| OD demand estimation problem falls within the category of problem-driven applied mathematics research.In this dissertation,the probability theory,mathematical statistics,optimization methods,statistical methods are comprehensively used to extend current OD estimation models.An optimization model is formulated to estimate the upper bound of OD demand based on prior OD information.Based on this,the turning flow information is used to modify the traditional least squares OD demand estimation model and the OD demand covariance estimation model.The observed link flow is the input of OD estimation model,which can be collected by the traffic sensors.In view of this,this dissertation establishes a sensor location model based on OD demand estimation,and verifies the effectiveness of the model through numerical experiments.The details of each chapter are as follows:The first chapter introduces the research background and significance of the proposed OD demand estimation model based on principal component analysis and its extension,introduces the existing research results of OD demand estimation,and briefly gives the basic knowledge of principal component analysis and stochastic user equilibrium model.In chapter 2,it is pointed out that there is a deficiency in an existing literature study,which is,principal component analysis is used to reduce the dimension of OD demand matrix and then solve the upper bound of OD demand.Then,based on the prior information of OD demand,an effective upper bound model of OD demand is given.In chapter 3,based on the estimated upper bound of OD demand and the relationship between OD demand and turning traffic flow,the traditional least square estimation model of OD demand and the covariance estimation model of OD demand is optimized.Then the optimization models are given,and are conducted on two traffic networks to verify the validity of the model.In the fourth chapter,a sensor location model based on OD demand estimation is presented.This model is an integer programming problem,and a simulated annealing algorithm based on the optimization of link weight is proposed to solve the model by using the link weight determined by the principal component analysis.Finally,the model is applied to two traffic networks to verify the effectiveness of the model.The fifth chapter summarizes the whole dissertation and plans the future research direction.This thesis includes 16 figures,14 tables and 81 references. |
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