交通流的非线性分析、预测和控制
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摘要
交通流中的非线性特征是近年来兴起的一个研究方向,其研究目地在于揭示交通流系统的各种非线性特征背后的形成机制,然后加以预测和控制。研究对象主要分为2类：一类是各种交通流模型,另一类是实际的交通流时间序列。本文以交通流的非线性分析、预测和控制为研究内容,重点进行了以下的研究：
(1)对宏观和微观的交通流时间序列进行非线性检验,检验方法有递归图、替代数据法、CLY方法和功率潜,检验结果表示宏观和微观交通流均具有周期性和随机性,均表现出混沌特征。
(2)从三个方面分析微观交通流时序的非线性特征。第一：采用提出的基于最小二乘支持向量机(LS-SVM)计算时间序列Lyapunov指数谱的方法分析了交通流的混沌和超混沌特征,计算结果表示交通流在拥挤状态下出现超混沌。第二：提出通过速度时间序列的算法复杂度估计系统周期性成分的比率,通过速度变化率序列的近似熵估计系统在结构变化上的复杂性。计算结果表明不同的复杂度值对应交通流的不同状态。第三：改进了hurst指数和多重分形谱的计算方法,然后采用hurst指数和多重分形谱分析不同状态下交通流序列的分形结构特征,结果表明交通流在不同状态下的分形特征量值存在差异,因此具有不同的分形结构。
(3)对交通流预测的研究包括：一、提出一种改进的基于最大Lyapunov指数的混沌时序预测方法。该方法选取了相空间中的多个邻近重构向量来提高预测精度,给出了计算步骤。对理论混沌序列预测的结果表明改进方法要优于原方法,讨论了噪声和邻近参考点数对预测结果的影响,并将该方法应用到了对交通流的预测当中。二,提出了基于最大Lyapunov指数的多变量混沌时间序列的预测方法。给出了算法步骤,并讨论了噪声、邻近参考点数和预测步长对预测效果的影响。对理论混沌序列预测的结果表明了提出方法的有效性,并将该方法应用到了对交通流的多变量预测当中。三,提出了一种预测交通流量的动态组合建模方法。该方法将流量时间序列分解成周期项、趋势项、混沌扰动项,采用季节性指数平滑法预测周期项和趋势项之和,计算时分别取周期为一天和一周,用带遗忘因子的递推最小二乘法确定权重,采用混沌预测的邻域法预测混沌项。仿真结果表明了该方法的合理性和有效性。
(4)依据变结构控制理论,通过设计速度控制器使得交通流趋于稳定和有序。提出了三种控制方法：连续宏观交通流模型的近似变结构控制；基于离散趋近律的离散交通流模型的变结构控制：基于离散趋近律的离散交通流模型的预测变结构控制。给出了算法步骤并进行了仿真实验,仿真结果表明提出的方法能够将交通流密度稳定在一定范围内。通过改变换道率实现车流在车道上的分配。
图69幅,表14个,参考文献176篇。
Nonlinear characteristics in traffic flow is one research area in recent years, the research object is to reveal formation mechanism of nonlinear characteristics of traffic system, and then prediction and control. The research targets include each kind traffic flow model and real traffic flow time series. The study contents of this dissertation are nonlinear characteristics, predication and control of traffic flow, the main aspects are as follow:
(1) Nonlinear characteristics of macroscopic and microscopic traffic flow time series had been tested, the test methods include:recurrence plot, surrogate time series method, CLY method and power spectrum, the results show that macroscopic and microscopic traffic flow contain nonlinear characteristics and are chaotic.
(2) Nonlinear characteristics of microscopic traffic flow time series are analyzed of three aspects. The firstly, method of calculation Lyapunov exponent spectrum of time series based on least-squared support vector machine(LS-SVM) is proposed, and chaos and super chaos characteristics in traffic flow are analyzed by this method, the results show that traffic flow is super chaotic in jam condition. The secondly, methods of estimation ratio of periodic ingredient in system by Kolmogrov Complexity(Kc) and estimation complexity of structure variation of system by Approximate Entropy(ApEn) are proposed. The results of calculation show that different Kc and ApEn compare with different traffic conditions. The thirdly, methods of computation hurst index and multi-fractal spectrum are improved, then, fractal structure of microscopic traffic flow analyzed by hurst index and multi-fractal spectrum. The results show that microscopic traffic flow have different fractal characteristic values in different conditions, so it have different fractal characteristic structure in different conditions.
(3) The research of traffic predication include:The firstly, method of forecast chaotic time series based on maximum Lyapunov exponent is improved, in which several neighbouring reference vectors are selected in reconstructed phase space to increase forecasting precision, and the algorithm is given. The result of predication theory chaotic time series show that the improved method has a higher than the original method, meanwhile the influence from noise and number of nearly neighbour vector on the predication results is discussed, and traffic flow is predicated by the improved method. A method for predication of multivariable chaotic time series is proposed, and the calculation process is given, the influence from the noise and number of nearly neighbour vector and the forecasting step on the predication results is discussed, and traffic flow are predicated by the method. A combined dynamic method of forecast traffic volume time series is proposed. The traffic flow is decomposed into cycle item and tendency item and chaotic disturbing item, the sum of the cycle item and the tendency item is forecasted by seasonal index smoothing method, in this process the cycle chosen one day and one week, and recursive least squares with forgetting factor determined the weights, and the chaotic disturbing item is forecasted by partial forecast method. The simulation results show the reasonability and the effectiveness of the method.
(4) Based on variable structure control theory, speed controller are designed to stabilized traffic flow, and three control methods are proposed:approximately variable structure control continuous macroscopic traffic flow model; control discrete macroscopic traffic flow model based on discrete approaching low; forecasting control discrete macroscopic traffic flow model based on discrete approaching low. the algorithms are proposed, the simulation results show that the proposed methods can make the traffic density in a certain range. Distribution of traffic flow on different lane was achieved by changing lane rate.
(1)对宏观和微观的交通流时间序列进行非线性检验,检验方法有递归图、替代数据法、CLY方法和功率潜,检验结果表示宏观和微观交通流均具有周期性和随机性,均表现出混沌特征。
(2)从三个方面分析微观交通流时序的非线性特征。第一：采用提出的基于最小二乘支持向量机(LS-SVM)计算时间序列Lyapunov指数谱的方法分析了交通流的混沌和超混沌特征,计算结果表示交通流在拥挤状态下出现超混沌。第二：提出通过速度时间序列的算法复杂度估计系统周期性成分的比率,通过速度变化率序列的近似熵估计系统在结构变化上的复杂性。计算结果表明不同的复杂度值对应交通流的不同状态。第三：改进了hurst指数和多重分形谱的计算方法,然后采用hurst指数和多重分形谱分析不同状态下交通流序列的分形结构特征,结果表明交通流在不同状态下的分形特征量值存在差异,因此具有不同的分形结构。
(3)对交通流预测的研究包括：一、提出一种改进的基于最大Lyapunov指数的混沌时序预测方法。该方法选取了相空间中的多个邻近重构向量来提高预测精度,给出了计算步骤。对理论混沌序列预测的结果表明改进方法要优于原方法,讨论了噪声和邻近参考点数对预测结果的影响,并将该方法应用到了对交通流的预测当中。二,提出了基于最大Lyapunov指数的多变量混沌时间序列的预测方法。给出了算法步骤,并讨论了噪声、邻近参考点数和预测步长对预测效果的影响。对理论混沌序列预测的结果表明了提出方法的有效性,并将该方法应用到了对交通流的多变量预测当中。三,提出了一种预测交通流量的动态组合建模方法。该方法将流量时间序列分解成周期项、趋势项、混沌扰动项,采用季节性指数平滑法预测周期项和趋势项之和,计算时分别取周期为一天和一周,用带遗忘因子的递推最小二乘法确定权重,采用混沌预测的邻域法预测混沌项。仿真结果表明了该方法的合理性和有效性。
(4)依据变结构控制理论,通过设计速度控制器使得交通流趋于稳定和有序。提出了三种控制方法：连续宏观交通流模型的近似变结构控制；基于离散趋近律的离散交通流模型的变结构控制：基于离散趋近律的离散交通流模型的预测变结构控制。给出了算法步骤并进行了仿真实验,仿真结果表明提出的方法能够将交通流密度稳定在一定范围内。通过改变换道率实现车流在车道上的分配。
图69幅,表14个,参考文献176篇。
Nonlinear characteristics in traffic flow is one research area in recent years, the research object is to reveal formation mechanism of nonlinear characteristics of traffic system, and then prediction and control. The research targets include each kind traffic flow model and real traffic flow time series. The study contents of this dissertation are nonlinear characteristics, predication and control of traffic flow, the main aspects are as follow:
(1) Nonlinear characteristics of macroscopic and microscopic traffic flow time series had been tested, the test methods include:recurrence plot, surrogate time series method, CLY method and power spectrum, the results show that macroscopic and microscopic traffic flow contain nonlinear characteristics and are chaotic.
(2) Nonlinear characteristics of microscopic traffic flow time series are analyzed of three aspects. The firstly, method of calculation Lyapunov exponent spectrum of time series based on least-squared support vector machine(LS-SVM) is proposed, and chaos and super chaos characteristics in traffic flow are analyzed by this method, the results show that traffic flow is super chaotic in jam condition. The secondly, methods of estimation ratio of periodic ingredient in system by Kolmogrov Complexity(Kc) and estimation complexity of structure variation of system by Approximate Entropy(ApEn) are proposed. The results of calculation show that different Kc and ApEn compare with different traffic conditions. The thirdly, methods of computation hurst index and multi-fractal spectrum are improved, then, fractal structure of microscopic traffic flow analyzed by hurst index and multi-fractal spectrum. The results show that microscopic traffic flow have different fractal characteristic values in different conditions, so it have different fractal characteristic structure in different conditions.
(3) The research of traffic predication include:The firstly, method of forecast chaotic time series based on maximum Lyapunov exponent is improved, in which several neighbouring reference vectors are selected in reconstructed phase space to increase forecasting precision, and the algorithm is given. The result of predication theory chaotic time series show that the improved method has a higher than the original method, meanwhile the influence from noise and number of nearly neighbour vector on the predication results is discussed, and traffic flow is predicated by the improved method. A method for predication of multivariable chaotic time series is proposed, and the calculation process is given, the influence from the noise and number of nearly neighbour vector and the forecasting step on the predication results is discussed, and traffic flow are predicated by the method. A combined dynamic method of forecast traffic volume time series is proposed. The traffic flow is decomposed into cycle item and tendency item and chaotic disturbing item, the sum of the cycle item and the tendency item is forecasted by seasonal index smoothing method, in this process the cycle chosen one day and one week, and recursive least squares with forgetting factor determined the weights, and the chaotic disturbing item is forecasted by partial forecast method. The simulation results show the reasonability and the effectiveness of the method.
(4) Based on variable structure control theory, speed controller are designed to stabilized traffic flow, and three control methods are proposed:approximately variable structure control continuous macroscopic traffic flow model; control discrete macroscopic traffic flow model based on discrete approaching low; forecasting control discrete macroscopic traffic flow model based on discrete approaching low. the algorithms are proposed, the simulation results show that the proposed methods can make the traffic density in a certain range. Distribution of traffic flow on different lane was achieved by changing lane rate.
引文
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