The reduction of fuel consumption in engines is always considered of vital importance. Along these lines, in this work, this goal was attained by optimizing the heavyduty commercial vehicle engine control strategy. More specifically, at first, a general first principles model for heavyduty commercial vehicles and a transient fuel consumption model for heavyduty commercial vehicles were developed and the parameters were adjusted to fit the empirical data. The accuracy of the proposed model was demonstrated from the stage and the final results. Next, the control optimization problem resulting in low fuel consumption in heavy commercial vehicles was described, with minimal fuel usage as the optimization goal and throttle opening as the control variable. Then, a timecontinuous engine management approach was assessed. Next, the factors that influence low fuel consumption in heavyduty commercial vehicles were systematically examined. To reduce the computing complexity, the control strategies related to the time constraints of the engine were parametrized using three different methods. The most effective solution was obtained by applying a global optimization strategy because the constrained optimization problem was nonlinear. Finally, the effectiveness of the lowfuel consumption engine control strategy was demonstrated by comparing the simulated and field test results.
It is wellknown that vehicle energy consumption and exhaust emissions harm sustainable development. The rapid growth of the automobile industry in developing countries has alarmingly exacerbated the environmental pollution caused by automobile exhaust emissions [
Although numerous methods for reducing vehicle fuel consumption have been proposed, they are influenced by several factors [
Fuel economy studies rely on specific scenarios and driving strategies that are more sensitive to speed and acceleration [
Since the creation of ecodriving techniques for heavyduty commercial vehicles is highly dependent on vehicle performance, road driving, and traffic environment availability, the relevant works in the literature are scarce. Although planning the optimal speed profile of a vehicle using a heavy vehicle driving model predictive control (MPC) [
Under this perspective, in this work, an engine control strategy for heavy commercial vehicles that use less fuel was proposed and optimized. The optimal driving strategy for heavyduty commercial vehicles that minimizes fuel consumption can be classified as optimal control, with the optimization objective of minimizing fuel consumption during vehicle operation. The factors causing low fuel consumption driving of heavyduty commercial vehicles were also thoroughly discussed, and a driving strategy based on speed profile and throttle opening was proposed. Three parameterization methods were used to optimize the engine control strategy. Interestingly, iterating with the global optimization algorithm yielded the best results. Finally, the effectiveness of the lowfuel consumption engine control strategy was demonstrated by comparing it to realworld vehicle test results.
The remainder of this article is divided into the following sections: the discussion of a generic firstprinciples model of heavyduty commercial vehicles in
The heavyduty commercial vehicle model derivation was divided into two parts: the longitudinal motion control model derivation and the model derivation for fuel consumption estimation. Because the fuel consumption estimation model is heavily reliant on the vehicle motion control model, the vehicle motion control model was first established, and then a singlestep solution for fuel consumption was realized. The fuel consumption optimization problem defined in
The evaluation of vehicle motion control was described using fundamental physics laws and the basic parameters of the experimental vehicle. Because the purpose of this part was to develop a mathematical model of how a vehicle operates, simple polynomial functions and heavy vehicle parameters were used to approximate the vehicle dynamics model [
To improve the model’s robustness and accuracy, the traditional power factor fuel consumption model contained more parameters and was more computationally intensive [
In this work, the heavyduty commercial vehicle was idealized as a mass point, with no regard for the shape or size of the vehicle. However, the aerodynamic effect is regarded as a critical factor in the vehicle model that affects vehicle movement, and the operating state of the vehicle, as well as specific parameters, such as the vehicle wind resistance coefficient, air density, and orthogonal projection area, must be considered.
Aerodynamic drag is determined by the wind drag coefficient
where
Rolling resistance and slope resistance are defined by
where
where
The forces on the heavyduty commercial vehicle in the longitudinal dynamics model are depicted in
According to
Parameter  Value  Parameter  Value 

Area of orthographic projection 
Density of air 

Gross vehicle mass 
Coefficient of wind resistance 
0.528  
Efficiency of machinery 
Coefficient of roll resistance 
0.0055  
Radius of tire 
At present, there are two models available for fuel consumption estimation in the field of economic driving, and the pursuit of fuel consumption economy lies between them. The power demand type model typically calculates the instantaneous power demand of a vehicle and then obtains the instantaneous fuel consumption of the vehicle while driving using the speed and acceleration of heavyduty commercial vehicles [
The instantaneous fuel injection rate of an engine is influenced by a variety of factors including engine throttle opening, coolant temperature, oxygen concentration at the intake valve position, engine speed, and torque [
where
The vehicle speed, and acceleration for estimating the statistical function are considered the key factors for assessing fuel consumption. In addition, they are used to analyze the connection between engine speed and vehicle speed. When the vehicle speed is stable, the commercial vehicles have the same gear, speed, and the proposed linear change. The speed estimation model can be used to fit a primary function, whereas the instantaneous speed estimation model function is shown in
In summary, the direct relationship between the instantaneous fuel injection rate of the vehicle and the engine interior was considered first, and the fuel estimation model was established using engine speed and throttle opening, followed by an analysis of the relationship between the vehicle speed and acceleration and the engine interior. Finally, using
The employed parameter optimization was based on realworld data collected from heavy commercial vehicle experiments. During the experiments, the road surface is flat, and the changes caused by road inclination during vehicle driving can be ignored. Because the designed control system does not include the position factor of the vehicle, the data set does not contain vehicle position data.
Depending on engine experimental data, the parameters of the fuel consumption model were updated. For vehicle engines shifting from 700 to 1900 rpm and throttle position changing from 0% to 100%, the vehicle instantaneous fuel injection rate dataset was gathered in the engine tests, and the changing pattern of the pace of vehicle fuel consumption as engine speed grew when the throttle opening was taken from 0%–100%, respectively, is displayed in
The instantaneous fuel consumption model is provided by
where
Parameter  

Value 
The data shown in
The given instantaneous fuel consumption estimation model can measure variables related to the engine, which cannot directly respond to the influence of speed factors on heavy vehicle fuel consumption. As a result, the following step was to examine the direct relationship between engine speed and vehicle speed.
Parameter  

Value  11.96218  16.24941 
The driveline transmits the torque produced by the car engine to the drive wheels, and the torque acting on the drive wheels creates a circular force on the ground, which is what propels the vehicle forward. As can be observed in
Parameter  

Value 
The verification of the model was based on an independent dataset obtained during the highway testing of the mentioned heavy trucks. The test conditions on this stretch of road were significantly different from the data used in the previous section.
The relevant data snippet was selected from the dataset under test. Furthermore, the vehicle speed and fuel consumption data from the relevant time segment were used as the comparison condition because the fuel consumption of engines fluctuates with operating time. The vehicle speed was entered, the fuel consumption model simulation was run, and comparisons between the simulation and realworld results were performed. The model of the engine speed estimation was validated first.
Following that, the model of fuel consumption estimation was validated. The desired speed, corresponding throttle opening, and total fuel consumption data were chosen from the dataset shown in
The strategy of creating a decision system based on objective laws, such as vehicle displacement, engine performance, fuel consumption, and other factors is appropriate given the existence of the longitudinal dynamics model of heavy commercial vehicles. The approach can compare many variables and reflect all that is available. The constraint of ordinary differential equations (ODE) formed by the vehicle motion equation, the engine speed model, and the fuel consumption estimation model are shown in
where
To summarize the optimal control problem, for a controlled system, the optimal amount of control was sought to minimize the performance index while satisfying the constraints. The goal of this work was to find the vehicle driving control trajectory with the least amount of fuel consumption. Hence, the control trajectory was defined as a function of the vehicle position, vehicle speed, engine speed, and total engine fuel consumption, where vehicle speed and throttle opening were the control variables. In the vehicle driving process, seeking the optimal control trajectory is a nonlinear optimization with constraints. To determine the best control trajectory while a vehicle is running, a restricted nonlinear optimization procedure was used. For a controlled system, if the constraints are satisfied, the first thing to look for is the control variable
The variables of state and control satisfy the following constraints:
The variables of state and control constraints were explained as follows:
The maximum vehicle engine torque was 2500 N.m., which corresponds to a speed range of 1000–1400 rpm. As a result, the speed range should satisfy
The rate of change in the driving acceleration of a vehicle is directly proportional to its fuel consumption, and the magnitude of the rate of change influences both driving comfort and safety. As a result, any period during vehicle operation must satisfy
The optimization of the controlled systems
Parameterization
Typically, the dynamic programming method is used to numerically solve the optimal strategy problem using the Behrman equation [
Therefore, in this work, a parametric approach was to solve the optimal policy problem [
Nonlinearity
Since the maximization fuel consumption problem is a nonconvex, multimodal nonlinear model, it is difficult to be constrained, leading to the possible unsolvability of this optimization problem. Therefore, the objective function was used as the cost function
The Particle Swarm Optimization algorithm (PSO) is regarded as one of the more prominent options, and it follows the same general algorithmic flow as the global optimization approach [
In the optimization of optimal fuel consumption strategy, the PSO algorithm has obvious advantages compared with other algorithms. More importantly, the best results can be obtained in a limited time through the PSO [
To stop the optimization, it is necessary to make the optimization function meet the iteration condition
In
Serial number  Day 1  Day 2  

Test mileage (km)  Fuel 
Test mileage (km)  Fuel 

1  100.01  25.586  100.03  25.206 
2  80  22.819  80.085  20.131 
3  50  13.715  50.01  13.409 
Serial 
Method 
Mileage (m)  Fuel consumption (mL)  Description  Fuel 

1  1  2570.651  602.209  2 startup cycles  23.426 
2  1  2570.678  593.253  3 startup cycles  23.077 
3  1  2575.711  624.171  1 startup cycles  24.232 
4  2  2537.978  617.505  1 startup cycles  24.330 
5  2  2543.524  606.629  3 startup cycles(gradually)  23.849 
6  2  2543.524  812.693  3 startup cycles(impatiently)  31.530 
7  2  2543.524  646.767  4 startup cycles(gradually)  25.427 
8  2  2544.911  636.630  2 startup cycles  25.016 
9  3  2498.611  608.431  1 startup cycles  24.351 
In parametric approach 1, which models the regulating trajectory as the vehicle starting at a constant throttle opening, the throttle starts and stop moments were used as optimization parameters [
Since the throttle must be opened before it can be closed, the parameters in the decision vector must be strictly monotonically increased according to the time series. Moreover, the moment when the throttle was last closed must be lower than the maximum experimental time. For this reason, additional time constraints were imposed on the decision vector.
Experiments with 1 and 3 operation periods were also performed, achieving remarkably comparable state and control paths. Particularly, the primary distinction was defined as the number of starts raised, and the length of the throttle opening cycle shortened, leading to an increase in the frequency of vehicle speed changes. The fuel economy was not improved by increasing the number of parameters in the decision vector. Consequently, more iteration cycles were necessary for the algorithm to converge. As a result, as the vector dimension of the parameters increased, the algorithm converged more slowly. When method 1 with two start cycles of throttle opening was used, the convergence process required 40 iteration cycles. However, the convergence with three start cycles of throttle opening required 60 iteration cycles. This finding clearly indicates that the cost of algorithm convergence is increased with the number of parameters.
Heavyduty commercial vehicles have a unique architecture, which makes air resistance and drive resistance important factors in evaluating fuel efficiency. The engine must have greater power to keep the car moving at a consistent speed. To avoid producing extra mechanical energy from rapid changes in vehicle speed, the running period of each cycle must be extended if more throttleopening running cycles are necessary.
As a development of the control strategy covered in
where
The maximum throttle opening constraint must be added to the constraints stated in parameterization method 1. The maximum throttle opening of 100% for heavy commercial vehicles provided by the experiment was specified. The periods of four consecutive throttle opening actions and the variable throttle opening for each period are displayed in
Different levels of throttle operation can also have a significant impact on the fuel consumption of heavyduty commercial vehicles. Aggressive throttle pressing results in much higher fuel usage than progressive throttle pressing for the same number of throttle operations, as indicated by the comparison of data sets 5 and 6 in
The convergence of the PSO algorithm to a variable throttle opening is illustrated in
The third parameterization method operated with a single variable throttle from the start and runs until the end of the experiment. This control method was different from the one described in the preceding section in that it calls for only one actuation of the throttle opening. In addition, during the driving of the experimental vehicle, the mechanical energy generated by the engine was always higher than the energy necessary to drive the vehicle [
In this work, an engine control strategy for heavy commercial vehicles that use less fuel was proposed and thoroughly examined. First, a firstprinciples model based on a heavyduty commercial vehicle was developed, and the model was validated using experimental data collected from a real vehicle. The engine control strategy model was then created. Finally, it was used to evaluate engine control strategies.
From the acquired results, it was demonstrated that an ideal driving strategy based on a multioperation strategy of nonvariable throttle opening and engine speed coordination can reduce the fuel consumption of a heavyduty commercial vehicle. Under highspeed road conditions, heavyduty commercial vehicles can minimize fuel consumption by controlling the speed at 85 to 92.5 km/h and the throttle opening at 16.107% to 32.773%.
By using the optimal driving strategy model, the speed curve was produced. The connection between the control variables, vehicle speed, and fuel consumption under dynamic engine conditions was examined to estimate the fuel consumption of heavyduty commercial vehicles under various driving conditions and experimental conditions. Moreover, an instantaneous fuel consumption model based on the engine speed and speed power was established. The experimental data collected by large commercial vehicles demonstrated the model’s efficacy. The ideal fuelconsumption strategy and the calculation technique for the fuel consumption pattern in the driving cycle were both based on the estimation findings of the model.
The results indicated that the optimal fuel consumption was about 23.077 L/100 km in contrast between the calculated results of the given multiple strategies and the actual test data, to improve fuel economy and driving comfort, the driving style of more starts, and gentle driving should be adopted as much as possible. Saving fuel is a theoretical calculation based on assumptions, and actual driving is limited by the rational behavior of the driver. As a result, in our future work, the main focus will lead on developing a hardwareembedded system dedicated to the driving of heavy commercial vehicles, capable of solving vehicle driving optimization tasks in realtime, and reducing the rational constraints arising from the driver’s operation.
This work was supported in part by the Science and Technology Major Project of Guangxi under Grant AA22068001, in part by the Key Research and Development Program of Guangxi AB21196029, in part by the Project of National Natural Science Foundation of China 51965012, in part by the Scientific Research and Technology Development in Liuzhou 2022AAA0102, 2021AAA0104 and 2021AAA0112, in part by Agricultural Science and Technology Innovation and Extension Special Project of Jiangsu Province NJ202121, in part by the Guangxi Key Laboratory of Manufacturing System and Advanced Manufacturing Technology, in part by the Guilin University of Electronic Technology 2006540004Z, in part by the Innovation Project of GUET Graduate Education 2022YCXS017.
The authors declare that they have no conflicts of interest to report regarding the present study.