pioneering work of Konishi et al. [Phys. Rev. E （1999） 60 4000], a new feedback control scheme is presented to suppress traffic jams based on the coupled map car-following model under the open boundary condition. The effect of the safe headway on the traffic system is considered. According to the control theory, the condition under which traffic jams can be suppressed is analyzed. The results are compared with the previous results concerning congestion control. The simulations show that the suppression performance of our scheme on traffic jams is better than those of the previous schemes, although all the schemes can suppress traffic jams. The simulation results are consistent with theoretical analyses.

A new car-following model with consideration of the traffic interruption probability

In this paper, we present a new car-following model by taking into account the effects of the traffic interruption probability on the car-following behaviour of the following vehicle. The stability condition of the model is obtained by using the linear stability theory. The modified Korteweg-de Vries （KdV） equation is constructed and solved, and three types of traffic flows in the headway sensitivity space-stable, metastable, and unstable--are classified. Both the analytical and simulation results show that the traffic interruption probability indeed has an influence on driving behaviour, and the consideration of traffic interruption probability in the car-following model could stabilize traffic flow.

Car-following models of vehicular traffic

The Car-following models is a kind of microscopic simulation model for vehicular traffic, which describe the one-by-one following behaviors of vehicles in the same traffic lane. As a common traffic phenomenon, following behavior is of great importance in the micro-study of intelligent traffic control. Compared with other traffic-flow models, car-following model embodies the human factors and reflects the real traffic situation in a better way. This paper gives a systematic review of the development and actuality of car-following models by introducing and analyzing in detail the advantages and disadvantages of GHR model, OV model, CA model and fuzzy-logic model. In addition, local stability and asymptotic stability of car-following models are discussed in this paper.

A new coupled map car-following model considering drivers' steady desired speed

Based on the pioneering work of Konishi et al., in consideration of the influence of drivers＇ steady desired speed ef/ect on the traffic flow, we develop a new coupled map car-following model in the real world. By use of the control theory, the stability condition of our model is derived. The validity of the present theoretical scheme is verified via numerical simulation, confirming the correctness of our theoretical analysis.

A control method for congested traffic in the coupled map car-following model

Based on the pioneer work of Konishi et al, a new control method is presented to suppress the traffic congestion in the coupled map （CM） car-following model under an open boundary. A control signal concluding the velocity differences of the two vehicles in front is put forward. The condition under which the traffic jam can be contained is analyzed. The results axe compared with that presented by Konishi et al [Phys. Rev. 1999 E 60 4000-4007]. The simulation results show that the temporal behavior obtained by our method is better than that by the Konishi＇s et al. method, although both the methods could suppress the traffic jam. The simulation results are consistent with the theoretical analysis.

An Improved Car-Following Model for Multiphase Vehicular Traffic Flow and Numerical Tests

This paper attempts to introduce an improved difference model that modifies a car-following model, which takes the next-nearest-neighbor interaction into account. The hnprovement of this model over the previous one lies in that it performs more realistically in the dynamical motion for small delay time. The traffic behavior of the improved model is investigated with analytic and numerical methods with the finding that the new consideration could further stabilize traffic flow. And some simulation tests verify that the proposed model can demonstrate some complex physical features observed recently in real traffic such as the existence of three phases： free flow, coexisting flow, and jam flow; spontaneous formation of density waves; sudden flow drop in flow-density plane; traffic hysteresis in transition between the free and the coexisting flow. Furthermore, th.e improved model also predicts that the stable state to relative density in the coexisting flow is insusceptible to noise.

An improved car-following model with consideration of the lateral effect and its feedback control research

A car-following model is presented, in which the effects of non-motor vehicles on adjacent lanes are taken into ac- count. A control signal including the velocity differences between the following vehicle and the target vehicle is introduced according to the feedback control theory. The stability condition for the new model is derived. Numerical simulation is used to demonstrate the advantage of the new model including the control signal; the results are consistent with the analytical ones

Pre-compensation of Friction for CNC Machine Tools through Constructing a Nonlinear Model Predictive Scheme

Nonlinear friction is a dominant factor afecting the control accuracy of CNC machine tools.This paper proposes a friction pre-compensation method for CNC machine tools through constructing a nonlinear model predictive scheme.The nonlinear friction-induced tracking error is frstly modeled and then utilized to establish the nonlinear model predictive scheme,which is subsequently used to optimize the compensation signal by treating the friction-induced tracking error as the optimization objective.During the optimization procedure,the derivative of compensation signal is constrained to avoid vibration of machine tools.In contrast to other existing approaches,the proposed method only needs the parameters of Stribeck friction model and an additional tuning parameter,while fnely identifying the parameters related to the pre-sliding phenomenon is not required.As a result,it greatly facilitates the practical applicability.Both air cutting and real cutting experiments conducted on an in-house developed open-architecture CNC machine tool prove that the proposed method can reduce the tracking errors by more than 56%,and reduce the contour errors by more than 50%.

A new coupled-map car-following model based on a transportation supernetwork framework

A new car-following model is proposed by considering information from a number of preceding vehicles with intervehicle communication. A supernetwork architecture is first described, which has two layers： a traffic network and a communication network. The two networks interact with and depend on each other. The error dynamic system around the steady state of the model is theoretically analyzed and some nonjam criteria are derived. A simple control signal is added to the model to analyze the criteria of suppressing traffic jams. The corresponding numerical simulations confirm the correctness of the theoretical analysis. Compared with previous studies concerning coupled map models, the controlled model proposed in this paper is more reasonable and also more effective in the sense that it takes into account the formation of traffic congestion.

A Model of Car-Following with Adaptive Headway

The performances of a well-known GHR car-following model was investigated by using numerical simulations in describing the acceleration and deceleration process induced by the motion of a leading car. It is shown that in GHR model vehicle is allowed to run arbitrarily close together if their speed are identical,and it waves aside even though the separation is larger than its desired distance. Based on these investigations, a modified GHR model which features a new nonlinear term which attempts to adjust the inter-vehicle spacing to a certain desired value was proposed accordingly to overcome these deficiencies. In addition, the analysis of the additive nonlinear term and steady-state flow of the new model were studied to prove its rationality.

A control method applied to mixed traffic flow for the coupled-map car-following model

In light of previous work [Phys. Rev. E 60 4000 （1999）], a modified coupled-map car-following model is proposed by considering the headways of two successive vehicles in front of a considered vehicle described by the optimal velocity function. The non-jam conditions are given on the basis of control theory. Through simulation, we find that our model can exhibit a better effect as p = 0.65, which is a parameter in the optimal velocity function. The control scheme, which was proposed by Zhao and Gao, is introduced into the modified model and the feedback gain range is determined. In addition, a modified control method is applied to a mixed traffic system that consists of two types of vehicle. The range of gains is also obtained by theoretical analysis. Comparisons between our method and that of Zhao and Gao are carried out, and the corresponding numerical simulation results demonstrate that the temporal behavior of traffic flow obtained using our method is better than that proposed by Zhao and Gao in mixed traffic systems.

Numerical Simulation of Motor Vehicles’ Courtesy Behavior on Crosswalk Based on Car-Following Model

In observing driver courtesy towards pedestrians at unsignalized crosswalks, a behavioral model was adopted in a simulation based on the GM Car-Following Model. The SIMI Motion Software was used to extract the vehicle operation data from Wenyi South Road and Hanyuan Road in Xi'an City. The parameters of the GM Car-Following Model were calibrated by genetic algorithm. The road simulation environment based on the Car-Following Model was constructed by MATLAB. In the case of no stopping, uniform deceleration avoidance with advance notice, emergency brake avoidance without advance notice, changes such as the displacement of the Car-Following queue, headway, speed, acceleration, and deceleration were analyzed by numerical simulation. The results show that when there is advance notice before the crosswalk, the minimum headway distances of Car1-Car2, Car2-Car3, Car3-Car4 and Car4-Car5 are 7.09 m, 7.38 m, 7.65 m, 7.91 m, and the average rates of change of the headway during deceleration are 0.78 m/s, 0.74 m/s, 0.71 m/s, 0.68 m/s respectively;in the absence of advance notice before the crosswalk, the minimum headway distances of Car1-Car2, Car2-Car3, Car3-Car4 and Car4-Car5 are 7.28 m, 7.75 m, 8.19 m, 8.59 m, and the average rates of change of the headway during deceleration are 1.57 m/s, 1.25 m/s, 1.04 m/s, 0.96 m/s, respectively. Therefore, in order to effectively prevent the occurrence of vehicle rear-end events, it's necessary to set traffic signs and markings on the preceding section of the intersection or road exhibiting behavioral comity.