Research On The Method Of Propagation Delays Of High-speed Railway Trains Based On Maximum Algebra And Ensemble Learning

The development of high-speed railway operation shows a trend of higher speed,higher density,and highly networked in China,which makes delays caused by sudden disturbances spread in more ways and more range in the system.This brings inconvenience to passengers.It can broaden the scheduling space,speed up the system’s response and reduce the impact of delays to make scheduling decision with the aid of joint delay prediction.This paper proposes a hierarchical delay propagation prediction model based on the Max-plus algebra and ensemble learning algorithm.The main work of the paper is as follows:(1)The actual operation record data of high-speed railway trains is obtained and processed.Based on the changes of the delay time between related train events,delay propagation phenomenon is classified.The evaluation indexes of the delay propagation characteristics of the railway nodes is formed considering the phenomenon occurrence frequency combine with its generation mechanism.(2)Based on the train schedule,the coupling relationships of train events is analyzed,and the main components are selected.The coupling relationship set of train events is formed to describe the coupling relationships.The redundancy time of the train schedule is extracted from the actual operation record data with a fluctuation-based method.On the basis of the two,a delay propagation prediction model based on maximal algebra is established to predict the joint delays.And a preliminary prediction results of delay time based on linear factors is produced.(3)The non-linear factors of delays analyzed.And the characteristic data set of nonlinear influencing factors of delays is formed based on the probability characteristics of railway nodes.Principal component analysis(PCA),linear discriminant analysis(LDA),and a wrapped feature selection method is employed to extract or filter features.A hyperparameter optimization algorithm based on cross validation and grid search is designed to optimize the extreme gradient boosting tree(XGBoost)model.The feature set and hyperparameters with the best performance are selected to establish an ensemble learning model for the prediction of the preliminary prediction results error as a delay time correction result based on non-linear factors.(4)Analyze the link and sequence of linear and non-linear factors in delay propagation and design an integrated framework of two models,based on which the proposed hierarchical prediction model is formed to predict the spread of the actual operation delay record.The superiority of the proposed algorithm is proved by comparing the prediction accuracy with the preliminary model.The delay propagation simulation test of the designed delay cases was carried out with the use of the proposed prediction model.The delay tolerance of railway nodes is quantitatively evaluated according to the model output,so as to provide decision-making suggestions for the optimization of the operation diagram.