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Modeling and Predicting Heavy-Duty
Vehicle Engine-Out and Tailpipe
Nitrogen Oxide (NO
x
) Emissions Using
Deep Learning
Rinav Pillai
1
, Vassilis Triantopoulos
1
,
2
, Albert S. Berahas
3
, Matthew Brusstar
4
, Ruonan Sun
4
,
Tim Nevius
5
and André L. Boehman
1
*
1
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, United States,
2
Plasma Science and Fusion
Center, Massachusetts Institute of Technology, Cambridge, MA, United States,
3
Department of Industrial and Operations
Engineering, University of Michigan, Ann Arbor, MI, United States,
4
National Vehicle and Fuel Emissions Laboratory, U.S. EPA,
Ann Arbor, MI, United States,
5
Horiba Instruments Inc., Saline, MI, United States
As emissions regulations for transportation become stricter, it is increasingly important to
develop accurate nitrogen oxide (NO
x
) emissions models for heavy-duty vehicles.
However, estimation of transient NO
x
emissions using physics-based models is
challenging due to its highly dynamic nature, which arises from the complex
interactions between power demand, engine operation, and exhaust aftertreatment
efficiency. As an alternative to physics-based models, a multi-dimensional data-driven
approach is proposed as a framework to estimate NO
x
emissions across an extensive set
of representative engine and exhaust aftertreatment system operating conditions. This
paper employs Deep Neural Networks (DNN) to develop two models, an engine-out NO
x
and a tailpipe NO
x
model, to predict heavy-duty vehicle NO
x
emissions. The DNN models
were developed using variables that are available from On-board Diagnostics from two
datasets, an engine dynamometer and a chassis dynamometer dataset. Results from
trained DNN models using the engine dynamometer dataset showed that the proposed
approach can predict NO
x
emissions with high accuracy, where R
2
scores are higher than
0.99 for both engine-out and tailpipe NO
x
models on cold/hot Federal Test Procedure
(FTP) and Ramped Mode Cycle (RMC) data. Similarly, the engine-out and tailpipe NO
x
models using the chassis dynamometer dataset achieved R
2
scores of 0.97 and 0.93,
respectively. All models developed in this study have a mean absolute error percentage of
approximately 1% relative to maximum NO
x
in the datasets, which is comparable to that of
physical NO
x
emissions measurement analyzers. The input feature importance studies
conducted in this work indicate that high accuracy DNN models (R
2
= 0.92–0.95) could be
developed by utilizing minimal significant engine and aftertreatment inputs. This study also
demonstrates that DNN NO
x
emissions models can be very effective tools for fault
detection in Selective Catalytic Reduction (SCR) systems.
Keywords: heavy-duty vehicles, nitrogen oxide emissions, data-driven modelling, deep learning, artificial neural
networks, optimization
Edited by:
Weiqi Ji,
Robert Bosch, United States
Reviewed by:
Florian Vom Lehn,
RWTH Aachen University, Germany
Weiyu Cao,
Rivian Automotive LLC, United States
Opeoluwa Owoyele,
Louisiana State University,
United States
*Correspondence:
André L. Boehman
boehman@umich.edu
Specialty section:
This article was submitted to
Engine and Automotive Engineering,
a section of the journal
Frontiers in Mechanical Engineering
Received: 21 December 2021
Accepted: 02 February 2022
Published: 03 March 2022
Citation:
Pillai R, Triantopoulos V, Berahas AS,
Brusstar M, Sun R, Nevius T and
Boehman AL (2022) Modeling and
Predicting Heavy-Duty Vehicle Engine-
Out and Tailpipe Nitrogen Oxide (NO
x
)
Emissions Using Deep Learning.
Front. Mech. Eng 8:840310.
doi: 10.3389/fmech.2022.840310
Frontiers in Mechanical Engineering | www.frontiersin.org March 2022 | Volume 8 | Article 8403101
ORIGINAL RESEARCH
published: 03 March 2022
doi: 10.3389/fmech.2022.840310
1 INTRODUCTION
Heavy-duty vehicles employ compression ignition engines due to
their high power density, reliability and powertrain efficiency.
Even with the anticipated changes in Greenhouse Gas
regulations, diesel engine-powered trucks will continue to be
used in heavy-duty transportation for several years, especially
in the legacy fleet (EPA, 2021b). Also, the heavy-duty
transportation sector is more challenging to electrify due to
the need for high energy storage, fast charging rates and high
ranges for long-haul movement of goods (Askin et al., 2015;
Brown et al., 2020). However, diesel engines emit significant
amounts of NO
x
(nitric oxide and nitrogen dioxide) which is
designated as a criteria pollutant by the EPA (Winkler et al.,
2018), and has been shown to cause respiratory illness such as
asthma and chronic lung disease upon prolonged exposure. NO
x
is also a contributor to the formation of smog, acid rain and ozone
at ground levels (Boningari and Smirniotis, 2016). Stringent
emissions regulations have therefore been put in place to curb
vehicular NO
x
emissions (EPA, 2021b). This has put tremendous
pressure on the diesel engine industry to design and develop
technologies that limit NO
x
emissions from the engine and from
the tailpipe using exhaust aftertreatment systems. Accurate
estimation of instantaneous engine-out NO
x
emissions has
therefore become essential to improve engine control strategies
for NO
x
reduction. From a regulations perspective, accurate
models for tailpipe NO
x
predictions are important in
understanding the potential for future emissions reductions,
and as a tool for identifying possible modes of non-
compliance during in-use operation.
Formation of engine-out NO
x
is the result of complex chemical
reactions at high temperature within the combustion chamber,
and therefore strongly depends on the engine operating
condition. On the other hand, tailpipe NO
x
emissions are
highly dependent on the performance of the Selective Catalytic
Reduction (SCR) aftertreatment system. Past studies have made
use of thermophysical and chemical models to estimate NO
x
emissions. Mentink et al. (2017) developed a virtual engine-out
NO
x
sensor using a physics-based nitric oxide (NO) formation
model and an empirical correlation to determine nitrogen dioxide
(NO
2
) fraction of NO
x
. A semi-empirical two-zone model was
developed by Provataris et al. (2017) that made use of measured
in-cylinder pressure data and a physics-based model to estimate
NO formation in the combustion chamber. Camporeale et al.
(2017) used in-cylinder pressure sensor signal to create a grey-
box NO
x
raw emissions model. The model uses combustion
parameters such as adiabatic flame temperature and heat
release rate to estimate engine-out NO
x
emissions. Multiple
studies have also used computational fluid dynamics models to
model the changes in temperature and composition in the
combustion chamber to better estimate NO
x
emissions
production (Mobasheri et al., 2012;Dahifale and Patil, 2017).
These models use first principles to estimate NO
x
emissions and
therefore can achieve high extrapolation capabilities. However,
they require high computational time and cost, large number of
assumptions and the need for laborious manual configuration for
different engines.
In the past several years, increasing large quantities of data is
being collected through engine and chassis dynamometer
laboratory tests due to complex powertrain units with greater
number of actuators and finer control. This has led to growing
interest in the use of machine learning to develop predictive
models for NO
x
emissions. Using machine learning, accurate
data-driven models can be developed without requiring explicit
solution to the governing equations that describe the physics of
the system. Selvam et al. (2021) used measurements from On-
board Diagnostics (OBD) sensors to calculate combustion
variables like adiabatic flame temperature, oxygen
concentration and combustion time. These variables were then
used as inputs to an ensemble based method called Random
Forests to estimate engine-out NO
x
emissions for five different
heavy-duty engines. The model was evaluated to have an average
R
2
value of 0.72 and a mean absolute error (MAE) of 78 parts per
million (ppm). A hybrid model consisting of a physics-based
model and a machine learning approach was proposed by
Mohammad et al. (2021). The model combined a physical and
chemical model developed in GT-Suite with a Support Vector
Machine and Feed-Forward Artificial Neural Network (FFNN).
The model was validated using 772 steady state operating points
for a 13L heavy-duty diesel engine and showed good accuracy
with an R
2
score of 0.99 and root mean square error (RMSE) of
23 ppm. However, this model was not tested on transient
operating conditions. Johri and Filipi (2014) describes the
development of a Neuro-Fuzzy Model to predict transient NO
x
and soot emissions. This model divides the problem into multiple
sub-problems which are individually identified using a simpler
class of models. Polynomial and neural network models were
used as choices for the local models with validity functions that
determine the regions of input space where the local model is
active. The model was tested on Unites States Federal city-driving
schedule (FTP75) cycle data for a 6.4L heavy-duty engine. The
model predictions were in good agreement with the total
cumulative NO
x
measured over the test cycle.
Deep Learning has been shown to be adept at discovering
intricate structures in high-dimensional data and has applications
in various domains such as science, business and government
(LeCun et al., 2015;Goodfellow et al., 2016). A virtual NO
x
sensor
using Recurrent Neural Network (RNN) was proposed by Arsie
et al. (2013). Data for training was collected by running different
test cycles like the New European Driving Cycle (NEDC) on a
1.3L light-duty diesel engine. Engine Control Unit (ECU)
variables including engine speed, air mass flow, boost pressure,
fuel mass, start of injection (SOI) and air fuel ratio (AFR) were
used as inputs to the network. Pruning techniques were used to
improve generalization capability of the model. The authors
reported R
2
values between 0.83–0.91 for different test sets
with RMSE values ranging from 47–122 ppm. Fischer (2013)
developed a virtual NO
x
sensor for a 2.2L light-duty diesel engine
using Self-Organizing Map algorithm—a type of ANN which
makes use of a selector and estimator layer. Six input parameters
including engine speed, fuel quantity, lambda, air mass flow,
boost pressure and exhaust gas temperature were used to estimate
engine-out NO
x
. The model showed good accuracy on the
Artemis Urban Test Cycle with an error of 1.57% between the
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Pillai et al. Modeling NOx Using Deep Learning
total measured and predicted NO
x
over the cycle. Zhang et al.
(2015) proposed using an ANN model to predict engine-out NO
x
emissions using ECU variables like engine speed, torque, injection
timing, air flow rate, rail pressure and oil temperature as inputs.
The train and test data consisted of a “Chirp”cycle, Hot and Cold
Start drive cycles collected from a 2L light-duty diesel engine.
Total NO
x
estimated from the model deviated on an average
about 5.8% from the measured total NO
x
over the test cycle.
Bellone et al. (2020) compared a Convolutional Neural Network
(CNN) and Long-Short Term Memory (LSTM) network models
to predict engine-out NO
x
emission, soot and fuel consumption
for a heavy-duty 8L diesel engine. Input parameters included
ECU variables such as engine speed, fuel flow/cyl., injection angle,
rail pressure, wastegate position, exhaust gas recirculation (EGR)
position, exhaust temperature, main, post and pre-injection
quantity, inlet pressure, pre-injection angle and throttle
position. The CNN model captured 98.64% of the total test
cycle NO
x
emissions with an R
2
of 0.993, while the LSTM
model captured 99% of the total test cycle NO
x
emissions with
and R
2
of 0.995.
Shin et al. (2020) developed an engine-out NO
x
emissions
model for 1.6L light-duty diesel engine using Deep Neural
Networks (DNN) by training the model on the Worldwide
Harmonized Light Vehicles Test Procedure (WLTP) cycle.
They used Bayesian hyperparameter optimization to find the
optimal DNN architecture. The accuracy of the model was
indicated by an R
2
value of 0.9675 and MAE of 17 ppm using
14 input variables from the ECU. Yu et al. (2021) presented a
method for estimating tailpipe NO
x
emissions by complete
ensemble empirical model decomposition with adaptive noise
and an LSTM network. They used on-road data from the OBD
sensors of a diesel bus to train the network. They reported good
model accuracy with an R
2
value of 0.98 with RMSE of 46.11 ppm
on the test data. A steady state engine-out NO
x
emissions model
was proposed by Lee et al. (2021) using a DNN model. The model
used 8 ECU parameters including engine speed, brake mean
effective pressure, EGR rate, air mass, fuel mass, injection timing,
boost pressure and injection pressure as inputs. 696 steady state
conditions were evaluated using the model with good accuracy
indicated by an R
2
of 0.98.
However, the previously conducted studies have developed
DNN models for engine-out and tailpipe NO
x
emissions without
taking into account the effect of SCR performance which is an
essential component affecting overall NO
x
production. With the
light-duty industry expected to be increasingly electrified in the
near future, more emphasis also needs to be placed on developing
accurate models for estimation of heavy-duty diesel engine NO
x
emissions - both engine-out and tailpipe. Additionally, many of
the models also make use of ECU variables, such as fuel injection
timing, swirl ratio, and injection angle (Bellone et al., 2020;Shin
et al., 2020;Lee et al., 2021), which may not be readily available
except with proprietary access. Deep Learning models can be
highly accurate, but are inherently considered to be black-box
models, and therefore it is difficult to interpret their predictions.
However, it is crucial to understand for example why NO
x
emissions are higher than expected under given engine
operating conditions. Multiple papers have used percent of
NO
x
captured or total test cycle NO
x
error as an evaluation
metric for NO
x
prediction using DNN (Fischer, 2013;Johri
and Filipi, 2014;Bellone et al., 2020). The limitations of using
this metric in evaluating DNN model accuracy for predicting NO
x
emissions has been discussed in the current work and new
improved instantaneous error metrics for this application have
been proposed.
This work tries to address the aforementioned shortcomings of
the existing work in the literature by developing accurate engine-
out NO
x
and tailpipe NO
x
models using DNN. The DNN models
were trained and tested using two different datasets - an engine-
aftertreatment dynamometer dataset and a chassis dynamometer
dataset on two 6.7L heavy-duty bus engines (different model
years) using non-proprietary variables that are available from the
OBD as model inputs. The outline and contributions of this work
are as follows:
•Application of DNN to develop engine-out and tailpipe NO
x
emissions models for heavy-duty diesel engines using
physics inspired inputs readily available from the OBD,
while demonstrating high accuracy on both train and test
datasets.
•Development of a DNN model for tailpipe NO
x
emissions
using SCR aftertreatment information such as SCR inlet and
outlet temperatures and exhaust mass flow rate that
captures the effect of SCR performance on tailpipe NO
x
emissions.
•Analysis and development of holistic error metrics that help
visualize instantaneous as well as total NO
x
emissions
prediction errors of DNN NO
x
models over the DNN
training process.
•Interpretability study of models to enhance the physical
understanding of NO
x
emissions estimation using DNN.
Evaluation of model accuracy using minimal number of
“relatively important”input parameters physically affecting
production of NO
x
emissions, thereby illustrating DNN
model interpretation of complex transient NO
x
emissions.
•Detailed analysis of a potential application of developed
DNN models to fault detection in SCR aftertreatment
systems.
Organization
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.
2 INPUT FEATURES AND DATA
DESCRIPTION
In this section, the thermophysical and chemical phenomena
affecting production of engine-out and tailpipe NO
x
emissions are
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Pillai et al. Modeling NOx Using Deep Learning
explained, which lays the groundwork for the selection of the
input parameters for each models. A detailed description of the
datasets used to train and test the DNN models is also provided.
2.1 Input Feature Selection
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.
2.1.1 Engine-Out NOx Formation
NO
x
is composed of nitric oxide (NO) and nitrogen dioxide
(NO
2
). Diesel engine NO formation is described by Three
mechanisms - Thermal NO, Prompt NO and Fuel NO
(Heywood, 2019). Prompt NO is formed in fuel-rich
conditions and is not highly temperature dependent. Fuel NO
formation is dependent on the presence of nitrogen-based
compounds in the fuel. However, the primary mechanism for
diesel NO formation within the combustion chamber is defined
by the Extended Zeldovich Mechanism (Lavoie et al., 1970)
referred to as Thermal NO. Thermal NO formation is due to
oxidation of nitrogen in the air. The principal reactions governing
the formation of Thermal NO are given by
N2+ONO +N(1)
N+O2NO +O(2)
N+OH NO +H.(3)
These reactions ((1),(2),(3)) are highly dependent on the
combustion temperature (>2000 K), in-cylinder oxygen (O
2
)
concentrations, and residence time of the reacting mixture at
peak temperatures and lean air-fuel mixtures (Bowman, 1975).
NO
2
on the other hand is formed due to partial oxidation of NO
further downstream of the cylinder which can be explained by the
following reaction (4) (Merryman and Levy, 1975):
NO +HO2NO2+OH.(4)
Engine-out NO
x
formation is primarily controlled by the
temperature of the burned gas and O
2
concentration in the
combustion chamber. These parameters vary based on
different engine operating and control variables such as intake
air mass flow rate, fuel flow rate, intake manifold temperature and
pressure, engine speed and load. Therefore, these variables were
selected as inputs for modeling engine-out NO
x
. Exhaust gas
recirculation (EGR) is an important engine-out NO
x
control
strategy typically employed on diesel engines. The
introduction of EGR, which is composed primarily of nitrogen
(N
2
), carbon dioxide (CO
2
), and water (H
2
O), displaces air in the
cylinder, and results in lower NO
x
formation. The primary
mechanisms for the decrease in NO
x
formation due to EGR
are the reduction in the mixture’s oxygen concentration, and
decrease in the combustion temperatures due to presence of
higher specific heat capacity triatomic molecules. As a result,
EGR mass flow rate was also included as an input to the DNN
when available.
2.1.2 Tailpipe NOx Emissions
Tailpipe NO
x
emissions are highly dependent on the performance
of the SCR. SCR uses ammonia (NH
3
) in the form of aqueous urea
as a NO
x
reduction reagent to convert NO
x
to N
2
and H
2
O.
However, the dominant catalytic reactions require a certain
optimal temperature range (520–725 K) (Khair and Majewski,
2006). There are three important SCR reactions given by (Koebel
et al., 2002):
4NO +4NH3+O24N2+6H2O(5)
4NH3+2NO +2NO24N2+6H2O(6)
4NH3+3NO23.5N2+6H2O.(7)
The standard SCR reaction (5) occurs in a NO dominant
environment and requires high temperature. At lower SCR
temperatures, a faster reaction rate conversion (6) takes place
using equimolar amounts of NO and NO
2
. This helps to improve
SCR performance at lower SCR temperatures. However, an excess
of NO
2
results in a slower reaction rate reaction (7). Therefore,
SCR conversion efficiency is highly dependent on the ratio of NO
2
to NO entering the SCR.
The SCR performance is greatly influenced by the residence
time available for reactants in the optimal temperature range,
which is a function of the space velocity. The space velocity of the
reactor is a function of the measured exhaust gas flow rate
through the SCR. The rate of NO
x
removal is also dependent
on the inlet NO
x
concentration, as NO
x
levels determine the rate
of reactions (Heywood, 2019). Therefore, exhaust aftertreatment
variables such as SCR inlet and outlet temperatures, exhaust mass
flow rate and measured engine-out NO
x
were considered as
inputs to the tailpipe NO
x
DNN model. Coolant temperature
was also included as an input to the model to provide information
regarding cold start or hot start conditions for the test cycles.
Other variables affecting SCR performance such as urea injection
quantity and timing, and ammonia (NH
3
) slip were not
considered, as they are not readily available from the OBD
data without proprietary access.
2.2 Data Sources and Dynamometer Test
Cycles
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.
2.2.1 Engine Dynamometer Data and Test Cycles
Engine dynamometer testing was conducted at the United States
EPA, National Vehicle and Fuel Emissions Laboratory (NVFEL),
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Pillai et al. Modeling NOx Using Deep Learning
Ann Arbor, on a 6.7L heavy-duty engine (2010) using
certification diesel fuel. Test data included engine parameters
as well as after-treatment parameters as described in Section 2.1.
Both engine-out and tailpipe-out NO
x
emissions were measured
using exhaust gas analyzers at 10 Hz frequency. All parameters
measured using test cell instruments were also recorded at 10 Hz
frequency. The dynamometer test cycles included three separate
runs of a cold Federal Test Procedure (FTP) cycle, a hot FTP cycle
and a Ramped Mode Cycle (RMC) as shown in Figures 1A,B.
These tests encompass a variety of engine operating conditions
including cold-start, hot-start and transient. This dataset will be
referred to as Dataset 1 in this paper. Dataset 1 had a total of
127,223 samples for training the DNN after pre-processing.
In literature, data for testing DNN NO
x
models was found to
be split from the dataset in two different ways: keeping a separate
run of a complete test cycle as test set (Arsie et al., 2013;Fischer,
2013;Zhang et al., 2015;Bellone et al., 2020) or randomly
selecting points from the dataset as test set (Shin et al., 2020;
Lee et al., 2021;Yu et al., 2021). In this study, both methods were
adopted to analyze and compare the effect they had on the model
performance. Subsequently. the dataset was first randomly
shuffled and then split into train, validation and test sets. 75%
of the data was used as train set, of which 25% was used as
validation set. The remaining 25% of the total data was used to
test the model after training and validation. Splitting of the
dataset was also done by using two runs of each test cycle as
train set and one run of each test cycle (unseen by the DNN
models) as test set.
2.2.2 Chassis Dynamometer Data and Test Cycles
Chassis dynamometer testing was conducted on a hybrid bus that
operates on a parallel hybrid architecture using a 6.7L heavy-duty
engine (2011) and a 650V nickel-metal hydride battery using
certification diesel fuel. The tests were conducted at the Heavy-
Duty Chassis Dynamometer Test Facility at the United States
EPA NVFEL, Ann Arbor. The facility is capable of simulating on-
road conditions for transient and loaded conditions with the help
of a road speed modulated vehicle cooling fan with high
precision. Continuous tailpipe exhaust measurements were
made using a heated dilution tunnel and a Horiba MEXA-One
gaseous emissions bench, while engine-out NO
x
measurements
were sampled directly from the exhaust prior to the SCR, both at
FIGURE 1 | Engine and Chassis dynamometer test cycles used to develop datasets for Deep Learning NO
x
Models. (A) Engine Dyno FTP Cycle. (B) Engine Dyno
RMC Cycle. (C) Chassis Dyno Cold Start Super Cycle. (D) Chassis Dyno Hot Start Cycles. (E) Chassis Dyno On Road Cycle. (F) Chassis Dyno Ramp Cycle.
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Pillai et al. Modeling NOx Using Deep Learning
10 Hz frequency. A Cold Start Super Cycle (CSSC), a Hot Start
Cycle which was a combination of New York Bus Cycle (NYBC),
Orange County Bus Cycle (OCBC), NREL Transient Cycle, an
On-Road bus cycle and a Ramp Cycle (Figures 1C–F) were
successfully run on the chassis dynamometer to generate a
comprehensive dataset encompassing different vehicle
operating conditions. OBD data was collected from the bus
using Controller Area Network (CAN) at 10 Hz frequency.
This included engine and after-treatment parameters similar to
the engine dynamometer tests as described in Section 2.1. Battery
parameters including state of charge, charging and discharging
current were also included as inputs to the engine-out NO
x
model
to incorporate the influence of hybridization on the NO
x
emissions of the bus (Bagheri et al., 2021). This dataset will be
referred to as Dataset 2 in this paper.
Dataset 2 had a total of 442,623 samples after pre-processing.
As described for Dataset 1, Dataset 2 was also split randomly into
equivalent train, validation and test set ratios. The data was also
split using 16 runs of complete test cycles as train set and 3
separate runs of test cycles (unseen by the DNN models) as test
set. Further details on the train, validation and test splits for both
the datasets has been provided in Table 1.
3 RESEARCH METHODOLOGY
In this section, the research methodology followed in this paper is
described. Specifically, we discuss the model and its associated
hyperparameters and the data pre-processing strategy employed.
3.1 Feed Forward Deep Neural Network
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)formore
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.
3.2 Data Pre-Processing
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.
TABLE 1 | Description of datasets (engine and chassis dynamometer. Types of
data splits (random and test cycles) and train/validation/test splits.
Dataset Engine dynamometer Chassis dynamometer
Type of Data split Random Test cycles Random Test cycles
Total Samples 127,223 127,223 442,623 442,623
Train 76,334 64,883 265,574 301,569
Validation 19,083 16,221 66,393 75,392
Test 31,806 46,119 110,656 65,662
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Pillai et al. Modeling NOx Using Deep Learning
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’sfit
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:
Xnorm X−Xmin
Xmax −Xmin
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.
3.3 Architecture of DNN Models
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.
3.3.1 Hyperparameter Selection and Optimization
In this study, hyperparameter optimization, a very important
ingredient of DNN training (Feurer and Hutter, 2019), is
implemented using a grid search where the search space is
defined by a grid of hyperparameter values. Every point in the
grid which represents a model configuration is then evaluated for
performance using appropriate evaluation metrics. Grid search was
performed using the GridSearchCV function in the “scikit-learn”
library, which allows to perform cross-validation (Refaeilzadeh et al.,
2009) in order to understand the generalization capability of each
model configuration being tested. The target hyperparameters for
optimization included the number of hidden layers, number of
nodes in each hidden layer, learning rate and batch size. The ranges
of hyperparameters considered for the two datasets are given in
Table 2.Table 3 summarizes the final architecture and
hyperparameters for each model.
For the hyperparameter optimization, initially a small DNN
network composed of two hidden layers with 20 and 10 nodes,
respectively, was set up to reduce computational burden. Some
hyperparameters were selected based on optimal values in literature
that used DNNs for similar supervised learning regression tasks. The
Adam optimizer (Kingma and Ba, 2014), a stochastic first-order
diagonally scaled method, was used as the optimization algorithm.
Associated with the optimization algorithm, the learning rate (a
parameter that controls the change in the DNN model weights), as
well as the batch size (the amount of data used in the Forward- and
Backward-Propagations) were also tuned. With respect to the DNN
model, the Rectified Linear Unit (ReLU) activation function (Nair
and Hinton, 2010) was considered appropriate for both the hidden
layers and the output layer. ReLU is a piece-wise linear function
which outputs the input itself if it is positive, but outputs zero if it is
FIGURE 2 | Deep neural network model architecture, inputs/outputs, and activation functions. (A) Engine Out NOx Model. (B) Tailpipe NOx Model.
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Pillai et al. Modeling NOx Using Deep Learning
negative. In this application all input values are non-negative, thus,
ReLU is an appropriate candidate for the hidden layers.
Moreover, the number of hidden layers and nodes in each
hidden layer were optimized using a separate grid search using
the optimized learning rate and batch size from the first grid
search. The different DNN hidden layer configurations for the
grid search were developed using a custom function that utilizes
three parameters as inputs to create different DNN hidden layer
configurations; number of hidden layers, number of neurons in
the first hidden layer and number of neurons in the last hidden
layer. Based on the number of hidden layers selected, the function
individually selects the number of neurons for first and last
hidden layers from the ranges provided in Table 2 and
linearly decreases the number of neurons in each layer based
on the number of hidden layers. For example, if we consider 5
hidden layers, 200 neurons in the first hidden layer and 20
neurons in the last hidden layer, a DNN hidden layer
configuration given by (200,155,110,65,20) is created by the
function. Each network in both the grid searches was run for
200 epochs with 5 fold cross-validation (Stone, 1978)to
determine the optimal batch size, learning rate and hidden
layer configuration based on the optimal mean MSE on the
cross-validation tests. Further tests were then carried out on
the optimal network architecture determined to evaluate the
effect of increasing the width of the network (i.e., number of
nodes in each hidden layer) and number of epochs on the
performance of the model. The number of epochs for training
the network was optimized based on the training and validation
loss curves to ensure that there was no overfitting of the model on
the train set. Number of epochs was used as a termination criteria
for the training of all the models. The optimal hyperparameters
based on the results from the grid searches have been summarized
in Table 3.
Learning Rate Decay
Learning rate decay is a mechanism by which the learning rate
(employed by the optimization algorithm) is set and adjusted as
the optimization progresses in help with learning. Specifically,
during the early stages of training large learning rates are
employed to allow for large steps, and in order to avoid
spurious local minima. In the latter stages of training, a
smaller, more refined learning rate is employed in order to
obviate the effects of noise, and in order to converge (to a
local minimum). Learning rate decay has been shown
empirically to improve model optimization and generalization
(Smith, 2018;Ge et al., 2019;You et al., 2019). In this study,
learning rate decay was used for all the models.
Dropout
Overparametrized DNNs, i.e., DNNs with large number of
parameter (weights), are prone to overfitting to the training
dataset (Sankararaman et al., 2020). Dropout is a
TABLE 2 | Ranges of hyperparameters explored for different models (Engine Dynamometer and Chassis Dynamometer).
Dataset Engine dynamometer Chassis dynamometer
Model Engine-out NO
x
Tailpipe NO
x
Engine-out NO
x
Tailpipe NO
x
Learning Rate [0.01,0.001,0.0001] [0.01,0.001,0.0001] [0.01,0.001,0.0001] [0.01,0.001,0.0001]
Batch Size [100, 500, 1,000, 95,417] [100, 500, 1 000, 95,417] [1,000, 5,000, 10,000, 3,31,967] [1,000,5,000, 10,000, 3,31,967]
Input Layer Nodes 8 5 9 5
Hidden Layers [2,3,4,5,6] [2,3,4,5,6] [2,3,4,5,6] [2,3,4,5,6]
First Hidden Layer Nodes [200,100,50,20] [200,100,50,20] [200,100,50,20] [200,100,50,20]
Last Hidden Layer Nodes [20,15,10,5] [20,15,10,5] [20,15,10,5] [20,15,10,5]
Hidden Layer Activation Function ReLU ReLU ReLU ReLU
Output Layer Nodes 1 1 1 1
Output Layer Activation Function ReLU ReLU ReLU ReLU
Epochs 200 200 200 200
TABLE 3 | Final optimal hyperparameters for engine-out and tailpipe NO
x
models for dataset 1 and 2.
Dataset Engine dynamometer Chassis dynamometer
Model Engine-out NO
x
Tailpipe NO
x
Engine-out NO
x
Tailpipe NO
x
Input Layer Nodes 8 5 9 5
Hidden Layer Nodes [200, 100, 50, 5] [1,000, 500, 250, 100, 5] [1,000, 500, 250, 100, 5] [2,000, 1,000, 500, 250, 100, 5]
Hidden Layer Activation Function ReLU ReLU ReLU ReLU
Output Nodes 1 1 1 1
Output Layer Activation Function ReLU LeakyReLU ReLU LeakyReLU
Learning Rate 0.001 0.001 0.001 0.001
Learning Rate Decay 1/5 every 200 Epochs 1/5 every 200 Epochs 1/10 every 400 Epochs 1/10 every 400 Epochs
Drop Out 0 0.1 0.1 0.1
Batch Size 500 500 1,000 1,000
Epochs 600 600 1,000 1,000
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Pillai et al. Modeling NOx Using Deep Learning
regularization technique often employed in DNN training to
mitigate this issue (Srivastava et al., 2014). The technique
involves randomly “dropping out”nodes along with their
connections from the network during training. Temporarily
“deactivating”nodes during training reduces the over-
adaptation of the network weights to the training data and
leads to improvement in network out-of-sample performance
and generalization (Baldi and Sadowski, 2013). The fraction of
nodes that are deactivated at every iteration of training (“dropout
rate”) is often treated as a hyperparameter. In this study a small
dropout rate of 0.1 was applied to the hidden layers of all models
during training except for the engine-out NO
x
model for
Dataset 1.
3.3.2 Loss Function and Evaluation Metrics
In this study, the following loss function and evaluation metrics
were used.
Mean Squared Error (MSE)
Mean Squared Error (MSE) is the default loss function used in
many DNNs for regression problems. It is calculated via
MSE 1
n
n
i1
yi−^
yi
2,
and is the average of the squared difference between the true
output value (y
i
) and the model’s predicted value (^
yi), also
referred to as the prediction error.
R-Squared (R
2
)
Coefficient of determination or R-Squared (R
2
), defined as
R21−n
i1yi−^
yi
2
n
i1yi−
y
2,
where
yis the mean of the true output value, is a statistical
measure used to determine the “goodness of fit”, i.e., how well the
predicted NO
x
values fit with the true NO
x
values. Using R
2
as an
evaluation metric indicates the model performance across
different points in the NO
x
distribution. The higher the R
2
value, the better the model prediction across the NO
x
distribution.
Total NO
x
Error
Another evaluation metric that has been used in the literature to
measure the predictive accuracy of NO
x
emissions models is Total
NO
x
error (%) (Fischer, 2013;Johri and Filipi, 2014;Bellone et al.,
2020). Total NO
x
error, defined as
Total NOxError %
()
Total NOxpredicted −Total NOxactual
Total NOxactual
*100,
is the difference between total true and predicted NO
x
emissions
in the dataset. Total cumulative NO
x
is calculated for train,
validation and test datasets for both true and predicted NO
x
values. The percent difference between total true and predicted
NO
x
over each dataset shows if the model has captured various
transient NO
x
conditions (both high and low) across the dataset
effectively and the percentage of total NO
x
emissions captured by
the model over the dataset.
Instantaneous NO
x
error
Since the DNN models developed in this study are used to
predict instantaneous NO
x
emissions, we propose a novel
instantaneous NO
x
error metric that captures the error at
every point in the training (validation, testing) set. The
absolute prediction error and percent absolute prediction
error(%)foreverytrainingpointiscalculatedatevery
epoch of training and is given by
Absolute Prediction Errori|yi−^
yi|
Absolute Prediction Errori%
()
|yi−^
yi|
yi
*100.
The maximum, minimum and mean absolute prediction error
and percent error is then calculated and reported for each epoch
over the training set. As the DNN learns to predict NO
x
emissions
at every instant (data point) in the training set, these error metrics
should reduce indicating improvement in the model’s
instantaneous NO
x
prediction capability.
3.3.3 Output Layer Activation Function for Tailpipe
NOx Model
Both engine-out and tailpipe NO
x
models have 1 node in the
output layer as the models are predicting one continuous non-
negative output (engine-out or tailpipe NO
x
emissions). ReLU
was considered as an appropriate candidate for the output
layer for both models. However, an interesting phenomenon
was observed while examining model predictions for tailpipe
NO
x
. Namely, the model predicted tailpipe NO
x
as “0”for
many true labels where the NO
x
emissions were smaller than
0.0001 g/s (70% of the training set). This resulted in
underprediction of total cycle NO
x
emissions since many
non-zero values were predicted as zero. Extracting the input
values to the output layer ReLU activation function showed
negative values for smaller true NO
x
labels ( <0.000 1 g/s),
which by the nature of ReLU are output as “0”,thereby
increasing total NO
x
prediction error. Thus, other activation
functions like LeakyReLU (Maas et al., 2013) and Exponential
Linear Unit (ELU) (Clevert et al., 2015) were tested for the
output layer. These activation functions are similar to the
ReLU activation function with minor differences (e.g.,
LeakyReLU has a small slope in the negative region;
nonzero gradient when the node is not active). It was found
that using LeakyReLU improved the tailpipe NO
x
model
predictions at lower NO
x
values at the expense of predicting
some negative NO
x
values ( <1%of the dataset). The small
negative slope helps to smoothen the hard threshold that ReLU
has to output “0”value and therefore helps the models predict
better at lower NO
x
values. LeakyReLU only outputs negative
values for very small NO
x
true labels ( <10−5g/s). These
negative values are negligible when compared to the total
training set NO
x
predicted (<0.01%), thereby improving
overall tailpipe NO
x
DNN model performance.
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Pillai et al. Modeling NOx Using Deep Learning
4 RESULTS
In this section, the main results for the engine-out NO
x
and
tailpipe NO
x
models are presented. Table 3 summarizes the final
architecture and hyperparameters for each model. The results are
divided into the following sub-sections: model evaluation metrics
(Section 4.1), error metrics (Section 4.2), and instantaneous
actual vs predicted NO
x
emissions (Section 4.3), on the train,
validation and test sets for each model and dataset.
4.1 Model Evaluation Metrics Results
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’sNO
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
,modelforthisdataset.
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
TABLE 4 | Evaluation metrics for train, validation and test set with 95% confidence intervals (all models).
Dataset Engine dynamometer Chassis dynamometer
Model Engine-out NO
x
Tailpipe NO
x
Engine-out NO
x
Tailpipe NO
x
Train MSE (g/s) 5.02E-06 ± 3.03E-07 7.79E-07 ± 2.14E-07 1.91E-05 ± 3.23E-07 4.21E-05 ± 2.07E-06
Val MSE (g/s) 7.35E-06 ± 2.47E-07 1.27E-06 ± 3.29E-07 4.30E-05 ± 8.60E-07 7.20E-05 ± 2.70E-06
Test MSE (g/s) 7.41E-06 ± 1.76E-07 1.43E-06 ± 3.37E-06 4.19E-05 ± 4.86E-07 7.07E-05 ± 9.22E-07
Train MAE (g/s) 1.22E-03 ± 2.41E-05 4.30E-04 ± 1.36E-04 2.48E-03 ± 2.61E-05 3.18E-03 ± 3.56E-05
Val MAE (g/s) 1.25E-03 ± 1.43E-05 4.44E-04 ± 1.32E-04 3.25E-03 ± 2.04E-05 3.94E-03 ± 7.02E-05
Test MAE (g/s) 1.34E-03 ± 1.77E-05 4.51E-04 ± 1.35E-04 3.27E-03 ± 2.20E-05 3.91E-03 ± 3.14E-05
Train R
2
0.998 ± 0.001 0.996 ± 0.001 0.987 ± 0.001 0.956 ± 0.002
Val R
2
0.997 ± 0.001 0.995 ± 0.001 0.971 ± 0.001 0.926 ± 0.003
Test R
2
0.997 ± 0.001 0.994 ± 0.001 0.972 ± 0.001 0.927 ± 0.001
Train MAE (%) 0.512 ± 0.010 0.080 ± 0.025 0.516 ± 0.021 1.487 ± 0.040
Val MAE (%) 0.566 ± 0.006 0.084 ± 0.025 0.950 ± 0.020 2.137 ± 0.222
Test MAE (%) 0.566 ± 0.006 0.085 ± 0.025 0.883 ± 0.028 1.797 ± 0.020
Train Total NO
x
Error (%) 0.086 ± 0.049 1.229 ± 1.250 0.116 ± 0.114 0.151 ± 0.231
Val Total NO
x
Error (%) 0.100 ± 0.058 1.304 ± 1.375 0.155 ± 0.114 0.368 ± 0.350
Test Total NO
x
Error (%) 0.084 ± 0.059 1.214 ± 1.313 0.167 ± 0.109 0.249 ± 0.195
Frontiers in Mechanical Engineering | www.frontiersin.org March 2022 | Volume 8 | Article 84031010
Pillai et al. Modeling NOx Using Deep Learning
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.
4.2 Error Metrics
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
FIGURE 3 | Evolution of MSE and R
2
curves over training and validation data (All Models). (A) Engine Out NOx Loss and R
2
Dataset 1. (B) Tailpipe NOx Loss and R
2
Dataset 1. (C) Engine out NOx Loss & R
2
Dataset 2. (D) Tailpipe NOx Loss and R
2
Dataset 2
FIGURE 4 | Train and Test R
2
fits with histograms showing distribution of errors (All Models). (A): Engine Out NOx Model R
2
Train Dataset 1. (B): Engine Out NOx
Model R
2
Test Dataset 1. (C): Engine Out NOx Model R
2
Train Dataset 2. (D): Engine Out NOx Model R
2
Test Dataset 2. (E): Tailpipe NOx Model R
2
Train Dataset 1. (F):
Tailpipe NOx Model R
2
Test Dataset 1. (G): Tailpipe NOx Model R
2
Train Dataset 2. (H): Tailpipe NOx Model R
2
Test Dataset 2.
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Pillai et al. Modeling NOx Using Deep Learning
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 10
7
) 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 10
1
) 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–Hand Table 4 which
shows the mean MAE and percent MAE with respect to the
maximum NO
x
over the train, validation and test sets.
4.3 Actual vs Predicted NOx Emissions
Figures 6,7depict 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–Dshow 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–Dindicates 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
FIGURE 5 | Progression of total NO
x
error in comparison with maximum, minimum and mean absolute error over training of all DNN NO
x
models. (A) Engine Out
NOx Train Errors (%) Dataset 1. (B) Tailpipe NOx Train Errors (%) Dataset 1. (C) Engine Out NOx Train Errors (%) Dataset 2. (D) Tailpipe NOx Train Errors (%) Dataset 2.
(E) Engine Out NOx Train Errors Dataset 1. (F) Tailpipe NOx Train Errors Dataset 1. (G) Engine Out NOx Train Errors Dataset 2. (H) Tailpipe NOx Train Errors Dataset 2.
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Pillai et al. Modeling NOx Using Deep Learning
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.
5 DISCUSSION
In this section, three different studies conducted have been described
which highlight some important aspects of the application of DNNs
to NO
x
emissions predictions. First, an analysis of the effect of type of
input data split on the accuracy of developed DNN models is
presented. Then, insights from an input feature importance study
are discussed. Finally, the effectiveness of the developed DNN models
to fault-detection in SCR aftertreatment systems is also presented.
5.1 Effect of Training Data on Model
Accuracy
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
FIGURE 6 | Improvement of instantaneous NO
x
prediction over DNN training (Engine-Out NO
x
model Dataset 1). (A) Engine Out NOx Training Epoch 1 Dataset 1.
(B) Engine Out NOx Training Epoch 200 Dataset 1. (C) Engine Out NOx Training Epoch 400 Dataset 1. (D) Engine Out NOx Training Epoch 600 Dataset 1.
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Pillai et al. Modeling NOx Using Deep Learning
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
FIGURE 7 | Actual vs Predicted NO
x
emissions for a portion of the test set (All Models). (A) Test Set Engine Out NOx Actual vs Predicted Dataset 1. (B) Test Set
Tailpipe NOx Actual vs Predicted Dataset 1. (C) Test Set Engine Out NOx Actual vs Predicted Dataset 2. (D) Test Set Tailpipe NOx Actual vs Predicted Dataset 2.
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Pillai et al. Modeling NOx Using Deep Learning
parameters such as fuel injection pressure and timing, urea
injection timing and quantity and NH
3
slip could be included
as inputs to the DNN models to capture the variation in NO
x
emissions.
5.2 Input Feature Importance Study
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 (~ 106model parameters vs ~ 105
training points) Therefore, the network is able to learn from
existing input features even if one input feature is removed. The
FIGURE 8 | Effect of type of data split on model performance. (A) Engine Out NOx Model Dataset 1. (B) Tailpipe NOx Model Dataset 1. (C) Engine Out NOx Model
Dataset 2. (D) Tailpipe NOx Model Dataset 2.
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Pillai et al. Modeling NOx Using Deep Learning
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.
5.3 DNN as a Fault Detection Tool for Engine
and Aftertreatment System
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
FIGURE 9 | Effect of variable removal on model performance (Engine out NO
x
model Dataset 1). (A) Effect of Variable Removal on R
2
—Engine Out NOx Dataset 1.
(B) Effect of Variable Removal on MSE—Engine Out NOx Dataset 1.
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Pillai et al. Modeling NOx Using Deep Learning
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.
5.4 Application of DNN Models to Other
Heavy-Duty Engines and Fuels
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
FIGURE 10 | Effect of variable removal on model performance (tailpipe NO
x
model Dataset 2). (A) Effect of Variable Removal on R
2
—Tailpipe NOx Dataset 2. (B)
Effect of Variable Removal on MSE—Tailpipe NOx Dataset 2.
FIGURE 11 | Application of DNN for fault detection in SCR aftertreatment Systems. (A) Tailpipe NOx Emission-faulty after treatment vs DNN model prediction. (B)
Cumulative Tailpipe NOx Emission.
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Pillai et al. Modeling NOx Using Deep Learning
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.
6 CONCLUSIONS AND FUTURE WORK
Deep Neural Network (DNN) models were developed using
physics inspired inputs to predict transient heavy-duty diesel
engine-out and tailpipe NO
x
emissions using engine and
aftertreatment variables. The study employed popular and
well-established techniques in machine/deep learning to
develop engine-out and tailpipe NO
x
emissions models with
high predictive power. Based on an in-depth analysis of the
DNN models for predicting NO
x
emissions developed in this
study, the following conclusions can be drawn:
1. DNN models using physics inspired inputs are capable of
effectively characterizing the complex, nonlinear nature of
transient engine-out and tailpipe NO
x
emissions. In this study,
simple and easily accessible OBD parameters (inputs) were
used to develop accurate DNN models. All the models
developed in this study have a mean absolute error
percentage within 1–2% of the maximum NO
x
measurement, which is comparable to physical NO
x
emissions measurement analyzer accuracy of 1% of full scale.
2. Novel tailpipe NO
x
models developed using SCR aftertreament
variables, such as SCR inlet and outlet temperature, engine-out
NO
x
and exhaust mass flow rate, showed good prediction
accuracy (R
2
= 0.99). However, the DNN tailpipe NO
x
model
developed using data from a faulty SCR system exhibited lower
prediction accuracy (R
2
= 0.92) on the test set.
3. This study analyzed the effect of type of dataset splitting on the
model accuracy. It was shown that randomly splitting the
dataset into train and test sets provides a better understanding
of cycle-to-cycle NO
x
emissions variation to the DNN model
while training—thereby improving model accuracy on the test
set. If the DNN models are trained using multiple runs of test
cycles as train data, it would be advisable to include more input
features that provide additional information to the DNN about
the cause of disparity in NO
x
emissions for similar test cycles.
4. The feature importance study conducted on the DNN models
showed the robustness of the models to removal of single input
features while training the network. It was also observed that
the DNN models had close understanding of the complex
transient nature of NO
x
emissions as they were trained using
physics inspired input features. Engine-out NO
x
models
showed good correlation with engine operating conditions
like engine speed and torque (R
2
= 0.93), while tailpipe NO
x
models exhibited good accuracy even with just three
aftertreatment variables as inputs (R
2
= 0.95). Interestingly,
the DNN models did not perform equally well when trained
using data from a poorly functioning aftertreatment system
(R
2
= 0.92). This indicated that when DNN models for NO
x
emissions are trained using physics inspired inputs, training
data that is not representative of the physics of NO
x
emissions
formation can lead to relatively poor DNN model
performance.
5. This work demonstrated that DNN NO
x
emissions models can
be very effective tools for fault detection in Selective Catalytic
Reduction (SCR) systems. Cumulative NO
x
predictions from
the DNN model detected that the engine with a faulty
aftertreatment (SCR) system produced 60% more total cycle
NO
x
(g) than the expected NO
x
emissions from a functioning
aftertreatment (SCR) system.
Future work in this domain will involve the application of
similar DNN models to on-road testing data from OBD
information and a Portable Emissions Measurement System
(PEMS). On-road emissions prediction presents an interesting
challenge as environmental variables such as road grade, ambient
temperature, pressure and humidity also affect NO
x
emissions,
but their effects are not necessarily captured in the controlled
environment of laboratory testing. Use of DNN models that are
trained using physics inspired inputs along with real-world
driving effects would help develop models for on-road NO
x
prediction, which should reduce the disparities in NO
x
emissions between on-road and laboratory type tests.
However, measurements from low cost production on-road
sensors are less repeatable than those taken from expensive
instruments used in engine and chassis dynamometer test
cells, and hence it would be challenging to achieve equally
high accuracy models using on-road data. The influence of
different type of fuels on DNN model NO
x
prediction could
also be explored by training the models on comprehensive
datasets including data from different fuels tested on a heavy-
duty vehicle. More heavy-duty engines and aftertreatment
systems could be incorporated into the DNN models to assess
the model’s robustness in predicting NO
x
emissions from
different engine sizes and SCR systems. Successful
implementation using comprehensive datasets available from
chassis and engine dynamometer testing regularly conducted
for compliance purposes could result in a database created to
measure cumulative NO
x
emissions over test cycles for different
heavy-duty engines using the DNN models. This would be
important to inform the development of future NO
x
emissions
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Pillai et al. Modeling NOx Using Deep Learning
regulations and for validating real-world emissions
measurements against expected performance.
DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article will be
made available by the authors, without undue reservation.
AUTHOR CONTRIBUTIONS
Specific contributions to the paper are as follows: RP: Data
Curation, Formal Analysis, Methodology, Software, Validation,
Investigation and Writing - original draft. VT: Investigation,
Methodology and Validation. ASB: Investigation,
Methodology, Software and Validation. MB: Resources and
Supervision. RS: Resources and Data Curation. TN: Resources,
Project Administration and Funding Acquisition. ALB:
Resources, Supervision, Project administration and Funding
Acquisition.
FUNDING
Funding for this study was provided by Horiba Instruments Inc.
ACKNOWLEDGMENTS
The authors would like to thank Maria Peralta, Advanced Testing
Center Director, United States EPA, NVFEL, Garrett Brown,
Scott Ludlam and Robert Caldwell at the United States EPA,
NVFEL for conducting the chassis dynamometer tests at the
Heavy-Duty Chassis Dynamometer Test Facility and providing
data for this study.
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Conflict of Interest: TN was employed by Horiba Instruments Inc. This study
received funding from Horiba Instruments Inc. The funder was involved in
resources, project administration and funding acquisition.
The remaining authors declare that the research was conducted in the absence of
any commercial or financial relationships that could be construed as a potential
conflict of interest.
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Pillai et al. Modeling NOx Using Deep Learning
