Optimization On Vertical Alignment Of Metro Track For Operation Cost Saving

Vertical Alignment of Metro Track(VAMT)design and energy-saving train control have significant impacts on the energy costs and maintenance cost.As energy-efficient design of VAMT is interdependent with train control,they can be cooperative optimized in the design stage,and the obtained train control scheme is implemented in the operation stage by adopting Automatic Train Operation.The cooperative optimization contributes to further reducing energy cost and maintenance cost compared to the optimization only on the train control or the VAMT,which leads to minimum operation cost and sustainable development of metro system.This paper focus on train control and VAMT optimization for a metro section constructed by shield tunneling,considering respectively the periodic maintenance and the condition-based maintenance.Firstly,under the periodic maintenance,VAMT and train control scheme is optimized cooperatively aiming at minimizing bi-directional traction energy.Secondly,this paper quantifies the impact of VAMT and train control scheme on maintenance cost that employs dynamics simulation,and then proposes the computation method of maintenance cost.Based on this,VAMT and train control scheme is optimized cooperatively under the condition-based maintenance,which aims to reduce energy cost and maintenance cost.The major content of the paper is introduced as below.(1)In the optimization of train control,energy-saving efficiency is limited by the VAMT.To further improve energy-saving efficiency under the periodic maintenance,a multi-phase optimization model is formulated to cooperatively optimizes train control scheme and VAMT that meets the design criteria in the Code for Design of Metro and construction constraints.The objective is to minimize the round-trip traction energy with a given horizontal alignment of metro track.Considering the nonlinearity of the proposed model,this study proposed an integrated algorithm combining the Brute force algorithm with the Pseudospectral method to find the optimal solution.The results of case studies indicate that,the proposed model reduces energy consumption compared to the optimization only on train control and the optimization only on the VAMT design,the energy-saving ratio is more than 20% and 14% respectively.(2)Considering factors of wheel-rail wear,a computational model of wheel-rail wear is proposed,which is applied to calculate wear of wheel/rail under vary gradients and train speeds with the determined curve radius.Principles of wheel/rail wear are summarized: when the curve radius is constant,the greater the absolute value of gradient or the train speed is,the amount wear of wheel and rail increase.The increased wear amount may reduce the usage time of wheel/rail,which lead to the maintenance cost growth.To save maintenance cost,the reduction of wheel/rail wear needs to be considered in the optimization of VAMT and train control.(3)Under the condition-based maintenance,the adjustment of train control scheme and VAMT aiming at energy saving only may increase the wear of wheel/rail and the corresponding maintenance cost.To solve this problem,a cooperative optimization model is formulated to minimize energy cost and maintenance cost,which optimize the VAMT and train control scheme satisfying the practical constraints in the VAMT design and train control.The model is solved by combining the wheel-rail dynamics simulation with the Brute force algorithm and the Pseudospectral method.Case studies show that,the proposed model reduces the energy cost and maintenance cost by 21% compared to the optimization only on train control.The model also creates 9% cost saving ratio when compare the maintenance cost with the cooperative optimization only aiming at energy saving.