考虑观测数据随机性的OD矩阵贝叶斯估计方法

OD matrices as important basic data for transportation planning and management are normally estimated based on observed link counts. With the development of detection technology, intersection turning movements and some path and/or sub-path flows can also be observed，and the observed values of these data have some randomness. How to estimate OD matrices using these multiple-source data has become an important problem for transportation planning and management. By relationship analysis, theoretical research, and real application, considering data randomness, this research try to synthesize these multiple sources of data to estimate OD matrices for urban road networks, in order to improve the accuracy and efficiency of estimation. .Analyze the relationships among multiple-source data、OD flow and path flow based on network equilibrium theorem, and construct Bayesian network. Under the assumption of multivariate normal distribution, variance-covariance matrices are adopted to represent randomness of all variables and their correlation. In the proposed Bayesian statistical model for OD matrices estimation, derive the prior distribution of all variables based on historical data; and according to the constructed Bayesian network, update the observed variables one by one to calculate the posterior means and variance-covariance matrices, and obtain the posterior distribution; give the estimates of OD matrices based on maximum posterior probability density norm, and provide the corresponding probability intervals according to the posterior probability density curve. Apply the proposed Bayesian statistical method to estimate the traffic demand for different time interval in real transportation network, analyze the influences of data randomness, network size, and different types of data on the accuracy and efficiency of OD matrices estimation, and realize the combination of theoretical research and real applications.

OD矩阵作为城市交通规划的重要基础数据，通常根据观测的路段流量进行估计。随着检测技术的发展，结点流量、转向流量或路径流量等也可以获得，许多城市积累了大量日复一日的观测数据。如何利用这些多类型数据进行OD矩阵估计，是交通规划所面临的重要研究课题。.基于交通网络流理论，对OD流、路段流、结点流和转向流等随机变量进行关系解析，并据此进一步构建贝叶斯网络。从日复一日的观测数据中提取观测量的先验信息，基于解析关系建立随机变量之间的方差协方差矩阵，并用来量化多元变量的随机性和相关性。基于贝叶斯统计模型，观测数据被逐个用于更新随机变量的后验分布，导出后验均值和方差协方差矩阵；采取后验概率密度最大准则给出OD矩阵估计值，并根据概率密度曲线得到相应的置信区间。对现实交通系统进行OD矩阵贝叶斯估计；观察数据随机性、观测量类型、检测器布局等因素对OD矩阵估计的影响，分析不同时间窗的城市交通需求的空间特征。

OD矩阵作为城市交通规划的重要基础数据，通常根据观测的路段流量进行估计。随着 检测技术的发展，结点流量、转向流量或路径流量等也可以获得，许多城市积累了大量日 复一日的观测数据。如何利用这些多类型数据进行OD矩阵估计，是交通规划所面临的重要 研究课题。 基于交通网络流理论，对OD流、路段流、结点流和转向流等随机变量进行关系解析， 并据此进一步构建贝叶斯网络。从日复一日的观测数据中提取观测量的先验信息，基于解 析关系建立随机变量之间的方差协方差矩阵，并用来量化多元变量的随机性和相关性。基 于贝叶斯统计模型，观测数据被逐个用于更新随机变量的后验分布，导出后验均值和方差 协方差矩阵；采取后验概率密度最大准则给出OD矩阵估计值，并根据概率密度曲线得到相 应的置信区间。对现实交通系统进行OD矩阵贝叶斯估计；观察数据随机性、观测量类型、 检测器布局等因素对OD矩阵估计的影响，分析不同时间窗的城市交通需求的空间特征。