Predictive Modeling of Energy and Exergy Effects from Injector Placement in HCCI Engines Running on Diethyl Ether and Biogas Using Machine Learning Techniques – Research and Reviews in Sustainability | Caravel Press
Predictive Modeling of Energy and Exergy Effects from Injector Placement in HCCI Engines Running on Diethyl Ether and Biogas Using Machine Learning Techniques
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1School of Mechanical Engineering, Vellore Institute of Technology, Chennai, India
* Correspondence: Feroskhan M, feroskhan.m@vit.ac.in
The global emphasis on sustainable energy has highlighted biogas as a viable alternative fuel for internal combustion engines. Among advanced engine technologies, Homogeneous Charge Compression Ignition (HCCI) engines stand out due to their notable efficiency and low emissions, making them well-suited for clean energy applications. A key aspect in maximizing the benefits of biogas in HCCI engines, especially when paired with diethyl ether (DEE) as a pilot fuel, involves determining the optimal injector location. This study employed machine learning techniques to identify the most effective injector position by analyzing variables such as engine load, biogas flow rate, methane content, and intake air temperature. Three injector configurations were tested: one at the intake port and two further upstream at 6 cm (Manifold 1) and 10 cm (Manifold 2) from the intake. To solve this complex optimization problem, five advanced machine learning models SVM, Random Forest, AdaBoost, CATBoost, and XGBoost were utilized to predict crucial performance metrics, including brake-specific energy use, exergy losses, thermal efficiency, fuel consumption, and exergy-based efficiency. XGBoost emerged as the most accurate model, consistently delivering the highest R² values. The findings underscore the potential of machine learning to enhance injector placement strategies, thereby improving the energy efficiency and overall performance of HCCI engines operating on biogas and DEE.
Growing global interest in sustainable energy has increased attention on renewable fuels like biogas, recognized for being a carbon-neutral choice for powering internal combustion engines. Produced through the anaerobic digestion of organic materials, biogas shows great promise, though conventional engines often struggle to balance efficiency with low emissions when using it. HCCI engines help address these challenges by integrating features from both spark-ignition and compression-ignition systems, leading to higher thermal efficiency and reduced emissions. A pivotal factor in optimizing biogas use in HCCI engines is determining the best injector position for pilot fuels such as diethyl ether (DEE), since it significantly influences metrics like brake thermal efficiency and exergy efficiency. While experimental research and CFD simulations have provided important insights, they may not effectively capture complex variable interactions. In this context, machine learning has become a valuable tool, offering the ability to uncover hidden patterns and accelerate the identification of optimal injector configurations for HCCI engines running on biogas and DEE.
Several researchers have explored machine learning (ML) techniques to predict and optimize the performance of various engine types, including HCCI engines. Hanuschkin et al. (2021) used ML to analyse in-cylinder flow fields and predict combustion engine performance, while Wong et al. (2013) applied advanced ML models to optimise biodiesel engines. Extending to CI engines, Ağbulut, Gürel and Sarıdemir (2021) employed ML for nanoparticle–diesel blends, and Wang et al. (2022) compared ML methods for gasoline Wankel engines.
In SI engines, Liu, Ulishney and Dumitrescu (2020, 2021) developed Random Forest-based ML models for natural gas engines, improving predictions of combustion metrics. ML has also been applied to gas turbines (Liu and Karimi 2020a) and extensively to HCCI engines. Çay et al. (2012) pioneered artificial neural network (ANN) models for alternative-fuelled engines, while Balki et al. (2018) and Çay (2013) expanded the use of ANNs in SI engines.
How to cite this article
Samavedam, A.S., CV, P., Sreekanth, M., P, T. and M, F. (2026). 'Predictive Modeling of Energy and Exergy Effects from Injector Placement in HCCI Engines Running on Diethyl Ether and Biogas Using Machine Learning Techniques'. Research and Reviews in Sustainability, 2, pp. 72-101. https://doi.org/10.65582/rrs.2026.006
Furthermore, Oğuz, Saritas and Baydan (2010), Patel, Azad and Khan (2019), and Ghobadian et al. (2009) modelled diesel engine performance and emissions using biofuels and ANN approaches. For diverse biofuel blends, Sebayang et al. (2017, 2022) and Gökalp et al. (2010) employed extreme learning machines and ANNs to predict engine performance and exhaust emissions.
Researchers have diversified machine learning (ML) approaches beyond artificial neural networks (ANNs). Kullolli, Sakthivel and Ilangkumaran (2016) applied neural networks to investigate the effects of injection timing in compression ignition (CI) engines, while Correa Gonzalez et al. (2021) predicted ignition characteristics in gasoline blends. Lionus Leo et al. (2024) employed Random Forest models to analyse an HCCI–DI engine operating with biodiesel–nano additives.
Studies by Sahoo, Kumar and Srivastava (2022) and Liu and Liu (2022) demonstrated the adaptability of ML techniques to compressed natural gas (CNG) and ammonia-fuelled engines, respectively. Furthermore, Makalesi et al. (2022) and Zandie et al. (2023) highlighted the capability of ML models for multi-fuel exhaust emission prediction and multi-output engine performance modelling.
Advanced techniques such as long short-term memory (LSTM) networks were employed by Liu et al. (2022) for micro gas turbine engines fuelled with microalgae blends. Broader ML applications include the prediction of fuel consumption and maintenance costs (Katreddi, 2023) and hybrid physical–ML modelling approaches for diesel engine emission prediction (Mohammad et al. 2021). Finally, closely aligning with the present study, Kale and Krishnasamy (2024) utilised ML techniques for performance prediction and optimisation of HCCI engines operating on biofuel–gasoline blends, underscoring the growing role of ML in modelling complex engine systems.
Extending prior studies, this work employs advanced machine learning techniques to optimize injector placement and fuel–air preparation parameters for biogas and diethyl ether fuelled HCCI engines under varying engine loads. Three injector locations are examined, namely direct injection at the intake port and two upstream manifold positions located 6 cm (Manifold 1) and 10 cm (Manifold 2) from the intake. Five machine learning models, including SVM, Random Forest, AdaBoost, CatBoost, and XGBoost, are used to predict key performance and exergy-based indicators such as brake-specific energy consumption, brake thermal efficiency, fuel consumption, exergy losses, and overall exergy efficiency. Although prior studies have applied machine learning models to energy systems for performance prediction, most have focused on output estimation and have rarely incorporated exergy-based analysis or design-level parameters such as injector placement. This study addresses this gap by integrating machine learning with exergy evaluation to quantify the influence of injector location and operating conditions on combustion irreversibility and efficiency, thereby offering new insights for the optimization of renewable-fueled HCCI engines.
2. Experimental Setup
The experimental framework, depicted in Figure 1, was established to investigate an HCCI engine running on simulated biogas alongside diethyl ether (DEE). This involved converting a Kirloskar 8 HP single-cylinder compression ignition engine into a water-cooled HCCI configuration. The synthetic biogas was created by carefully mixing methane and carbon dioxide streams, which were then blended with intake air before entering the engine. DEE was introduced as a pilot fuel via injectors positioned both at the intake port and further upstream to explore different injection strategies. Power output was tracked using an eddy current dynamometer, while DEE consumption was precisely measured with a digital balance. Injection timing control was managed electronically. By systematically varying conditions such as engine load, biogas flow rate, methane concentration, intake air temperature, and DEE injection characteristics, a robust dataset was developed for training the machine learning models.
Fig. 1.Experimental setup used in this study.Full size
3. Methodology
This section outlines the comprehensive methodology employed to meticulously prepare the dataset, enabling the machine learning model to undergo effective training and subsequently deliver accurate predictions.
3.1. Data Acquisition and Machine Learning Modelling
During the experimental phase, the engine operated on air and simulated biogas, with diethyl ether (DEE) used as a pilot fuel introduced through the intake manifold. DEE was supplied at three different points: directly at the intake port, 6 cm upstream (Manifold 1), and 10 cm further upstream from Manifold 1 (Manifold 2), as illustrated in Figure 2. To comprehensively assess engine performance, tests were carried out by systematically varying several intake parameters, including the injector location (port, Manifold 1, Manifold 2), methane concentration (60% CH₄–40% CO₂ and pure CH₄), and engine load levels of 5, 10, 15, and 20 Nm, while maintaining constant intake air and coolant temperatures of 35°C. The biogas flow rate was also varied across different operating conditions. Data collected included five input parameters namely injector position, methane fraction, engine load, intake temperature, and biogas flow rate and five output metrics namely brake specific energy consumption, brake thermal efficiency, brake specific fuel consumption, exergy loss, and exergy efficiency. In total, this experimental design resulted in 60 distinct engine test runs covering all combinations of the selected operating parameters. This dataset was used to train and validate multiple machine learning models to predict engine performance under diverse operating conditions and to identify the optimal injector location. These input parameters were selected as they directly affect mixture formation, combustion characteristics, and in cylinder thermodynamic behavior, which in turn govern exergy destruction and efficiency. Their inclusion enables the models to capture the influence of operating conditions and fuel composition on exergy based performance. The overall methodology adopted in this study, along with a correlation heatmap of all variables, is presented in Figures 3 and 4.
Fig. 2.Layout of the experimental setup used in the study.Full size
Fig. 3.Workflow employed in the current study.Full size
Fig. 4.Correlation Heatmap for the input and output features.Full size
3.2. Performance Analysis
This section outlines the comprehensive methodology employed to meticulously prepare the dataset, enabling the machine learning model to undergo effective training and subsequently deliver accurate predictions.
3.2.1. Energy Analysis
In the comprehensive analysis, key parameters were meticulously evaluated to gain in-depth insights into the engine's performance capabilities. Through a thorough assessment, three critical energy parameters were identified as offering the most valuable opportunities for optimization and efficiency enhancement: brake power output, brake thermal efficiency, and Brake Specific Fuel Consumption.
Brake Power Output:
(1)
Where is the brake power output, is the engine speed in revolutions per second, and is the torque measured by the dynamometer. This parameter quantifies the actual useful work output of the engine, serving as a direct measure of its overall performance. As such, it is an indispensable metric for evaluating the engine's capabilities
Brake Thermal Efficiency:
(2)
Where is the brake thermal efficiency, is the brake power output, is the mass flow rate of fuel, and is the lower heating value of the fuel. This parameter characterizes the engine's ability to convert the chemical energy stored in the fuel into useful work. It provides invaluable insights into fuel utilization and energy conversion efficiency, making it a crucial aspect for identifying potential areas for improvement.
Brake Specific Fuel Consumption:
(3)
Where BSFC is the Brake Specific Fuel Consumption, is the mass flow rate of fuel, and is the brake power output of the engine. This parameter measures the fuel efficiency of the engine, indicating how much fuel is required to produce a certain amount of power. A lower BSFC value indicates a more efficient engine.
Brake Specific Energy Consumption (BSEC)
(4)
Where BSEC is the brake specific energy consumption, is the mass flow rate of fuel, is the lower heating value of the fuel, and is the brake power output.
Brake Specific Energy Consumption (BSEC) quantifies the amount of fuel energy needed to generate one unit of brake power. It is determined based on the fuel mass flow rate, lower heating value (LHV), and brake power. While BSFC assesses fuel efficiency, BSEC offers a more complete picture by accounting for fuel energy content, making it useful for comparing different fuels. Together, these metrics provide valuable insight into engine efficiency and fuel utilization.
3.2.2. Exergy Analysis
To complement the energy analysis, exergy analysis was performed to evaluate engine irreversibilities and the quality of energy conversion. Two key exergy parameters were considered: exergy destruction and exergy efficiency, as they capture inefficiencies not reflected by brake power, brake specific fuel consumption, or brake thermal efficiency.
Exergy Destruction:
(5)
Where is the mass flow rate, and are the specific enthalpy and entropy of the working fluid, and is the reference environment temperature. Exergy destruction quantifies the loss of useful work due to irreversibilities such as combustion, heat transfer, and friction within the engine.
Exergy Efficiency:
(6)
This parameter evaluates the effectiveness of the engine in converting the available exergy of the fuel into useful work. The exergy analysis is based on the assumptions of steady-state operation, negligible kinetic and potential energy effects, uniform reference environmental conditions, and idealized thermodynamic properties of the working fluid. Together, these exergy parameters provide a clearer understanding of internal losses and energy utilization, enabling identification of optimization potential across different operating conditions.
4. Observed Trends
This section presents a detailed analysis of the key trends and patterns observed during the experimental investigation of HCCI engine performance using biogas and diethyl ether (DEE) as fuels, building upon observations reported in our previous study (Samavedam et al. 2024). All figures presented in this section are taken from (Samavedam et al. 2024).
4.1. Trends of Brake Specific Energy Consumption
This subsection looks at how injector location, engine load, methane fraction, and biogas flow rate affect Brake Specific Energy Consumption (BSEC) in a biogas engine, based on detailed experiments. Tests were carried out with three injector positions: port injection, Manifold 1 (6 cm away), and Manifold 2 (10 cm away). As shown in Figure 5, BSEC drops steadily as engine load increases for all injector setups. Port injection consistently showed the lowest BSEC, indicating better fuel efficiency. Although Manifold 1 and 2 had higher BSEC, they followed the same trend. Interestingly, Manifold 2 often performed better than Manifold 1, even though it was placed farther from the port, which goes against the usual expectation that closer injection is always more efficient. Injector placement had the biggest effect at low loads, where port injection clearly outperformed the other two. At higher loads, the differences became smaller. Along with injector location and load, the study also examined how biogas flow rate and methane fraction influence BSEC. A higher biogas flow rate generally led to increased BSEC, but BSEC still went down with load, showing why it is important to fine-tune the flow rate. Surprisingly, increasing the methane fraction raised BSEC, as seen in Figures 6 and 7, which means the methane content also needs careful adjustment depending on engine load.
Overall, these results show that injector location, load, methane level, and flow rate all interact in complex ways to influence BSEC. Considering all these factors together is key to improving fuel economy and engine performance.
Fig. 5.BSEC vs Load at various injector locations.Full size
Fig. 6.BSEC vs Load at various methane fractions.Full size
Fig. 7.BSEC vs Load at various Biogas flow rates.Full size
4.2. Trends of Brake thermal Efficiency
In the experimental study, it was observed that Brake Thermal Efficiency (BTE), also known as 1st law efficiency, serves as a crucial performance metric for internal combustion engines. It indicates how efficiently an engine transforms the chemical energy of the fuel into usable mechanical output, with higher values indicating better performance. The experiments involved three injector locations: Port injection, Manifold 1 (6 cm from the port), and Manifold 2 (10 cm from the port). Results indicated that BTE increases with engine load for all locations, a typical trend since engines generally operate more efficiently under higher loads. Port injection consistently demonstrated the highest efficiency, suggesting superior fuel-air mixing and combustion. Counterintuitively, Manifold 2 outperformed Manifold 1 despite being further from the port, indicating that the relationship between injector distance and efficiency is not linear as per Figure 8. The efficiency curves for all locations showed steeper increases at lower loads, with diminishing improvements at higher loads. This suggests that the greatest efficiency gains occur in the transition from low to medium loads. Furthermore, the experiment indicated that methane fraction and biogas flow rate significantly influence BTE. Higher methane fractions lowered efficiency when compared to lower methane fractions while increased biogas flow rates also led to lower BTE, especially at higher loads as per figures 9 and 10. The impact of these factors became more pronounced as engine load increased.
Fig. 8.Brake thermal efficiency vs Load at different injector locations.Full size
Fig. 9.Brake thermal efficiency vs Load at different biogas flow rates.Full size
Fig. 10.Brake thermal efficiency vs Load at different methane fractions.Full size
4.3. Trends of Brake Specific Fuel Consumption
This subsection examines how injector location, engine load, methane fraction, and biogas flow rate together influence Brake Specific Fuel Consumption (BSFC) in an internal combustion engine. Using a detailed experimental dataset and a machine learning model, the study aimed to uncover trends among these parameters and their effects on BSFC. Three injector positions were tested: port injection, Manifold 1 (6 cm from the port), and Manifold 2 (10 cm from the port). As shown in Figure 11, BSFC consistently decreased with increasing engine load across all injector locations and parameter combinations. Port injection emerged as the most efficient, showing the lowest BSFC throughout the load range, which points to better energy conversion and fuel economy. While Manifold 1 and Manifold 2 had higher BSFC, they followed the same downward trend. Interestingly, Manifold 2 often showed intermediate BSFC values despite being farther from the port, which challenges the common assumption that placing injectors closer always improves efficiency. The influence of injector location on BSFC was most noticeable at lower loads, where port injection clearly outperformed the manifold setups. At higher loads, this difference became much smaller, suggesting that injector positioning matters less as load increases. Beyond injector placement and load, the study also looked at how biogas flow rate and methane fraction affect BSFC. A higher biogas flow rate generally led to increased BSFC, though BSFC still dropped with higher loads, highlighting why it is important to carefully set the flow rate. Likewise, a higher methane fraction was linked to increased BSFC, as seen in Figures 12 and 13, which shows that the methane content needs to be adjusted based on expected load conditions for the best performance.
Fig. 11.BSFC vs Load at all injector locations.Full size
Fig. 12.BSFC vs Load at different methane fractions.Full size
Fig. 13.BSFC vs Load at different biogas flow rates.Full size
4.4. Trends of Exergy Destroyed
This subsection examines how injector location, engine load, methane fraction, and biogas flow rate influence exergy destruction in an internal combustion engine. Using a detailed experimental dataset, the study analyzed the relationships between these parameters to support the development of a machine learning model for optimizing engine efficiency. Three injector positions were tested: port injection, Manifold 1 (6 cm from the port), and Manifold 2 (10 cm from the port). The results, shown in the graph, plot exergy destruction against engine load for each injector location at a methane fraction of 100% and a biogas flow rate of 12 lpm. Exergy destruction decreased with increasing engine load for all injector setups. Port injection consistently showed the lowest exergy destruction, indicating more efficient energy use. Manifold 1 and Manifold 2 recorded higher values but followed the same downward trend. Notably, Manifold 1 often showed intermediate performance despite being closer to the port, challenging the assumption that closer injector placement always reduces exergy destruction. At lower loads, differences between injector locations were more pronounced, with port injection performing best as shown in Figure 14. As load increased, these differences became smaller, suggesting that injector placement is less critical at higher loads. The study also evaluated how biogas flow rate and methane fraction affect exergy destruction. Higher flow rates generally led to more exergy destruction, although values still decreased with increasing load. A higher methane fraction usually resulted in lower exergy destruction at low loads, but this trend reversed at higher loads, as seen in Figures 15 and 16.
Fig. 14.Exergy Destroyed vs Load at various injector locations.Full size
Fig. 15.Exergy Destroyed vs Load at various Biogas flow rates.Full size
Fig. 16.Exergy Destroyed vs Load at various Methane fractions.Full size
4.5. Trends of Exergy Efficiency
This section examines how injector location, engine load, methane fraction, and biogas flow rate affect exergy efficiency in the internal combustion engine. By studying both exergy destruction and efficiency, the analysis gives a clearer picture of energy use and supports building a stronger machine learning model. Tests were carried out with three injector positions: port injection, Manifold 1 (6 cm), and Manifold 2 (10 cm). The results, shown in the graph, plot exergy efficiency against engine load for a methane fraction of 100% and a biogas flow rate of 12 lpm. Exergy efficiency increased with load for all setups. Port injection consistently showed the highest efficiency across loads, as seen in Figure 17. Manifold 1 and 2 had lower efficiency but followed the same trend, with Manifold 2 often performing between the other two despite being farther from the port. At low loads, differences between injector locations were more pronounced, while at higher loads these gaps narrowed. Higher biogas flow rates generally led to lower efficiency, though efficiency still rose with load. Lower methane fractions slightly improved efficiency at higher loads, as shown in Figures 18 and 19, highlighting the need to carefully balance these factors for better engine performance.
Fig. 17.Exergy Efficiency vs Load at various injector locations.Full size
Fig. 18.Exergy Efficiency vs Load at various biogas flow rates.Full size
Fig. 19.Exergy Efficiency vs Load at various methane fractions.Full size
5. Pseudocode and Parameter Specifications for Model Training
This section presents the pseudocode and key parameters for each machine learning model employed in this study, namely Support Vector Machine (SVM), Random Forest, AdaBoost, CATBoost, and XGBoost.
5.1. Support Vector Machine (SVM)
The first machine learning model utilized in this study was the Support Vector Machine (SVM), which identifies a decision boundary, or hyperplane, that best separates different classes by maximizing the margin between them. Thanks to this approach, SVM excels with high-dimensional data and is versatile enough to manage both linear and non-linear classification tasks through the application of various kernel functions. For predicting continuous outputs, the Support Vector Regression (SVR) variant relies on the same foundational concept. Table 1 outlines the pseudocode for this model, with key parameter configurations detailed below (Suthaharan 2016):
Table 1.Pseudocode for the support vector machine algorithm for prediction.
Pseudocode for SVR
Input: Training dataset with corresponding labels and parameters: kernel type, (regularization parameter), (for RBF kernel)
Output: Predicted output value for new input
Begin
Define kernel function based on the chosen kernel type (linear, polynomial, RBF, etc.).
Initialize regularization parameter to control the trade-off between margin width and error.
For RBF kernel, set to determine the influence of a single training example.
Optimize: a. Calculate weights and bias by minimizing regression error. b. Use an optimization algorithm (e.g., Sequential Minimal Optimization) to solve for Lagrange multipliers. c. Identify support vectors based on non-zero Lagrange multipliers.
Calculate Prediction Value:
For new input , compute:
Return Predicted Output Value: for .
End
Working Parameters:
Kernel Type: Determines how data is projected into higher-dimensional space to achieve clearer separation. Common kernels include Linear (ideal for data that is linearly separable), Polynomial (captures polynomial relationships), Radial Basis Function (RBF, effective for non-linear patterns by considering distance-based similarity), and Sigmoid (comparable to neural network activation functions).
Regularization parameter (C): Balances the goal of maximizing the margin with minimizing classification errors. Larger values of C impose stricter penalties on misclassifications, while smaller values allow for a wider margin at the expense of tolerating some errors.
Gamma (γ): Mainly used with the RBF kernel, this parameter dictates how much influence a single training example has. Lower gamma leads to a broader, more generalized influence, whereas higher gamma concentrates the model’s focus on nearby points.
Epsilon (ϵ): Defines a tolerance zone for errors in SVR, within which no penalty is applied. This helps adjust the model’s sensitivity to small deviations in data.
5.2. Random Forest
The study also incorporated the Random Forest algorithm, an ensemble learning approach that boosts prediction reliability and accuracy by constructing multiple decision trees. During training, Random Forest generates many such trees and combines their outputs taking a majority vote for classification problems or averaging (mean or median) for regression tasks. This ensemble strategy significantly enhances robustness and helps mitigate overfitting. Table 2 presents the pseudocode for the Random Forest model, while the associated working parameters are provided in the subsequent section (Breiman 2001).
Table 2.Pseudocode for the Random Forest algorithm.
Pseudocode for Random Forest (Prediction)
Input: Trained Random Forest model, new input data Output: Predicted output value for
Begin
For each decision tree in the Random Forest: a. Pass the input through decision tree to get a prediction .
For classification, compute the mode (most common) of the predicted classes . For regression, compute the mean or median of the predicted values .
Return the final predicted output value.
End
Working Parameters of Random Forest:
Number of Trees (K): The total trees in the forest; more trees usually improve performance but increase computation time.
Max Depth: Limits how deep each tree can grow, preventing overfitting.
Min Samples Split: Minimum samples required to split a node; higher values lead to simpler trees.
Min Samples Leaf: Minimum samples in a leaf node to ensure adequate data for generalization.
Max Features: Number of features considered for splits; adds randomness and reduces overfitting.
Bootstrap: Indicates if samples are drawn with replacement when building trees; true adds diversity.
Random State: Seed for reproducibility of results.
Criterion: Measures split quality, with options for classification ('gini', 'entropy') and regression ('mse', 'mae').
5.3. AdaBoost
The third model utilized was the AdaBoost algorithm. AdaBoost is an ensemble learning method that combines multiple weak classifiers to enhance the accuracy and robustness of predictions. It operates by sequentially training classifiers, adjusting the weights of misclassified instances to focus on difficult cases. The final prediction is made by aggregating the weighted outputs of all classifiers. Table 3 shows the pseudocode for the AdaBoost algorithm, while the working parameters for the same are presented below (Schapire 2013).
Table 3.Pseudocode for the AdaBoost algorithm.
Pseudocode for AdaBoost
Input: D, a set of d class-labeled training tuples, , the number of rounds, a classification learning scheme. Output: Predicted output value for tuple .
Begin:
Initialize weights of tuples in D to . For to : a. Sample D with replacement based on weights to obtain . b. Derive model using . c. Compute error . d. If , go back to step 2a. e. Update weights of correctly classified tuples: i. Multiply by . ii. Normalize weights.
To predict output for tuple :
Initialize weight for each class to 0. For to : a. Compute classifier weight: . b. Get prediction . c. Add to the weight for the predicted value . Return the final predicted output value based on aggregated weights.
End:
Working Parameters for AdaBoost:
Number of Rounds: This parameter defines the total number of weak classifiers to be combined. More rounds can enhance performance but may lead to overfitting.
Weak Classifier: A basic model used in each round. Common choices include decision stumps or any classifier that performs slightly better than random guessing.
Weight Adjustment: Each training instance has a weight that is updated after each round based on the classifier's performance. Misclassified instances receive higher weights to increase their importance in subsequent rounds.
Error Rate: The error rate of each weak classifier is considered to adjust the weights of the classifiers in the final prediction.
5.4. CatBoost
The fourth model employed in the study was CatBoost, a powerful gradient boosting library that is specifically designed to handle categorical features seamlessly without extensive preprocessing. CatBoost stands for Categorical Boosting and it excels at improving the performance of decision tree-based algorithms by utilizing an ordered boosting technique, which assists in preventing overfitting. One of CatBoost's key strengths is its ability to efficiently deal with a diverse array of data types, including high cardinality categorical features. Table 4 shows the pseudocode for the CATboost algorithm, while the working parameters for the same are presented below (Prokhorenkova et al. 2018).
Table 4.Pseudocode for the CATboost.
Pseudocode for CatBoost Prediction
Input: Trained CatBoost model, new input data x Output: Predicted output value for x Begin
Initialize the prediction value to 0 .
For each decision tree in the CatBoost model: a. Pass the input through decision tree to get a prediction . b. Update the prediction value: .
Return the final predicted output value: .
End
Working Parameters for CatBoost:
Learning Rate: Controls the step size at each iteration while moving toward a minimum of the loss function. A smaller learning rate can improve model performance but may require more iterations.
Depth of Trees: Defines the maximum depth of the trees in the ensemble. Deeper trees can capture more complex patterns but are prone to overfitting.
Number of Iterations: Specifies the total number of trees to be built. More iterations can enhance model performance but may also lead to overfitting if not properly managed.
L2 Leaf Regularization: A regularization parameter that helps to prevent overfitting by penalizing large weights in the model.
Loss Function: Determines how the model evaluates its predictions during training. Common choices include mean squared error for regression tasks and log loss for classification tasks.
5.5. XGBoost
The final model employed in the study was XGBoost, or Extreme Gradient Boosting - a powerful machine learning algorithm that enhances the traditional gradient boosting framework. XGBoost constructs an ensemble of decision trees, where each new tree focuses on correcting the errors of its predecessors using gradient computations. By incorporating advanced regularization techniques, XGBoost effectively mitigates overfitting, a common challenge with tree-based models. The pseudocode for the XGBoost algorithm is provided in Table 5, while the key working parameters are presented below (Chen and Guestrin 2016).
Table 5.Pseudocode for the XGBoost.
Pseudocode for XGBoost
Input: Training dataset , learning rate , number of trees , loss function Output: Ensemble model Begin
Initialize model
For to do: a. Compute the residuals: b. Fit a new decision tree to the residuals c. Calculate the tree's contribution: d. Update the model:
Return the ensemble model
End
Working Parameters for XGBoost:
Learning Rate: Also referred to as eta, this parameter determines how much each tree contributes to the overall prediction. Using a lower learning rate often improves the model’s performance but typically requires more boosting iterations.
Max Depth: Sets the maximum depth of the individual trees. Deeper trees are capable of capturing more intricate patterns but may also increase the risk of overfitting.
Number of Estimators: Specifies how many trees are included in the ensemble. While increasing this number can boost model accuracy, it is important to monitor closely to avoid overfitting.
Subsample: Indicates the fraction of the training data used to grow each tree. Values below 1 introduce randomness, which can help mitigate overfitting.
Col sample by tree: Defines the proportion of features selected randomly for each tree, further helping to control overfitting.
Gamma: A regularization parameter that sets the minimum reduction in loss needed to make an additional split on a leaf node, thereby managing model complexity.
Loss Function: Determines the objective to be minimized during training. Typical choices include mean squared error for regression and binary logistic loss for classification tasks.
6. Analysis of Machine Learning Models
This segment of the research evaluates the performance of five machine learning algorithms Support Vector Machine (SVM), Random Forest, AdaBoost, CATBoost, and XGBoost in correlating input variables such as injector location, methane ratio, engine load, intake air temperature, and biogas flow with essential output metrics. These outputs encompass brake specific energy consumption, exergy destruction, brake thermal efficiency, brake specific fuel consumption, and exergy efficiency. The main objective is to pinpoint the most influential set of input parameters that lead to enhanced engine efficiency and performance across different loading conditions. All models were systematically tuned using a Grid Search with ten fold cross validation to identify optimal hyperparameters and ensure robust predictive performance.
6.1. Model Performances in Predicting brake specific energy consumption
Brake Specific Energy Consumption (BSEC) serves as a crucial metric for assessing the energy efficiency of an engine. To predict BSEC, five machine learning models were trained using data obtained from the experimental trials and were assessed based on RMSE, MAE, and R² values. As illustrated in Table 6, the Random Forest algorithm delivered the best results, achieving the lowest RMSE (0.5402) and MAE (0.2879), along with the highest R² of 0.9501, which indicates it could account for approximately 95% of the variability in BSEC. The optimal Random Forest configuration consisted of 300 estimators with a maximum tree depth of 6, as identified through grid search optimization. XGBoost also showed strong performance with an R² of 0.9285 and slightly higher error metrics, while ADABoost followed with an R² of 0.9115. CatBoost demonstrated moderate predictive ability with an R² of 0.7451 and higher RMSE (1.2205) and MAE (1.1200). In contrast, the SVM model performed poorly, with the highest RMSE (3.8684), high MAE (3.4005), and a negative R² (-1.5609), meaning it did worse than simply predicting the mean. Because engine experiments are time-consuming and data extraction is challenging, the dataset used was relatively small. This makes it especially important to choose robust models and tune them carefully. Grid search was used to find the best hyperparameters for each algorithm to ensure the models performed as well as possible on the available data. Figure 20 shows the actual vs predicted BSEC values for the Random Forest model, clearly illustrating its high prediction accuracy.
Fig. 20.Actual vs Predicted plot for BSEC for the Random Forest model.Full size
Table 6.Performance metrics of all 5 Machine Learning Models for Brake specific energy consumption Prediction.
Metric
SVM
Random Forest
ADAboost
CatBoost
XGBoost
RMSE
3.8684
0.5402
0.7192
1.2205
0.6464
MAE
3.4005
0.2879
0.4029
1.1200
0.4272
R2
-1.5609
0.9501
0.9115
0.7451
0.9285
6.2. Model Performances in Predicting Brake Thermal Efficiency
Brake Thermal Efficiency is a key parameter that influences overall engine performance and energy use. To predict this parameter, five machine learning models were tested: Support Vector Machine (SVM), Random Forest, ADABoost, CatBoost, and XGBoost. These models were trained on data from the experimental setup and evaluated using RMSE, MAE, and R² metrics. As shown in Table 7, the XGBoost model performed best, achieving the lowest RMSE (3.2662) and MAE (1.4464) along with the highest R² score of 0.9262, capturing about 93% of the variance in Brake Thermal Efficiency. The optimal XGBoost configuration obtained through grid search used 300 estimators with no restriction on maximum tree depth. Random Forest followed closely with an R² of 0.9136, while SVM and ADABoost also performed well with R² scores slightly above 0.91. CatBoost showed weaker results, with the highest RMSE (5.3956) and a lower R² of 0.7987. Since engine experiments are time-consuming and often produce smaller datasets, grid search was used to carefully tune model parameters and improve accuracy. Figure 21 shows the actual vs predicted plot for the XGBoost model, highlighting its ability to closely match real Brake Thermal Efficiency values. These results indicate that XGBoost, along with Random Forest, SVM, and ADABoost, can reliably predict this parameter, while CatBoost was less effective for this dataset.
Fig. 21.Actual vs Predicted plot for brake thermal efficiency for the XGboost model.Full size
Table 7.Performance metrics of all 5 Machine Learning Models for Brake Thermal Efficiency Prediction
Metric
SVM
Random Forest
ADAboost
CatBoost
XGBoost
RMSE
3.5453
3.5345
3.6232
5.3956
3.2662
MAE
2.0964
1.5644
1.6593
4.1822
1.4464
R2
0.9131
0.9136
0.9092
0.7987
0.9262
6.3. Model performances in predicting Brake Specific Fuel Consumption
Brake Specific Fuel Consumption (BSFC) serves as an important indicator of how efficiently an engine utilizes fuel. To predict BSFC, this study employed five machine learning models Support Vector Machine (SVM), Random Forest, AdaBoost, CatBoost, and XGBoost which were trained using the experimental dataset and evaluated with RMSE, MAE, and R² metrics. As detailed in Table 8, XGBoost demonstrated the strongest predictive capability, achieving the lowest RMSE (0.0187) and MAE (0.0149), along with the highest R² value of 0.9947 The optimal XGBoost configuration obtained through grid search used 200 estimators with maximum tree depth of 6, explaining nearly 99.5% of the variation in BSFC. Random Forest also performed robustly, attaining an R² of 0.9501, followed by AdaBoost with an R² of 0.9076. CatBoost showed moderate performance (R² = 0.7451), whereas SVM struggled significantly, yielding the highest RMSE (0.3837), highest MAE (0.3376), and a negative R² (-1.2345), indicating it failed to reliably capture the data patterns. Because experimental engine studies often generate relatively small datasets due to the complexity of data acquisition, grid search techniques were employed to fine-tune model parameters and enhance prediction accuracy. Figure 22 illustrates the actual versus predicted BSFC values for the XGBoost model, showing a close match to experimental data. Overall, these findings underscore that ensemble methods, particularly XGBoost, along with Random Forest and AdaBoost are highly effective for modeling BSFC, while SVM proved less suitable for this application.
Fig. 22.Actual vs Predicted plot for brake thermal efficiency for the XGboost model.Full size
Table 8.Performance metrics of all 5 Machine Learning Models for Brake Specific Fuel Consumption Prediction
Metric
SVM
Random Forest
ADAboost
CatBoost
XGBoost
RMSE
0.3837
0.0574
0.0780
0.1296
0.0187
MAE
0.3376
0.0306
0.0445
0.1189
0.0149
R2
-1.2345
0.9501
0.9076
0.7451
0.9947
6.4. Model Performances in Predicting Exergy Destroyed
The Exergy Destroyed parameter, critical for assessing engine performance, was modeled using Support Vector Machine (SVM), Random Forest, ADABoost, CatBoost, and XGBoost algorithms. As shown in Table 9, the ADABoost model delivered the best results, achieving the lowest RMSE (0.5999) and MAE (0.4467), along with the highest R² score of 0.8818 with 100 as its number of rounds, indicating it could explain about 88% of the variance in Exergy Destroyed. XGBoost also performed well, with an RMSE of 0.7603, MAE of 0.5293, and R² of 0.8102. SVM and CatBoost showed moderate predictive ability, with R² scores of 0.7085 and 0.6494, respectively, while Random Forest performed the weakest, recording an R² of just 0.2698. Grid search was used to optimize hyperparameters for all models. Figure 23 illustrates the actual vs predicted values for the ADABoost model, highlighting its strong fit. These results show that ADABoost, followed by XGBoost, is best suited for predicting Exergy Destroyed with this feature set.
Table 9.Performance metrics of all 5 Machine Learning Models for Exergy Destroyed Prediction
Metric
SVM
Random Forest
ADAboost
CatBoost
XGBoost
RMSE
0.9421
1.4912
0.5999
1.0333
0.7603
MAE
0.6127
1.1602
0.4467
0.8164
0.5293
R2
0.7085
0.2698
0.8818
0.6494
0.8102
Fig. 23.Actual vs predicted plot for Exergy Destroyed for the ADAboost model.Full size
6.5. Model Performances in Predicting Exergy Efficiency
Exergy Efficiency, a key parameter affecting engine performance, was modeled using Support Vector Machine (SVM), Random Forest, ADABoost, CatBoost, and XGBoost. As shown in Table 10, the XGBoost model delivered the best results, achieving the lowest MAE (1.5157), an RMSE of 3.2778, and the highest R² score of 0.9189 with 300 estimators and maximum depth of 10, explaining about 92% of the variance in Exergy Efficiency. Random Forest, SVM, and ADABoost showed similar performance, with R² values between 0.9042 and 0.9156, while Random Forest also achieved a notably low MAE of 1.4805. In contrast, CatBoost performed the weakest, with an RMSE of 5.2108, MAE of 4.0571, and an R² of 0.7951. Grid search was used to tune hyperparameters for all models to enhance prediction accuracy. Figure 24 shows the actual vs predicted plot for XGBoost, highlighting its strong fit. Overall, XGBoost proved most effective for predicting Exergy Efficiency, with Random Forest also showing competitive results.
Fig. 24.Actual vs predicted plot for Exergy Efficiency for the XGboost model.Full size
Table 10.Performance metrics of all 5 Machine Learning Models for Exergy Efficiency Prediction
Metric
SVM
Random Forest
ADAboost
CatBoost
XGBoost
RMSE
3.4026
3.3451
3.5635
5.2108
3.2778
MAE
2.0518
1.4805
1.6044
4.0571
1.5157
R2
0.9126
0.9156
0.9042
0.7951
0.9189
6.6. Comparison of all 5 machine learning models for best predictive capabilities
The performance of various machine learning models in predicting key engine parameters was evaluated across five critical outputs: Brake Specific Energy Consumption, Brake Thermal Efficiency, Brake Specific Fuel Consumption, Exergy Destroyed, and Exergy Efficiency. As shown in Table 11, XGBoost achieved exceptional accuracy for Brake Specific Fuel Consumption with an R² of 0.9947, while Random Forest performed best for Brake Specific Energy Consumption at 0.9501. XGBoost also delivered strong results for Brake Thermal Efficiency and Exergy Efficiency, with R² scores of 0.9262 and 0.9189 respectively. For Exergy Destroyed, ADABoost showed the highest predictive performance, reaching an R² of 0.8818. Although the datasets were relatively small, which is typical given the time and effort required for detailed engine experiments, the models were carefully tuned using grid search to achieve the best possible results. The high R² values across most parameters indicate that the models effectively captured the main relationships between inputs and outputs. These relationships were often monotonic, such as efficiency generally increasing with load and specific consumptions decreasing, which is consistent with well-established engine behavior. Tree-based ensemble models such as XGBoost and Random Forest are particularly effective in capturing nonlinear interactions and threshold effects between engine operating parameters, which explains their superior performance for most outputs. Random Forest showed strong generalization for energy-based metrics due to its robustness against overfitting, while XGBoost benefited from gradient-based boosting to refine predictions for efficiency-related parameters. ADABoost performed better for exergy destruction likely because it emphasizes difficult-to-predict samples, which is useful for capturing losses influenced by subtle thermodynamic variations.
Table 11.Best performing models for prediction of each of the 5 output parameters.
Parameter
Model with highest R2 score
R2 Score
Brake specific energy Consumption
Random Forest
0.9501
Brake Thermal Efficiency
XGBoost
0.9262
Brake Specific Fuel Consumption
XGboost
0.9947
Exergy Destroyed
ADAboost
0.8818
Exergy Efficiency
XGBoost
0.9189
7. Conclusion
The predictive performance of multiple machine learning models was evaluated for five key engine outputs: brake specific energy consumption, brake thermal efficiency, brake specific fuel consumption, exergy destroyed, and exergy efficiency. Support Vector Machine (SVM), Random Forest, AdaBoost, CatBoost, and XGBoost models were trained and compared. As summarized in Table 11, XGBoost achieved the highest accuracy for several metrics, with R² values of 0.9947 for brake specific fuel consumption, 0.9262 for brake thermal efficiency, and 0.9189 for exergy efficiency. Random Forest performed best for brake specific energy consumption (R² = 0.9501), while AdaBoost yielded the highest accuracy for exergy destroyed (R² = 0.8818). The strong predictive performance indicates that the models successfully captured the dominant relationships between engine inputs and outputs, which were largely monotonic and consistent with established engine performance behavior (e.g., increased load leading to improved efficiency and reduced specific consumption). This agreement with known physical trends suggests that the models are learning meaningful system behavior rather than overfitting. Although the dataset was limited, as is typical in experimental engine studies, systematic hyperparameter tuning using grid search ensured near-optimal model performance. The consistently high R² values demonstrate that ensemble-based models, particularly XGBoost and Random Forest, are well suited for modeling complex thermodynamic and exergy-based engine characteristics. Beyond offline prediction, these trained models can be integrated into real-time engine monitoring frameworks by mapping readily available sensor inputs (such as load, speed, and fuel flow) to key efficiency and exergy indicators. This enables continuous estimation of otherwise difficult-to-measure parameters like exergy destruction and exergy efficiency, supporting early fault detection, performance degradation monitoring, and adaptive control strategies. Such real-time capability can help operators optimize operating conditions, reduce energy losses, and improve overall engine efficiency without requiring additional physical instrumentation.
Conflict of interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data availability. The data used in this study will be made available upon request.
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