1. Introduction
The diesel vehicle is the main source of NO
x emission. In China, according to the 2019 China Mobile Source Environmental Management Annual Report, diesel vehicles account for 9.1% of motor vehicles in China, but the contribution rate of NO
x emission reaches 70% of the total vehicle emissions [
1]. At the same time, China has implemented NO
x emission reduction regulations, which limit the NO
x emission of motor vehicles strictly, and put forward higher requirements for automobile manufacturers to adjust the engine component parameters. Traditionally, in order to reduce emissions by adjusting engine component parameters, it is necessary to go through the engine test bench or actual driving. It is very expensive and inefficient to evaluate the success of the adjustment process by means of PEMS (Portable Emission Measurement System). Therefore, in the actual road driving process, it is very important to understand the causal relationship between vehicle operating parameters and emissions and to establish relevant reliable models.
In recent years, some scholars have used the chassis dynamometer or the engine test bench to collect the engine working data and construct the models according to the data obtained in the steady-state.
Table 1 presents the results of some recent studies on NO
x steady-state prediction by some authors.
These studies have achieved ideal experimental results, but the data obtained under steady-state conditions cannot capture the transient behavior of the engine from part load to full load as well as the hysteresis effect of the engine under start, stop, or cold start conditions [
2], which is often quite different from the emission data generated by diesel vehicles driving on the real road.
In actual road driving, the NO
x emission data of the diesel engine is a highly nonlinear, complex, and changeable sequence. Coupled with the complexity of engine characteristics and the uncertainty of drivers in the actual road operation process, it is very difficult to construct a highly nonlinear equation group for NO
x emission modeling. Traditional modeling methods for NO
x transient emissions include physical or chemical as well as empirical or semi-empirical assumptions. For example, Maurya et al. [
8] used the commercial 3D CFD (Computational Fluid Dynamics) engine simulation tool STAR-CD, combined with the mesh generator es-ice, to analyze the combustion process of a dual-fuel engine using a computational fluid dynamics (CFD) model, and derived the effect of EGR on the combustion and performance of the dual-fuel engine. Stelios A et al. [
9] used a semi-empirical zero-dimensional two-zone model to predict NO
x variation with engine load/speed, fuel injection timing, EGR rate, boost pressure, and fuel injection pressure at a relatively low cost. CFD models based on physical chemistry are commonly used for NO
x predictions. By calculating the physical and chemical process of fuel combustion, NO
x emission can be estimated accurately. However, due to the complex structure, high computational cost, and long time required, CFD models cannot be applied in real time [
10,
11]. Based on physical and chemical properties and empirical assumptions, these methods are very difficult to model instantaneous NO
x emissions [
12] and have limited performance in predicting NO
x emissions during actual road driving [
13].
With the gradual rise of machine learning, as it is unnecessary to understand the complex physical and chemical knowledge behind the research object, any additional complexity will be incorporated into the models when having enough data. At the same time, the method can consider the impact of environmental conditions on emissions that are difficult to analyze by physical and chemical models [
14], so it is widely used by scholars. Liu et al. [
15] used the integrated method of PCA (Principal Component Analysis) and genetic algorithm to search for the best super parameters of support vector machine to predict the steady-state and transient NO
x emissions of diesel engines. Ideal results can be achieved by making predictions of the steady-state emission, but the results of transient emissions still have large errors at some operating points. Sáez et al. [
16] used a single artificial neural network to predict the transient NO
x emission of diesel engines with input variables of vehicle speed and acceleration, engine speed and torque, intake temperature as well as air mass flow, which the best result of
R2 was only 0.82. In view of the characteristics of the NO
x transient emission time series of diesel vehicles, such as highly non-stationary, irregular fluctuation frequency as well as internal complexity and variability, as time goes on, the traditional machine learning algorithm may lose learning abilities [
17]. Deep learning has better learning performance for the highly complex nonlinear data, showing more excellent performance, but at present, few scholars use deep-learning methods to model transient NO
x emissions of diesel vehicles. Shin et al. [
18] used the DNN (Deep Neural Network) and Bayesian optimization method to optimize the hyper-parameter and predict the NO
x transient emission, which improved the prediction accuracy and model stability significantly. However, compared with the single deep neural network, researchers found that signal processing can extract signal features effectively [
19] and machine learning algorithms have been used in the field of wind speed prediction, power load forecasting, and financial field. For instance, Ma et al. [
20] predicted wind speed using double decomposition, error correction strategies, and long- and short-term memory neural networks. Tong et al. [
21] proposed a deep learning-based model that refines features from historical load data and associated temperature parameters by stacking denoised self-encoders and then training a support vector regression (SVR) model to predict the total load for the coming day. Niu et al. [
22] used a combination of variational modal decomposition and LSTM to predict stock price changes with good predictive performance.
In this study, the vehicle exhaust online monitoring platform is used to obtain the NOx emission data of two buses in the actual road driving process, and the in-depth learning model GRU (Gated Recurrent Unit) is used to establish the instantaneous NOx emission model. Since there are noises in the collected data, SSA (Singular Spectrum Analysis) and ICEEMDAN (Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) are used to filter the noise in the data. Considering that the subsequences generated by the ICEEMDAN decomposition increase the computational cost, the SVR (Support Vector Regression) models of the differentiation models are used to replace the low-frequency subsequence GRU models.
4. Results and Discussion
In order to verify the prediction performance of the multiple noise-reduction deep-learning differentiated model SSA-ICEEMDAN-SVR-GRU proposed in this paper, a comparative analysis was carried out. First, compare the model with five single models of GRU, LSTM, SVR, Bayes, and RF without noise reductions; then compare the model with GRU, LSTM, and SVR that have undergone SSA one-step noise reduction; in addition, ICEEMDAN-GRU, ICEEMDAN-LSTM, and ICEEMDAN-SVR models are added for comparison, involving a total of 12 different models for comparison.
Table 6 lists the multi-index evaluation results of two buses using different models.
4.1. Comparative Analysis of Single Models
It is not possible to achieve ideal results in the transient NOx emission. Taking the transient NOx emission prediction results of bus 2 as an example, the RMSE, MAE, and R2 of the SSA-ICEEMDAN-SVR-GRU models are increased by 52.613, 43.202, and 9.932% respectively compared to the GRU models. Compared with the random forest model, the RMSE, MAE, and R2 of the SSA-ICEEMDAN-SVR-GRU model are improved by 50.354, 45.727, and 9.685%, respectively.
In order to further analyze and verify the predictive ability of the SSA-ICEEMDAN-SVR-GRU models on the instantaneous emission of NO
x from two buses,
Figure 6 shows the comparison results for the five single models of Bayes, RF, SVR, LSTM, and GRU. Combining
Table 6, it can be found that the predictive ability of single models is limited and cannot accurately capture the significant characteristics of transient NO
x concentration emissions, and the prediction error is relatively large. Single models can predict the overall trend of changes in NO
x transient emissions, but there are huge gaps between the predicted result and the actual value. The main reason for this result is that in the actual road operation of diesel vehicles, the road conditions are complex and changeable. The driver needs to adjust the fuel supply and emergency braking constantly. The engine presents an irregular and rapid change state, which directly affects diesel combustion and NO
x emissions. It is difficult for single models to capture the transient emission law of NO
x, and it is impossible to model and predict accurately.
4.2. Comparative Analysis of SSA Single Treatment Results
After the original data is processed by SSA noise reduction, the prediction accuracy is significantly higher than that of a single model. For example, in bus 2, the RMSE, MAE, and R2 of SSA-GRU are improved by 18.122, 11.347, and 3.500%, respectively. However, compared with the SSA-ICEEMDAN-SVR-GRU model, satisfactory prediction results are still not achieved. In the transient NOx emission prediction results of bus 2, the SSA-ICEEMDAN-SVR-GRU model is better than the RMSE of the SSA-GRU model, in which the values of MAE and R2 increased by 42.124, 35.932, and 6.181% respectively.
Figure 7 shows the modeling results after processing the transient NO
x emission results of two buses using singular spectrum analysis. Through comparative analysis of
Figure 7 and
Figure 6, it can be found that the noise after the original sequence is reduced by SSA and the NO
x sequence shows a more obvious trend. The regularity of the NO
x transient sequence can be found more easily by using a machine learning model, and the stability and generalization of the model can be enhanced. By comparing the first mock exam with the SSA model, the
R2 of SVR, LSTM, and GRU increased by 2.587, 3.964, and 3.533% respectively, which means that SSA can enhance the interpretability and prediction ability of the model.
Table 3 shows the influence of different values of SSA-SVR model m on the prediction results. In the process of SSA noise reduction, if the m value is too large, the noise in the NO
x emission sequence may not be filtered completely, which will directly affect the basic information of the NO
x emission sequence; if the value of m is too small, the correct, and useful information in the original sequence will be filtered out. Therefore, selecting an appropriate m value to filter the transient emission data of NO
x can improve the data quality, reduce the influence of random interference, and enhance the prediction accuracy and stability of the model. The experimental results show that SSA noise reduction is very helpful to extract useful information from the original NO
x sequence and improve the prediction accuracy of NO
x transient emission.
4.3. Comparative Analysis of Single Treatment Results of ICEEMDAN
The original data is decomposed by ICEEMDAN and then modeled. The prediction accuracy and stability are significantly higher than the single model and the SSA noise reduction processing model. For example, for bus 2, the RMSE, MAE, and R2 of the ICEEMDAN-GRU model are improved by 42.44%, 32.442, and 8.58%, respectively, compared with the single model GRU. The RMSE, MAE, and R2 of the ICEEMDAN-GRU model are increased by 29.701, 23.795, and 4.907%, respectively, compared to the SSA-GRU noise-reduction model SSA-GRU. Through the comparison of the above two groups, it is found that the ICEEMDAN decomposition has a better noise-reduction effect on nonlinear and unstable data, and it is easier to mine the internal information and characteristics of the data. However, the dual noise-reduction SSA-ICEEMDAN-SVR-GRU model increased the RMSE, MAE, and R2 of ICCEMDAN-GRU by 17.672, 15.927, and 1.248%, respectively.
Figure 8 shows the comparison results of modeling and comparison of the original NO
x emission sequences of two buses after ICEEMDAN processing.
Figure 6,
Figure 7 and
Figure 8 are compared and analyzed. The original sequence of NO
x emissions is processed by ICEEMDAN and then modeled and predicted. The predicted result is closer to the experimental value, and more accurate prediction results can be obtained under high-load and high-speed conditions of diesel vehicles. Combining
Table 6, it is found that the prediction performance of the model processed by ICEEMDAN is higher than that of SSA noise reduction. For example, in the GRU model of bus 2, the RMSE of the SSA-GRU model is 18.122% higher than that of the GRU model, and the ICEEMDAN-GRU is 42.441% higher than the GRU. This improvement is mainly due to the fact that ICEEMDAN decomposes the transient NO
x emission sequence into multiple subsequences with different frequency fluctuations. From
Table 4, it is found that these subsequences have lower sample entropy, that is, they have lower sample entropy. The complexity of the model can better capture the changing law of the sequence, thereby improving the predictive ability.
The comparison of the dual noise-reduction differential model SSA-ICEEMDAN-SVR-GRU with the single model and single-processing model shows that the prediction accuracy of the model proposed in this paper is higher than other models. Among them, a single model has the worst performance. This is because the originally collected NOx emission sequence contains a lot of noise and a variety of fluctuating frequencies. A single model cannot learn its laws well and accurately. After the noise of the original NOx emission sequence is reduced by SSA, the noise in the sequence is significantly reduced, the model can better capture the sequence information, and the accuracy of the model is improved. The original data is directly processed by ICEEMDAN, which can obtain better prediction results. However, because ICEEMDAN directly decomposes the original sequence, the subsequence is less complex than the original sequence, and the sampling results of different frequencies are distributed in different subsequences, which is easier to find than the law but does not filter the noise, so the prediction accuracy is still insufficient. After the noise of the original sequence is reduced by SSA, ICEEMDAN is used to decompose, and the accuracy of the model is further improved. At the same time, the complexity of subsequences is analyzed through sample entropy, and SVR is used to replace low-complexity subsequences, which reduces the calculation cost and prediction time while maintaining model stability and prediction accuracy. Therefore, the SSA-ICEEMDAN-SVR-GRU model proposed in this paper is a prediction method with excellent performance. By comparing different models, using SSA to reduce the noise of the transient NOx emissions for diesel vehicles, and ICEEMDAN decomposition can effectively improve the prediction accuracy of the model.
5. Conclusions
This research proposes a differential model SSA-ICEEDMAN-SVR-GRU with dual noise reduction to improve the prediction of transient NOx emissions of diesel vehicles. In the proposed SSA-ICEEDMAN-SVR-GRU model, SSA is used for noise reduction, ICEEMDAN is used to decompose the data, and sample entropy is used to calculate the subseries complexity, using a differentiation model depending on the complexity. The proposed model is validated with data from two buses and compared with five single models, three SSA processing models, and three ICEEMDAN processing models. Based on the comparison of three sets of experiments, the following conclusions are drawn:
- (1)
After noise reduction by SSA, the prediction model is established. The accuracy is higher than that of a single model. It shows that SSA can remove the outliers in the original sequence. It also shows that noise has a great influence on the prediction results of NOx transient emissions of diesel vehicles.
- (2)
Using ICEEMDAN to process the original data and then modeling, the prediction accuracy is significantly improved, indicating that ICEEMDAN’s decomposition method can effectively extract the trend law and useful information of the original sequence, which helps the model learn its internal laws and improve the performance of the model.
- (3)
After comprehensively considering SSA noise reduction and ICEEDAN decomposition, the combined model SSA-ICEEMDAN-SVR-GRU has the best prediction performance. The results show that double noise reduction has better prediction performance than the single-processing method in improving the accuracy of transient NOx emission prediction.
- (4)
The use of SVR in the low-frequency sequence instead of the GRU model with higher computational cost can reduce the prediction time and maintain the prediction performance of the model.
Overall, the SSA-ICEEMDAN-SVR-GRU model proposed in this paper helps to analyze the diesel vehicle’s NOx emissions on actual roads, replacing physical NOx emissions sensors with virtual NOx emissions sensors, etc., to provide transient NOx emissions for diesel vehicles A new method.
The model proposed in this paper shows excellent performance in the prediction of NOx transient emissions from diesel vehicles. In the future, we will consider the method proposed in this paper to predict other pollutants of diesel vehicles, such as HC, PM, CO, etc., to reduce the cost of experimental measurement and experimental complexity.