The Start of Combustion Prediction for Methane-Fueled HCCI Engines: Traditional vs. Machine Learning Methods

Namar, Mohammad Mostafa; Jahanian, Omid; Koten, Hasan

doi:https://doi.org/10.1155/2022/4589160

Mathematical Problems in Engineering

On this page

Abstract Introduction Results and Discussion Conclusion Abbreviations Data Availability Conflicts of Interest References Copyright Related Articles

Special Issue

Mathematical and Numerical Improvements in Internal Combustion Engines

View this Special Issue

Research Article | Open Access

Volume 2022 | Article ID 4589160 | https://doi.org/10.1155/2022/4589160

The Start of Combustion Prediction for Methane-Fueled HCCI Engines: Traditional vs. Machine Learning Methods

Mohammad Mostafa Namar,¹Omid Jahanian,¹and Hasan Koten²

Academic Editor: Adriana Del Carmen Téllez-Anguiano

Received19 Feb 2022

Revised26 Apr 2022

Accepted30 Apr 2022

Published30 May 2022

Abstract

In this work, 11 regression models based on machine learning techniques were employed to provide a fast-response and accurate model for the prediction of the start of combustion in homogeneous charge compression ignition engines fueled with methane. These regression models are categorized into linear and nonlinear types. Although the robust random sample consensus (RANSAC) model is a nonlinear type as well as SAM (simple algebraic model), the prediction accuracy is enhanced from 89.3% to 98.4%. Such accuracy is also achieved for the linear models, namely, ordinary least squares, ridge, and Bayesian ridge models. Indeed, due to the linear hypothesis (the correlation for the start of combustion prediction), the presented models have an acceptable response time to be used in real-time control applications like the electronic control units of the engines.

1. Introduction

Using environmentally friendlier devices is one of the most important approaches to have a green atmosphere for the next decades. Homogeneous charge compression ignition (HCCI) engines are considered as more efficient and cleaner engines than both conventional types, spark ignition (SI) and compression ignition (CI), in the engine industry [1]. These engines release less NOx emission due to the employed low temperature combustion (LTC) process and consume less fuel as they are designed in lean burnt mode [2]. Furthermore, the carbon-based emissions such as CO₂, CO, and HC may be decreased or even removed thanks to the ability of these engines in running by the light hydrocarbons such as methane or hydrogen [3, 4]. In consequence, the target of having a cleaner environment can be achieved by extending the applications of this type of engine in the automotive industry [5, 6] as well as the other approaches such as reactivity controlled compression ignition (RCCI) [7, 8], catalyst converter development [9, 10], and engine downsizing [11, 12].

One of the most challenging issues for the industrial applications of HCCI engines is the combustion stability, especially in high-speed operation conditions, and it is needed to be controlled by the start of combustion (SOC) timing [13]. There is no direct controller actuator for the SOC, such as the spark plug at the SI and injector (injection timing) at the CI engines, and the SOC will be affected by the engine inlet parameters like the pressure and temperature of the inlet charge, equivalence ratio, and engine speed [14]. Consequently, the real-time exact prediction of SOC may lead to extending the usage of these types of engines in movement applications, as it is considered as one of the key parameters in combustion stability [15, 16].

A wide range of SOC predictors has been presented in the literature. To study the effects of key parameters on the SOC, fundamentally, the three-dimensional computational fluid dynamics (3D-CFD) models are used [17, 18]. These models present high accuracy due to employing detailed chemical kinetics mechanism while they need a long run time. The 0D thermodynamic models are considered as the second type of SOC predictors which have much better run time than 3D-CFD models [19, 20]. Although the run-time is noticeably declined by the 1D thermodynamic models, developing the predictor models leads the researcher to provide the third type called semiempirical models for the faster ones [21, 22]. These models generally use the engine performance data and provide an algebraic correlation to predict the SOC. The primary efforts caused the models which need to unmeasurable parameters as seen in literature [23, 24] and then they are developed for the models with measurable inputs [25, 26]. Although the accuracy of these models is acceptable for control application, the run time is still needed to be improved in the real-time applications.

Flourishing the machine learning (ML) techniques is a promising achievement to enhance the performance of SOC predictors. These techniques have been recently used by researchers to develop control models in the engine industry [27–29]. Using ML, it is possible to provide the numerical models to predict the SOC timing employing the engine performance dataset. These models may have better run times than the modified knock integral model (MKIM) [25] and simple algebraic model (SAM) [26] if the proposed correlations have less nonlinearity.

In this work, employing the dataset consists of the performance and operating conditions of 3 different HCCI engines fueled with Methane, adopted from a thermodynamic model, and using different regression ML techniques and several SOC prediction models are presented. The performance of them is compared with Simple Algebraic Model (SAM) model. The main novelty of this work is providing a simple linear model with higher accuracy thanks to the ML techniques. It is completely sufficient for control applications and to use in the Electronic Control Unit (ECU) via the linearity of the model.

2. Model Description

In general, three different types of numerical models are employed in this research, namely, SAM, virtual engine, and ML regressor models. In this study, 6 linear and 5 nonlinear supervised type regressor models were used. In this section, these models are described in detail.

2.1. SAM

The SOC time of methane-fueled HCCI engines will be predicted via a simple algebraic correlation due to the engine inlet parameters [26]:where is the engine rotary speed, is the equivalence ratio, is the mass ratio of exhaust gas recirculated (EGR) to inlet charge, and and refer to the inlet charge pressure and temperature at the inlet valve closing (IVC) time, respectively. The constants A, B, D, E, and F relate to the used fuel, and and depend on the real compression ratio (CR).

2.2. Virtual Engine

Each control-oriented model uses the experimental dataset to provide its own semi-empirical correlations. In this research, the results of a stand-alone thermodynamic model of engine closed-cycle [3, 5, 26] are employed instead of the experimental data. This model includes a detailed chemical kinetics mechanism of methane oxidation called “GRI 3.0 [30]” which consists 325 reactions and 53 species. The validity of the employed model has been evaluated by several engines and different operation conditions, and SOC is defined at a crank angle where 5% of the fuel is consumed. The main excellence of this model is SOC detection with acceptable accuracy; therefore, it is sufficient to be used as the virtual engine for this study. The virtual engine is run for a wide range of engine inlet parameters, namely, engine speed, equivalence ratio, EGR, charge pressure and temperature at IVC, relative humidity (RH), and real CR.

2.3. ML Regressor Model

ML regressor models generally use a hypothesis to define the target value (SOC). For the multivariate linear regression, the hypothesis is defined as [31]where is the independent variable and is the coefficient of the related variable. The subscript refers to the number of independent variables. It should be noted that the is considered equal to 1.00. Using the training dataset, the target of ML techniques is to find the best vector of which has the least residual for the test dataset. So, the type of considered cost function, which should be minimized, is the base of the definition of different ML techniques; as an example, the cost function of ordinary least squares (OLS) method is defined as [32]where is the vector of dependent variable of the problem (target value of each case) and the superscript is the number of train cases. A variety of approaches are used to minimize the cost function, but generally, they can be divided into two categories, namely, noniterative and iterative. In noniterative approach, the best vector of is calculated by in the train dataset domain as [33]

For the iterative approach, the vector of is simultaneously updated based on the learning rate () in each iteration [34].

3. Results and Discussion

Considering the validated virtual engine [3, 5, 26], demanded dataset is constructed by running the virtual engine for 3 engines defined in Table 1. This dataset consists of 1177 sample train cases and 253 sample test cases which are adopted from the results of running the virtual engine for each engine at different operating conditions. Considered independent parameters are engine speed, equivalence ratio, EGR, charge pressure and temperature at IVC, RH, and real CR, and the dependent parameter is SOC. For the training dataset, the dispersion of SOC is between 10 CAD before Top Dead Center (TDC) and 10 CAD after TDC, as shown in Figure 1, however, it is mainly (more than 67%) occurred before TDC.

(a)

(b)

The performance of the SAM in SOC prediction for both the train and test samples is studied in the first step, as shown in Figure 2. The accepted range of SOC prediction in control applications is reported as the residual () with less than 2 CAD [26]. For the test samples, SAM predicted the SOC with 89.3% in the acceptable range as well as 70.6% for the train samples reported in Table 2. In addition, the root mean squared error (RMSE) is reported as 1.64 and 1.84 for the test and train samples, respectively.

(a)

(b)

In the next step, both linear and nonlinear ML regression methods are applied to the training dataset and the results are illustrated in detail. The built-in Python code has been used for such an investigation, and the employed models are reported in Table 3. Achieved coefficient vector (vector of ) for linear methods is presented in Table 4. The most effective parameter on SOC variations is reported the equivalence ratio by the OLS, Ridge, Support Vector Regression (SVR), and Bayesian Ridge (BR) models while the CR is considered with a more important role by Lasso and Huber models, as shown in Figure 3.

(a)

(b)

(c)

(d)

(e)

(f)

In Figure 3, the impact factors of independent parameters on SOC for the ML linear regressors; OLS, Lasso, ridge, SVR, BR, and Huber were shown. Looking more detail in Figure 3 and Table 4, and considering the out of rage intercepts of SVR and Huber models, it seems, these models are not converged, and the learning is failed. In addition, the considered impact factor for equivalence ratio (0.00) in the Lasso model shows that the effect of equivalence ratio can be ignored which is not acceptable in real applications. However, the main parameters of comparing these models are considered the acceptable residual (less than 2 CAD) percentage and the score of the model (the best score is equal to 1.00) in the test dataset. Table 5 reports the performance of defined models in Table 3 on the test dataset. Considering reported scores and the acceptable residual percentage, it can be concluded that among the nonlinear models, the Robust RANSAC model is greatly learned and has outstanding accuracy by predicting up to 98.4% in the acceptable range. The same noticeable performance is achieved by the OLS, ridge, and BR models from the linear models; however, the performance of the Lasso model is still acceptable by predicting up to 99.6% with less than 3 CAD errors. The scatter plots of achieved residuals by the models are shown in Figures 4 and 5 for the test and train datasets, respectively. Due to these plots, it can be concluded that the main reason for found errors in the Lasso model is approaching the learning process to overfitting. The same trend has existed for the nonlinear SVR and nearest neighbors models. Complete overfitting has occurred for the decision tree model, and the reason for the pretty weak performance of MPL neural network, Huber, and linear SVR models is the convergence issue.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

4. Conclusion

In this work, 11 regression models based on machine learning techniques were employed to provide a fast-response and accurate model for the prediction of the start of combustion in homogeneous charge compression ignition engines fueled with methane. The dataset for such an investigation is adopted from validated virtual engines which used the detailed chemical kinetics of methane combustion. The main achievements of the work are listed in the following:(i)The robust RANSAC model as a nonlinear model enhanced the accuracy of SOC prediction to 98.4%.(ii)The linear models, namely, ordinary least squares, ridge, and Bayesian ridge models, presented outstanding accuracy in SOC prediction (up to 98% correct predictions).(iii)For the linear hypothesis (the correlation for SOC prediction), the presented models have acceptable response time to be used in the real-time control applications as the engine ECU.

Abbreviations

0D:	0-dimensional
3D:	3-dimensional
BDC:	Bottom dead center
BR:	Bayesian ridge
CAD:	Crank angle degree
CFD:	Computational fluid dynamics
CI:	Compression ignition
CR:	Compression ratio
ECU:	Electronic control unit
EGR:	Exhaust gas recirculated
EVO:	Exhaust valve opening
HCCI:	Homogeneous charge compression ignition
IVC:	Inlet valve closing
LTC:	Low temperature combustion
MAE:	Mean absolute error
MKIM:	Modified knock integral model
ML:	Machine Learning
MSE:	Mean squared error
OLS:	Ordinary least squares
RCCI:	Reactivity controlled compression ignition
RH:	Relative humidity
RMSE:	Root mean squared error
SAM:	Simple algebraic model
SI:	Spark Ignition
SOC:	Start of combustion
SVR:	Support vector regression
TDC:	Top dead center

N:Engine speed (rpm)

P:	Pressure (kPa)
T:	Temperature (K)]
:	Learning rate
:	Vector of coefficients
:	Equivalence ratio.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conﬂicts of interest.

References

J. Moradi, A. Gharehghani, and M. Mirsalim, “Numerical comparison of combustion characteristics and cost between hydrogen, oxygen and their combinations addition on natural gas fueled hcci engine,” Energy Conversion and Management, vol. 222, Article ID 113254, 2020.
View at: Publisher Site | Google Scholar
H. Solmaz, “A comparative study on the usage of fusel oil and reference fuels in an hcci engine at different compression ratios,” Fuel, vol. 273, Article ID 117775, 2020.
View at: Publisher Site | Google Scholar
M. M. Namar and O. Jahanian, “Energy and exergy analysis of a hydrogen-fueled hcci engine,” Journal of Thermal Analysis and Calorimetry, vol. 137, no. 1, pp. 205–215, 2019.
View at: Publisher Site | Google Scholar
M. Rabeti, O. Jahanian, A. A. Ranjbar, S. M. Safieddin Ardebili, and H. Solmaz, “Potential of semi-empirical heat transfer models in predicting the effects of equivalence ratio on low temperature reaction and high temperature reaction heat release of an hcci engine,” Journal of Applied and Computational Mechanics, 2021.
View at: Google Scholar
M. Namar and O. Jahanian, “Defining start and duration of combustion in hcci engines using mean-value method for control applications,” Amirkabir Journal of Mechanical Engineering, vol. 50, no. 6, pp. 1265–1276, 2019.
View at: Google Scholar
M. Fathi, O. Jahanian, D. D. Ganji, S. Wang, and B. Somers, “Stand-alone single-and multi-zone modeling of direct injection homogeneous charge compression ignition (di-hcci) combustion engines,” Applied Thermal Engineering, vol. 125, pp. 1181–1190, 2017.
View at: Publisher Site | Google Scholar
A. P. Singh, V. Kumar, and A. K. Agarwal, “Evaluation of comparative engine combustion, performance and emission characteristics of low temperature combustion (pcci and rcci) modes,” Applied Energy, vol. 278, Article ID 115644, 2020.
View at: Publisher Site | Google Scholar
S. S. Motallebi Hasankola, R. Shafaghat, O. Jahanian, S. Talesh Amiri, and M. Shooghi, “Numerical investigation of the effects of inlet valve closing temperature and exhaust gas recirculation on the performance and emissions of an rcci engine,” Journal of Thermal Analysis and Calorimetry, vol. 139, no. 4, pp. 2465–2474, 2020.
View at: Publisher Site | Google Scholar
S. Pandiaraj, D. Subbaiyan, T. Ayyasamy, and S. Nagarajan, “Design, development and analysis of mullite catalytic converter for ci engines,” SAE Technical Paper, 2019.
View at: Publisher Site | Google Scholar
T. Agrawal, V. K. Banerjee, B. S. Sikarwar, and M. Bhandwal, “Optimizing the performance of catalytic convertor using turbulence devices in the exhaust system,” Advances in Interdisciplinary Engineering, Springer, Berlin, Germany, 2019.
View at: Google Scholar
M. M. Namar, O. Jahanian, R. Shafaghat, and K. Nikzadfar, “Numerical/experimental study on downsized iranian national engine (ef7) performance at low engine speeds,” International Journal of Engineering, vol. 34, no. 9, pp. 2137–2147, 2021.
View at: Google Scholar
M. M. Namar, O. Jahanian, R. Shafaghat, and K. Nikzadfar, “Feasibility study for downsizing ef7 engine, numerical and experimental approach,” The Journal of Engine Research, vol. 61, no. 61, pp. 73–85, 2021.
View at: Google Scholar
X. Duan, M.-C. Lai, M. Jansons, G. Guo, and J. Liu, “A review of controlling strategies of the ignition timing and combustion phase in homogeneous charge compression ignition (hcci) engine,” Fuel, vol. 285, Article ID 119142, 2021.
View at: Publisher Site | Google Scholar
S. Khandal, N. Banapurmath, and V. Gaitonde, “Performance studies on homogeneous charge compression ignition (hcci) engine powered with alternative fuels,” Renewable Energy, vol. 132, pp. 683–693, 2019.
View at: Publisher Site | Google Scholar
M. Taghavi, A. Gharehghani, F. B. Nejad, and M. Mirsalim, “Developing a model to predict the start of combustion in hcci engine using ann-ga approach,” Energy Conversion and Management, vol. 195, pp. 57–69, 2019.
View at: Publisher Site | Google Scholar
Z. Wang, G. Du, Z. Li, X. Wang, and D. Wang, “Study on the combustion characteristics of a high compression ratio hcci engine fueled with natural gas,” Fuel, vol. 255, Article ID 115701, 2019.
View at: Publisher Site | Google Scholar
H. Ezoji and S. S. M. Ajarostaghi, “Thermodynamic-cfd analysis of waste heat recovery from homogeneous charge compression ignition (hcci) engine by recuperative organic rankine cycle (rorc): effect of operational parameters,” Energy, vol. 205, Article ID 117989, 2020.
View at: Publisher Site | Google Scholar
J. Moradi, A. Gharehghani, and M. Mirsalim, “Numerical investigation on the effect of oxygen in combustion characteristics and to extend low load operating range of a natural-gas hcci engine,” Applied Energy, vol. 276, Article ID 115516, 2020.
View at: Publisher Site | Google Scholar
G. Du, Z. Wang, D. Wang, X. Wang, and X. Fu, “Study on the effect of water addition on combustion characteristics of a hcci engine fueled with natural gas,” Fuel, vol. 270, Article ID 117547, 2020.
View at: Publisher Site | Google Scholar
M. Fathi, O. Jahanian, and M. Shahbakhti, “Modeling and controller design architecture for cycle-by-cycle combustion control of homogeneous charge compression ignition (hcci) engines–a comprehensive review,” Energy Conversion and Management, vol. 139, pp. 1–19, 2017.
View at: Publisher Site | Google Scholar
X. Han, P. Divekar, M. Zheng, and J. Tjong, “Empirical investigation and control-oriented modeling of n-butanol hcci for improving combustion controllability,” Fuel, vol. 280, Article ID 118551, 2020.
View at: Publisher Site | Google Scholar
M. Nazoktabar, S. A. Jazayeri, M. Parsa, D. D. Ganji, and K. Arshtabar, “Controlling the optimal combustion phasing in an hcci engine based on load demand and minimum emissions,” Energy, vol. 182, pp. 82–92, 2019.
View at: Publisher Site | Google Scholar
M. Shahbakhti and C. R. Koch, “Dynamic modeling of hcci combustion timing in transient fueling operation,” SAE International Journal of Engines, vol. 2, no. 1, 2009.
View at: Publisher Site | Google Scholar
K. Swan, M. Shahbakhti, and C. R. Koch, “Predicting start of combustion using a modified knock integral method for an hcci engine,” SAE Transactions, pp. 611–620, 2006.
View at: Google Scholar
M. Shahbakhti, R. Lupul, and C. R. Koch, “Predicting hcci auto-ignition timing by extending a modified knock-integral method,” SAE Technical Paper, 2007.
View at: Publisher Site | Google Scholar
M. M. Namar and O. Jahanian, “A simple algebraic model for predicting hcci auto-ignition timing according to control oriented models requirements,” Energy Conversion and Management, vol. 154, pp. 38–45, 2017.
View at: Publisher Site | Google Scholar
C. Mishra and P. M. V. Subbarao, “Machine learning integration with combustion physics to develop a composite predictive model for reactivity controlled compression ignition engine,” Journal of Energy Resources Technology, vol. 144, no. 4, Article ID 042302, 2021.
View at: Publisher Site | Google Scholar
C. Mishra and P. Subbarao, “Design, development and testing a hybrid control model for rcci engine using double wiebe function and random forest machine learning,” Control Engineering Practice, vol. 113, Article ID 104857, 2021.
View at: Publisher Site | Google Scholar
Z. H. Zheng, X. Lin, M. Yang et al., “Progress in the application of machine learning in combustion studies,” ES Energy & Environment, vol. 9, pp. 1–14, 2020.
View at: Publisher Site | Google Scholar
G. P. Smith, D. M. Golden, M. Frenklach et al., Gri 3.0 mechanism, Gas Research Institute, Chicago, IL, USA, 1999, http://combustion.berkeley.edu/gri-mech/version30/text30.html.
M. Alizamir, S. Kim, O. Kisi, and M. Zounemat-Kermani, “A comparative study of several machine learning based non-linear regression methods in estimating solar radiation: case studies of the USA and Turkey regions,” Energy, vol. 197, Article ID 117239, 2020.
View at: Publisher Site | Google Scholar
A. Almaghrebi, F. Aljuheshi, M. Rafaie, K. James, and M. Alahmad, “Data-driven charging demand prediction at public charging stations using supervised machine learning regression methods,” Energies, vol. 13, no. 16, 2020.
View at: Publisher Site | Google Scholar
R. Li, J. M. Herreros, A. Tsolakis, and W. Yang, “Machine learning regression based group contribution method for cetane and octane numbers prediction of pure fuel compounds and mixtures,” Fuel, vol. 280, Article ID 118589, 2020.
View at: Publisher Site | Google Scholar
G. Hackeling, Mastering Machine Learning with Scikit-Learn, Packt Publishing Ltd, Birmingham, United Kingdom, 2017.
M. Ishida, S. Jung, H. Ueki, and D. Sakaguchi, Combustion Characteristics of Hcci Engines Fuelled with Natural Gas and Dme, 2007.
S. B. Fiveland and D. N. Assanis, “Development and validation of a quasi-dimensional model for hcci engine performance and emissions studies under turbocharged conditions,” SAE Transactions, pp. 842–860, 2002.
View at: Google Scholar
S. B. Fiveland, R. Agama, M. Christensen et al., “Experimental and simulated results detailing the sensitivity of natural gas hcci engines to fuel composition,” SAE Transactions, pp. 2123–2134, 2001.
View at: Google Scholar

Copyright

Copyright © 2022 Mohammad Mostafa Namar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies

Views

395

Downloads

303

Citations