Construction of a NOx Emission Prediction Model for Hybrid Electric Buses Based on Two-Layer Stacking Ensemble Learning

Abstract

To enhance the management of NOx emissions from hybrid electric buses, this paper develops an instantaneous NOx emission prediction model for hybrid electric buses based on a two-layer stacking ensemble learning method. Seventeen parameters, including operational characteristic parameters of hybrid electric buses, engine operating parameters, and emission after-treatment device operating parameters are selected as input features for the model. The correlation analysis results indicate that the Pearson correlation coefficients of engine coolant temperature and selective catalytic reduction (SCR) after-treatment device temperature show a significant linear negative correlation with instantaneous NOx emission mass. The Mutual Information (MI) analysis reveals that engine intake air volume, SCR after-treatment device temperature and engine fuel consumption have strong nonlinear relationships with instantaneous NOx emission mass. The two-layer stacking ensemble learning model selects eXtreme Gradient Boosting (XGBoost), Random Forest (RF), and an optimized BP neural network as base learners, with a linear regression model as the meta-learner, effectively predicting the instantaneous NOx emission mass of hybrid electric buses. The evaluation metrics of the proposed model—mean absolute error, root mean square error, and coefficient of determination—are 0.0068, 0.0283, and 0.9559, respectively, demonstrating a significant advantage compared to other benchmark models.

1. Introduction

To mitigate environmental pollution caused by vehicle emissions, countries worldwide have implemented various measures aimed at reducing emissions of greenhouse gases and harmful pollutants. Developing public transportation can effectively alleviate the increasingly severe issues of urban air pollution and traffic congestion. Relevant reports indicate that diesel vehicles account for 88.4% of the total NOx emissions from vehicles [1]. Currently, hybrid electric buses, predominantly powered by diesel fuel, are available in the market. Therefore, studying the NOx emissions of hybrid electric buses is particularly important.

Since the implementation of China VI emission standards, many regions across China have established remote monitoring platforms utilizing remote data transmission technology to collect on-board diagnostic (OBD) data for the real-time supervision of heavy-duty vehicle emissions. Using remote transmission technology to obtain OBD data is more efficient than employing the Portable Emission Measurement System (PEMS) and allows for long-term monitoring of vehicle operation and emissions. Therefore, adopting this technology is more advantageous for the daily management of vehicle emissions. Researchers analyzed the NOx emission data which was obtained from remote monitoring platforms and PEMS. The results demonstrated strong consistency between these two datasets [2,3]. Wang et al. [4] utilized remote transmission technology to acquire data and developed a computational method for quantifying NOx emissions from vehicles under prolonged operation. Applying this method, they demonstrated that the NOx emission factor for heavy-duty vehicles under the China VI standard (1.420 g/km) decreased by 2.474 g/km compared to those under the China V standard (3.894 g/km). Cao [5] proposed a comprehensive analytical framework for NOx emissions from heavy-duty diesel vehicles using OBD remote transmission technology, integrating data processing, identification of high-emission vehicles, and analysis of emission causes. This framework used a fuel-based window method to identify high-emission vehicles and utilizes binning and machine learning techniques to investigate the causes of NOx emissions. Currently, developing vehicle-level NOx emission prediction models using machine learning, neural networks, and other techniques has become an essential research direction to assist in supervising emissions from heavy-duty diesel vehicles.

Researchers have constructed neural networks to perform emission predictions for various engines from multiple perspectives. Studies [6,7] employed artificial neural networks to predict emissions from gasoline engines, and the results consistently indicated a high accuracy of neural networks in predicting pollutant emissions from gasoline engines. Odufuwa [8] constructed an artificial neural network (ANN) model for a small diesel engine to predict fuel consumption, effective thermal efficiency, and emissions of four pollutants—CO₂, NOx, CO, and PM. The ANN model demonstrated excellent performance in predicting pollutant emissions. Amit [9] compared diesel engine performance and emissions by adding various substances to diesel fuel. In their study, an artificial neural network was utilized to predict pollutant emissions such as NOx, and the model demonstrated good predictive performance. However, these researchers relied solely on data obtained from engine bench tests to construct neural networks for pollutant emission predictions. Given that actual driving conditions involve numerous additional parameters; it is essential to conduct on-road vehicle tests to develop more accurate pollutant emission prediction models.

Based on real-world vehicle road tests, researchers have developed appropriate pollutant emission prediction models using various algorithms. Sampaio [10] integrated carbon dioxide emissions and operational costs for heavy-duty truck loads using Genetic Algorithms (GA) combined with artificial neural network optimization. Their model balanced environmental sustainability and economic efficiency to determine the optimal vehicle driving patterns. Ambuj [11] optimized the architecture and parameters of neural networks for agricultural vehicles using the Particle Swarm Optimization (PSO) algorithm. The optimized neural network demonstrated improved efficiency and accuracy in predicting energy consumption for agricultural vehicles. Several researchers [12,13] have investigated the selection of input parameters for neural networks, generally finding that increasing the number of input parameters can improve the overall model accuracy. Seo [12] selected six parameters—vehicle speed, engine speed, engine torque, engine coolant temperature, fuel-to-air ratio, and intake air mass flow—as inputs for neural networks predicting exhaust emissions, constructing seven different neural networks by varying input parameters. Notably, their study did not include the temperature of the SCR after-treatment device as an input parameter. Tang [13] utilized Genetic Algorithms (GA) to optimize a Back Propagation neural network (BP) for predicting various gas emissions during the cold-start phase of small hybrid vehicles, analyzing the accuracy of emission prediction models by comparing different input parameters. Their results demonstrated that the optimized model significantly improved prediction accuracy compared to the original model. Wen [14] constructed a Gated Recurrent Unit (GRU) neural network —a variant of the Long Short-Term Memory (LSTM) neural network—for emission prediction, analyzing and ranking ten NOx-related features by importance. They identified air flow, exhaust flow, and CO₂ concentration as the top three influential features affecting NOx models for urban, suburban, and highway driving conditions. In their analysis, CO₂ was used as a proxy feature partially substituting for fuel consumption. However, selecting a higher number of input parameters does not necessarily guarantee improved model performance, as excessive parameters may lead to computational inefficiency, high feature correlation, and overfitting. Therefore, careful consideration regarding the number of input parameters is particularly important.

Wang [15] utilized Mutual Information (MI) to select input parameters and developed a BP neural network to predict NOx emissions without considering after-treatment systems. However, this approach has limitations, as it does not represent actual vehicle emissions. Wang [16] employed the GRU and optimized its hyper parameters using a combined Bayesian optimization and k-fold cross-validation approach, establishing a NOx prediction model suitable for smaller datasets. Their training process involved a learning rate adjustment strategy that combined cosine annealing and exponential decay, achieving a determination coefficient (R²) of 0.9569. Nevertheless, the test dataset used in their study consisted of non-steady-state data, making it unsuitable for instantaneous per-second NOx emission prediction. Wei [17] developed transient emission prediction models for CO₂ and NOx using the super-learner framework, incorporating algorithms such as RF, XGBoost, LightGBM (Light Gradient Boosting Machine), and CatBoost. Their research primarily focused on medium-duty diesel vehicles. However, fuel consumption was not considered in the selection of input features for their models.

Yu [18] also utilized a Genetic Algorithm (GA) to optimize a BP neural network for predicting emissions from light-duty vehicles. However, the number of comparative models used for evaluation was limited. To address noise issues within the data, Li et al. [19] developed a time-series neural network prediction model, ultimately predicting NOx concentration. However, their study did not consider parameters related to after-treatment systems in selecting input features. Arsie et al. [20] conducted bench tests on diesel engines and optimized a recurrent neural network (RNN) using the least squares method, but their research similarly lacked comparative analysis with other models.

Based on the analysis above, several limitations in previous studies can be summarized as follows: (1) The current research on NOx emission prediction models for hybrid electric buses remains insufficient. (2) Input features selected for engine emission prediction differ significantly among various studies. (3) Horizontal comparisons among different predictive models are lacking.

Based on the operating characteristic parameters of hybrid electric buses, engine operating parameters, and after-treatment system parameters, this paper develops a two-layer stacking ensemble learning model for transient NOx emission prediction in hybrid electric buses. The proposed model is compared against mainstream predictive models developed in previous studies. This research aims to identify the most influential feature parameters affecting NOx emissions from hybrid electric buses, providing insights and guidance for constructing NOx prediction models applicable to other types of heavy-duty diesel vehicles. The NOx prediction model is integrated into enterprise or government platforms for remote monitoring of urban bus emissions, aiming to improve urban air quality and control the operation of vehicles with excessive emissions. By integrating this prediction algorithm into the platform, it can partially address issues such as malfunctioning NOx sensors (due to damage, etc.) or the loss of critical data during transmission.

2. Materials and Methods

2.1. Data Collection

This paper utilizes OBD remote transmission technology to obtain relevant operational parameters of hybrid electric buses, with a data acquisition frequency of 1 Hz. The relevant technical parameters of the hybrid electric buses are presented in

Table 1. The relevant technical parameters of the hybrid electric buses.

Parameter Name	Specification
Traveling range	urban
Type of fuel	diesel-electric
Emission standard	China VI
Powertrain	Series
Rated engine speed (rpm)	2300
Maximum engine torque (N·m)	700
Rated engine power (kW)	140
Vehicle weights (kg)	18,000
Windward area (m2)	8.16
Battery capacity (kW·h)	86.44

. The test hybrid electric bus travels approximately 16 km from the first station to the terminal station, with a total of 36 bus stops along the route.

2.2. Calculation of Related Supplementary Parameters

Based on the collected data, this paper introduces several additional parameters related to vehicle operation and emissions, such as acceleration. The definitions and calculation formulas for parameters such as the air-to-fuel ratio, the instantaneous NOx emission mass, total vehicle power, Vehicle Specific Power (VSP), and engine effective power are as follows.

The NOx sensor transmits concentration data (in ppm) to the OBD system. However, researchers typically analyze vehicle NOx emissions using either mass-based emissions per kilometer (g/km) or NOx emission rates (mg/s) [4]. To enable more intuitive analysis, this study converts the per-second NOx concentration readings into instantaneous NOx mass emissions, which are then used as the output of the predictive model. The calculation of the instantaneous NOx emission mass of vehicles is shown in Equation (1) [21].

$$E_{NOx,i}={\displaystyle \frac{0.001587\times e_i}{3600}}\times \left(f_{Fuel,i}\times \rho +f_{Air,i}\right)$$

(1)

where, $E_{NOx,i}$ is the instantaneous NOx emission mass (g), $e_i$ is the instantaneous NOx emission concentration (ppm), $f_{Air,i}$ is the instantaneous air mass flow rate (kg/h), $f_{Fuel,i}$ is the instantaneous fuel volume flow rate (L/h), and $\rho$ is the fuel density (for diesel, typically 0.86 g/cm³).

The air-to-fuel ratio is defined as the ratio of intake air mass flow to engine fuel mass flow, calculated as shown in Equation (2).

$${AFR}_i={\displaystyle \frac{f_{Air,i}}{f_{Fuel,i}\times \rho }}$$

(2)

where ${AFR}_i$ is the instantaneous air-to-fuel ratio of the engine, $f_{Air,i}$ is the instantaneous air mass flow rate (kg/h), $f_{Fuel,i}$ is the instantaneous fuel volume flow rate (L/h), and $\rho$ is the fuel density (for diesel, typically 0.86 g/cm³).

Vehicle power is determined using the vehicle power balance equation [22,23]. By substituting the respective power calculation methods into this equation, the final form of vehicle power is presented in Equation (3).

$$\left\{\begin{array}{c}{P}_e={\displaystyle \frac{1}{{\eta }_T}}\left(P_f+P_w+P_i+P_j\right)\\ P_e={\displaystyle \frac{1}{{\eta }_T}}\left[{\displaystyle \frac{Gfv}{3.6}}+{\displaystyle \frac{Giv}{3.6}}+{\displaystyle \frac{C_{D}A{\rho }_{Air}}{2}}{\left({\displaystyle \frac{v}{3.6}}\right)}^3+{\displaystyle \frac{\delta Mv}{3.6}}{\displaystyle \frac{du}{dt}}\right]\times {\displaystyle \frac{1}{1000}}\end{array}\right.$$

(3)

where $P_e$ is the estimated vehicle power (kW), ${\eta }_T$ is the mechanical transmission efficiency, $g$ is the gravitational acceleration (9.80 m/s²), $f$ is the rolling resistance coefficient, $v$ is the speed (km/h), $i$ represents the road gradient (since the bus is driving on flat terrain, $i$ is taken as 0). $C_D$ is atmospheric drag coefficient, $A$ is windward side (m²), ${\rho }_{Air}$ is the air density (1.2258 kg/m³), and $\delta$ is automotive rotating mass conversion factor.

Vehicle Specific Power (VSP) is defined as the power demand per unit mass of the vehicle. In this paper, the VSP calculation formula from Yang [24] is adopted, as shown in Equation (4).

$$VSP=0.0643·v+0.000279·v^3+a·v+g·v·\mathit{sin}\theta$$

(4)

where $a$ is the acceleration of the vehicle (m/s²), $g$ is the gravitational acceleration (9.80 m/s²), $\theta$ is the angle between the road and the horizontal plane, which is taken as 0.

The engine’s effective power is calculated as shown in Equation (5) [25].

$$P_{me}=T_{tq}{\displaystyle \frac{2\pi n}{60}}\times {\displaystyle \frac{1}{1000}}={\displaystyle \frac{T_{tq}n}{9550}}$$

(5)

where $T_{tq}$ is the engine net output torque (N·m), and $n$ is the engine speed (rpm).

To investigate the factors influencing NOx emissions, this paper selects a total of 10 directly read feature parameters and seven calculated feature parameters for correlation analysis. The specific parameters and their corresponding symbols are listed in

Table 2. Feature Parameters and Symbols.

Index	Input Features	Unit	Abbreviations
1	Vehicle speed	km/h	v
2	Atmospheric pressure	kPa	Patm
3	Engine net output torque	N·m	Ttq
4	Friction torque	N·m	Tfric
5	Engine speed	rpm	N
6	Engine fuel flow	L/h	Ffuel
7	Intake air mass flow	kg/h	Fair
8	SCR inlet temperature	°C	TSCR-in
9	SCR outlet temperature	°C	TSCR-out
10	Engine coolant temperature	°C	Tcool
11	Acceleration	m/s2	a
12	Real-time fuel consumption	L/s	FC
13	Air-to-Fuel Ratio	/	AFR
14	Vehicle power	kW	Pe
15	Vehicle Specific Power	kW/t	VSP
16	Engine effective power	kW	Pme
17	SCR temperature difference	°C	ΔTSCR

. Superficially, operational characteristic parameters such as speed and acceleration, along with energy consumption parameters including total vehicle power and VSP specific power, reflect the vehicle’s energy usage patterns. These indirectly determine the charging duration and frequency in hybrid electric buses. In contrast, engine parameters (e.g., engine speed and fuel flow rate) and SCR system parameters (including inlet and outlet temperatures) directly govern NOx emission characteristics.

2.3. Data Preprocessing

To reduce the impact of dimensional differences among input features on model performance and to accelerate the convergence of the prediction model’s weight parameters, this study employs the Z-score normalization method to preprocess the input features.

The Pearson Correlation Coefficient is a statistical measure used to quantify the linear correlation between two continuous variables. It is widely applied in data analysis and feature selection in machine learning. In this study, the Pearson correlation coefficient is utilized to initially identify features linearly correlated with NOx emissions. Meanwhile, Mutual Information (MI) is employed to analyze the nonlinear relationships between each input feature and the target feature, instantaneous NOx emissions. MI is a statistical measure from information theory that quantifies the dependency between two variables, capturing both linear and nonlinear relationships. Unlike the Pearson correlation coefficient, which only measures linear correlation, MI is applicable to a broader range of data relationships, making it particularly valuable for engine emission analysis. The MI calculation formula is presented in Equation (6).

$$I\left(X;Y\right)=\sum _{\left(x,y\right)\in X\times Y}p\left(x,y\right)log\left({\displaystyle \frac{p\left(x,y\right)}{p\left(x\right)p\left(y\right)}}\right)$$

(6)

where $I\left(X;Y\right)$ represents the mutual information, $p\left(x,y\right)$ is the joint probability distribution of X and Y, and $p\left(x\right)$ and $p\left(y\right)$ are the marginal probability distributions of X and Y, respectively.

2.4. Two-Layer Stacking Ensemble Learning Model

The Back Propagation Neural Network (BPNN) offers advantages in simplicity and computational efficiency, making it well-suited for static features or short-sequence prediction tasks. In contrast, the LSTM algorithm demonstrates superior capability in temporal sequence modeling, though with higher model complexity. This study focuses on series hybrid electric buses, whose operational characteristics involve engines operating primarily at just a few high-efficiency working points. Therefore, the BPNN is prioritized for the predictive model. In this study, a two-layer stacking ensemble learning model is adopted. By combining multiple base models as inputs for prediction results and training a meta-model, the final prediction is obtained. Employing the BPNN as a base model in the ensemble enables the fitting of highly nonlinear relationships between input features and target variables, significantly improving prediction accuracy.

The first layer consists of three types of heterogeneous base models: eXtreme Gradient Boosting (XGBoost), Random Forest (RF), and BPNN. The second layer utilizes a linear regression model as the meta-learner for final prediction. To enhance computational efficiency, the Principal Component Analysis (PCA) is applied to reduce input feature dimensionality while preserving essential information. In the base models, Bayesian optimization is used for the adaptive search of BPNN hyper parameters to determine optimal configurations. The prediction results obtained from the base models are subjected to K-fold cross-validation. The average values from the K predictions are used to generate meta-features, which are then utilized for meta-model training to produce the final prediction results. The overall model architecture is illustrated in Figure 1.

XGBoost is an improved version of the Gradient Boosting Decision Tree (GBDT) and is a highly adaptive machine learning algorithm widely used for regression and classification tasks in data mining. Based on the boosting concept, GBDT constructs weak learners and aggregates their results to achieve better regression or classification performance. The objective function of XGBoost is formulated as shown in Equation (7).

$$obj\left(t\right)=\sum _{i=1}^{n}L\left(y_i,{\widehat{y}}_i^t\right)+\Omega \left(f_t\right)+c$$

(7)

where $L\left(y_i,{\widehat{y}}_i^t\right)$ is the loss function, $y_i$ is the true NOx emission value for the ith sample, and ${\widehat{y}}_i^t$ is the predicted NOx emission value for the ith sample at the ith iteration. $\Omega \left(f_t\right)$ is the regularization term, which helps control model complexity and prevent overfitting, and c is a constant term.

RF is an ensemble learning method that integrates multiple decision trees using the Bootstrap Aggregating (Bagging) algorithm. It performs regression by averaging predictions from multiple decision trees and classification using majority voting. By combining multiple base learners, Random Forest effectively reduces overfitting and enhances generalization performance, making it widely applicable in regression and classification tasks across various disciplines [26].

The BPNN is a classical feedforward neural network that adjusts network weights through the Back Propagation algorithm and is widely used in regression and classification tasks. The BP neural network consists of an input layer, hidden layer, and output layer, as shown in Figure 2. The PCA-reduced data is input into the BP neural network, and the prediction value is obtained through forward propagation layer by layer, as expressed in Equation (8).

$$\widehat{y}=f_2(W_2·f_1(W_{1}X+b_1\left)b_2\right)$$

(8)

where $W_1$ and $W_2$ are the weight matrices, $b_1$ and $b_2$ are the biases, $f_1$ is the activation function, and $f_2$ is the linear activation function. The back propagation process includes loss calculation and weight updates along the gradient direction using the chain rule to compute gradients layer by layer. In this study, the ReLU (Rectified Linear Unit) function is used as the activation function, as expressed in Equation (9), with its function graph shown in Figure 3.

$$ReLU=max(0,x)$$

(9)

2.5. Model Evaluation Methods

To compare model accuracy, this study evaluates the prediction performance using Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and the Coefficient of Determination (R²).

3. Results and Discussions

3.1. Input Feature Analysis

This study uses the Pearson correlation coefficient to analyze the linear relationships between input features and the instantaneous NOx emission mass of hybrid electric buses. Additionally, Mutual Information (MI) scores are used to examine the nonlinear relationships between input features and instantaneous NOx emission mass.

Figure 4a illustrates the Pearson correlation coefficients between different input features. As shown in the figure, some input features exhibit a high degree of linear correlation, highlighting the importance of applying PCA for dimensionality reduction [27]. Figure 4b presents the relationships between various input features and instantaneous NOx emission mass. The Pearson correlation coefficients for engine coolant temperature and SCR after-treatment system temperature are both lower than −0.5, indicating a negative correlation with instantaneous NOx emissions. Under frequent engine start–stop conditions, the after-treatment system is forced into an intermittent operation mode. The resulting multiple cold-start conditions, combined with the dynamic response lag of the catalyst temperature field, create a synergistic effect that significantly increases transient NOx emissions. This phenomenon is primarily attributed to the reduced ammonia storage capacity and kinetic limitations of the reduction reaction caused by incomplete activation of catalytic active sites during cold conditions. The effect is more pronounced in winter.

The Mutual Information (MI) score assessment of feature relationships with instantaneous NOx emission mass highlights the intake air mass flow (MI = 1.67) as having a particularly strong nonlinear impact on NOx emissions. The MI scores for various feature parameters are shown in Figure 5. Additionally, the SCR after-treatment system temperature and fuel flow-related parameters exhibit MI scores above 0.9, indicating a strong nonlinear relationship with instantaneous NOx emission mass.

The contribution rates and cumulative contribution rates of the principal components obtained through PCA are illustrated in Figure 6. When the cumulative contribution rate of the selected principal components exceeds 80%, it is considered reasonable and effective. However, to enhance the model’s accuracy, it is necessary to determine the number of principal components to extract. When the number of extracted principal components exceeds 12, the improvement in model accuracy becomes marginal. Therefore, taking these factors into account, the first 12 principal components are selected to form the input of the model.

3.2. Model Optimization Results

The base models selected in this study are XGBoost, RF, and BPNN. Among these, Bayesian optimization is employed to optimize the BP neural network with two hidden layers to determine the number of hidden layer neurons, the number of samples per training iteration, and the learning rate. In this research, the Bayesian optimization process is implemented through a custom objective function. This function constructs the neural network architecture based on the input parameters and uses 3-fold cross-validation to calculate the MSE. Ultimately, it returns the negative MSE to the optimizer, which determines the final result within the given range of parameters to be optimized. After five initial random searches and 20 iterations of Bayesian optimization, the best parameter combination was obtained in the seventh iteration, as shown in Figure 7. The final optimized values for batch size, number of neurons in the two hidden layers, and learning rate are summarized in

Table 3. The parameter search range and final results of Bayesian optimization.

Optimization Parameters	Search Range	Optimized Values
Batch size	16~128	106
Units of Hidden Layer 1	32~256	105
Units of Hidden Layer 2	16~128	67
Learning rate	0.0001~0.01	0.0019

.

In this study, 5-fold cross-validation is used to obtain the optimal meta-features. During each cross-validation iteration, the base models are trained on the training subset, and the predictions on the validation set are used as meta-training features. Simultaneously, predictions on the full test set are averaged across folds to generate meta-test features. The final Mean Squared Error MSE values for the three base models—XGBoost, RF, and BP Neural Network—are 0.0026, 0.0012, and 0.0010, respectively. The distribution of MSE values for the three base models across the 5-fold cross-validation process is shown in Figure 8.

3.3. Model Prediction Results Comparison and Analysis

In this study, MAE, MSE, RMSE, and R² are used to comprehensively evaluate the Stacking ensemble learning model and six other common NOx prediction models. All models utilize PCA for feature dimensionality reduction, and the data set is divided using the same method. The Stacking ensemble learning model achieves an MAE of 0.066, RMSE of 0.0270, and R² of 0.9580, with prediction results shown in Figure 9. The remaining six NOx prediction models are: (1) BP neural network optimized with GA algorithm, (2) BP neural network optimized with PSO algorithm, (3) LSTM model, (4) GRU model, (5) RF model, and (6) XGBoost model. The results for these models are presented in Figure 10.

Table 4. Evaluation metrics for seven models.

Model	MAE	RMSE	R2
GA-BP	0.0132	0.0359	0.9104
PSO-BP	0.0093	0.0577	0.9212
LSTM	0.0128	0.0577	0.7473
GRU	0.0126	0.0516	0.7981
RF	0.0111	0.0402	0.9066
XGBoost	0.0084	0.0340	0.9271
Stacking	0.0066	0.0270	0.9580

presents the three evaluation metrics for seven models. It can be observed that the two time-series prediction models, LSTM and GRU, perform poorly in predicting the instantaneous NOx emissions of hybrid electric buses, with R² values below 0.8. The models using GA (Genetic Algorithm) and PSO (Particle Swarm Optimization) to optimize BP neural networks exhibit significantly better R² values than the time-series models, with Root Mean Squared Errors (RMSE) of 0.0359 g/s and 0.0577 g/s, respectively. The Stacking model proposed in this study outperforms all other models across all three evaluation metrics, demonstrating its effectiveness in predicting NOx emissions for hybrid electric buses.

To enhance the credibility of the model, this study selected an additional 1200-s segment of operational and emission data from the tested bus beyond the original modeling dataset. This segment includes a 140-s period of pure electric driving (with zero NOx emissions) and the remaining duration with the engine active. A comparison between the actual and predicted values is shown in Figure 11. The R² value for this segment is 0.9601, demonstrating the model’s effectiveness to some extent. Future research could further validate the model’s applicability by incorporating hybrid buses of different vehicle types.

4. Conclusions

This study constructs a two-layer stacking ensemble learning model for transient NOx emission prediction in hybrid electric buses. Seventeen parameters, including operating characteristics of hybrid electric buses, engine operating parameters, and after-treatment system parameters, are selected as input features for the model. The model predicts the transient NOx emissions of hybrid electric buses and is compared with mainstream predictive models developed in previous studies. This research is applicable to vehicle remote monitoring technology and provides insights into NOx emission regulation of heavy-duty diesel vehicles.

Pearson correlation analysis reveals a significant negative correlation between instantaneous NOx emission mass and three key parameters: engine coolant temperature (r = −0.565), SCR after-treatment system inlet temperature (r = −0.593), and outlet temperature (r = −0.686), with absolute correlation coefficients exceeding 0.56. This indicates a strong association between the decrease in these parameters and the increase in instantaneous NOx emissions. MI analysis shows that the MI score for intake air mass flow is 1.67, while the MI scores for SCR after-treatment system temperature and engine fuel consumption are both greater than 0.9, suggesting a strong nonlinear relationship between these features and instantaneous NOx emission mass. These findings highlight the significant impact of SCR after-treatment system operating characteristics on the transient NOx emission flux of hybrid electric buses. Under frequent engine start–stop conditions, the after-treatment system is forced into an intermittent operation mode. The resulting multiple cold-start conditions, combined with the dynamic response lag of the catalyst temperature field, create a synergistic effect that significantly exacerbates transient NOx emissions. In the future, preheating the SCR system by supplying power in advance through the hybrid system could be an effective strategy to maintain its operating temperature within the effective working range.

The two-layer stacking ensemble learning model constructed in this study selects XGBoost, RF, and an optimized BPNN as base models, with a linear regression model as the meta-model, effectively predicting the instantaneous NOx emission mass of hybrid electric buses. The model is compared with two optimized BP prediction models, two time-series neural network models, an RF model, and an XGBoost model. The evaluation metrics—MAE, RMSE, and R²—are 0.0066, 0.0270, and 0.9580, respectively, demonstrating a significant advantage over all compared models. In the future, an appropriate prediction model can be developed for the steady-state NOx emissions of hybrid electric buses.