出行分布观测数据中的稀疏矩阵问题研究

摘要

The problem of sparse matrix in the trip distribution observational data are analyzed, and three different methods are put forward to calibrate the parameters of the double restraint gravitational model, as Parted Matrix Estimation, Zero Replaced Matrix Estimation and Incremental Matrix Estimation. By defining the Estimate Accuracy Index and the Estimate Effectiveness Index to measure the effects of estimation, this paper through the double restraint gravitational model equivalent mathematical programming with constraints, and compares three different analytical method of the estimation precision of the calibration method. On the basis of analysis, it used the methods of numerical simulation calculation, and contrasted the three estimation methods in accuracy and effectiveness. The conclusion finds that the calibration parameters by the method of the Zero Replaced Matrix Estimation have the best results in accuracy, and the calibration parameters by the method of the Incremental Matrix Estimation have the best results in effectiveness. The research results can be used as a theoretical basis of parameters calibration of observation sparse matrix in urban traffic planning in practical.%对出行分布观测数据中的稀疏矩阵问题进行分析,提出了部分矩阵估计、补零矩阵估计和增量矩阵估计3种不同方法来标定双约束重力模型的参数.通过定义估计的精确性和有效性两个不同的估计效果测度,将双约束重力模型等价为带有约束的数学规划,并采用解析方法比较3种不同标定方法的估计精度差异.在此基础上,通过数值方法模拟计算,并比较3种标定方法的估计有效性.通过研究可以发现,补零矩阵估计的参数精确性最好,而增量矩阵估计的有效性最好.研究成果能够作为实际城市交通规划中观测稀疏矩阵参数标定工作的理论依据.