Article citation information:
Khuong Thi,
H., Nguyen Cao, V. Artificial neural network-based prediction of
in-cylinder pressure and pressure rise rate in a PCCI diesel engine. Scientific Journal of Silesian University of
Technology. Series Transport. 2026, 132,
185-196. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2026.132.10
Ha KHUONG THI[1],
Van NGUYEN CAO[2]
ARTIFICIAL NEURAL NETWORK-BASED PREDICTION OF
IN-CYLINDER PRESSURE AND PRESSURE RISE RATE IN
A PCCI DIESEL ENGINE
Summary. This study
experimentally collected in-cylinder pressure data from a diesel engine
operating under premixed charge compression ignition (PCCI) conditions. The
input parameters included advanced ignition timings of 40°, 45°, 50°, 55°, and
60° CA BTDC, and a crank angle range of 320°-420° CA. Accordingly, pressure
traces corresponding to each ignition timing were obtained, yielding a total of
505 data points, with 101 points per pressure trace. Based on the experimental
dataset, an artificial neural network (ANN) model was developed for pressure
prediction and accuracy assessment. The results indicate that the model
achieves very high accuracy, with R², RMSE, and MAE values of 0.9983,
0.9397 bar, and 0.6937 bar, respectively, for the training dataset, and 0.9981,
1.0115 bar, and 0.7268 bar for the testing dataset. These results confirm the
strong generalization capability and reliability of the ANN model. Given the
validated accuracy, the ANN model was further applied to predict four
additional pressure traces at ignition timings of 30°, 35°, 65°, and 70° CA
BTDC, corresponding to 404 predicted pressure points. By combining the
experimental and predicted datasets (909 pressure points in total), the
pressure rise rate was calculated and a three-dimensional (3D) model was
established. This model clearly illustrates the distribution and variation
patterns of key combustion-related parameters in a PCCI diesel engine, thereby
providing a valuable database and scientific foundation for future studies on
combustion analysis, optimization, and AI-based engine prediction and control.
Keywords: PCCI
combustion, in-cylinder pressure, artificial neural network, pressure rise rate
1.
INTRODUCTION
Emissions generated by internal
combustion engine (ICE)-powered vehicles pose significant threats to both human
health and the environment [1]. Nevertheless, more than 1.4 billion vehicles
worldwide were still powered by ICEs as of 2023 [2], indicating their continued
dominance in current transportation systems. Among these technologies, diesel
engines remain difficult to replace due to their high thermal efficiency,
durability, and operational reliability, particularly in heavy-duty
applications. Consequently, improving diesel engine technologies to mitigate
environmental impacts has become an urgent and widely studied research topic.
High emissions from conventional diesel engines primarily originate from
inhomogeneous air-fuel mixing and heterogeneous combustion processes, which
simultaneously generate fuel-rich and fuel-lean regions as well as strong
temperature gradients within the combustion chamber. To address these issues,
low-temperature combustion (LTC) strategies have been extensively investigated.
Among them, premixed charge compression ignition (PCCI) has attracted
considerable attention due to its potential to improve combustion
characteristics and significantly reduce emissions [3,4]. PCCI combustion,
derived from the homogeneous charge compression ignition (HCCI) concept,
involves early fuel injection to promote premixing before auto-ignition during
the compression stroke. This approach leads to a relatively homogeneous mixture
prior to ignition, resulting in lower peak combustion temperatures and reduced
formation of nitrogen oxides (NOₓ) and soot compared to conventional
diesel combustion. In practical applications, PCCI operation is typically
combined with injection timing control, exhaust gas recirculation (EGR), and
multi-stage injection strategies to enhance mixture preparation and combustion
controllability [5-7]. Although recent studies have demonstrated that optimized
injection strategies and EGR rates can extend the operating load range and
reduce HC/CO emissions, challenges related to combustion control and limited
operating range remain [8-9]. With rapid advancements in computational
technologies, internal combustion engine research has increasingly incorporated
artificial intelligence (AI)-based approaches alongside traditional experimental
methods. Artificial neural networks (ANNs), in particular, have demonstrated
strong capabilities in modeling highly nonlinear
systems with multiple interacting parameters. For instance, Foroutani
et al. [10] successfully applied ANN models to predict performance and
emissions of a heavy-duty diesel engine fueled with
syngas, achieving high prediction accuracy across different operating
conditions. Similarly, Odufuwa [11] developed an
ANN-based predictive framework for small diesel engines, demonstrating
significant improvements in performance optimization and emission reduction.
AI-based approaches have also been applied to advanced combustion concepts such
as PCCI. Cheng Ma et al. [12] combined long short-term memory (LSTM) networks
with NSGA-II optimization to enhance performance and emission characteristics
of a CNG/diesel dual-fuel engine operating in PCCI mode, achieving substantial
reductions in NOₓ and fuel consumption. Despite these advancements,
studies focusing on ANN-based modeling and prediction
of in-cylinder pressure under PCCI combustion remain relatively limited. Given
the strong nonlinear behavior and complex combustion
kinetics inherent to PCCI operation, ANN models offer a promising solution due
to their computational efficiency and adaptability. Motivated by this research
gap, the present study develops an ANN-based model to predict in-cylinder
pressure at new injection advance angles using experimentally measured pressure
data. Furthermore, the predicted pressure data are utilized to calculate the
pressure rise rate, providing deeper insights into combustion characteristics
and enabling identification of optimal operating regions for PCCI diesel
engines.
2. METHODOLOGY
2.1.
Experimental Setup
Figure 1 illustrates the schematic
diagram of the experimental engine test bench, which consists of major
components such as an AC electric dynamometer, an exhaust gas analysis system,
a fuel supply system, an engine control system, and various measuring
instruments. The test engine is a Changchai 192FA
diesel engine (2), a single-cylinder four-stroke engine, directly coupled to a
DW16 dynamometer (1) and equipped with a Common Rail fuel injection system.
Intake air is drawn from the ambient environment through an air filter and an
intake air flow meter (7), then passes through a surge tank (8) to attenuate
pressure fluctuations caused by the cyclic intake process of the engine. Diesel
fuel is supplied to the Common Rail injection system, where the fuel pressure
is compressed to a high level, monitored by a pressure sensor (11), and
controlled by the electronic control unit (ECU) (15). In-cylinder combustion is
analyzed using a combustion analysis system, which
employs signals from a speed sensor (3) and a crankshaft position sensor (4) to
determine the engine speed and crank angle position, thereby enabling
combustion analysis and measurement data synchronization. A lambda sensor (5)
is installed in the exhaust line to measure the excess air ratio, while the
exhaust gases are directed to an exhaust gas analyzer
(6) to determine the emission components. The overall operation of the system
is monitored and managed by the ECU (15) and the central control computer (14),
allowing for data acquisition, processing, and synchronization throughout the
experimental campaign.
Table 1 summarizes the main
technical specifications of the Changchai 192FA
engine used in the experimental study.
Tab. 1
Technical specifications of the test engine
|
Specification |
Changchai 192FA engine |
|
Cylinder bore, [mm] |
92 |
|
Stroke [mm] |
76 |
|
Displacement volume [cm3] |
504 |
|
Compression ratio |
19 |
|
Rated power [kW] |
8.2 |
|
Rated speed [rpm] |
3600 |
Fig. 1. Schematic diagram of the experimental
engine test bench
2.2.
Predictive Capability Evaluation
Artificial Neural Networks (ANNs)
are machine learning models inspired by the structure and functional mechanisms
of the human brain. ANNs are developed to efficiently address tasks such as
prediction, classification, complex pattern recognition, and data processing,
particularly in systems characterized by nonlinear relationships [13].
Evaluating the predictive capability and accuracy of any machine learning
model, in general, and artificial neural network models, in particular, is a
crucial step to ensure the reliability of the model. In this study, the model
performance is assessed using the coefficient of determination (R²), root
mean square error (RMSE), and mean absolute error (MAE). These metrics are
widely used to compare prediction errors in forecasting problems [14].
Root Mean Squared Error (RMSE)
calculates the average deviation between predicted values and actual values.
Mean Absolute Error (MAE) calculates
the average of the absolute errors between the actual and predicted values.
R² (Coefficient of
Determination): A statistical indicator that shows the proportion of variance
in the target to be predicted that is explained by the input variables in the
model.
yi is the actual value and
2.3. Theoretical Basis for Boost Pressure
Calculation
The rate of pressure change with
respect to the crank angle is determined to evaluate the pressure development
during the combustion process. This parameter reflects the intensity of
combustion and is commonly used to analyze the
combustion characteristics of internal combustion engines. In this study, the
rate of pressure rise with respect to the crank angle is calculated using the
finite difference method. The influence of crank angle resolution on
pressure-derived parameters has been thoroughly investigated by Brunt and Lucas
[14].
where:
θ is the crank angle (°CA – crank angle);
𝑃1 is the in-cylinder pressure at crank angle 𝜃1;
𝑃2 is the in-cylinder pressure at crank angle 𝜃2.
The above expression represents a
finite-difference approximation of the derivative:
2.4. Dataset Used for the Model
Figure 2 shows the distribution of
in-cylinder pressure as a function of crank angle for different advanced
injection timings (40°, 45°, 50°, 55°, and 60° CA BTDC), corresponding to 101
data points for each injection timing. Consequently, a total of 505 pressure
data points were collected during the experimental campaign. It can be observed
that the pressure curves exhibit relatively similar shapes, with the peak
pressure occurring around the TDC region (~360-370° CA), which is
characteristic of PCCI combustion dominated by premixed combustion. Variations
in injection timing result in only minor changes in the peak pressure
magnitude, indicating that the compression and auto-ignition processes are
relatively stable. This behavior is consistent with
the low-temperature combustion and mixture stratification characteristics of
PCCI. The experimental in-cylinder pressure data corresponding to injection
timings ranging from 40° to 60° CA BTDC were selected for processing and
analysis, as this range represents a stable operating region characteristic of
the PCCI combustion mode. This injection timing interval clearly reflects
premixed mixture formation, auto-ignition, and hybrid combustion
characteristics (premixed-diffusive), while ensuring good repeatability and
reliability of the experimental data. Therefore, this dataset was used as the
basis for training and evaluating the predictive model, as well as for
subsequent analyses of pressure rise rate and in-cylinder pressure trends. The
dataset was divided into 80% for training (404 data points) and 20% for testing
the predictive accuracy of the model (101 data points).
The evaluation results presented in
Table 3 indicate that the ANN model achieves high accuracy and exhibits stable
performance on both the training and testing datasets. Specifically, the
coefficient of determination R2 reaches 0.9983 for the training set
and 0.9981 for the testing set, with a negligible difference of only 0.0002
(approximately 0.02%), demonstrating the excellent generalization capability of
the model. The RMSE increases slightly from 0.9397 for the training dataset to
1.0115 for the testing dataset, corresponding to an increase of approximately
7.64%, while the MAE rises from 0.6937 to 0.7268, with a difference of about 4.77%.
These deviations remain below 10%, which is within the acceptable range for
nonlinear prediction models. These results confirm that the ANN model not only
provides high prediction accuracy but also ensures good stability and
reliability, with no evidence of overfitting, making it well suited for
in-cylinder pressure prediction in PCCI engines. The discrepancies between the
experimental and ANN-predicted pressure values are illustrated in detail in
Figure 3.
Fig. 2. In-cylinder pressure as a function of
crank angle for different advanced injection timings
Tab. 2
Performance of the pressure prediction model
|
Pharse |
R² |
RMSE |
MAE |
|
Train |
0.9983 |
0.9397 |
0.6937 |
|
Test |
0.9981 |
1.0115 |
0.7268 |
The error distributions for both the
training and testing datasets are centered around
zero, indicating the absence of systematic bias in the model. The mean error
values of the two datasets are nearly identical, with a central deviation of
less than 0.1 pressure units, reflecting the stability of the ANN model. The
error distribution of the testing dataset is slightly wider than that of the
training dataset, but the difference is not significant, as evidenced by the
increase in RMSE (approximately 7.64%) and MAE (about 4.77%) compared to the
training dataset. The majority of errors in both datasets fall within ±1
pressure unit, accounting for approximately 98% of the data. Large errors
(|error| > 2) occur only at a very low frequency in both datasets. Overall,
the model exhibits very small error dispersion and high reliability.
Figure 4 presents a comparison
between the experimental pressure and the predicted pressure for both the
training and testing datasets. The results show that the predicted curves
closely follow the variation trends of the experimental data in both datasets,
demonstrating the model’s strong capability to capture the nonlinear
characteristics of the combustion process. Discrepancies occur only locally at
a few outlier points; however, their magnitudes are small and do not
significantly affect the overall pressure range. Notably, the strong similarity
in trends and fitting quality between the two datasets indicates that the model
not only achieves high prediction accuracy but also exhibits good
generalization capability, thereby confirming the reliability of the model for
predicting subsequent in-cylinder pressure values.
Fig. 3. Distribution of errors between
experimental and ANN-predicted pressure
Fig. 4. Comparison of experimental and
ANN-predicted in-cylinder pressure for
the training and testing datasets
3. RESULTS AND DISCUSSION
The injection timing range of
40°-60° CA BTDC was selected as the training dataset because it represents a
stable and typical operating region of the PCCI combustion mode. Within this
range, the premixing, auto-ignition, and hybrid combustion processes are
clearly manifested and exhibit high repeatability in the experimental data,
ensuring good data quality, low noise, and strong representativeness of the
engine combustion kinetics. Based on 505 in-cylinder pressure data points
collected at injection timings of 40°, 45°, 50°, 55°, and 60° CA BTDC, the ANN
model was developed and its predictive accuracy was validated. Subsequently,
the trained model was employed to predict an additional 404 pressure data
points at new injection timings of 30°, 35°, 65°, and 70° CA BTDC, which lie at
the boundaries of the data space, in order to evaluate the extrapolation
capability, stability, and generalization performance beyond the training
domain. This approach enables simultaneous assessment of prediction accuracy
within the interpolation domain and forecasting capability under new operating
conditions, thereby confirming the generalization ability, reliability, and
practical applicability of the ANN model for in-cylinder pressure prediction in
PCCI engines. Figure 6 presents the complete data distribution consisting of
990 pressure data points, including 550 experimental points and 440 points
predicted by the ANN model. This combined dataset forms a large-scale input
database that comprehensively covers advanced injection timings across the
engine operating space. The dataset enables a continuous representation of
pressure characteristics as a function of crank angle and injection strategy.
Based on thermodynamic theory describing the relationship among pressure,
volume, and crank angle, the 990 pressure data points are subsequently used to
calculate the engine pressure rise rate.
Fig. 5. Distribution of experimental and
predicted pressure data
The in-cylinder pressure
distribution of the PCCI engine reveals the formation of a distinct and
continuous high-pressure band for all advanced injection timings, primarily
concentrated within the range of 360°-380° CA, with peak values reaching
approximately 85-90 bar. Notably, this high-pressure region does not occur at a
single operating point but extends across a control parameter domain,
reflecting a characteristic feature of premixed combustion in which a
relatively homogeneous fuel-air mixture is formed prior to auto-ignition.
During the crank angle interval of 320°-355° CA, the pressure rises rapidly
from approximately 8 bar to about 65-68 bar due to the combined effects of
compression and low-temperature chemical reactions. The pressure then increases
sharply and reaches its maximum within the 360°-380° CA range, corresponding to
the main heat release phase associated with volumetric auto-ignition throughout
the combustion chamber. Subsequently, in the range of 400°-420° CA, the
pressure gradually decreases as a result of expansion work, reduced combustion
reaction rates, and thermal energy dissipation. The presence of a broadened
peak pressure region across the control domain, rather than a localized
maximum, indicates that PCCI combustion tends to distribute energy more
uniformly, with a controlled pressure rise rate and lower peak temperatures
compared to conventional diesel combustion. These characteristics contribute to
reduced NOₓ and soot formation while improving combustion quality and
overall engine efficiency. The relationship between the in-cylinder pressure
curve (Figure 6) and the pressure rise rate (PRR) curve (Figure 7) demonstrates
a direct mathematical and physical dependence; therefore, the shape of the PRR
curve is inherently governed by the geometry of the pressure curve. During the
crank angle interval of 320°-355° CA, the in-cylinder pressure increases
rapidly from approximately 8 bar to about 65-68 bar due to the combined effects
of compression and early heat release, with the corresponding PRR rising from
approximately −0.076 MPa/°CA to about 3.3 MPa/°CA. As the combustion
process enters the main heat release phase around 360° CA, the pressure
increase rate reaches its maximum, resulting in a peak PRR of approximately
5.860 MPa/°CA. After the pressure reaches its maximum, the pressure curve
enters a saturation region, and the slope decreases, causing the PRR to drop
toward zero. Following the pressure reversal, the PRR becomes negative and
reaches a minimum of approximately − 2.620 MPa/°CA at around 380° CA,
reflecting the decreasing pressure with respect to crank angle. The pressure
continues to decline at subsequent crank angles; however, the rate of decrease
becomes more gradual, with PRR values ranging from approximately −0.9240
to − 0.0760 MPa/°CA between 390° CA and 400° CA. Consequently, the
characteristic trend of the PRR curve increase → peak → decay to
zero → negative region → gradual recovery is an inevitable
consequence of the geometric form of the pressure curve as a function of crank
angle. This behavior fully reflects the physical
stages of the PCCI combustion cycle and confirms the strong consistency between
combustion kinetics and in-cylinder pressure dynamics.
Fig. 6. Comparison between experimental and
predicted values for the training and
test datasets obtained from the ANN and GBM models
Fig. 7. Residual error distributions of the ANN
and GBM models
4. CONCLUSION
This study applied an artificial neural network (ANN) to evaluate the
accuracy of an in-cylinder pressure prediction model for a PCCI engine under
advanced ignition timing conditions ranging from 40° to 60° CA BTDC, within a
crank angle domain of 320-420° CA, corresponding to a total of 505 data points.
The results demonstrate that the ANN model achieves very high prediction
accuracy, as confirmed by the statistical metrics R², RMSE, and MAE.
Specifically, for the training dataset, the model yielded R² = 0.9983,
RMSE = 0.9397 bar, and MAE = 0.6937 bar. Similarly, the testing dataset
maintained comparable performance, with R² = 0.9981, RMSE = 1.0115 bar,
and MAE = 0.7268 bar, indicating strong generalization capability and the
absence of overfitting. Based on these results, it can be concluded that the
ANN model is reliable and well suited for predicting in-cylinder pressure in
PCCI engines using ignition timing and crank angle as input parameters.
Leveraging the validated accuracy, the model was further trained and employed
to predict new pressure profiles at the boundary regions of ignition timing,
namely 30°, 35° and 65°, 70° CA BTDC, while maintaining the same crank angle
range of 320-420° CA. For each ignition timing condition, 101 pressure data
points were predicted, resulting in a total of 404 newly generated pressure
data points, thereby substantially expanding the pressure dataset beyond the
original training domain. Following the construction of the generalized
pressure dataset, three-dimensional (3D) models were established to represent
the distributions of the heat release rate (HRR) and the pressure rise rate,
based on established thermodynamic formulations. These models describe the
variation of HRR and pressure rise rate as functions of ignition timing within
the range of 40°-60° CA BTDC and crank angle from 320° to 420° CA. The results
reveal smooth and continuous distributions of both parameters, which are
consistent with the combustion dynamics of PCCI engines. Overall, the study
confirms the high accuracy and reliability of the ANN-based pressure prediction
model and further demonstrates its capability for extrapolation beyond the
original training dataset. The proposed approach contributes to reduced
experimental costs and computational time for processing large datasets while
providing effective input data for calculating key engine parameters,
particularly the pressure rise rate. However, the present study is limited to
characterizing the distribution of the pressure rise rate derived from the predicted
pressure data and does not yet identify the optimal operating regions of the
engine at specific pressure levels. Therefore, this work serves as a scientific
foundation for future research on AI-based combustion optimization, aiming to
determine optimal pressure distribution regions to enhance engine power,
improve thermal efficiency, and reduce emissions in PCCI engines.
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Scientific
Journal of Silesian University of Technology. Series Transport is licensed
under a Creative Commons Attribution 4.0 International License
[1] University of Transport and Communications, No. 3 Cau Giay Street,
Lang Ward, Hanoi, Vietnam. Email: khuongha82@utc.edu.vn. ORCID:
https://orcid.org/0009-0009-5790-5584
[2] University of Transport and Communications, No. 3 Cau Giay Street,
Lang Ward, Hanoi, Vietnam. Email: caovan87@utc.edu.vn. ORCID:
https://orcid.org/0000-0002-5335-6073