1. Introduction
The transportation system is an intricate ecosystem consisting of the interactions and limitations among people, vehicles, roads, and the environment. As the most cost-effective transportation method, road transportation involves substantial consumption of fossil fuels by heavy-duty vehicles, resulting in a growing contribution of greenhouse gases and other pollutants to global pollution sources year after year [
1]. The transportation sector is responsible for generating the highest amount of greenhouse gases [
2], with an estimated 30% of anthropogenic emissions attributed to it. Furthermore, the transportation sector accounts for approximately 20–25% of total energy consumption, with 65–75% of this energy being utilized for road transportation [
3,
4,
5]. In recent years, many measures have been taken to optimize fuel consumption and reduce pollutants and greenhouse gas emissions in the transportation sector, including engine optimization, transmission optimization, and electric vehicle development. However, these advances are limited by technology, manufacturing conditions, and costs, making it difficult to achieve significant breakthroughs in the short term.
Vehicle technology and road environmental conditions are fundamental requirements for attaining energy-saving driving [
6,
7]. Speed control is a crucial component of vehicle technology development, ensuring safety while driving and reducing fuel consumption. The vehicle longitudinal control algorithm is a controller designed for speed regulation, utilizing reference and actual speeds as inputs, and throttle angle and brake position as outputs [
8,
9]. Several methods are available for achieving stable longitudinal control of autonomous vehicles. Simorgh [
10], for instance, devised an adaptable PID controller founded on model reference, and implemented resilient update law and slope correction control in order to enhance the model’s control efficiency. As technology continues to advance, numerous studies have demonstrated that modern data-based control methods can more precisely regulate vehicle speed, thereby enhancing the safety of driving. Aziziaghdam [
11] devised a longitudinal controller consisting of two parts. The external controller determines the target speed, whereas the internal controller is responsible for determining the throttle and brake. Ji et al. [
12] introduced a highly effective system linearization scheme that integrates a novel real-time point updating method with traditional linearization techniques. This integration leads to a reduction in steady-state errors and overshoot, ultimately improving the control performance of MPC controllers. Yang et al. proposed a new integral robust format for the asymptotic tracking of mismatched uncertain nonlinear systems [
13] and a neural adaptive learning algorithm for constrained nonlinear systems with interference suppression [
14], achieving the stability and accuracy of the control systems under multi-source disturbances. Li et al. [
15] suggested an integrated braking and steering MPC controller that can execute accurate path tracking while retaining high computational efficiency, thereby enhancing the precision of speed control and vehicle safety.
Meanwhile, ecological driving technology [
16,
17], which is often overlooked, has the potential to significantly improve vehicle fuel consumption. According to research, ecological driving can decrease fuel consumption by 15% to 25% and reduce greenhouse gas emissions by at least 30% [
18]. In contrast, engines and vehicles utilizing the latest technology are estimated to save approximately 10% to 12% in total fuel costs [
19]. Ecological driving encompasses various factors, such as driving speed, acceleration, deceleration, route selection, and idle speed [
20,
21,
22]. The variations in these factors have resulted in diverse driving styles. Deml et al. introduced a driving style classification system [
23] which utilizes lateral and longitudinal acceleration behavior. Biral et al. [
24] developed an objective function for risk measurement during driving, which integrates driving style and relevant safety factors into ADAS through optimal control. The concept of safe operation was integrated into the optimal control problem in the form of a penalty function. To obtain the optimal reference operation strategy, certain parameters in the driving style were utilized to optimize the control parameters.
With its robustness and easy-to-understand characteristics, fuzzy logic (FL) improves the efficiency of driving style recognition and is frequently utilized in such applications [
25,
26,
27]. An FL algorithm was proposed by Syed et al. [
28] to assess the ideal pedal operation of hybrid vehicles. This algorithm continuously monitors the accelerator and brake pedal operations, performs necessary corrections, and provides tactile feedback to the driver. The findings indicate that fuel consumption is cut by at least 3.5% without any impact on the vehicle’s performance. Given that the initial design of fuzzy rules typically necessitates continuous experimental verification, modification, and optimization, which is both time-consuming and inefficient, machine learning methods have been widely adopted and advanced in the research of driving style recognition. By combining feature selection, machine learning models can effectively select the most representative features of the driving style from a vast array of behavioral data, resulting in a more precise identification of the driver’s style. To determine the features that significantly affect fuel consumption, Jakov et al. [
29] suggested a linear regression model that takes into account ten features that directly reflect fuel consumption, aiming to identify variations in driving behavior. Tao et al. [
30] investigated the features of driving cycles by employing genetic algorithms, wherein they selected six out of twelve features under sampling windows of 146 s and 80 s. Yang et al. [
31] employed a Gaussian mixture model to determine the feature distribution that influences driving style and employed Bayesian information to evaluate and analyze the correlation of the selected features.
It is necessary to take into account the road slope for eco-friendly driving while on the road. When compared to the traditional adaptive cruise control (ACC) system, the ecological driving technology that incorporates road slope information in advance has been found to enhance fuel economy by 4.5%. Consequently, the integration of road slope factors into the longitudinal control methods of automobiles has garnered significant research interest. Sun et al. [
32] introduced a hybrid model predictive control (HMPC) theory and employed a mixed logic dynamic (MLD) framework, a specialized hybrid system modeling technique, for the development of the upper controller. The proposed control method’s effectiveness was verified through the use of speed tracking at various slopes and NEDC loops for speed tracking. Andreas et al. [
33] proposed an energy-optimal adaptive cruise control method that takes into account factors such as speed limits, road slope, and travel time during the optimization process, resulting in the planning of an optimal speed trajectory. Zhai et al. [
34] proposed a distributed model predictive control method for vehicles driving on highways with various slopes. When compared to benchmark testing, the proposed strategy can result in saving more than 21% of fuel for the entire vehicle.
This article aims to improve the speed control accuracy of heavy-duty truck driving assistance systems and simultaneously reduce fuel consumption by constructing a high-precision vehicle longitudinal control model guided by ecological driving. The structure of this article is as follows. In
Section 2, the process of establishing an MPC speed control model that integrates driving style recognition methods and road slope is discussed in detail. In
Section 3, the data sources are examined and the efficacy of the model is confirmed. Subsequently, the model built in this article was simulated and validated by setting different road slope conditions. Simultaneously, in
Section 4, an accurate analysis is conducted on the effectiveness of the DS-MPC control method under real driving conditions. Finally, the main findings are summarized and future work is discussed in
Section 5.
2. The Design of the Control System
2.1. Calculation of the Slope
In this paper, the slope of the actual road is calculated based on the vehicle speed and GPS elevation information collected by the CAN bus, and the calculation is shown in Equation (1).
At low slope angles,
where,
is the GPS elevation,
is the actual distance travelled by the vehicle, and
is the straight-line distance between GPS elevations. Then the slope
can be expressed as Equation (2).
where
is the time taken to travel from
to
.
and
are the speed at
and
, respectively.
As can be seen from Equation (2), GPS elevation and vehicle speed are important indicators for determining slope and in the actual data collection process, there may be cases of missing or abnormal data. In the case of missing or abnormal elevation data, the process shown in
Figure 1 is used for elevation correction. For vehicle speed, when the vehicle is in the parking state (
), its GPS elevation should remain unchanged, so its slope remains unchanged, and the slope of the current position is filled with a similar reasonable value. In the abnormal state of vehicle speed data, linear interpolation is used for the correction.
2.2. Feature Selection
A feature selection method based on a sigmoid function-based whale optimization algorithm is used according to the requirement for the feature selection of natural driving data. The features most relevant to driving style expression are selected by limiting the range of output values in the location update phase in order to reduce the size of the dataset used for driving style recognition while retaining relevant information. In this paper, the k-means method is used to construct the initial features for driving style feature recognition.
To complete the feature selection associated with driving style, the continuous WOA must be converted to its corresponding binary space [0, 1]. The use of a sigmoid transfer function can force the search agent to move through the binary space [
35,
36], thus improving the whale optimization algorithm for driving style feature selection. The equation is defined as shown in Equation (3).
where,
denotes the step vector of the search space at. Thereafter the current search agent uses Equation (4) to complete the position update.
where,
denotes a random number in (0, 1).
The objective of feature selection is to find the minimum number of features to select and to obtain the maximum classification accuracy. Based on this objective, both objectives are aggregated and transformed into a single objective problem as in Equation (5), and the minimum fitness value is defined as the sum of the small classification error rate and the minimum number of selected features.
where,
denotes the classification error rate and
,
are the length of the selected feature subset and the number of all features, respectively.
,
are the degree of importance of classification accuracy and feature subset length, and
. In this paper, we take
. The fitness value of each solution is continuously calculated during the iterative process and the subset with the smallest fitness value is treated as the optimal solution, based on which the classification accuracy is calculated as in Equation (6).
To avoid over-fitting in subsequent calculations, highly correlated features need to be removed. In this paper, the Pearson correlation, a measure of linear correlation between two variables, is used to identify and remove highly correlated features from the dataset, allowing the model to focus on the most informative features, thereby improving generalization and performance. It is calculated as in Equation (7).
where,
are the covariances of the variables
and
.
,
are the standard deviations of the variables
and
.
are the arithmetic mean of the samples
and
. The value ranges from [−1, 1], where the closer it is to 1 or −1, the stronger the linear relationship between the features, and the closer it is to 0, the weaker or no relationship between the features.
2.3. Driving Style Recognition
The spectral clustering algorithm, derived from graph theory [
37], is a method that utilizes the spectral properties of data to simultaneously perform dimensionality reduction and clustering. The basic idea behind spectral clustering is to convert the data into a graph representation and use the eigenvectors of the graph Laplacian to project the data into a low-dimensional space where clustering can be performed more efficiently. Spectral clustering is flexible and can handle complex and nonlinear data structures, so it is commonly used with driving style recognition. Spectral clustering is highly scalable, can handle large datasets, is computationally efficient, and is well suited to handle large amounts of driving data. In addition, spectral clustering is robust to noise and outliers, which makes it accurate in recognizing driving styles even when natural driving data is noisy.
The combination of Bi-LSTM and a self-encoder is shown in
Figure 2. The self-encoder compresses the data to low dimensions and later uses the compressed data as input, and the trained Bi-LSTM network learns the temporal dependencies between the sequence data points. In the training phase, the auto-encoder and Bi-LSTM networks are jointly trained, and this joint training process helps the model to learn a more informative and compact representation of the input data, which improves the performance of the driving style recognition task.
Currently, the use of machine learning for driving style recognition is inefficient, costly, and weak in practical applications under large data conditions. Natural driving data is a continuous time series, and the state of the data at the current moment is related to the state of the moments before and after. Therefore, a spectral clustering driving style recognition method based on a Bi-LSTM autoencoder is proposed, which firstly determines the original labels from the cleaned data using k-means, and then uses a whale optimization algorithm combined with a sigmoid function to compress the size of the data set and use it for The selected features are fed into an auto-encoder with Bi-LSTM to learn the feature values and feature vectors required for spectral embedding, and spectral clustering is used to determine the driving style, as shown in
Figure 3 and
Figure 4. The red and green lines in
Figure 4 represent the flow of data at different layers.
In order to enable real-time feedback control of the vehicle based on the driver’s driving style and road slope, this chapter proposes a model predictive control method with adaptive weights for the longitudinal control of the vehicle based on the driver’s driving style and changes in road slope, thus achieving real-time feedback on changes in driving operation requirements based on optimization control.
2.4. Fuzzy Logic
Traditional control methods require the establishment of a mathematical model of the control system, but for some control objects with complex structures and unknown mechanisms, traditional control methods cannot be controlled. Fuzzy control is a control technique that uses fuzzy logic to deal with uncertainties and inaccuracies in control systems. Fuzzy logic reasoning is a method based on empirical summaries whose rules can be expressed in natural language without the need to know the mathematical model of the control object. Therefore, fuzzy logic reasoning is particularly suitable for control objects where it is difficult to obtain mathematical models and dynamic characteristics and has the advantages of robustness and adaptability. In MPC, the use of fuzzy logic reasoning can improve the accuracy of the models used for prediction and control. A driver’s driving style can be thought of as a set of preferences and rules that govern the way the driver operates the vehicle. Incorporating these preferences and rules into the control system through fuzzy control allows the control system to adapt to the driver’s style, improving driving comfort and safety.
The basic idea of fuzzy logic reasoning in MPC is to improve the accuracy of the predictive model by adjusting the subordination function used in fuzzy logic to deal with the relationship between the various variables in the control system, and thus predict and control the actions more accurately. Traditional predictive control models with fixed parameters do not respond quickly enough to the driver’s actions, which can affect the smoothness of the driving operation. In addition, road slope conditions affect driver performance and fuzzy logic reasoning can improve the adaptability of the model predictive control model to the environment. Therefore, this paper uses a fuzzy control approach to adaptively adjust the weighting factors with changing operating conditions and uses the Fuzzy Logic Designer tool in MATLAB to complete the construction of the model.
2.4.1. Fuzzy Logic Reasoning Framework Design
In MPC, the model parameters mainly include the prediction time domain
, the control time domain
, the error weight matrix
, and the control weight matrix
in the objective function equation. The selection of the parameters directly affects the effectiveness of the MPC. To this end, weights that reflect the system’s ability to follow the reference trajectory are controlled in the objective function to be optimized to reflect the influence of driving style and road environment. The driving style and road slope have a certain stability in the secular data, and to assist in reflecting the influence of driver behavior and road environment, the actual vehicle speed and acceleration rate of change are added as errors along with the input to the fuzzy logic. Therefore, a four-dimensional fuzzy controller was designed based on driving style, current road slope, current vehicle speed, and acceleration rate of change, as shown in
Figure 5.
The driving style is based on the above recognition results, the slope can be calculated in real time based on the vehicle speed and GPS information, while the acceleration rate of change and the vehicle speed can be obtained based on the vehicle’s motion state, and then the error weighting factor can be obtained after fuzzy inference, and the corresponding weighting factor can be obtained after defuzzification. Therefore, the adjustment of the error weight factor is carried out adaptively in real time and the results are fed into the model predictive control model in real time.
2.4.2. Fuzzification
Fuzzification is the process of converting explicit inputs into fuzzy variables or fuzzy sets. In fuzzy control, the aim of fuzzification is to map explicit inputs into linguistic variables that can be used for fuzzy rule bases and inference.
Combined with the input fuzzy control in this paper, represents driving style whose discrete domain is [−1, 0, 1], represents slope whose continuous domain is [−8, 8], Jerk represents rate of change in acceleration whose continuous domain is [0, 10], Vel represents vehicle speed whose continuous domain is [0, 100] and the continuous domain of the output variable is [10, 20].
Based on the changes in the input and output variables, the corresponding fuzzy linguistic variables are defined so that the corresponding knowledge base can be constructed, as in Equation (8).
where,
is negative big,
is negative small,
is positive medium,
is positive small, and
is positive big.
The affiliation function selected for driving style is a triangular distribution, while the remaining input and output variables use a combination of triangular and trapezoidal distributions. The affiliation function for each input and the affiliation function for the output are shown in
Figure 6.
2.4.3. Fuzzy Rule Design
The rate of change in acceleration is most pronounced when the driver has an aggressive driving style and is more similar for different slope conditions. The driver’s output increases from 0 (Z) to positive (PB) in the acceleration rate of change domain when driving uphill or downhill, depending on their speed change, where a more conservative output is favorable if the slope is gentle. The effect of speed variation is more pronounced when the driver is a normal type of driving style. Drivers in this category usually have limited acceleration variation, i.e., they do not accelerate or decelerate as often, and are considered to be operating more steadily up and down hills, so their output is maximized only at high slopes, high speeds, and high rates of changes in acceleration. When the driver has a conservative driving style, in order to show the difference from a normal driver, it is assumed that he or she will adopt the most conservative operating strategy in the uphill and downhill conditions and will usually adopt a low speed and low change in acceleration strategy to pass, so the output usually varies from negative big (NB) to positive small (PS). Similar to the moderate driver, the maximum is only reached at high slope, high speeds, and high rates of changes in acceleration. Based on the above design of the fuzzy rules, a total of 135 fuzzy rules were designed and
Figure 7 shows the design surface corresponding to the fuzzy rules.
According to different driving styles, slope changes, speed, and rates of changes in acceleration, the value of the error weight Q is adjusted in real time and the optimization problem can be solved through quadratic planning, so that the design of the model prediction control model based on driving style is completed.
2.5. Model Predictive Control Considering Driving Style and Slope
Model predictive control is a feedback control algorithm that solves a multi-objective optimization problem in the predictive time domain in real time online based on a dynamic mathematical model of the system, and then calculates the most appropriate control action and achieves control of the system through continuous iterative operations. The algorithm has the advantages of generalization, immunity to disturbances, robustness, and excellent dynamic performance, without the need for an exact model. Therefore, model predictive control can be a good solution to the problems of model mismatch, time lag, and non-linearity caused by the complex environment of the vehicle.
The basic principle of model predictive control is to predict the future output of the system based on the existing model, the current state of the system, and the future control quantities, and to achieve the control purpose by solving the constrained optimization problem on a rolling basis, with three basic properties: predictive model, feedback correction, and rolling optimization.
Due to the time lag in the braking system, the engine system, and the acquisition and processing of sensor signals, there is a delay between the actual acceleration and the desired acceleration during the longitudinal motion of the car. In order to track the desired acceleration more accurately, the tracking of the car’s acceleration can be considered as a first-order inertial link and incorporated into the control system, whose transfer characteristics can be expressed as Equation (9).
where,
is the link gain. In model predictive control based on driving style, the influence of driving style constraints on the state and control quantities of the system needs to be considered. In this study, the driving style constraints are mainly manifested as the effects of acceleration and acceleration rate of change, with different constraints for the acceleration and deceleration conditions, respectively.
For an aggressive driving style, drivers will use greater throttle opening, faster acceleration, and a higher rate of change in acceleration when accelerating, higher deceleration, and a wider opening of the brake pedal when decelerating, while normal and calm drivers will be more cautious, so the constraints on acceleration and the rate of change in acceleration are shown in Equations (10)–(12).
In the above equations,
is the acceleration constraint and the lower two rows are the acceleration change constraint on acceleration and the acceleration constraint on deceleration, respectively. For the effect of driving style,
= 1.2 for aggressive drivers,
= 1 for moderate drivers and
= 0.8 for calm drivers, as below. Equations (13) and (14) were used to make decisions about their rate of change in acceleration.
In this section, according to the aforementioned adaptive model predictive control with driving style recognition and fuzzy rule construction, an adaptive model predictive control model considering driving style and slope was constructed using Carsim 2019.1 and MATLAB/Simulink 2018a. The model built in this paper was validated by setting different road conditions of slope and real driving conditions.
An adaptive model predictive control model considering driving style as shown in
Figure 8 was constructed by means of Carsim, MATLAB/Simulink.
The joint simulation platform is divided into four main parts, including the upper model predictive control part, the lower speed controller part, the vehicle model part, and the fuzzy inference part. The upper controller, lower speed controller and fuzzy inference sections were implemented in the main runtime environment of MATLAB/Simulink, and the vehicle model section was built in the Carsim 2019.1 simulation software. The vehicle model is used to transmit the vehicle configuration and parameter states to the upper model predictive control and fuzzy inference logic in real time during simulation time. The upper controller transmits the desired acceleration decision to the lower control strategy based on the results of the fuzzy inference, the desired speed sequence, and the actual vehicle longitudinal speed. The lower-level speed controller obtains the corresponding brake cylinder pressure or throttle opening according to the desired acceleration and inputs it to the vehicle model, which determines the braking or driving state of the vehicle according to the input signal, forming closed loop control.
This section takes the fuzzy inference module and uses driving style, slope, rate of change in acceleration, and speed as inputs to the fuzzy controller and thus obtains the control quantity weights Q for the model predictive control, which in turn expresses the effect of driving style on vehicle control. In this condition, the vehicle is simulated for uphill and downhill conditions at 0% and 5% slopes.
4. On-Road Test Results
To verify the effectiveness of the control strategy proposed in this article, vehicles located in an actual driving dataset of a continuous 9000 m on National Highway 236 were selected as the basis for simulation, as
Figure 18 shows. The labels for the driving styles of the vehicles on this section were acquired by classifying the driving styles in the preceding section, and the simulation platform incorporated the actual speed and road conditions. The approach put forth in this paper (DS-MPC) should be contrasted with that of PID control in a system for fixed speed cruise control.
Figure 19 and
Figure 20 display the speed tracking and corresponding error curves under real operating conditions. The results indicate that the control method proposed in this paper effectively tracks the speed changes of heavy trucks, maintaining a low deviation in speed. The average error is 0.03147 m/s, indicating an improvement of 80.56% over the accuracy of PID control. Furthermore, the standard deviation is 0.03210 m/s, indicating an improvement of 65.81% over the speed maintenance performance of PID control. Consequently, the proposed control method significantly enhances the power performance and road safety of the intelligent driving assistance system for heavy-duty trucks.
Figure 21 shows the fuel consumption comparison results of vehicles using DS-MPC control and PID control on this road section. As shown in the figure, during continuous changes in road slope, the total fuel consumption of vehicles using DS-MPC control method was 319.111g, while the fuel consumption of vehicles using the traditional control method was 329.881, with an average fuel saving rate of 3.27%, which constitutes a good fuel saving effect. In addition, the fuel consumption using the DS-MPC control method varied slightly under different driving styles, which is consistent with the fuel consumption results of the simulation results. But the fuel saving effects varied under different driving styles, with aggressive driving styles having a more significant reduction in fuel consumption. This is because after the DS-MPC control method accurately identifies the driving style, the changes in throttle opening and brake pressure of the aggressive driving style are smoother than those of the PID control method, thus achieving higher fuel efficiency. In summary, heavy-duty vehicles using the DS-MPC control method have high fuel efficiency and will effectively reduce emissions.
The elevation changes of the vehicle under actual operating conditions are depicted in
Figure 22. To further illustrate the correlation between elevation changes and vehicle speed,
Figure 23 presents typical slope sections along with their corresponding changes in vehicle speed. The proposed method outlined in this paper exhibits superior speed tracking performance on typical slope sections within the same road section. DS-MPC can enhance the precision of speed tracking during the deceleration process, thereby ensuring a uniform speed change. During the deceleration process, the vehicle has the ability to reach its predetermined target ahead of schedule and then enhance its acceleration. In comparison to PID control, it can achieve the desired vehicle speed in a shorter time. Furthermore, the DS-MPC algorithm is capable of effectively tracking the target speed during the deceleration phase, with a minimal overshoot and error, thereby achieving rapid tracking. It maintains good stability during the phase of increasing speed and further enhances the safety of road driving.