Optimizing Gear Shifting Strategy for Off‐Road Vehicle with Dynamic Programming

<div class="section abstract"><div class="htmlview paragraph">By installing an automated mechanical transmission (AMT) on heavy-duty vehicles and developing a reasonable shift strategy, it can reduce driver fatigue and eliminate technical differences among drivers, improving vehicle performance. However, after detaching from the experience of good drivers, the current shifting strategy is limited to the vehicle state at the current moment, and cannot make predictive judgment of the road environment ahead, and problems such as cyclic shifting will occur due to insufficient power when driving on the ramp. To improve the adaptability of heavy-duty truck shift strategy to dynamic driving environments, this paper first analyzes the shortcomings of existing traditional heavy-duty truck shift strategies on slopes, and develops a comprehensive performance shift strategy incorporating slope factors. Based on this, forward-looking information is introduced to propose a predictive intelligent shift strategy that balances power and economy. The vehicle power demand is calculated based on the possible future working conditions and road information, and the rotation speed, torque and impact degree are constrained to ensure the rationality of the shift range under the premise of meeting the vehicle dynamic performance. Finally, the optimal gear sequence planning is carried out with the cumulative fuel consumption in the next 5 seconds as the economic objective and output at the corresponding time. Based on GT-Suite simulation platform, the vehicle object model and gearshift control strategy are established. Under different driving conditions and road scenes, the gearshift strategy of the real vehicle is compared with the gearshift strategy built in this paper. The simulation results show that compared with the real vehicle gearshift strategy, the predictive intelligent gearshift strategy improves the fuel consumption by about 0.2% ~ 0.78%, and has better adaptability in the dynamic driving environment; Compared with the comprehensive performance shift strategy, this strategy reduces the frequent gear shift caused by the gradient change of the comprehensive shift strategy, and the fuel consumption is reduced by about 1.22% under the actual road test condition.</div></div>

<div class="section abstract"><div class="htmlview paragraph">The gear shifting strategies strongly influence the vehicle fuel consumption because they change the powertrain inertia and the engine operation point. The literature normally presents gear shifting strategies based on the engine power and torque to improve the vehicle acceleration performance. Strategies based on fuel economy are difficult to determine due to a large number of factors that influence the engine behavior such as the available transmission ratios, required acceleration and vehicle speed. In this paper it was evaluated the influence of the addition of more gear ratios in the vehicle gearbox, which initially contains five available gear ratios. For each proposed gearbox configuration, the gear shifting strategy was optimized through an algorithm developed to improve the engine fuel consumption in the Brazilian standard urban driving cycle NBR6601. The simulations were performed by means of co-simulation between the multibody dynamics software Adams<sup>TM</sup> (where is located the model based on a conventional 1.0L vehicle) and Matlab/Simulink<sup>TM</sup> (where is implemented the vehicle longitudinal dynamics equations). The optimization algorithm elaborated in Matlab<sup>TM</sup> utilizes previous simulations results, stored in a database, to compare them with the results obtained performing new strategies.</div></div>

An asymptotic error analysis of the conventional discrete dynamic programming (DDP) method is presented, and upper bounds of the error in the control policy (i.e., the difference of the estimated and true optimal control) at each operation period are computed. This error is shown to be of the order of the state discretization interval (ΔS), a result with significant implications in the optimization of multistate systems where the “curse of dimensionality” restricts the number of states to a relatively small number. The error in the optimal cost varies with ΔS2. The analysis provides useful insights into the effects of state discretization on calculated control and cost functions, the comparability of results from different discretizations, and criteria about the required number of nodes. In an effort to reduce the discretization error in the case of smooth cost functions, a new discrete dynamic programming method, termed gradient dynamic programming (GDP), is proposed. GDP uses a piecewise Hermite interpolation of the cost‐to‐go function, at each stage, which preserves the values of the cost‐to‐go function and of its first derivatives at the discretization nodes. The error in the control policy is shown to be of the order of (ΔS)3 and the error in the cost to vary with ΔS4. Thus as ΔS decreases, GDP converges to the true optimum much more rapidly than DDP. Another major advantage of the new methodology is that it facilitates the use of Newton‐type iterative methods in the solution of the nonlinear optimization problems at each stage. The linear convergence of DDP and the superlinear convergence of GDP are illustrated in an example.

This study proposes an integrated eco‐driving controller, in which speed profile and power split optimisation are simultaneously treated. A speed profile controller is designed based on a multi‐phase dynamic programming (DP) algorithm, which is utilised to optimise speed trajectories with the detailed model of the traction power system, vehicle dynamics system, and signal constraints at intersections. The optimised speed and demand power profiles are designed as the reference of the power split optimal controller. A DP algorithm is presented to determine voltage trajectories of supercapacitors with power plant voltage limitations and dynamic power losses. The performance of the proposed integrated method is evaluated by numerical simulation based on an actual route of Chengdu Tramway Line 2. The energy reduction can be achieved by the speed profiles controller, compared to the eco‐cruising benchmark strategies. Energy efficiency can be further improved by the integrated eco‐driving controller. Moreover, the influences of green signal time windows and trip time on the shape of the optimised solution are investigated. For a given journey, the trip time with minimum energy consumption can be obtained. The integrated eco‐driving control method can be implemented by driver assistant systems or automatic train operation systems.

Parallel dynamic programming and automata theory

Dynamic programming algorithms are developed for optimal capital allocation subject to budget constraints. We extend the work of Weingartner [Weingartner, H. M. 1966. Capital budgeting of interrelated projects: Survey and synthesis. Management Sci. 12(7, March) 485–516.] and Weingartner and Ness [Weingartner, H. M., D. N. Ness. 1967. Methods for the solution of the multi-dimensional 0/1 knapsack problem. Oper. Res. 15(1, January–February) 83–108.] by including multilevel projects, reinvesting returns, borrowing and lending, capital deferrals, and project interactions. We are able to handle dynamic programming models with several state variables because the optimal returns are monotone non-decreasing step functions. Computational experience with a variety of problems is reported.

Real-time vehicle guidance effectively reduces traffic jams and improves the operational efficiency of urban transportation. The trip time on a route is considered as a random process that changes with time, and the shortest path selection requires a random dynamic model and the solution of a decision-making problem. Thus, the shortest trip time is the criterion to determine the dynamic path selection by a random dynamic programming (DP) model which discretizes the trip times in the continuous segments on the route. In this study, a numerical model of random dynamic programming is established by using a probability tree model and an AND/OR (AO∗) algorithm to select the path of the shortest trip time. The results show that the branches of the probability tree are only accumulated on the “quantity” and do not cause a “qualitative” change. The inefficient accumulation of “quantity” affects the efficiency of the algorithm, so it is important to separate the accumulation of “quantity” from node expansion. The accumulation of “quantity” changes the trip time according to the entering time into a segment, which demands an improved AO∗ algorithm. The new AO∗ algorithm balances between efficiency and the trip time and provides the optimal real-time vehicle guidance on the road.

To solve the problem of the multi-dimensional dynamic programming model which including three state variables and three decision variables in each stage, we have been using discrete differential dynamic programming (DDDP) algorithm. In this paper, considering the particularity of each variable of the objective function is independent in the same stage and the variables of the constraint condition is increasing step by step, we propose a one-dimensional dynamic programming recursive optimization method to obtain the initial solution of the DDDP algorithm.

Purpose. To develop a new approach to the design of mining production processes with limited resources. Methods. Combinatorial optimisation methods were used to develop a new approach. The problem of designing technological processes can be solved by interpreting the problem “knapsack problem” with a private solution “backpack 0-1”. Dynamic programming algorithms are used to find the optimal solution. Findings. A new approach to the design of mining production management processes with limited resources has been developed. If the target goal is to obtain the maximum effect at minimum costs, then the direct run method is used. If there are restrictions on bandwidth, energy characteristics, specific cost, then the reverse run method is used. In the final part of the study, the proposed approach was verified. The task consisted in the development of recommendations regarding the choice of the structure of the technological chain of the cleaning pit under the given technological and mining-geological development parameters. The amount of specific production cost was imposed as a limitation. As a result of solving the design problem by the reverse run method, recommendations for replacing the cleaning equipment were developed. This made it possible to ensure the specified level of productivity and reduce the unit cost by 10.6%. The use of combinatorial optimisation methods made it possible to obtain an optimal solution in the field of given parameters. Originality. The scientific novelty of the work consists in establishing regularities in the formation of the efficiency of mineral deposit development processes. For the first time, combinatorial optimization methods were used to design the processes that accompany the development of mineral deposits, and the scope of their application was determined, as well as a number of dynamic programming tasks and algorithms were formalised: backtracking, spanning tree. Practical implication. Verification of the developed approach was carried out in relation to the design of mining production processes with limited resources. The obtained approach makes it possible to find optimal solutions under the constraints set at the design stage. As limitations can be: throughput capacity of the transport chain, energy characteristics of technological processes accompanying mining, specific cost of mining, etc. The design problem can be solved in a direct order – if the objective function is to maximise the parameter, or in the opposite way – if there are restrictions.

7 - Numerical optimization in allocation, storage, and recovery of thermal energy and resources

Recently, as the market share of electric vehicles (EVs) has increased, how to handle the increased electricity demand for EV charging in the power grid and how to use EV batteries from a grid-operating aspect have become more important. Also, from the perspective of individual EVs, Vehicle-to-Grid (V2G) technologies that reduce the cost for each vehicle’s charging in conjunction with the power grid are significant. In this paper, the V2G control problem at the individual vehicle level is studied using a Dynamic Programming (DP) algorithm that considers EVs’ charging efficiency. The DP algorithm is developed to generate an optimized charging/discharging power profile that minimizes electricity costs, while satisfying the constraints of the initial and final battery states of charge, for given a time-of-use electricity price. To show the effectiveness of the proposed algorithm, simulation is conducted for three different charging scenarios (unidirectional charging, bidirectional charging, and unidirectional charging with cost variations based on electricity usage), and the results showed that DP can achieve significant cost savings of about 30% compared to the normal charging method. Also, the result of DP is compared with that of Linear Programming, demonstrating that DP outperforms Linear Programming in cost savings for the V2G control problem.

This paper investigates the computation of transient-optimal policies in discrete dynamic programming. The model, is quite general: it may contain transient as well as nontransient policies. and the transition matrices are not necessarily substochastic. A functional equation for the so-called transient-value-vector is derived and the concept of superharmonicity is introduced. This concept provides the linear program to compute the transientvalue-vector and a transient-optimal policy. We also discuss the elimination of suboptimal actions, the solution of problems with additional constraints, and the computation of an efficient policy for a multiple objective dynamic programming problem.

An integrated energy-efficient train operation approach based on the space-time-speed network methodology

A data-driven energy management method for parallel PHEVs based on action dependent heuristic dynamic programming (ADHDP) model

The shift strategy of automatic transmission plays a vital role in the smoothness and economy of heavy-duty mining trucks. In this paper, an engine fuel consumption model, a 6 + 2 speed automatic transmission model, and a vehicle resistance model are built in MATLAB. Combined with the development of smart mining technology, the traditional two-parameter economic shift strategy is corrected based on vehicle load and road slope. The dynamic programming optimization algorithm is used to extract the best economical shift strategy under known working conditions to reduce the fuel consumption and the number of shifts. Finally, simulation experiments of the optimized shift strategy by dynamic programming in a typical mine work cycle are carried out. The simulation results show that the engine speed and output torque are maintained in a relatively stable and efficient working range by using the proposed shift strategy. Compared with the traditional two-parameter shift strategy, dynamic programming has advantages in reducing fuel consumption and shift numbers.