FREEWAY TRAFFIC FLOW MODELING BASED ON RECURRENT NEURAL NETWORK AND WAVELET TRANSFORM基于递归神经网络和小波变换的高速公路交通流建模6 Conclusions 结论The highly nonlinear and dynamic characteristics of the macroscopic traffic flow require a modeling approach, which can deal with the complex nonlinear relationships among the speed, flow and density.宏观交通流的高度非线性和动态特性，需要一个建模方法，它可以处理的速度，流量和密度之间的复杂的非线性关系。

At the same time, effective measures have to be taken to eliminate traffic noise and disturbance. In this paper, a method of wavelet denoising and traffic flow modeling by an Elman recurrent neural network is presented.同时，必须采取有效措施来消除交通噪声和干扰。

在本文中，一种小波去噪和交通流的Elman神经网络建模这工作了。

Simulation results show that the wavelet transform can effectively eliminate the noise signal, and that the Elman network can accurately describe the real behavior of freeway traffic flow.仿真结果表明，小波变换可以有效地消除信号中的噪声，和Elman神经网络能够准确地描述高速公路交通流的真实行为。

This method is of great importance to realize on-line modeling and control of freeway traffic flow.此方法对实现高速公路交通流的在线建模与控制具有重要意义。

Fuzzy Self-Adaptive PID Controller for Freeway Ramp Metering高速公路匝道控制的模糊自适应控制器Abstract:Aiming at the nonlinear and time-varying characteristics of freeway traffic system, a fuzzy self-adaptive PID controller is designed and applied to freeway ramp metering in this paper.摘要：针对高速公路交通系统的非线性、时变特性，设计了一种模糊自适应控制器，并将其应用于高速公路匝道控制系统。

A traffic flow model to describe the freeway flow process is firstly built. Based on the model and in conjunction with nonlinear feedback theory, a fuzzy-PID ramp controller is then designed. The ramp metering rate is determined by the PID controller whose parameters are tuned by fuzzy logic according to the density tracking error and error variation.首先建立了一个交通流模型来描述高速公路的流程。

基于该模型，并结合非线性反馈理论，一个模糊的控制器，控制器，然后设计。

斜坡根据密度跟踪误差和误差变化情况，通过模糊逻辑对控制器参数进行调整，确定了测量速度。

Gauss and triangle curves are used for the membership functions of the fuzzy variables. The rule base including 49 fuzzy rules is also established. Finally, the control system is simulated in MATLAB software. The results show that this controller designed has fast response, good dynamic and steady-state performance. It can achieve a desired traffic density along the mainline of a freeway, and can make vehicles travel more efficiently and safely. This approach is quite effective to freeway ramp metering.高斯和三角曲线用于模糊变量的隶属函数。

还建立了包括49个模糊规则的规则库。

最后，对控制系统进行了仿真研究的软件。

结果表明，该控制器具有响应快、动态性能和稳态性能。

它可以实现所需的交通密度，高速公路主线，并能使车辆行驶更安全、更安全。

这种方法是相当有效的高速公路匝道控制。

2. Freeway Traffic Flow Model高速公路交通流模型Consider a multiple lane (λ) freeway section with a single entry ramp, as shown in figure 1. 考虑多车道（λ）具有单一入口匝道路段，如图1所示。

Assume that at time slice k, vehicles flow into a given section at a rate of qu(k) vehicles per hour per lane from its upper boundary and r(k) vehicles per hour from the entry ramp.假设在时间片上，车辆进入一个给定的区段在一个区段（克）每车道从它的上边界和（钾）车辆每小时从入口匝道的速度。

They discharge at a rate of q(k) vehicles per hour per lane at its lower boundary. 他们以每小时的速度在其较低的边界处排放一个问（克）的车辆。

By the conservation principle, the number of vehicles in this freeway segment at time 按养护原则，在这条高速公路的车辆数量在时间 k+1, N(k+1) would be )]()()([)()1(k r k q k q t k N k N u +-∆+=+λλ (1)Δxq u ρ v qrFigure 1 A freeway section )]()()([)()1(k r k q k q t k N k N u +-∆+=+λλ (1)Define traffic density as , where is length of the road segment. Equation (1) can now be written in terms of density 定义交通密度，哪里是公路段的长度。

方程（1）现在可以用密度来书写]/)()()([)/()()1(λρρk r k q k q x t k k u +-∆∆+=+(2)Empirical evidence suggests that a relationship between flow and traffic density exists. This relationship, denoted as is generally referred to as the fundamental diagram of traffic flow. Many forms of fundamental diagrams have been proposed, all of which share some common features: 经验证据表明，流量和交通密度之间的关系存在。

这种关系，表示为通常被称为交通流基本图。

许多形式基本图已经被提出，所有这些都有一些共同的特点：(1) flow is zero when density is zero; (2) there is a maximum density (often referred to as jam density) that corresponds to bumper-to-bumper traffic (at which flow is also zero); and (3) there exists a traffic density at which flow is maximal (often referred to as critical density). （1）密度为零时的流量为零；（2）有一个最大密度（通常称为果酱密度），对应于保险杠到保险杠的流量（在流量也是零）；（3）存在流量最大的交通密度（通常称为临界密度）。

When traffic density is below critical density, flow increases with density; and when traffic density is above critical density, flow decreases with density.交通密度低于临界密度时，流量随密度增大而增大；当交通密度超过临界密度时，流量随密度的增加而减小。

Equation (2) and the fundamental diagram constitute a discrete form of the well known traffic flow model called LWR model [4]. 方程（2）和基本图构成的离散的众所周知的交通流模型的LWR模型[ 4 ]形式。