Dynamic Model And Mixed Regression Based On Metro Swipe Data

With the rapid development of urban rail transit,subway has become an important means of public transportation.The increase in passenger traffic has led to crowding problems,congestion leads to the improvement of safety problems,the decline of service quality,poor travel experience and so on.Aiming at the problem of subway passenger flow analysis,A dynamic statistical model and a robust mixed linear regression model are established for the data of passenger card swiping time.The EM algorithm corresponding to the model is proposed.used to calculate maximum likelihood estimates of parameters.The accuracy of the algorithm was evaluated by computer simulation experiment,applying the proposed model to real data,construct the prediction interval,The cross-validation method is used to verify the validity of the model.The main results are as follows:(1)Applying dynamic statistical models,the train time in peak and off-peak hours,the probability of passengers taking each train,the distribution of passengers’ departure time,and the distribution of passengers’ travel time can be inferred based on the data of passengers’ swipe time in and out of the station.The simulation results show that the EM algorithm can accurately estimate the unknown parameters in the dynamic statistical model.(2)By analyzing the actual data of Beijing Metro Line 6 through dynamic statistical model,A number of quantitative indicators are given to describe the passenger flow characteristics in peak and off-peak hours.The results show that the travel time has a significant effect on the travel probability and the distribution of departure time.Based on the dynamic statistical model,the dynamic prediction interval of passengers’ outbound card swiping time is constructed.The calculation results on the test set show that the actual coverage of the interval is consistent with the nominal coverage,it shows the validity of dynamic statistical model.(3)Using a robust mixed linear regression model,It can infer the probability of passengers choosing each bus path,predict the bus time of each bus path and other indicators to describe the subway system.The model assumes that the errors follow the modified Huberloss distribution.No longer paying attention to the passenger’s ride.An EM algorithm is proposed to solve the maximum likelihood estimation of unknown parameters in the model.The simulation results show that the EM algorithm can accurately estimate the unknown parameters in the robust mixed linear regression model.(4)Based on the experiment of different distribution of errors and the comparison experiment with the traditional method,the robustness of the model and the robustness of the algorithm are verified.The actual data of Beijing subway are analyzed by the proposed model.Some quantitative indexes of passenger flow characteristics in morning peak period are given,The results show that the train running time has a significant effect on the route choice of passengers.The fitting is evaluated by the coefficient of determination and the corrected coefficient of determination,the results show that the model fits the data well,this also shows the effectiveness of the robust mixed linear regression model.