The paper is organized as follows. In Section 2 we discuss engine-out and tailpipe NO _x formation, our choice of input features, and the data. Our research methodology is described in Section 3. In Section 4 we present our results followed by an in depth discussion of input feature importance and potential application of developed DNN models in Section 5. We conclude with final remarks in Section 6.

In the current study, a DNN model using physics inspired features as inputs has been developed. Therefore, significant engine and vehicle parameters from literature that affect engine-out and tailpipe NO _x formation were measured in the tests conducted to develop the datasets used to train the DNN models, while also taking into consideration their ease of availability from vehicle OBD. A brief description of engine-out NO _x and tailpipe NO _x formation has been provided in the following sections to explain the different inputs selected for each model.

Data was collected from two different sources: engine dynamometer testing and chassis dynamometer testing. A 6.7L heavy-duty bus engine (different model years) was tested on an engine and chassis dynamometer using multiple dynamometer test cycles representative of urban, highway, idle, transient and cold start conditions, thereby comprehensively encompassing known sources of transient NO _x emissions.

An Artificial Neural Network (ANN) makes use of representative data to establish empirical relationships between input features and some target output (LeCun et al., 2015; Goodfellow et al., 2016). ANNs have been shown to be adept at establishing complex relationships without the need of strict assumptions or mathematical equations, and as a result have had tremendous success in applications such as image classification (Ciregan et al., 2012), speech recognition (Amodei et al., 2016), and games (Silver et al., 2016); see (Bishop, 1994; Abiodun et al., 2018) for more examples. In its most primitive form, an ANN is a composition of connected neurons arranged in an input layer, possibly a set of hidden layers, and an output layer. Neurons in adjacent layers are connected through edges, or weights. Information flows from the input layer to the output layer through activation functions at each neuron that attempt to capture nonlinearity in the input-output relationship. This process is called “Feed-Forward Propagation”. Training an ANN amounts to adjusting the weights, commonly via the process of “Back Propagation” (Rumelhart et al., 1986), in order to minimize the “objective or loss” function which measures the deviation between the true target output and the predicted output of the network. One Feed-Forward and one Back-Propagation constitute one training “epoch” of the ANN.

Deep Learning Neural Networks (DNN) are a multi-layer manifestation of ANNs (i.e., more than one hidden layer). The predictive power of DNNs is positive correlated with the volume of data and the size of the network, i.e., both the height (number of neurons per layer) and the width (number of layers) (Sun et al., 2017). An important aspect of DNNs is their capability to learn good representations of complex phenomena using “feature learning” (Bengio, 2012). This enables DNNs to learn nonlinear mappings of input features to outputs by generating “high level” features using “low level” (input) training data. These intrinsic characteristics of DNNs make them suitable for modeling and predicting NO _x emissions using simple accessible data.

In this study, DNNs are used in a supervised learning regression task, i.e., the training data has a labelled output and the output (NO _x emissions) is continuous. The proposed DNNs are trained over multiple epochs to develop NO _x emissions models with high predictive power using the different training datasets (see Section 2.2). The DNNs have multiple “hyperparameters” (e.g., number of hidden layers and nodes, batch size, learning rate) that determine the structure of the neural network and guide the learning process. These parameters are tuned, using exhaustive grid searches (Feurer and Hutter, 2019), to give the best possible performance for a given model, dataset, and computational budget. Prior to training the DNNs, the available datasets are pre-processed in order to help with the training (learning), and as a result increase the predictive power of the DNNs for the given computational budget (Yu et al., 2021); see Section 3.2 for more details. Figure 2 shows the schematic for the DNN engine-out (2a) and tailpipe NO _x (2b) models to describe the DNN architecture.

Transient data was collected from the engine and chassis dynamometer testing, therefore, it is necessary to eliminate time delay between the input parameters and the measured NO _x emissions before training the DNN models to improve model performance (Arsie et al., 2013; Fischer, 2013; Johri and Filipi, 2014; Zhang et al., 2015). For the engine dynamometer data, the dataset was time-aligned according to 40 Code of Federal Regulations (CFR) Part §1,065 to account for delays in exhaust gas transport and instrument responses (EPA, 2021a). An empirical time constant was derived by cross-correlating the input parameters with the measured NO _x emissions for the chassis dynamometer data for time-alignment of the complete dataset. The effectiveness of the time alignment method was demonstrated with a Pearson’s correlation coefficient of 0.99.

Further, any data points that had negative values due to instrument or calibration errors were removed. This ensures that noisy or unreasonable data does not contaminate the DNN models. The application of DNN to instantaneous NO _x prediction is difficult as it involves the prediction of a continuous variable at every point. To mitigate this issue several studies in the literature have used box plots or median methods to determine and remove “outliers” in the data to improve network performance (Donateo and Filomena, 2020; Yu et al., 2021). In this study, it was found that eliminating outliers also removed a large number of “peak” NO _x conditions which are significant in predicting different transient and “rare” events that occur during vehicle operations. Thus, in order to promote robustness in the DNN models, in this study, data associated with outliers (e.g., “peak” NO _x conditions) was included in the training.

Each dataset was divided into train, validation and test sets as described in Section 2.2. The train set is used to train the models. The validation set provides an unbiased evaluation of the model’s fit on the training samples while tuning the different hyper-parameters of DNN models. The test set is used to evaluate the final model to determine model accuracy and generalization capability.

Feature Scaling is an essential step in data pre-processing for DNN models. The basis for feature scaling is to transform the data such that all the inputs have similar distributions, i.e., a common scale, and equal importance is given to each variable ensuring that no variable influences the model solely due to magnitude (Kotsiantis et al., 2006). Scaling the features helps with the stability, efficiency and robustness of gradient-based optimization algorithms (Wan, 2019). In this study, normalization was used which shifts and rescales the input values to a range between 0 and 1 (also known as   min−max scaling) given by: X norm = X − X min X max − X min

In all the datasets, min −max scaling was fit on the train set and then used to normalize both the validation and test set. This was done to ensure unbiased testing predictions.

An Intel^® Core^TM i7-10750H CPU @ 2.60 GHZ (12 cores) with 16 GB RAM and an NVIDIA GeForce RTX 2060 GPU were used for computation. Python 3.60 programming language was used to develop the model with the help of “Keras” deep learning library using TensorFlow (Abadi et al., 2016) as backend. The Python library “scikit-learn” (Pedregosa et al., 2011) was used for pre-processing data, dataset splitting, hyperparameter grid search and model evaluation using different metrics.

The evaluations metrics used to measure the prediction accuracy and overall performance of the models on the train, validation and test sets are reported in Table 4. Cross-validation (5 fold), a popular tool used in machine learning to evaluate a model prediction and generalization capability (Refaeilzadeh et al., 2009), was employed in this study. The results presented in Table 4 are the average MSE, MAE, R ² and MAE (%) over the maximum NO _x values over the 5 fold cross-validation for each model along with their respective 95% confidence intervals. Overall, the confidence interval values reported in Table 4 indicate that the models were robust to changes in training inputs.

The selection of evaluation metrics was directed at analyzing different aspects of the model’s NO _x prediction capability. First, MSE and MAE were chosen to evaluate if the models were generalizing well to unseen data, i.e., validation and test sets. For all the models, the training and validation MSE and MAE values are very close indicating good model generalization. The test and validation set MSE and MAE values are comparable indicating model robustness to predicting NO _x for conditions unseen by the model when training.

One of the holistic metrics used in the literature to capture NO _x , emissions model accuracy is R ² (Arsie et al., 2013; Bellone et al., 2020; Shin et al., 2020; Yu et al., 2021). As can be seen from Table 4, R ² values on train, validation and test sets are high for both engine-out and tailpipe models for Dataset 1 and engine-out model for Dataset 2 even with the inclusion of peak NO _x , conditions (Yu et al., 2021). Contrary to (Arsie et al., 2013; Zhang et al., 2015; Bellone et al., 2020; Shin et al., 2020) that used ECU variables which are comprehensive but not easily accessible, the models developed in this study achieved comparable high model accuracy while utilizing only simple OBD, parameters as inputs to the models. The aftertreatment system on the bus used to collect data for Dataset 2 has been subject to a product recall due to a manufacturing defect (EPA, 2018). Therefore, the data is not completely representative of a working SCR, system and subsequently the production of tailpipe NO _x , emissions. This could explain the relatively lower R ² values for the tailpipe NO _x , model for this dataset. However, the model still captured a significant portion of the transient tailpipe NO _x , emissions as indicated by Test R ² of 0.9275 shown in Table 4.

Linearity of the models was evaluated using mean absolute error (percent) with respect to the maximum NO _x in the dataset. As can be seen from Table 4, the percent MAE with respect maximum NO _x for all the models are well within 1–2%, which is comparable to the NO _x measurement accuracy of NO _x emissions analyzers which have linearity of 1% of full-scale NO _x (Gluck et al., 2003).

Figure 3 presents the training and validation MSE (loss) and R ² curves for each model. These curves help to visualize the progress of the MSE function and R ² as the network is trained over a set number of epochs. The training loss over the epochs shows how well the model is learning using the given dataset, while the validation loss shows how well the model is generalizing to a smaller validation set that is not being used to train the DNN. For all the models, it can be seen that MSE decreases as the network learns, while R ² increases which indicates improvement in model prediction. The sudden drops in the loss curves indicate where the learning rate decay was implemented for each model.

The results of Regression Analysis (R ² fit) for train and test datasets of the different models are shown in Figure 4. The models show high degrees of agreement with the measured engine-out and tailpipe NO _x emissions demonstrated by high R ² values on both train and test sets. The points are well distributed on both sides of the regression fit line which indicates normal distribution of prediction errors with a mean around 0, which is further confirmed by the histogram of errors shown for all the models. The large scatter of points on either side of the regression fit line in Figures 4G,H can be attributed to the large number of data points which causes the “few” outliers in the plot to cover a larger region in the plots.

Figure 5 shows the total NO _x error (%) (Arsie et al., 2013; Johri and Filipi, 2014; Bellone et al., 2020) for train and validation sets (orange line) on a log scale. The error was consistent on average over the training. From Table 4 it can be observed that total NO _x error (%) for lower accuracy models (R ² = 0.93–0.95) is lower than that of higher accuracy models (R ² = 0.99). A simple reason for this could be due to the fact that the lower accuracy models overpredict and underpredict instantaneous NO _x more than the higher accuracy models. The results from Table 4 show that there is no clear correlation between R ² values and the total NO _x error, i.e., higher R ² models do not show lower total NO _x error. The studies conducted on the models indicate that the magnitude of overprediction and underprediction in lower R ² models, sufficiently balance out when the cumulative total true and predicted NO _x over the train, validation and test set is calculated, resulting in a lower total NO _x error (see histograms in Figure 4). This suggests that the total NO _x error metric alone is not a good indicator of a model’s instantaneous NO _x predictive capability.

Therefore, in order to better understand the progression of the instantaneous prediction error at every epoch, the (maximum, minimum and mean) absolute prediction error and percent absolute prediction error over the train set were used as additional evaluation merits; see Section 3.3.2 for definition. From Figure 5, it can be seen that all metrics decrease as the model is trained, indicating improvement in model accuracy. The large maximum percent absolute prediction errors (of the order 10⁷) can be attributed to a few very low NO _x emissions points being significantly overpredicted, however, this represents a very small portion of the entire dataset ( < 5 % ) . Subsequently, it can be observed that the mean absolute error (%) is low (in the order of 10¹) indicating higher overall instantaneous prediction capability. Also, it is important to consider the scale of the NO _x emissions while evaluating percentage absolute error. Very small errors in predictions can be blown up when calculating absolute error with respect to the true NO _x emissions which are at the scale of 1E-04 and lower. These absolute errors however are still small when compared to the average value of NO _x emissions in the datasets (0.03–0.05 g/s) as can be seen from Figures 5E–H and Table 4 which shows the mean MAE and percent MAE with respect to the maximum NO _x over the train, validation and test sets.

Figures 6, 7 depict the actual NO _x emissions in red and the predicted NO _x emissions in blue. Such visualizations aid in understanding the predictive capabilities of the models over the course of training, and clearly highlight points for which the model is overpredicting or underpredicting NO _x emissions.

As an example, Figure 6 depicts the improvement in the predictions of the engine-out NO _x DNN model for Dataset 1, over a small section of the train set as the network learns. Figures 6A–D show the actual and predicted NO _x emissions for the DNN model at epochs 1, 200, 400 and 600 respectively. It can be observed that as the network is trained, subsequently the predictions (dashed blue line) approach the true values of NO _x emissions (red line). The increasing overlap of the two lines in Figures 6B–D indicates significant improvement in the model predictive capabilities over the course of training.

Figure 7 shows the NO _x prediction results for a portion of the test set for all the models. Sections of the test set have been enlarged below each sub-plot to provide more clarity to the profile for measured and predicted NO _x emissions. Figure 7B also includes an enlarged log-scale plot to show the peak tailpipe NO _x predictions more clearly. The DNN models are able to capture both dips and peaks in the engine-out and tailpipe NO _x emissions effectively as observed from the enlarged plots. The DNN models were successfully able to capture high frequency oscillations in previously unseen test data, while having MAE within 1–2% of the full scale of the NO _x emissions available in the dataset. Overall, the results are very promising, and the models appear to be suitable for transient NO _x emissions estimation in engine-out NO _x control and tailpipe NO _x compliance applications.

In this section, the effect of model training data for NO _x prediction on the DNN model accuracy has been analyzed. DNN models were trained using data split by two different approaches as described in Section 2.2. The results for this experiment on each of the models is presented in Figure 8. It was observed that when the models were trained using randomly selected training data, they had good accuracy (both R ² and MSE) on train, validation and test sets. However, when the models were trained using complete test cycles and then tested on different (unseen) complete runs of the same test cycles, the models had less prediction accuracy on the test set. However, the models are not overfitting on the training data, as R ² and MSE of the “hold-out” validation set is comparable to that of the train set, as can be seen from the striped bars in Figure 8.

One explanation for this phenomenon could be that there are variations in NO _x emissions measurements across multiple runs of the same test cycle, either due to instrument measurement deviations or accuracy limits or due to the effect of an engine or aftertreatment parameter that is not included in the input features for the DNN models - for eg. fuel injection pressure and timing, urea injection or NH ₃ slip. The results from this study suggest that DNN models trained using randomly selected data, are capable of learning the different variations in NO _x measurements that occur at similar inputs much better than when the model is trained using whole test cycles. The variation in NO _x emissions at the same point in the dataset between the test cycle runs in the train set and the test set are unknown to the models when the data is not split randomly. This could be causing the higher error between the model prediction and the true NO _x measurement in the test cycle. Therefore, to improve model prediction when using multiple runs of whole test cycles to train the DNN, it could be advisable to add more input features to explain the variation in true NO _x measurements. Fuel injection strategies affect the formation of NO _x emissions (Agarwal et al., 2013). SCR performance is also affected by NH ₃/NO _x ratio, while NH3 slip could also affect the effectiveness of engine-out to tailpipe NO _x conversion (Girard et al., 2007). Therefore, proprietary ECU parameters such as fuel injection pressure and timing, urea injection timing and quantity and NH₃ slip could be included as inputs to the DNN models to capture the variation in NO _x emissions.

DNN’s are inherently black-box models due to their multi-layer nonlinear architecture. DNN’s are capable of modelling complex problems with high accuracy but at the expense of losing “explainability”, i.e., how transparent the model’s predictions are to a human (Fan et al., 2021). In the application of predicting NO _x emissions, especially for engine control and compliance purposes it is important to discern where and why the model is predicting incorrectly. Therefore, an attempt has been made to determine “important” inputs to the DNN models presented in this paper that affect model prediction. This study does not completely make the DNN models transparent, but tries to gain some understanding into the inner workings of the DNN’s characterization of various engine and aftertreatment parameters to the production of NO _x emissions.

The DNN models make use of input engine or aftertreatment parameters to learn the complex transient nature of NO _x emissions. Therefore, by removing an input feature that is important to the DNN to learn, would result in decrease in the model accuracy. This was the underlying principle used to develop an understanding of relative importance of engine or aftertreatment variables for the DNN models to predict NO _x emissions. In this study, few (5–9) input features were used to train the models, and as a consequence this method was easier to implement. After the DNN models were trained, the models (with the same hyperparameters and architecture) were trained again by removing one input feature at a time to find the input feature which when removed reduced the model prediction accuracy, i.e., R ² and MSE. As an example, results for the experiments have been presented for the engine-out NO _x model using Dataset 1 in Figure 9.

However, as can be seen from the R ² and MSE values for both train and test sets, removal of any single input variable did not seem to affect the model prediction accuracy. The actual physics of NO _x formation and engine operation could provide an explanation for this phenomenon. NO _x emissions are formed due to highly complex chemical and physical phenomena which are affected by parameters that are highly dependent on each other. Therefore, even if one variable or input is removed from the DNN model, information provided by other engine or aftertreatment variables help the DNN to capture the complex process of NO _x formation in diesel engines. The observed independence could also be because the DNN was sufficiently over-parameterized, i.e., number of parameters in the network exceeds the training points ( ∼ 1 0 6 model parameters vs ∼ 1 0 5 training points) Therefore, the network is able to learn from existing input features even if one input feature is removed. The two hypotheses could be responsible in conjunction for the observed independence of model accuracy on the removal of single input features.

Further testing was therefore conducted by removing multiple sets of inputs till a significant reduction in model prediction accuracy was achieved to test the model’s capability to model NO _x emissions with only the most “important” variables. For the engine-out NO _x model, it was observed that just providing engine speed and torque as inputs to the DNN still resulted in model accuracy (R ²) of 0.93. This is consistent with the diesel engine operation—as the engine speed and torque essentially determine the engine operating conditions which is highly related to the production of engine-out NO _x emissions. However, the significant reduction in accuracy suggests that the other input features also contribute to the DNN prediction accuracy on a smaller scale when compared to engine speed and torque. Similarly, using chassis dynamometer data which was collected from a hybrid bus, model accuracy, i.e., R ² of 0.93 was achieved using engine speed and torque along with state of charge and charging current as input features.

For the tailpipe NO _x model using the engine dynamometer dataset, utilizing SCR inlet temperature, exhaust mass flow rate and engine-out NO _x as inputs resulted in a model prediction accuracy with R ² of 0.95 on the test set. However, for the tailpipe NO _x model for the hybrid bus, removing even a single input feature resulted in significant reduction in model prediction accuracy as shown in Figure 10. This could be attributed to incorrect functioning of the SCR system for this hybrid bus (EPA, 2018). Subsequently, the data collected to train this tailpipe NO _x DNN model, is not a true representation of the effect of SCR parameters on tailpipe NO _x emissions. Considering that this particular DNN model is much “deeper” and “wider” than the other tailpipe NO _x DNN model, over-parameterization of the network was inadequate for the network to completely capture incorrect operation of the SCR system.

The variable importance study however suggests that the DNN models are capable of capturing some aspects of the physics of engine-out and tailpipe NO _x emissions without the need for any physical or chemical equations. Important engine and aftertreatment variables guide the DNN models to predict with higher accuracy. The study conducted also demonstrates that utilizing minimal information, i.e., two to four physics inspired inputs, the DNN models developed in this study are capable of capturing complex trends of NO _x emissions in heavy-duty vehicles as indicated by the R ² values of 0.92 for engine-out and 0.95 for tailpipe NO _x model.

This section presents an example of the application of DNN models such as the ones developed in this paper for detection of anomalies or faults in diesel vehicles. If DNN models using physics inspired inputs are trained using data from functioning engine and aftertreatment systems, the predictions of the model can compared with data that is obtained from in-use vehicles. This can be applied to detect abnormal NO _x emissions occurring either due to a faulty engine operation, incorrectly operating aftertreatment systems or defeat devices. Fault detection can therefore be performed on an engine-level, as well as, aftertreatment-level.

As an example, data was collected from an poorly-functioning aftertreatment (SCR) system for the same engine as the one used for engine dynamometer testing in this paper. The DNN model trained using data from a functioning aftertreatment system was used to predict the tailpipe NO _x emissions for this engine. The tailpipe NO _x emissions predictions for all three engine dynamometer test cycles (Section 2.2) were then compared with the “faulty” aftertreatment system data. In Figure 11A, the blue dashed line indicates the DNN prediction (using functioning aftertreatment system data) and the red line indicates NO _x emissions measurements collected from the faulty aftertreatment system. The cumulative total tailpipe NO _x emissions over the 3 test cycles for the faulty aftertreatment system was 29.81 g while, the DNN model predicted the expected total tailpipe NO _x emissions (if the aftertreatment was functioning correctly) of 18.6 g, as shown in Figure 11B. The engine with a faulty aftertreatment system produced 60% higher tailpipe NO _x emissions which was successfully detected by the DNN model. This example demonstrates the capability of optimized DNN models to detect NO _x emissions anomalies or faults in diesel vehicles and their application for testing and compliance purposes.

This section discusses the application of similar DNN models to other heavy-duty engines and fuels. Even though the models developed in this paper have been trained on data from one particular engine, it is expected that due to the use of physics inspired features, the models are capable of capturing the significant features and trends that affect transient NO _x emissions in other heavy duty diesel engines. However, from an instantaneous engine-out NO _x perspective, since it is a continuous variable and highly dependent on engine design and calibration and fuel injection strategies, trained model accuracy would be reduced when tested directly on other engines not used to train the models developed in this study. Also, from a tailpipe NO _x model perspective, SCR aftertreatment systems with different catalysts have different NO _x conversion dependencies on the inputs used in the DNN models developed in this study. Therefore, using comprehensive datasets such as the ones developed in this study for other engines and aftertreatment systems, and subsequently applying a similar training process as described in this study should theoretically result in accurate DNN NO _x emissions models for different heavy-duty engines. The current DNN models could also be modified to include other inputs that capture the effect of different engine designs and calibration and SCR catalysts along with comprehensive datasets for other engines to evaluate model performance on other heavy-duty engines.

The type of fuel tested to develop the datasets used to train the DNN models in this study could influence the performance of the trained models. The models in this study were trained using data from engine and chassis dynamometer testing running on certification diesel fuel. Therefore, the dataset used to train the DNN models captures the NO _x emissions trends for certification diesel fuel. Capturing NO _x emissions trends for other fuels such as biodiesel or other higher oxygenated renewable fuels would require subsequent training and optimization using vehicle testing data using these fuels. DNN models developed in this study could be utilized as a base model for initial training using data from a different fuel and then optimized for NO _x emissions prediction. A larger dataset that encompasses NO _x emissions trends using different fuels on a single engine can be used to train similar DNN models with fuel type as an input. The model performance could then be evaluated to capture the influence of fuels on the DNN NO _x emissions predictions.