Combined Prediction for Vehicle Speed with Fixed Route

Plug-in hybrid electric vehicles (PHEVs) are gradually becoming the main mode of transportation to replace fuel vehicles. Energy-saving and emission reduction has received increased attention [1, 2]. Energy management is a key technology, necessary to improve PHEVs fuel economy [3, 4]. The rule-based energy management strategy is mature [5, 6]; however, it has a lot of restrictions, such as the changes in vehicle parameters, driving conditions and driver habits [7, 8], and difficulty achieving significant optimization results. The optimized energy management strategy can achieve better control effects for improving vehicle fuel economy [9], but the real-time performance of the strategy is poor. For example, the global optimization control can optimize the most reasonable energy management strategy under the condition of grasping the overall driving conditions [10]. However, the actual driving conditions cannot be obtained during vehicle travel; therefore, the application of the optimized energy management strategy is limited. The development of intelligent transportation systems has provided opportunities for improving the performance of energy management strategies for PHEV [11]. Considering the characteristics of the abovementioned energy management strategies, a predictive control [12, 13], with both optimization and real-time, is presented and widely followed, which is based on the predictive energy management strategy [14, 15]. Furthermore, the vehicle speed prediction model becomes a necessary module.

The vehicle speed prediction model can be divided into real-time learning and offline learning. Each model is most suitable for different types of problems. Real-time learning [16] is a data prediction model for online learning. Offline learning [17] is a data prediction model based on historical data. Real-time learning is more varied and offline learning is simple to use, but the real-time learning build environment is more complex when developing energy management strategies. Nowadays, people’s lives are gradually regularized. Vehicles, as a means of transportation for people’s daily travel, are on a fixed route. With the passage of time, the vehicle speed data on the fixed route begins to reflect the characteristics of the fixed driving cycle. The offline learning model perfectly reflects these inherent characteristics after incorporating this feature. Therefore, it is not necessary to repeat real-time learning of vehicle speed data on the fixed route. In this case, offline learning is more appropriate than real-time learning.

For the study of offline learning models, two commonly used models are utilized, namely, random prediction represented by Markov [18] and machine learning represented by a neural network [19]. Ref. [20] proposed a vehicle speed prediction method based on driving data, using deep learning of a neural network to predict future short-term vehicle speed. However, deep learning relies heavily on driving data, and the prediction accuracy will drop sharply because of driving data that occurs outside of learning. Ref. [21] proposed three methods for vehicle speed prediction based on neural networks, BP, layer recurrent (LR), and radial basis function (RBF). However, the prediction power of neural networks is limited by fitting, and the prediction error is a little large, such that the RMSE is about 2.28 km/h. Ref. [22] designed a high-order Markov velocity predictor combined with a linear programming algorithm, and the speed prediction accuracy was significantly improved compared with the first-order Markov. Although the predicting vehicle speed within the training speed can ensure high accuracy, the predicted vehicle speed outside the training speed cannot be followed well. In this case, the prediction accuracy is 4.47 km/h, which is relatively large. Ref. [23] designed an algorithm based on the velocity constrained Markov stochastic model to predict vehicle speed. The generated velocity trajectory was used to predict the speed of each cycle on the fixed route ahead, but the predicted velocity error is large, such that the RMSE is about 3.8 km/h. Ultimately, prediction accuracy has become a key issue in predictive models. In a word, achieving accurate vehicle speed prediction is a challenge.

From the above research, it can be found that many vehicle speed prediction models have their advantages, but also reflect their shortcomings. For example, contradiction between the high accuracy and generalization exists in the vehicle speed prediction model of the neural network structure; Markov is good at grasping the global speed change state, but the prediction accuracy is poor. Therefore, the research can proceed toward the direction of exploring the advantages of each prediction model to form a new combined prediction algorithm. However, in recent years of research on vehicle speed prediction, the combined prediction model has been rarely studied. Ref. [24] uses a neural network model based on historical speed to predict the average traffic speed of a road segment. Then, the Hidden Markov models (HMMs) are used to represent the statistical relationship between the average vehicle speed and the vehicle speed. However, the prediction curve derived from the combination is not very good.

This paper intends to make full use of the characteristics of Markov and BP neural network prediction models to form a combined prediction model. The predicted vehicle speed obtained from Markov with the characteristics of the following state of speed change, and then local high-accuracy fitting through the BP neural network, will be utilized to obtain better prediction results of the vehicle speed than the two prediction methods. The arrangement of this article is as follows: The second part introduces the source of road driving cycle data used by the prediction model. The third part describes the vehicle speed combined prediction model and the Markov speed prediction model, as well as the BP neural network model used in the model. The fourth part shows the effect of the vehicle speed prediction model and analyzes the characteristics of the prediction model. Finally, the fifth part draws conclusions.

The data acquisition experiment of road driving cycle needs to be carried out in the actual traffic environment. Nowadays, people’s lives are relatively regular, and it is more common to travel on a fixed route in daily life. The paper decides to select the driving condition information extracted by a fixed route as the data foundation of the research [25], which can reduce the amount of data used by the model and improve work efficiency. Vehicle speed data with multiple features is not the focus of this paper. According to the research needs, a modified vehicle equipped with a global positioning system (GPS) is used to obtain road driving cycle.

The route selected in the paper is the travel route commonly used by the population in the region. In order to facilitate the extraction of experimental data, the one-way travel plan is replaced by a round-trip cycle plan, which can also reflect the vehicle speed characteristics of the route. The characteristics of the route selected by the experiment are that there are many pedestrians and deceleration zones on the road, the traffic volume is small, and the driving speed of the vehicle is not allowed to exceed 60 km/h. Because the modified test car is not allowed to drive on the city road, a section of road in Yanshan University is selected as the test route. Experimental equipment is used to extract vehicle speed and GPS location information on this test route, as shown in Figure 1. The vehicle is traveling from the starting point and drives around until reaching the initial position, while the driving trajectory will be generated and the vehicle speed can be collected. In the experiment, it should be noted that the vehicle speed with a fixed step size is extracted within a fixed time interval, which is beneficial to reduce the complexity of the data. Elimination of duplicate data can improve subsequent prediction efficiency, and it paves the way for the construction of the prediction model.

On the basis of the above experimental methods, it is also necessary to repeat the experiment several times at a fixed time every day to obtain sufficient speed characteristics of the route. Some of the vehicle speed data is plotted as shown in Figure 2. It can be seen from the figure that it takes about 10 minutes to perform a driving cycle on this section, and the maximum speed during the driving cycle does not exceed 45 km/h. The speed-distance relationship curve after integration processing is shown in Figure 3. Different sections will begin to show a fixed speed characteristic, which is the characteristic of the road driving cycle. Finally, the received vehicle speed data is collated, combined, and segmented for use in predictive models. The road condition data obtained will become the basis of the prediction model and support the verification of the accuracy of the prediction model.

For vehicles on a given route, mathematical statistics and machine learning methods, based on historical driving data, can be used to predict future speeds, such as neural networks [26, 27]. It is also possible to predict future speeds by means of random prediction, such as Markov [28]. The following discusses research on the vehicle speed prediction model.

The simulation analysis of this paper is based on the fixed route speed data and selects the other three sets of road driving cycles on the fixed route to verify the prediction effects of BP, Markov, MBNN1, MBNN2, and MBNN3. The following is a comparative analysis with a set of results data.

Figures 12 and 13 are the prediction effect diagrams of single prediction models. The initial 90 s is mainly influenced by the parameter of the historical vehicle speed, so the initial time of the prediction is selected at 89 s. In order to verify the prediction effect of the model, the speed prediction of the future 1‒5 s is performed every second.

The final predicted speed curves overlap together with the actual vehicle speed curves to form the comparison figures of vehicle speed prediction. From these two figures, we can see the predicted characteristics of the Markov and BP neural network. The BP neural network has a slower response to the change state, but the local variation trend has a good fitting effect. It is often fitted to the trend of the speed of the next few seconds, but there is no actual follow-up to the actual speed curve. Therefore, the speed predicted by the BP neural network in Figure 13 is mostly attached to the surface of the actual speed curve. On the contrary, in Figure 12 Markov better follows the global speed change state. Most of the predicted vehicle speeds can coincide with the actual vehicle speed curve, but the local variation trend fitting effect is poor, resulting in large error.

The initial conditions of MBNN are the same as for a single prediction model. Figures 14, 15 and 16 are the diagrams showing the speed prediction effects of the three MBNNs. It can be seen from the figure that MBNN better combines the advantages of the Markov model and BP neural network model. The predicted speed curve better follows the change state of the actual speed curve, and can overlap better than the BP neural network speed prediction. Furthermore, the fluctuation of the locally fitted speed curve is smaller than that of the Markov prediction.

In order to see the above predicted performance more clearly, these images are partially enlarged, as shown in Figure 17. The results are consistent with the characteristics of the single prediction model analyzed above. The results of the neural network perform well linearly, while Markov fluctuates greatly. The use of the combination method balances the predicted performance of the two models and the predicted performance is better. Intuitively, the predictions of the three MBNN are not very different. The following analysis is based on the data.

Figure 18 compares the vehicle speed prediction errors of the five prediction algorithm models. The prediction error is calculated from the mean of the prediction bias within the 5 s prediction duration recorded every second. As can be seen from the figure, MBNN can reduce the fluctuation range of error compared to a single prediction model. At the moments of large error, the prediction error of MBNN is smaller than that of a single prediction model, and other times can be kept at an average level.

The paper uses Root Mean Square Error (RMSE) to further evaluate the accuracy of speed prediction [38]. The expression of RMSE is as shown in Eq. (11), and the evaluation time of RMSE can be adjusted by changing the value of n:where v_p,i is the predicted speed of the i seconds after time p, v_r,i is the actual speed of the i seconds after time r, time r, and time p are the same time point. In order to distinguish between predicted and actual values, different symbols are used: n represents the RMSE evaluation steps.

The vehicle speed prediction evaluation results obtained by Eq. (11) are listed in Table 2, which summarizes the prediction accuracy of the five prediction models in the fixed route and the three groups of 5 s within the vehicle speed prediction simulation. Taking the first set of predictions as an example, the RMSE in a single BP prediction model and a Markov prediction model within 5 s is 2.3775 m/s and 2.2123 m/s, while the RMSE performances in the three MBNN combined prediction models within 5 s are 1.7880 m/s, 1.5420 m/s, and 1.5366 m/s, respectively. Compared to the better performing Markov prediction model, the improvement ratios of the combined prediction models are about 19%, 30%, and 31%, respectively. Furthermore, in the other two groups of speed prediction, the improvement ratios are 17%, 26%, 27% and 20%, 28%, and 28%. On the whole, the performance improvement ratios of the three combined prediction algorithms are 19%, 28%, and 29%. Among them, MBNN2 and MBNN3 performed better, and MBNN3 performed best in most cases. Summarizing the performance of the combined prediction algorithms, the MBNN prediction models can improve the accuracy by 25.3% on average. Furthermore, it can be seen from the law of Table 2 that within a small prediction step, the accuracy of the prediction model is not much different because the prediction accuracy is high. However, as the prediction step length is extended, the accuracy advantage of MBNN will become larger and larger.

In order to improve the energy management effect of plug-in hybrid vehicles, this paper studies the problem of vehicle speed prediction in the control strategy. An experiment on a fixed route was conducted and a set of road driving cycle extraction methods were designed. The BP neural network and Markov prediction model were adopted and analyzed. Although the speed prediction of the fixed route can be realized by a single prediction model, the prediction accuracy of a single prediction model reaches a certain range; therefore, it is difficult to obtain an improvement in prediction effect by only debugging a single prediction model. Better speed prediction accuracy has an impact on the energy management effect of plug-in hybrid vehicles. Therefore, this paper proposes a combined prediction algorithm that can efficiently improve prediction accuracy. Based on the advantages of a BP neural network and Markov prediction algorithm, the prediction model is improved, and three combined prediction models, MBNN1, MBNN2, and MBNN3, are designed. The prediction results show that the predicted speed curves obtained by the three MBNN models follow the change state of the actual speed curve better, and the fluctuation of the prediction error is reduced. Finally, the predictive value of MBNN is evaluated via RMSE from the perspective of generalization ability and accuracy. The RMSE performance in 5 s is distributed between 1‒2 m/s. Compared with the preferred single prediction model adopted in this paper, the MBNN prediction models can improve accuracy by 25.3% on an average. This proves that the MBNN prediction models have obvious advantages. In summary, the designed combined prediction model can give full play to the prediction advantages of a Markov and BP neural network, which will play an important role in speed prediction and energy optimization of plug-in hybrid vehicles.