基于热力学熵和混沌理论的城市道路交通系统的研究
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摘要
城市道路交通系统的研究是依据一定的科学理论、科学思想和科学方法，对系统的结构、特性以及系统状态进行分析，对系统内部各个方面以及系统与外界的相互关系和相互作用规律从不同角度不同层面进行研究，并建立相关的数学和物理模型，从而揭示交通系统的发展演化规律。研究城市道路交通系统的特性及其发展演化规律对于城市道路交通系统的控制与管理、系统的规划与建设、甚至对整个城市的经济发展与建设都有着十分重要的意义。
城市道路交通系统的研究是交通工程基础科学理论研究的重要课题之一，长期以来，人们从不同方面对其进行了研究，并获得了相应的研究成果，对社会和经济产生了积极的促进作用。但是采用物理学方法(包括动力学理论、热力学熵理论、混沌理论等)从系统特征入手对其进行较全面和较深入的研究还不多见。本文在借鉴国内外成熟研究成果的基础上，采用物理学原理和方法从不同角度对包括交通流系统在内的城市道路交通系统的多个方面进行了深入研究。
论文从系统入手，首先分析了交通系统以及交通流系统的特点和特性，提出了交通系统演化的基本原理。在此基础上，进一步阐述了道路交通系统的热力学特征，构造了该系统的热力学熵。
在分析道路交通系统特性的基础上，引入了交通势的概念，阐述了交通势的物理意义；分析了交通势的影响因素，通过定义交通势梯度，使相对交通压力得到量化；论文根据交通流基本特性以及交通流与路网相互作用规律，提出了城市道路交通系统供需关系演化的蛛网模型，并基于混沌理论对该蛛网模型相关问题进行了讨论，从中得到了相应的结论。
基于城市道路交通与城市发展的相互作用中所存在的负反馈特性，提出了道路交通系统发展演化的动力学模型；对城市道路交通系统发展演化的逻辑斯蒂(S形)曲线的特性进行了分析，特别是对曲线上的三个关键点进行了深入分析，得出了有益的结论；最后根据混沌分形理论对其进行了进一步阐述和分析。
论文依据动力学原理对交通流模型进行了研究。首先，对路段交通压力进行了深入分析，明确了它的物理意义；通过引入相对交通压力和相对动量的概念，并依据动量定理推导得出交通流微分方程；其中粘滞阻力项是在公式推导过程中自然导出的，避免了人为引入参数的随意性，此项的获得对实际交通流的微分方程的应用和相关公式的推导具有重要意义；在推导交通流微分方程的基础上，进一步考虑到实际应用条件，从而导出了格林希尔治方程和一维线性跟驰模型，从而使得交通流理论中的几个重要公式获得了理论上的统一。
采用热力学熵理论的方法对交通流系统进行了研究。首先，对热力学熵的构成进行了分析研究，总结归纳出了构造方法，并以此建立了交通流系统的热力学熵；然后通过分析熵理论中广义流产生的原因，进而揭示了交通流系统中热力学熵产生的内部机制；最后根据熵理论，推导得出了具有动力学特征的道路交通系统中的交通流微分方程。由于是首次引入了热力学熵对交通流系统进行研究，加之已有的关于交通流系统的统计熵研究和讨论，从而构成了一个较为完整的交通流熵理论体系。
本文对交通波进行了研究，首先对交通波进行了三个状态的划分，通过分析前后两个断面交通流的流入和流出率，导出交通波的扩展和收缩方程；以此为基础，讨论了起动波及消散时间、停车波及停车长度等问题，还对交通流通过交叉口进行了动态分析。
以可持续发展为目标，提出了城市路网结构布局评价的基本思想和原则，分析和确定了评价指标以及相应的影响因素和修正系数；建立了路网结构布局的评价模型；并将其应用于实际评价当中，效果良好。
在分析城市路网结构及其功能的基础上，将路网划分为主通路和连接路段；在分析主通路、连接路段以及交叉口可靠性的基础上，通过引入连通度修正因子，导出了OD路网可靠性公式；通过实例应用和深入分析，揭示了连通度在实际路网中具有的双重效应。
通过定义路网的微观态、时效及其时效熵，建立了路网系统的时效熵公式，并给出了计算步骤；根据实测数据拟合的通行时间概率分布曲线，定义了路径选择风险和路径选择风险熵，实现了对出行路径选择风险的量化描述。
在混沌吸引子原理的基础上，通过对交通流时间序列进行相空间重构，分析了临近点与预测点相关性，确定了相关权重；通过对综合权重的确定，建立了修正后的一阶线性预测模型；通过进一步地深入分析指出，预测结果与演化过程中相邻相点间各维分量之间的相互转化关系有关；通过合理地利用转化关系，将实际值的预测转化为了分量百分比的预测，并通过综合分析，建立了基于混沌吸引子的多元线性回归预测模型，其预测结果与实际情况较为接近。
采用灰关联度和信息熵结合的方法对交通影响因素进行了排序。由于用灰关联度法进行排序可能造成突出个别大关联测度值对结果的影响，进而使排序结果与实际情况不符。本文通过采用灰色数据处理方法对参考列和比较列分别进行数据处理，并在其关联值的基础上进一步定义和确定了灰关联熵，建立了交通影响因素排序公式。实际应用表明，排序效果良好。
The study of urban road traffic system,based on scientific theory and idealogy,throughanalyszing the constructure and features of the system and exploring the mechanism of theinteraction among factors forming the system and reciprocity between the system and theoutside,biuld up a variety of model fiting into practical conditions to reveal the law ofevolution of urban road traffic system.No doubt,it is very important researching on the urbanroad traffic system not only to improvment of the system self but also to development ofwhole city economy.
The study of urban road taffic system is one of important research items relating totrasportation engineering。In the passed time,it had been studied more widely and deeply,according to different view points.However it is relevent rare to study it further throughmaking use of physics methods,including dynamic theory,entropy theory,and chaos theory.In this paper,different parts of urban road traffic system have been studied synthetically bymeans of physical method and thought.
At first,based on the chaostic character of traffic system,this paper put forward theprinciple for the development of urban road traffic system,discussed thermodynamicsfeatures of the system,and constructed the thermodynamics entropy of it.
In order to describe urban road traffic system effectively,through analysing charactersof traffic flow system,the concept of the traffic potential was established in this paper.Inaddition,the factors affecting traffic potential was discussed.At the same time,the relaventtraffic pressure was quantited by means of defination of the traffic potential grade,whichwould contribut a lot to furthermore describtion of road traffic sustem.According to thecharacters of traffic flow,the cobweb model of the supply-need relationship of urban roadtraffic system was built up,and some problems about the model was discussed on bassis ofchaos theory.
On the basis of the analysis of thermodynamics entropy,this paper discussed the way tobuild up the thermodynamics entropy of traffic flow,and then established the traffic flowentropy.Through the analysis of the entropy variation of road traffic system,this paperrevealed the mechanism of the traffic flow entropy producing,and set up the equation of theentropy producing.At last,according to the entropy theory,the differentiating equation of thestate and the model of traffic flow were derived.The above method can be used widely todeal with the problem relating to traffic flow,which is meaningful to the development of traffic flow theory.
Aimed at the problem of traditional traffic flow differentiating equation in theory and inpractical use,the traffic pressure was analysed synthetically,and it was pointed out that trafficpressute results from matual effect between traffic flow and road.According to the idea ofmomentum law,the traffic flow defferentiating equation based on kinetic theory was derivedthrough the introduction of relative traffic pressure and relative momentem,and the factor ofthe viscosity resistance is obtained.Under practical conditions of road and traffic flow,Greenshields equation and car following model were derived by means of the traffic flowdifferentialing equation.The results show that the traffic flow differentiating equation isunitive in theory,clear in concept,and overcome the disadvantage of the man-identified factorof viscosity resistance,which is meaningful to the development of traffic flow theory.
Based on the principle of sustainable development,this paper put forward the principleof urban road network layout.Through further analyzing,this paper proposed effectioncoefficients of urban road network layout,and finally established the equation for theevaluation of urban road network layout.The results show that the method is feasible inpractice.
In order to reflect the reliability of urban road network objectively,on the basis of theanalysis of urban road network structure and function,it was put forward that OD roadnetwork consists of main roads and connection roads.According to the principle of reliabilityengineering,the relative influence factors on the reliability was analyzed,and the method ofthe reliability calculation was studied.Based on the main roads reliability,the reliabilityequation of OD road network was derived through introducing OD connectivity.Theinfluence of the node number on OD road network reliability and the method of how toimprove OD road network reliability were discussed further.Analysis and calculation resultsshow that the reliability of the OD road network is 0.621 when main roads are not connectedeffectively,the reliability will be 0.704 through the connection of main roads when thecontinuance of main road is not influnced.It was indicated that the reliability of OD roadnetwork depends on not only the continuance and the validity of main road but also theconnectivity of OD road network,so this method is feasible and effective.
In order to predict chaotic time series of traffic flow accurately,according to theprinciple of chaotic attractor,this paper analyzed correlativity between the central phase pointand the neibour phase point in the region of chaotic attractor,and pointed out that thecorrelativity plays an important role in the prediction.Making use of the principle and method of grey system,this paper obtained the correlativity weight,and established the forecastmodel with the correlativity weight.At last,incorperating distance weight and correlativityweight as synthetic weight,this paper derived the one-order linear prediction model withsynthetic weight and established the multi-dimensional forecast model of chaotic time seriesof traffic flow.The analyzed result shows that it is feasible and effective.
This paper pointed out the shortcoming of the original grey relation analysis method inranking of influnece factors,which may cause the tendence controlled by relation value ofparticular points and make some useful information lost.In order to overcome theshortcoming,through introducing grey entropy and connecting it with grey relation degree,this paper established the coincidence degree.The applicaton of practical example showsthat the ranking order of thanspoetation factor based on the coincidence degree method isbasically accord with based on others,so it is feasible.
城市道路交通系统的研究是交通工程基础科学理论研究的重要课题之一，长期以来，人们从不同方面对其进行了研究，并获得了相应的研究成果，对社会和经济产生了积极的促进作用。但是采用物理学方法(包括动力学理论、热力学熵理论、混沌理论等)从系统特征入手对其进行较全面和较深入的研究还不多见。本文在借鉴国内外成熟研究成果的基础上，采用物理学原理和方法从不同角度对包括交通流系统在内的城市道路交通系统的多个方面进行了深入研究。
论文从系统入手，首先分析了交通系统以及交通流系统的特点和特性，提出了交通系统演化的基本原理。在此基础上，进一步阐述了道路交通系统的热力学特征，构造了该系统的热力学熵。
在分析道路交通系统特性的基础上，引入了交通势的概念，阐述了交通势的物理意义；分析了交通势的影响因素，通过定义交通势梯度，使相对交通压力得到量化；论文根据交通流基本特性以及交通流与路网相互作用规律，提出了城市道路交通系统供需关系演化的蛛网模型，并基于混沌理论对该蛛网模型相关问题进行了讨论，从中得到了相应的结论。
基于城市道路交通与城市发展的相互作用中所存在的负反馈特性，提出了道路交通系统发展演化的动力学模型；对城市道路交通系统发展演化的逻辑斯蒂(S形)曲线的特性进行了分析，特别是对曲线上的三个关键点进行了深入分析，得出了有益的结论；最后根据混沌分形理论对其进行了进一步阐述和分析。
论文依据动力学原理对交通流模型进行了研究。首先，对路段交通压力进行了深入分析，明确了它的物理意义；通过引入相对交通压力和相对动量的概念，并依据动量定理推导得出交通流微分方程；其中粘滞阻力项是在公式推导过程中自然导出的，避免了人为引入参数的随意性，此项的获得对实际交通流的微分方程的应用和相关公式的推导具有重要意义；在推导交通流微分方程的基础上，进一步考虑到实际应用条件，从而导出了格林希尔治方程和一维线性跟驰模型，从而使得交通流理论中的几个重要公式获得了理论上的统一。
采用热力学熵理论的方法对交通流系统进行了研究。首先，对热力学熵的构成进行了分析研究，总结归纳出了构造方法，并以此建立了交通流系统的热力学熵；然后通过分析熵理论中广义流产生的原因，进而揭示了交通流系统中热力学熵产生的内部机制；最后根据熵理论，推导得出了具有动力学特征的道路交通系统中的交通流微分方程。由于是首次引入了热力学熵对交通流系统进行研究，加之已有的关于交通流系统的统计熵研究和讨论，从而构成了一个较为完整的交通流熵理论体系。
本文对交通波进行了研究，首先对交通波进行了三个状态的划分，通过分析前后两个断面交通流的流入和流出率，导出交通波的扩展和收缩方程；以此为基础，讨论了起动波及消散时间、停车波及停车长度等问题，还对交通流通过交叉口进行了动态分析。
以可持续发展为目标，提出了城市路网结构布局评价的基本思想和原则，分析和确定了评价指标以及相应的影响因素和修正系数；建立了路网结构布局的评价模型；并将其应用于实际评价当中，效果良好。
在分析城市路网结构及其功能的基础上，将路网划分为主通路和连接路段；在分析主通路、连接路段以及交叉口可靠性的基础上，通过引入连通度修正因子，导出了OD路网可靠性公式；通过实例应用和深入分析，揭示了连通度在实际路网中具有的双重效应。
通过定义路网的微观态、时效及其时效熵，建立了路网系统的时效熵公式，并给出了计算步骤；根据实测数据拟合的通行时间概率分布曲线，定义了路径选择风险和路径选择风险熵，实现了对出行路径选择风险的量化描述。
在混沌吸引子原理的基础上，通过对交通流时间序列进行相空间重构，分析了临近点与预测点相关性，确定了相关权重；通过对综合权重的确定，建立了修正后的一阶线性预测模型；通过进一步地深入分析指出，预测结果与演化过程中相邻相点间各维分量之间的相互转化关系有关；通过合理地利用转化关系，将实际值的预测转化为了分量百分比的预测，并通过综合分析，建立了基于混沌吸引子的多元线性回归预测模型，其预测结果与实际情况较为接近。
采用灰关联度和信息熵结合的方法对交通影响因素进行了排序。由于用灰关联度法进行排序可能造成突出个别大关联测度值对结果的影响，进而使排序结果与实际情况不符。本文通过采用灰色数据处理方法对参考列和比较列分别进行数据处理，并在其关联值的基础上进一步定义和确定了灰关联熵，建立了交通影响因素排序公式。实际应用表明，排序效果良好。
The study of urban road traffic system,based on scientific theory and idealogy,throughanalyszing the constructure and features of the system and exploring the mechanism of theinteraction among factors forming the system and reciprocity between the system and theoutside,biuld up a variety of model fiting into practical conditions to reveal the law ofevolution of urban road traffic system.No doubt,it is very important researching on the urbanroad traffic system not only to improvment of the system self but also to development ofwhole city economy.
The study of urban road taffic system is one of important research items relating totrasportation engineering。In the passed time,it had been studied more widely and deeply,according to different view points.However it is relevent rare to study it further throughmaking use of physics methods,including dynamic theory,entropy theory,and chaos theory.In this paper,different parts of urban road traffic system have been studied synthetically bymeans of physical method and thought.
At first,based on the chaostic character of traffic system,this paper put forward theprinciple for the development of urban road traffic system,discussed thermodynamicsfeatures of the system,and constructed the thermodynamics entropy of it.
In order to describe urban road traffic system effectively,through analysing charactersof traffic flow system,the concept of the traffic potential was established in this paper.Inaddition,the factors affecting traffic potential was discussed.At the same time,the relaventtraffic pressure was quantited by means of defination of the traffic potential grade,whichwould contribut a lot to furthermore describtion of road traffic sustem.According to thecharacters of traffic flow,the cobweb model of the supply-need relationship of urban roadtraffic system was built up,and some problems about the model was discussed on bassis ofchaos theory.
On the basis of the analysis of thermodynamics entropy,this paper discussed the way tobuild up the thermodynamics entropy of traffic flow,and then established the traffic flowentropy.Through the analysis of the entropy variation of road traffic system,this paperrevealed the mechanism of the traffic flow entropy producing,and set up the equation of theentropy producing.At last,according to the entropy theory,the differentiating equation of thestate and the model of traffic flow were derived.The above method can be used widely todeal with the problem relating to traffic flow,which is meaningful to the development of traffic flow theory.
Aimed at the problem of traditional traffic flow differentiating equation in theory and inpractical use,the traffic pressure was analysed synthetically,and it was pointed out that trafficpressute results from matual effect between traffic flow and road.According to the idea ofmomentum law,the traffic flow defferentiating equation based on kinetic theory was derivedthrough the introduction of relative traffic pressure and relative momentem,and the factor ofthe viscosity resistance is obtained.Under practical conditions of road and traffic flow,Greenshields equation and car following model were derived by means of the traffic flowdifferentialing equation.The results show that the traffic flow differentiating equation isunitive in theory,clear in concept,and overcome the disadvantage of the man-identified factorof viscosity resistance,which is meaningful to the development of traffic flow theory.
Based on the principle of sustainable development,this paper put forward the principleof urban road network layout.Through further analyzing,this paper proposed effectioncoefficients of urban road network layout,and finally established the equation for theevaluation of urban road network layout.The results show that the method is feasible inpractice.
In order to reflect the reliability of urban road network objectively,on the basis of theanalysis of urban road network structure and function,it was put forward that OD roadnetwork consists of main roads and connection roads.According to the principle of reliabilityengineering,the relative influence factors on the reliability was analyzed,and the method ofthe reliability calculation was studied.Based on the main roads reliability,the reliabilityequation of OD road network was derived through introducing OD connectivity.Theinfluence of the node number on OD road network reliability and the method of how toimprove OD road network reliability were discussed further.Analysis and calculation resultsshow that the reliability of the OD road network is 0.621 when main roads are not connectedeffectively,the reliability will be 0.704 through the connection of main roads when thecontinuance of main road is not influnced.It was indicated that the reliability of OD roadnetwork depends on not only the continuance and the validity of main road but also theconnectivity of OD road network,so this method is feasible and effective.
In order to predict chaotic time series of traffic flow accurately,according to theprinciple of chaotic attractor,this paper analyzed correlativity between the central phase pointand the neibour phase point in the region of chaotic attractor,and pointed out that thecorrelativity plays an important role in the prediction.Making use of the principle and method of grey system,this paper obtained the correlativity weight,and established the forecastmodel with the correlativity weight.At last,incorperating distance weight and correlativityweight as synthetic weight,this paper derived the one-order linear prediction model withsynthetic weight and established the multi-dimensional forecast model of chaotic time seriesof traffic flow.The analyzed result shows that it is feasible and effective.
This paper pointed out the shortcoming of the original grey relation analysis method inranking of influnece factors,which may cause the tendence controlled by relation value ofparticular points and make some useful information lost.In order to overcome theshortcoming,through introducing grey entropy and connecting it with grey relation degree,this paper established the coincidence degree.The applicaton of practical example showsthat the ranking order of thanspoetation factor based on the coincidence degree method isbasically accord with based on others,so it is feasible.
引文
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