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.

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.

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.

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.

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.

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.

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.

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):

Working Parameters:

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).

Working Parameters of Random Forest:

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).

Working Parameters for AdaBoost:

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).

Working Parameters for CatBoost:

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).

Working Parameters for XGBoost:

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.

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.

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.

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.

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.

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.