Optimal Road Grade Design Based On Historical Data For Minimizing Transportation Energy Consumption

With the rapid increase of the number of automobiles,worldwide energy consumption and greenhouse gas emissions have risen greatly.It is a challenge for the automotive industry to reduce energy consumption and carbon emissions.For this purpose,academia and industry have paid much attention to the energy consumption minimization of ground vehicles.There are numerous technologies being improved and innovated,however all these methods concentrate exclusively on the improvement or control of the vehicle,but take the road grade as external influences.The innovation of this thesis is to consider the road conditions,particularly the road grade,as design parameters.We optimize the road to reduce the energy consumption of vehicles running on the road.The main contributions are listed as follows.The aim is to find an optimal road grade profile such that the total energy consumption of all vehicles is the minimal in the case when all vehicles running on the road follow a given acceleration trajectory.The optimization problem is solved both analytically by Pontryagin's minimum principle and numerically by dynamic programming(DP).The analytical solution is obtained through three steps.Firstly,the energy consumption model is simplified and the Hamiltonian of the control problem is developed.Subsequently,this minimization problem is solved in three cases depending on the value of acceleration.Finally,an example is used to verify that the vehicle consumes the least energy on the optimal road.We find the numerically by dynamic programming through two steps.First of all,we transform the continuous–time road grade optimal control problem into a discrete–time optimal control problem and use dynamic programming to find the optimal road angle profile.Secondly,we validate the correctness and advantage of the DP solution via Monte Carlo simulations on a large number of vehicles with various weights.When the given trajectory is unknown,but we have historical data of a large of vehicles,the stochastic speed model based on Markov chain is established and the total energy consumptions of all vehicles is defined as the objective function.The optimal road grade is determined by dynamic programming with Markov model.This approach consists of three steps.Firstly,the discrete–time model of the optimal road grade design problem is presented.Secondly,the deterministic dynamic programming with Markov speed profile is applied to solve two cases.Finally,the advantage of the proposed road design method for reducing transportation energy consumption is verified via the Monte Carlo method.The previous Markov chain model does not consider the influence between road grade to vehicle's speed.If the influence between road grade and vehicle's speed is considered,the stochastic speed model based on Markov decision process is developed and the expected value of the average energy consumptions of all vehicles is defined as the objective function.First,it is proved that the road grade affects the speed profile.Next,we use the recursive deterministic dynamic programming with Markov Chain to determinate the optimal road grade.The optimal road grade is achieved by repeating two steps iteratively.Firstly,the MDP model of stochastic speed trajectories is transformed into a Markov chain under the initial approximation road grade.Secondly,deterministic dynamic programming with the Markov model is utilized to find the optimal road grade that is considered as initial road grade for the next iteration.Finally,a large number of Monte Carlo simulations show that the optimal road grade improves fuel economy.