Optimization Model On Design Of Vertical Alignment Of Subway Track Considering The Construction Cost And Operation Energy Consumption

Vertical Alignment design of subway line not only affects the construction cost,but has a non-negligible impact on the energy consumption of train operation.Therefore,it is necessary to conduct a research on the optimization design of the longitudinal section for the subway line from the perspective of the minimum life cycle cost by considering the cost of construction and operation energy consumption.Firstly,the basic principles and influencing factors of the vertical alignment design of the subway line is introduced.Train operation effect under different station elevation differences,station spacing,and vertical alignment design schemes is analyzed through the traction simulation calculation software.And the general strategies of vertical alignment design are summarized.Then,on this basis,the optimization model of vertical alignment for underground lines is formulated based on the minimum train traction energy consumption,and the model is solved by Brute Force algorithm and dynamic programming algorithm.Finally,considering the change of line laying methods,the vertical alignment optimization model for subway lines is formulated with the objective of minimizing the life cycle cost,and the corresponding two-layer algorithm is designed to solve the model.The main research contents include:(1)Summarizing the main principles and general laws of the subway vertical alignment design.For vertical alignment design of different stations,the common-used slope types are listed for qualitative analysis and simulated under different station spacing.When the station elevation difference is similar,the "V" slope is adopted if the station spacing is short,and the "W" slope is adopted if the station spacing is long;when the station elevation difference is large,the single-sided slope alignment design scheme is adopted.(2)For urban rail transit underground lines,establishing a single inter-station vertical alignment optimization model with the objective of minimizing train traction energy consumption and the variable slope mileage and elevation as the decision variables.A two-layer algorithm is designed to satisfy the requirements of subway design specifications and practical design constraints.For the above model,Brute Force algorithm is used to find the horizontal position of the slope point at the upper layer,and dynamic programming algorithm to find the elevation of the slope point at the lower layer.Case studies show that the vertical alignment scheme obtained by the model in this paper can save 4-11% of train traction energy consumption compared withthe practical scheme,which verifies the effectiveness of the model.Compared with the single-direction optimization of the vertical alignment,the optimization of vertical alignment considering bi-direction traction energy consumption facilitates the improvement the energy-saving performance.The maximum optimization rate can be up to 10.12%;when the station elevation difference is similar,this method can be used to optimize the vertical alignment by using different slope types according to the station spacing."V" slope and "W" slope alignments can get better energy-efficient performance when the station spacing is about 1000 to 1500 m and greater than1500 m,respectively.(3)Considering the change of line laying methods,constructing the optimization model of the vertical alignment design of subway line with the aim of minimizing the life cycle cost(construction cost and operating energy cost)and the station elevation,the mileage and elevation of the slope points as decision variables Design characteristics of urban rail transit and practical engineering design requirements are considered.A simulated annealing algorithm is used to calculate the station elevation and the slope point mileage at the upper layer,and dynamic programming algorithm is used to find the slope point elevation at the lower layer.Case studies show that the optimized vertical alignment obtained by using the model in this paper can save 5.26% of the total cost compared with the original scheme;only considering the construction cost or operation energy consumption cost during the vertical alignment design process is not conducive to cost savings,therefore it is necessary to consider the both.