Prediction of Diesel Engine Performance and Emissions Under Variations in Backpressure, Load, and Compression Ratio Using an Artificial Neural Network

Abstract

Excessive exhaust backpressure (EBP) in modern diesel engines disrupts gas exchange, increases residual gas fraction (RGF), and reduces combustion efficiency. Traditional experimental approaches, including simulations and bench testing, are often time-consuming and costly, which has driven growing interest in artificial neural networks (ANNs) for accurately modelling complex engine behavior. This research introduces an ANN model designed to predict the impact of EBP on the performance and emissions of a diesel engine across varying compression ratio (CR) of 12, 14, 16, and 18 and engine load (25%, 50%, 75%, and 100%) conditions. The ANN model was developed and optimised using genetic algorithms (GA) and particle swarm optimisation (PSO). It was then trained using data from an experimentally validated one-dimensional computational fluid dynamics (1D-CFD) model developed through GT-Power GT-ISE v2024, simulating engine responses under variation CR, load, and EBP conditions. The optimised ANN architecture, featuring an optimal (3-14-10) configuration, was trained using the Levenberg–Marquardt back propagation algorithm. The performance of the model was assessed using statistical criteria, including the coefficient of determination (R²), root mean square error (RMSE), and k-fold cross-validation, by comparing its predictions with both experimental and simulated data. Results indicate that the optimised ANN model outperformed the baseline ANN and other machine learning (ML) models, attaining an R² of 0.991 and an RMSE of 0.011. It reliably predicts engine performance and emissions under varying EBP conditions while offering insights for engine control, optimisation, diagnostics, and thermodynamic mechanisms. The overall prediction error ranged from 1.911% to 2.972%, confirming the model’s robustness in capturing performance and emission outcomes.

1. Introduction

1.1. Background

Diesel engines are widely used in various applications due to their high efficiency and durability. However, they are also a significant source of harmful emissions, such as nitrogen oxides (NO_X), particulate matter (PM), carbon monoxide (CO), and hydrocarbons (HC) [1,2,3]. These emissions contribute to air pollution and pose serious health risks. Variable compression ratio (VCR) diesel engines offer a promising approach to optimise engine performance and reduce emissions by adjusting the compression ratio (CR) based on operating conditions [4,5]. Exhaust backpressure (EBP) is another critical factor that affects engine performance and emissions. Understanding and predicting the impact of EBP on VCR diesel engines when under varying engine load conditions is essential for achieving optimal engine control and minimising environmental impact. Artificial neural networks (ANNs) have emerged as a powerful tool for modelling complex systems and predicting engine performance and emissions due to their ability to learn non-linear relationships from large datasets.

1.2. Related Work

Aydin et al. [6] utilised ANN to predict the performance and emission parameters of a single-cylinder diesel engine fuelled by biodiesel–diesel blends. Their data, obtained from various engine loads and injection pressures, indicated that the ANN effectively modelled emissions and performance, achieving R² values between 0.8663 and 0.9858. Rezaei et al. [7] compared radial basis function (RBF) and feedforward (FF) ANNs for engine prediction, finding FF models simpler but requiring twice the training time of RBF models. In contrast, other studies [8,9,10] have favored backpropagation-based methods, indicating their stability and superior accuracy despite longer training requirements, highlighting a recurring contradiction in the literature between algorithm efficiency and predictive reliability. Çay et al. [11] applied ANN to predict BSFC, CO, HC, and air-fuel ratio (AFR) in a spark ignition engine using methanol and gasoline, determining that the backpropagation algorithm was optimal, with correlation coefficients exceeding 0.97 across all parameters. Similarly, Rao et al. [12] employed ANN with backpropagation for predicting performance and exhaust emissions in an indirectly injected (IDI) diesel engine, reporting strong predictive capability with high correlation coefficients for exhaust gas temperature (EGT), BSFC, and NO_X. These findings collectively underscore the agreement that ANNs are highly effective at capturing non-linear engine behavior.

Noor et al. [13] further validated ANN’s applicability by predicting marine diesel engine performance using a backpropagation Levenberg–Marquardt algorithm, achieving an R² of 0.99 against both experimental data and a mathematical model. Boruah et al. [14] also demonstrated ANN’s suitability as a black-box model for variable compression ratio (VCR) diesel engines, effectively forecasting performance parameters across diverse operating conditions. Similarly, Muralidharan and Vasudevan [15] confirmed that feedforward backpropagation networks can reliably predict performance, emissions, and combustion behavior across varying CRs, reinforcing agreement in the literature on ANN’s general robustness. Additional research on ANN modelling and prediction concerning diesel engine performance and emissions with VCR includes works by Karthickeyan et al. [16], Behera and Hotta et al. [17], Kakati et al. [18], and Manimaran et al. [19]. These studies consistently emphasize the necessity of accurate experimental data to ensure reliable predictions. In the same manner, Saravanamuth et al. [20], Hosamani et al. [21], Kumar et al. [22], and Taye [23] highlight the importance of preprocessing, architecture selection, and learning process optimisation as critical factors in ANN model development. Yang et al. [24] advanced this by showing that genetic algorithms (GA) can significantly improve prediction accuracy by optimising ANN weights, reducing errors compared to conventional training.

Although these studies confirm ANN’s strong predictive capability, several limitations persist. Contradictions remain regarding the dominance of specific algorithms. While RBF networks are sometimes reported as faster and simpler [7], backpropagation approaches are generally favored for their accuracy [8,9,10,11,12]. Moreover, the wide range of fuels (biodiesel, methanol, gasoline) and engine types (SI, DI, IDI, VCR, marine) complicates direct comparison and generalisation of findings. More importantly, the literature overwhelmingly focuses on prediction accuracy, often overlooking mechanistic interpretation.

1.3. Research Gap

While ANNs have been widely applied to predict diesel engine performance and emissions, comprehensive modeling frameworks that capture the combined effects of CR, load, and EBP are still underdeveloped. Existing studies either model VCR diesel engines without considering EBP or examine fluctuating EBP and load in fixed CR engines, thereby overlooking the complex interactions among these parameters [25,26,27]. The accuracy and reliability of ANN models are also highly dependent on the quality and representativeness of the training data, highlighting the need for optimisation using advanced techniques such as genetic algorithms (GA) and particle swarm optimisation (PSO), which have not been fully reported in previous work. Furthermore, although ANN models often demonstrate strong statistical accuracy as reflected by R² and RMSE values, few studies establish clear links between ANN predictions and fundamental combustion and thermodynamic processes. Similarly, benchmarking ANN models against alternative machine learning (ML) approaches and employing rigorous validation methods such as k-fold cross-validation remain underexplored, raising concerns about model robustness and generalisability.

1.4. Contribution and Novelty

This study makes several key contributions. First, it presents the development of an optimised ANN model (3-14-10 architecture) that uniquely integrates CR, load, and EBP as simultaneous inputs, addressing a notable research gap where these parameters have largely been studied individually. By incorporating GA and PSO, the model achieved high predictive accuracy (R² ≈ 0.991) with RMSE of 0.011, while rigorous k-fold cross-validation ensured strong generalisability and resistance to overfitting. Importantly, the predictions were not only statistically resilient but also consistent with fundamental thermodynamic and combustion mechanisms, thereby bridging data-driven modelling with physical interpretability. Furthermore, by validating the ANN using both experimentally validated 1D-CFD simulations and physical data, this work advances beyond conventional ANN studies and demonstrates a framework capable of supporting real-time engine management systems for performance optimisation and emission compliance under varying operating conditions.

2. Materials and Methods

2.1. Experimental Work for Data Simulation

The research employed a single-cylinder, four-stroke variable VCR diesel engine operating on conventional diesel fuel to gather research data. A 1D-CFD model validated by experiments was developed utilising the advanced GT-Power GT-ISE v2024 software. This model simulates an engine’s response under a spectrum of EBPs and a variety of engine loads and CRs, while engine speed remained constant at 1500 rpm, facilitating a comprehensive analysis of its performance and emission characteristics. These measurements, derived from the validated 1D-CFD model, provide critical insights into the engine’s operational efficiency and environmental impact. The VCR technology enables adjustable CRs, thereby optimising the engine’s performance in varying load conditions and improving its operational adaptability. The performance and emissions parameters that were of interest for this study are listed in

Table 1. Performance parameters and emission characteristics that are of interest for this study.

Performance Parameter	Emission Characteristic
Brake power (BP)	Carbon monoxide (CO)
Brake torque (BT)	Carbon dioxide (CO2),
Brake specific fuel consumption (BSFC)	Nitrogen oxides (NOX)
Brake thermal efficiency (BTE)	Hydrocarbons (HC),
Exhaust gas temperature (EGT)	Particulate matter (PM)

.

Table 2. Specifications of the proposed single cylinder 4-stroke diesel engine.

Engine Parameters	Units	Values
Make		Kirloskar
Type		1-cylinder, 4-stroke, VCR diesel
Cooling system		Water cooled
Rated power	kW	3.5
Speed	Rpm	1500
Bore diameter	Mm	87.5
Stroke	Mm	110
Connecting rod	Mm	234
Compression ratio		Variable (12–18)
Displacement	Cc	661
Loading		Eddy current dynamometer

depicts the specifications of the VCR diesel engine used for this study.

To provide further details, an EBP mechanism was developed using 304 stainless steel orifice plates with varying restriction diameters ranging from 32 mm to 17 mm. These orifices were consecutively placed along the exhaust pipe of the diesel engine. A Rosemount 3051S Series differential pressure (DP) transmitter, installed in conjunction with the orifice plates, was employed to measure the resulting EBP and transmit the corresponding signals to the data acquisition system. This configuration enabled the generation of EBPs over a broad spectrum, ranging from 5.4 kPa to 73.5 kPa. Nevertheless, for the present study, the results were specifically recorded at incremental values of 15, 30, 45, and 60 kPa. The selection of these discrete points was motivated by the need to balance experimental feasibility with representativeness: they incorporate the critical mid-range EBPs where performance and emissions effects are most pronounced, while avoiding redundant data collection at extreme ends of the spectrum that are either less practically relevant or imposes excessive strain on the test setup. This approach ensured both experimental efficiency and the generation of meaningful insights into the interaction between EBP, CR, and load.

The experimental investigation was conducted across four test cases, in which the CR and EBP were systematically varied. Specifically, the CR was adjusted in increments of 12, 14, 16, and 18, while the EBP was set to 15, 30, 45, and 60 kPa in all cases, respectively. In Case 1, the engine load was fixed at 25% and subsequently increased by 25% in each successive case, reaching 100% in Case 4 (i.e., Case 1 = 25%, Case 2 = 50%, Case 3 = 75%, Case 4 = 100%). This structured approach was designed to interpret the complex interactions between excessive EBP and the performance benefits generally associated with varying loads and CRs in diesel engines. Throughout the experimental testing, performance parameters were accurately measured using the EnginesoftLV 6.0 software and K-type thermocouple, while emissions data were acquired through a combined PUC gas analyzer. The engine test rig employed in the study is illustrated in Figure 1. Subsequently, the experimental findings were simulated using GT-Power GT-ISE v2024, with the corresponding simulation model shown in Figure 2. Ultimately, an ANN model was developed to predict engine performance and emissions behavior under these combined and complex operating conditions. The employed research design is suitable as it combines a flexible VCR diesel engine, controlled EBP generation, and precise measurement techniques, ensuring representative and reliable experimental data. The integration of GT-Power simulations further validates and extends the analysis, while the ANN model enhances predictive robustness under complex operating conditions. This hybrid approach ensures both methodological rigor and practical relevance to real-world diesel engine performance.

2.2. Artificial Neural Network Modelling

The application of ANNs within the field of I.C engine research demonstrates considerable potential due to their capacity for pattern recognition and data-driven modelling. ANNs possess an inherent self-learning capability, enabling them to extract and generalize complex relationships from large datasets. In the present study, a Levenberg–Marquardt backpropagation neural network, widely recognized in the literature as a reliable and effective approach for predicting engine-related parameters [28,29,30,31] was employed to predict the performance and emission characteristics of the VCR diesel engine. The network parameters were successively updated using the fast gradient descent algorithm, whereby the weights were modified along the negative gradient with a variable step size, ensuring convergence towards the minimum of the loss function. Model development was carried out using the Neural Network Toolbox in MATLAB R2024b, and the number of training epochs was set to 1000 to ensure adequate convergence and accuracy. The specifications of the ANN model are depicted in

Table 3. Specifications of the ANN model.

Parameter	Specification
Input layer neuron	3
Hidden layer (single) neuron	4 to 44
Output layer neuron	10
Training function	Levenberg–Marquardt
Performance function	Mean square error
Activation function	Log-sigmoid, Linear
Performance goal	$1.0\times {10}^{-3}$

.

Among the various factors influencing the performance of ANN, the network structure significantly impacts prediction outcomes. To identify an appropriate ANN structure, a script was developed in MATLAB R2024b. In this study, the R², RMSE, and complementary error indices such as MAE and MAPE were employed as evaluation indicators to ensure comprehensive statistical validation of the ANN’s predictive accuracy. These techniques have been previously proven to effectively enhance the accuracy of the baseline ANN in several studies [32,33,34]. Furthermore, cross-validation was introduced alongside the standard 70-15-15 dataset split, providing additional resilience against overfitting and enhancing generalisability across unseen data. During the training process, the number of neurons in the hidden layer varied from 4 to 44 to determine the optimal structure. It was observed that the RMSE was minimum at 0.013 and R² was maximum 0.984.

To strengthen the ANN optimisation process, neuron variation was further supported by the incorporation of advanced optimisation approaches such as genetic algorithms (GA) and particle swarm optimisation (PSO), as depicted in

Table 4. Comparison of baseline ANN and ANN optimized with GA and PSO.

Model Configuration	RMSE	${\mathit{R}}^2$	MAE	Convergence Epochs
ANN (baseline, neuron variation only)	0.013	0.984	0.017	640
ANN + GA optimization	0.0128	0.989	0.012	520
ANN + PSO optimization	0.011	0.991	0.010	500

. These techniques assisted in refining hyperparameter selection and enhancing convergence efficiency, ensuring that the network avoided local minima and achieved higher predictive reliability. Moreover, benchmarking against alternative ML algorithms (support vector machines, random forest, and deep learning architectures) was performed to contextualise the performance of the ANN within a broader modelling framework. This comparative assessment as seen in

Table 5. Benchmarking of ANN against alternative ML models.

Model Configuration	RMSE	${\mathit{R}}^2$	MAE	MAPE (%)
Support Vector Machine (SVM)	0.026	0.965	0.020	3.5
Random Forest (RF)	0.022	0.972	0.018	3.1
Deep Neural Network (DNN)	0.018	0.978	0.013	2.7
ANN (GA/PSO optimized)	0.011	0.991	0.010	2.1

, confirmed the superior adaptability of the ANN in capturing the non-linear relationships governing engine performance and emissions. The optimised ANN (with GA and PSO) achieved a substantial improvement over the baseline ANN, reducing RMSE by nearly 15% from 0.013 to 0.011 and improving $R^2$ from 0.984 to 0.991. When benchmarked against alternative ML algorithms, the optimised ANN consistently demonstrated exceptional performance, particularly in terms of accuracy (lowest RMSE and MAE) and generalisability (lowest MAPE), thus validating its robustness and suitability for predicting diesel engine performance and emissions under complex operating conditions of load, CR, and excessive EBP. This variation in the optimised RMSE and R² with respect to the number of neurons in the hidden layer are illustrated in Figure 3. The number of neurons for which the RMSE was minimum (0.011) and was R² was maximum (0.991) was selected to be the number of neurons in the hidden layer. Based on Figure 3, the best learning capability and minimum error were found when the number of neurons chosen was 14. Consequently, the 3-14-10 ANN architecture was determined to be the most suitable choice for predicting VCR diesel engine responses, owing to its superior generalisation capability under the operating conditions investigated in this study. Figure 4 presents the selected architecture of the optimised ANN model.

Approximately 1000 sets of data generated from the validated simulation model were systematically divided into three distinct datasets. A randomly selected 70% of the data (700 sets) was designated as the training dataset, which was utilised to train the ANN model on various parameters. The validation set comprised 15% (150 sets) of the total data, serving to tune the model’s hyperparameters and monitor its performance throughout the training process. This validation set played a crucial role in preventing overfitting, a scenario in which the model learns the training data too effectively but fails to generalise to new, unseen data. The remaining 15% (150) of the data was allocated as the test set, a separate dataset was not used during the training or validation phases. This test set was instrumental in evaluating the final performance of the trained model, providing an unbiased assessment of the ANN’s ability to generalise to new, unseen data. To complement this split, k-fold cross-validation was also applied to further minimise data bias and ensure statistical rigor. This evaluation was critical for assessing the model’s real-world performance and its capacity for making accurate predictions on the independent datasets, which had not been obtained with the split on simulated data. Several studies have demonstrated that this rigorous dataset division method, which effectively mitigates overfitting, is well-suited for applications of this nature [35,36,37,38]. To ensure balanced learning, all input and output variables were subjected to feature scaling prior to model development. Specifically, the input parameters (EBP, load, and CR) and the output parameters (performance and emission characteristics) were normalized using a min–max scaling approach to map their values within the range [0, 1]. This preprocessing step was essential given the use of a log-sigmoid activation function in the hidden layer, which is highly sensitive to input magnitudes. Normalization ensured that no single parameter dominated the learning process, thereby improving gradient stability, accelerating convergence, and enhancing generalization capability. After prediction, the ANN outputs were rescaled back to their original physical units to allow direct interpretation and comparison with experimental and simulated results.

The predictive capability of the ANN, supported by advanced optimization and benchmarking, was evaluated through the $R^2$, RMSE, MAE, and MAPE. Under these optimized conditions, an $R^2$ value approaching unity, in conjunction with a low RMSE, indicates the model’s ability to accurately capture the underlying relationships within the dataset. The corresponding mathematical formulations are presented in Equations (1)–(4), as detailed in [39]. In this context, the sum of squared residuals (SSres) and the total sum of squares (SStot) are defined as follows:

$${SS}_{res} =\sum _{i=1}^n{\left(y^i-\overline{y}\right)}^2$$

(1)

$${SS}_{tot}=\sum _{i=1}^n{\left(y^i-\overline{y}\right)}^2$$

(2)

The $R^2$ is mathematically expressed as follows:

$$R^2=1-{\displaystyle \frac{\mathrm{ }\mathrm{ }\mathrm{ }{SS}_{res}}{\mathrm{ }{SS}_{tot}}}$$

(3)

The RMSE, a common parameter for evaluating model prediction accuracy, is expressed as follows:

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left(y^{\left(i\right)}-{\widehat{y}}^{\left(i\right)}\right)}^2}$$

(4)

where ${\widehat{y}}^{\left(i\right)}$ denotes the predicted output of the ANN model; $\overline{y}$ represents the mean value of the experimentally validated data; $y^{\left(i\right)}$ corresponds to the data extracted from experimental tests and 1D-CFD model; and $n$ is the total number of data points.

To enhance the clarity of the ANN model structure, a flow chart has been developed, as illustrated in Figure 5.

3. Results and Discussion

In the present study, an ANN was designed utilising the data collected in the using simulated data, which was validated against experimental results to estimate the VCR diesel engine performance parameters and emission characteristics under EBP varying from 5.4 kPa to 73.5 kPa. Load, CR, and EBP were selected as input parameters while BP, BT, BSFC, BTE, EGT, CO, CO₂, NO_X, HC, and PM were chosen as output variables. The overall regression information for training, validation, and testing showed $R^2$ values of 0.99259, 0.98840, 0.97989, and 0.98408, respectively, as depicted in Figure 6. The fact that the $R^2$ is close to 1 is an indication of the ANN’s high accuracy and correctness in modelling the outputs. The detailed analysis for each parameter and characteristic is discussed in Section 3.1 and Section 3.2, respectively.

3.1. Performance Parameters

Figure 7 presents a comparative analysis of the predicted outcomes derived from the optimised ANN model against the actual values for five key performance parameters. This comparison serves as a basis for assessing the indicative efficiency of the optimised ANN model through the parameter of $R^2$ and RMSE. Notably, the distribution of the blue points shows a proximity to the black dashed line at a 45-degree angle, indicative of the trained ANN model’s powerful predictive capabilities and strong alignment between the predicted results and the actual measurements.

Evaluation of the performance parameters highlighted a significant correlation between the predicted and measured values for BP, EGT, BTE, BSFC, and BT. The regression plots illustrate a strong positive correlation, as evidenced by the high $R^2$ values of 0.9906, 0.9934, 0.9712, 0.9829, and 0.9774 for BP, BT, BSFC, BTE, and EGT, respectively. Furthermore, the RMSE values were notably low: 0.01911 kW for BP, 0.01981 N.m for BT, 0.01919 g/kW.h for BSFC, 0.02711% for BTE, and 0.02972 °C for EGT. These RMSE values incorporate the overall performance of the model, including its training, validation, and testing phases. These findings emphasise the efficiency of the optimised ANN model across multiple performance parameters, underscoring its precision in forecasting the performance parameters of a VCR diesel engine operating under conditions of significantly varying EBP.

Throughout both the validation and training phases, the observed $R^2$ and RMSE values demonstrate a notable similarity, suggesting that there is no indication of overfitting in the development of the ML model. Typically, overfitting arises from the presence of noise within the dataset; however, this study utilised data derived from an experimentally validated 1D-CFD model that is devoid of such noise due to the split, k-fold cross-validation that was applied to further minimise data bias and ensure statistical rigor. Furthermore, an analysis of the positional relationship between the blue points and the black dashed line reveals that the blue points consistently cluster near this reference line across all plots. This proximity further supports the stability of the model’s performance. The high $R^2$ values, ranging from 0.9712 to 0.9934, across all parameters indicate that the optimised ANN model is highly effective in capturing the relationships between input variables and the predicted engine performance parameters, with low RMSE values further supporting the model’s accuracy. However, it is crucial to consider potential limitations, the main one being that the model’s accuracy is depended on the quality and representativeness of the training data.

When observing Figure 8, there is a close agreement between the experimental data and the predictions made by both simulation and optimised ANN models, indicating that these modelling approaches effectively capture the performance characteristics of the VCR diesel engine across variation in loads, and under increasing EBP, a critical factor influencing engine efficiency and emissions. While ANN models excel at identifying complicated non-linear dependencies between input parameters and engine performance due to their data-driven nature, simulation models grounded in physical principles offer valuable insights into the underlying processes within the engine, enabling optimisation of design and operating parameters. This good agreement indicates that the optimised ANN model generalises well to unseen data, rather than simply memorising the training set. This was further observed during the validation and testing phases. In addition, the smooth trends in the ANN predictions, similar to the experimental and simulation data, further suggest that the model is not fitting noise or displaying the unpredictable behaviour typical of overfitted models.

Beyond statistical accuracy, the physical interpretation of these results highlights the thermodynamic processes underpinning the predicted performance. For instance, the reduction in BP and BTE under excessive EBP conditions can be explained by increased residual gas fraction (RGF), which restricts fresh air intake and lowers effective oxygen availability. This residual gas recirculation compromises combustion quality and increases pumping losses, thereby raising BSFC and reducing thermal efficiency [40]. The accurate prediction of EGT further reflects the optimised ANN’s ability to capture the thermal coupling between trapped hot residual gases and in-cylinder temperature rise. High EGT values observed under high EBP correspond to reduced heat release rate (HRR) and compromised combustion phasing, which not only reduce efficiency but also contribute to higher NO_X formation.

3.2. Emission Characteristics

When observing Figure 9a–e, the optimised ANN model demonstrates considerable predictive capabilities across all investigated emission parameters, specifically CO, CO₂, NO_X, HC, and PM as indicated by the high $R^2$ values. This strong correlation suggests that the model effectively captures the fundamental relationships between the input variables, namely CR, load and EBP, and the resulting emission outputs. However, a thorough critical analysis necessitates an analysis of each parameter individually, particularly regarding the relative magnitude of the RMSE in the context of the emission levels being predicted. This enables a deeper understanding of the model’s strengths and potential areas for enhancement. The observed $R^2$ values for the respective emissions are 0.9893 for CO, 0.9874 for CO₂, 0.9639 for NO_X, 0.9801 for HC, and 0.9701 for PM, coupled with RMSE values of 0.01970 ppm, 0.02912 ppm, 0.02122 ppm, 0.02098 ppm, and 0.01972 mg/m³. This overall critical assessment effectively highlights the strengths of the optimised ANN model, which include its impressive predictive capabilities and accuracy, as reflected by ${\mathrm{R}}^2$ values nearing unity and RMSE values approaching zero. These findings underscore the optimised ANN model’s substantial predictive power for diesel engine emissions under varying operational conditions (CR, load and EBP). On the other hand, Figure 10 aligns with the trends observed in Figure 8, demonstrating a strong agreement between the experimental measurements and the predictions obtained from both the simulation and the optimized ANN models. This close correlation indicates that the employed modelling approaches reliably capture the performance characteristics of the VCR diesel engine across varying load conditions and under progressively increasing EBP, a parameter that plays a pivotal role in determining engine efficiency and emissions.

Importantly, these predictions also align with combustion fundamentals. The rise in CO and HC under higher EBP conditions can be attributed to oxygen deficiency and incomplete combustion caused by restricted exhaust path, leading to partial oxidation. In contrast, higher CR improves these effects by promoting increased in-cylinder pressures and temperatures, thereby facilitating more complete combustion and lowering CO and HC emissions, a trend correctly reflected by the optimised ANN outputs. For NO_X, the optimised ANN effectively captured its sensitivity to the thermodynamic trade-off between combustion temperature and RGF dilution: higher load and CR increase peak temperatures, increasing NO_X, while increased EBP introduces dilutive effects that partially suppress its formation. The agreement between forecasted and experimental PM trends reinforces the reliability and robustness of the model, with high soot formation at higher EBP related to reduced air/fuel mixing efficiency and incomplete combustion, mechanisms consistent with established diesel combustion theory. Collectively, these insights indicate that the optimised ANN not only provides highly accurate statistical predictions but also reflects the fundamental thermodynamic and combustion mechanisms governing engine behaviour under varying CR, load, and EBP conditions.

4. Summary of the Study

4.1. Conclusions

In this study, an ANN model optimised with GA/PSO was developed using simulated data, which was validated against experimental results from a diesel engine operating under various CRs (12, 14, 16, and 18) and loads (25%, 50%, 75%, and 100%), while the EBP was varied between 5.4 kPa to 73.5 kPa. The ideal network architecture for the proposed ANN model was identified as (3-14-10), signifying the inclusion of three neurons in the input layer, fourteen neurons in a single hidden layer, and ten neurons in the output layer. The performance of the optimal network was evaluated through a comprehensive set of statistical measures, including error analysis and correlation, in comparison with both experimental and simulated outcomes. Based on the findings of this study, the following conclusions are presented:

• The findings confirm that excessive EBP adversely influences both performance and emissions, and that these effects are strongly modulated by load and compression ratio variations.
• The model outputs could be used to support emission compliance strategies by forecasting pollutant formation under diverse EBP and load conditions, thus aiding in the development of cleaner diesel technologies.
• The predictions obtained from the optimized ANN model, configured with fourteen neurons in the hidden layer, displayed a strong correlation with both the experimental data and the validated simulation results.
• The data point distribution for the optimized ANN model closely resembled that of the experimental and simulation data, achieving an overall $R^2$ value of 0.991. This high $R^2$ indicates that the developed ANN model was proficient in making predictions that aligned well with both experimental and simulated results.
• The overall prediction error percentage for the ANN model was found to range from 1.911% to 2.972%, validating the accuracy and consistency of the model in predicting performance results.

These results demonstrate the promising potential of the developed ANN optimised with GA/PSO for modelling and predicting diesel engine performance under combined varying operational parameters, specifically CR and load, while the engine experiences increasing EBP conditions. This capability can be highly valuable for enhancing engine control, optimizing performance, and improving analytical processes.

4.2. Recommendations

Future studies should extend the operating domain to include variable engine speeds, alternative fuels, and transient conditions. Furthermore, hybrid approaches that are not incorporated within the current study combining ANN with optimization algorithms are recommended to further enhance predictive robustness and generalizability. Drawing on these advancements, the developed optimised ANN model holds strong potential for integration into real-time engine management systems, where it could dynamically adjust the CR and load to mitigate the adverse effects of EBP. Such integration would not only improve fuel efficiency but also reduce pollutant emissions, thereby supporting more sustainable diesel engine operation.

4.3. Liminations

The study is limited by its focus on a single engine speed (1500 rpm) and restriction to steady-state conditions with conventional diesel fuel. These constraints may limit generalisability to other fuels, engine speeds, and transient operating regimes. Additionally, the computational performance of the ANN under real-time embedded applications was not assessed.