Department of Mechanical Engineering , Kongunadu College of Engineering and Technology , Tiruchirappalli , Tamil Nadu , 621215 , India , kongunadu.ac.in

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Chandrasekaran M.,

Chandrasekaran M.

orcid.org/0000-0002-5163-2513

Department of Mechanical Engineering , Vels Institute of Science Technology and Advanced Studies , Chennai , India

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Shaisundaram V. S.,

Shaisundaram V. S.

orcid.org/0000-0001-8642-0986

Department of Automobile Engineering , Vels Institute of Science Technology and Advanced Studies , Chennai , India

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Saravanakumar Sengottaiyan,

Corresponding Author

Saravanakumar Sengottaiyan

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Faculty of Engineering and Technology , Villa College , Male , 20002 , Maldives

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Gunasekaran Raji,

Gunasekaran Raji

orcid.org/0009-0006-8262-2859

Department of Mechanical Engineering , Dr. Mahalingam College of Engineering and Technology , Pollachi, Coimbatore , India , mcet.in

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Kumaravel S.,

Kumaravel S.

orcid.org/0000-0003-4902-7864

Department of Mechanical Engineering , Kongunadu College of Engineering and Technology , Tiruchirappalli , Tamil Nadu , 621215 , India , kongunadu.ac.in

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Chandrasekaran M.,

Chandrasekaran M.

orcid.org/0000-0002-5163-2513

Department of Mechanical Engineering , Vels Institute of Science Technology and Advanced Studies , Chennai , India

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First published: 28 June 2025

https://doi.org/10.1155/er/2329925

Academic Editor: Sanjay Basumatary

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Abstract

The rising dependence on fossil fuels, depleting renewable resources, and increasing oil costs necessitate alternative energy sources. Biofuels, such as pumpkin seed biodiesel, offer environmentally friendly solutions with lower greenhouse gas emissions. This is the first study to integrate pumpkin seed oil–based biodiesel blended with cerium oxide (CeO₂) nanoparticles and machine learning (ML) models for optimizing diesel engine performance and emission characteristics. The study uses response surface methodology (RSM) and XGBoost ML to maximize engine performance and predict emissions of carbon monoxide (CO), hydrocarbon (HC), nitrogen oxide (NO_x), and smoke opacity. The optimal blend, achieving a brake thermal efficiency (BTE) of 24.99% with minimal emissions, was 18.32% biodiesel, 63.84% engine load (operating at 75% of maximum capacity), and 48.55 ppm CeO₂. This study demonstrates the effectiveness of combining RSM and ML, providing new insights into the sustainable optimization of biodiesel blends for compression ignition engines.

1. Introduction

The development of biodiesel blends for compression ignition engines has gained significant momentum due to the global drive toward sustainable and environmentally friendly fuels, aligning with key initiatives, such as the sustainable development goals (SDGs), particularly SDG 7 (affordable and clean energy), and the broader net-zero emissions targets set by governments worldwide [1–3]. Biodiesel, derived from vegetable oils and waste biomass, is a renewable diesel fuel that produces fewer carbon monoxide (CO), unburned hydrocarbons (HCs), and particulate matter (PM) emissions during combustion [4–7]. These benefits make biodiesel a promising alternative to traditional fossil fuels, contributing to a reduction in greenhouse gas emissions and aiding efforts to mitigate climate change [8–11]. However, biodiesel’s higher viscosity, lower volatility, and reduced heating value compared to conventional diesel fuel often lead to increased specific fuel consumption (SFC) and changes in combustion behavior [12–14]. The research community has focused on optimizing biodiesel blend ratios to address performance challenges, ensure efficient operation, and minimize emissions [15–17]. Pumpkin seed oil biodiesel, in particular, has emerged as a beneficial fuel candidate, offering advantageous properties, abundant availability, and substantial environmental benefits, contributing to the global transition toward sustainable energy sources [18–21]. Further development is required to enhance combustion efficiency and improve emission characteristics, which remain critical to meeting international climate goals [22–24].

Biodiesel’s performance can be significantly improved when nanoparticles are added as fuel additives [25, 26]. Cerium oxide (CeO₂) nanoparticles, in particular, have demonstrated superior catalytic properties that enhance combustion efficiency, reduce ignition delay, and lower harmful emissions [27, 28]. The oxygen-donating properties of CeO₂ nanoparticles improve both air-fuel mixing quality and oxidation rates to achieve higher brake thermal efficiency (BTE) and diminished nitrogen oxide (NO_x) and smoke emissions [29, 30]. Finding the perfect mix ratio between biodiesel and nanoparticle concentration is difficult as fastening the degradation of their components causes faulty measurements to create irregular combustion of engines [31]. Response surface methodology (RSM) is a widely used statistical technique for optimizing engine performance and emissions, including biodiesel blends. RSM helps explore the relationships between multiple input variables and output responses, offering efficient solutions to complex optimization problems. Recent studies have highlighted RSM’s effectiveness in optimizing biodiesel blends, engine parameters, and emission reductions, particularly when using alternative fuels like biodiesel blends and nanoparticles [32, 33]. RSM has also shown promising results in reducing pollutants and improving fuel efficiency in diesel engines fueled by biodiesel blends [34, 35]. RSM combined with machine learning (ML) models for engine performance prediction provides the solution for current challenges in biodiesel blend and nanoparticle analysis [36–38]. While XGBoost regression models coupled with other ML algorithms generate enhanced prediction accuracy by the detection of complicated nonlinear patterns, RSM serves for experimental design and parameter relationship discovery [39–41].

The research combines two performance optimization techniques through a CI engine analysis to reach maximum efficiency objectives with minimum emission results. This research aims to assess how CI engine performance and emissions respond when using blends of biodiesel from pumpkin seeds with CeO₂ nanoparticle additives. The research seeks to use RSM for blend ratio optimization and ML for accurate predictions of SFC, BTE, CO, HC, NO_x, and smoke emission values under various engine load and CeO₂ concentration conditions. Experimental validation of the optimized fuel blend is performed using RSM and ML prediction analysis. The research establishes optimal biodiesel blend ratios together with nanoparticle concentrations to advance fuel efficiency and decrease engine emissions in CI engines, resulting in sustainable fuel alternatives with improved performance. Summary of contemporary research on biodiesel blends with nanoparticle additives compares recent studies focusing on biodiesel blends with different nanoparticle additives, as listed in Table 1, including CeO₂ and cupric oxide, across various engine performance and emission characteristics. These studies provide a snapshot of the effectiveness of nanoparticle additives in improving fuel efficiency and reducing emissions in diesel engines.

Table 1. Summary of contemporary research on biodiesel blends with nanoparticle additives.

S. no.	Tested fuel	Nano additive used	Particle size	Engine performance and emission characteristics in percentage (%)							Reference paper
S. no.	Tested fuel	Nano additive used	Particle size	BTE	SFC	CO	CO₂	NO_x	HC	Smoke	Reference paper
1	Jatropha biodiesel	Cerium oxide	20–80 ppm	1.5↑	—	37↓	—	30↓	40↓	—	[42]
2	Jatropha biodiesel	Cerium oxide	40–80 ppm	6.2↑	4.5↓	29.7↓	—	33.6↓	18.75↓	—	[43]
3	Waste cooking oil	Cerium oxide	40–50 nm	—	4.51↓	38.8↓	—	18.9↓	71.4↓	—	[44]
4	Diesel	Cerium oxide	50 and 40 ppm	6↑	—	—	—	30↓	—	—	[45]
5	Diesel, ethanol, and castor oil	Cerium oxide	30 nm	7.9↓	8.7↓	31.8↓	—	54↓	—	—	[46]
6	Calophyllum inophyllum biodiesel	Cerium oxide	20–60 ppm	5.4↑	17.6↓	—	—	—	14.7↓	—	[47]
7	Ethanol and biodiesel	Cerium oxide	10–20 g	38↓	1.4↓	—	—	25↓	60↓	—	[48]
8	Waste cooking oil	Cerium oxide	30 nm	32↓	—	—	—	30↓	—	—	[49]
9	Waste cooking oil	Cerium oxide and aluminum oxide	50 and 100 ppm	11.39↑	13.74↑	15.06↓	—	18.29↓	—	—	[50]
10	Waste cooking oil	Cerium oxide	100 ppm	—	24↓	30↓	—	—	—	52↓	[51]
11	Waste plastic oil	Cerium oxide	25–50 ppm	3↑	—	—	—	—	—	—	[52]
12	Pumpkin seed biodiesel	Cupric oxide	25–50 ppm	—	—	11↓	—	—	—	—	[12]
13	Pumpkin and teak seed oil	Diethyl ether	5%	—	—	—	12.96↓	26.57↓	67.16↑	9.84↑	[53]

Previous studies have thoroughly documented the use of biodiesel blends, nanoparticle additives, and RSM for engine parameter optimization. However, scientists have yet to determine the optimal ratio of biodiesel blends and CeO₂ nanoparticles for achieving maximum efficiency and minimizing emissions in a CI engine. While prior research has focused on individual optimization techniques like RSM or ML, there is a gap in the combined application of these methods for enhanced accuracy and optimization. Research has also shown that NO_x emissions tend to increase when biodiesel blends are used, and more advanced techniques are needed to improve both engine performance and emission reductions simultaneously.

This study presents a novel approach by combining RSM and ML algorithms, specifically XGBoost, to systematically analyze biodiesel blend ratios, CeO₂ concentrations, and engine load conditions for optimization. Unlike traditional research, which typically uses linear models, this study incorporates both quadratic and linear models to improve the accuracy of predictions for engine performance parameters. The optimal blend of 18.32% biodiesel, 63.84% engine load, and 48.55 ppm CeO₂ yields better fuel economy and lower emissions compared to standard diesel–biodiesel mixes. The use of XGBoost regression as an ML technique offers superior predictive accuracy compared to RSM alone, resulting in a more reliable model for optimizing biodiesel blends. This is the first study to integrate pumpkin seed oil–based biodiesel blended with CeO₂ nanoparticles and ML models for optimizing diesel engine performance and emission characteristics. By combining RSM with XGBoost ML, this work presents a novel approach to analyzing and optimizing biodiesel blends and nanoparticle concentrations, focusing on enhancing engine efficiency and reducing emissions. This unique methodology contributes significantly to the field by offering accurate predictions for complex engine performance and emissions parameters, such as CO, HC, NO_x, and smoke opacity, making a substantial advancement toward sustainable fuel technologies.

2. Materials and Methods

2.1. Pumpkin Seed Biodiesel (Pumpkin Seed Oil Methyl Ester [PSOME])

Pumpkins rank among Cucurbitaceae plants and offer healing plus nutritious traits to human health. Pepita seeds contain about half an oil that is highly useful for biodiesel production because they contain linoleic acid and vitamin E [54]. The local market provided pumpkin seed oil that was processed through filtration to remove solid impurities. Temperature at 60°C removed water content so that the substance could proceed with the transesterification treatment [55]. The low acid content of 0.40 mg KOH/g in the oil required a base-catalyzed transesterification process as per ASTM D6751 standards (Figure 1). The filtered oil received sodium methoxide treatment when sodium hydroxide was mixed with methanol to form the sodium methoxide solution [56].

Details are in the caption following the image — **Figure 1**
Open in figure viewer PowerPoint

Production of pumpkin seed biodiesel.

The stirring mixture heated between 55 and 66°C remained active for 1 h. The biodiesel product known as PSOME rose to the top after 24 h of settling in a separation funnel. The biodiesel underwent several water-washing steps to purify itself at a temperature of 65°C. This study filtered the product to achieve its highest possible quality. Pumpkin seed biodiesel (B100) has its physical and chemical attributes measured and compared to conventional diesel through the standard ASTM standards. Table 2 provides a comprehensive inventory of the properties of Pumpkin seed biodiesel [57].

Table 2. Properties of pumpkin seed biodiesel (PSOME).

Property	Diesel	Pumpkin seed biodiesel (B100)	ASTM standards
Density (kg/m³)	823.1	901.2	D 1298
Kinematic viscosity at 40°C (CST)	3.9	5.8	D 445
Flashpoint (°C)	57	174	D 93
Gross calorific value (MJ/kg)	43.4	40.3	D 240
Fire point (°C)	69	190.2	D 93

The product needs fewer safety measures when you store and handle it because of its high ignition resistance. Higher oil viscosity affects isomethane fuel atomization quality and raises brake-SFC (BSFC), which is in line with biodiesel research.

2.2. CeO₂ Additive

To improve combustion efficiency and lower pollutants, the biodiesel mixes included CeO₂. Table 3 lists the CeO₂ nanoparticles’ physicochemical characteristics [58].

Table 3. Properties of cerium oxide (CeO₂).

Properties	Values
Molecular formula	CeO₂
Molar mass	172.115 g (mol)
Appearance	White/pale yellow solid, slightly hygroscopic
Density	7.215 g/cm³
Melting point	2400°C
Boiling point	3500°C
Solubility in water	Insoluble
Particle size	<25 nm
Crystal structure	Cubic (fluorite)

2.3. Test Fuel Samples

The sample size for this study was determined to balance statistical power with practical considerations, such as available resources and the complexity of the experimental setup. To detect meaningful differences in engine performance and emission characteristics, four biodiesel blends were evaluated, mixed with pure diesel at CeO₂ nanoparticle concentrations ranging from 35 to 55 ppm. The tested biodiesel blends included B10 (10% PSOME + 90% diesel), B20 (20% PSOME + 80% diesel), and B30 (30% PSOME + 70% diesel), along with pure diesel as a baseline. These blends were carefully tested to assess their influence on combustion characteristics, fuel efficiency, and pollutant emissions such as CO, HC, NO_x, and smoke opacity, highlighting the potential of PSOME as a sustainable fuel alternative.

To ensure statistical reliability, the study employed an L27 orthogonal array design for RSM, involving 27 experimental runs [59]. This design was chosen to minimize the number of experiments while exploring the main effects and interactions of multiple variables, such as biodiesel blend ratios, nanoparticle concentrations, and engine load conditions. The 27 experimental runs (with triplicates) were determined using the Design Expert software v13 to optimize the experimental conditions efficiently [60, 61]. The use of RSM in this software allowed for a compelling exploration of the experimental space, ensuring robust and statistically significant results. This sample size aligns with prior studies, including Singh et al. [62] and Bhan et al. [50], demonstrating its adequacy for optimizing biodiesel blends and achieving meaningful findings. The experimental runs were selected based on the design of experiment (DOE) approach in Design Expert software v13, using an RSM user-defined model. This methodology helped systematically analyze the interactions between biodiesel blend ratios, CeO₂ nanoparticle concentrations, and engine load conditions, ensuring the results’ reliability and reproducibility.

2.4. Experimental Setup and Procedure

The study utilized a single cylinder taken from a four-stroke DI diesel engine, together with an eddy current dynamometer for engine load control (Figure 2). The sensing equipment underwent improved technology updates for accurate measurement during the experimental procedures. The instrument used a piezoelectric pressure sensor to track both internal engine combustion and fuel flow through the delivery system. The system enabled precise measurement of pressure data correlated with crankshaft position information.

The test engine relied on a combination of a mass airflow sensor for intake air detection and a strain sensor for engine operation checks under load conditions. The tested fuel consumption resulted from the calculations performed by the fuel flow meter. The study utilized an nondispersive infrared (NDIR) technologically equipped AVL 444 DI gas analyzer to test exhaust emissions of CO, HC, and NOx. The primary purpose of the AVL 437C smoke meter is to serve during smoke testing operations. The engine testing framework functioned with data acquisition hardware for functional monitoring of combustion feedback, which verified biodiesel mixture operational precision. The table below lists the test engine specifications (Table 4).

Table 4. Test engine specifications.

Parameters	Specification
Engine type	Four stroke, single cylinder water-cooled
Cylinder bore	87.5 mm
Stroke length	110 mm
Power output	5.2 kW
Displacement	661 cc
Speed	1500 rpm
Compression ratio	17.5:1
Gas analyzer	AVL DI 444N
Smoke meter	AVL 437C
Dynamometer	Eddy current, water cooled
Software used	Engine soft

Testing took place while the engine ran steadily at 50%, 75%, and 100% load levels. The system took readings after the engine established its stable mode of operation. The research conducted a structured analysis to show how mixing different biodiesel blends and CeO₂ nanoparticles affects how well an engine runs and burns fuel while controlling exhaust emissions.

2.5. Experimental Uncertainty Analysis

Experimental uncertainty analysis is essential for understanding the variability in the measurements obtained during experimentation. This variability can arise due to factors, such as environmental conditions, equipment used, instrument calibration, and observation precision. The propagation of error method, as outlined by Holman [63], was used to quantify the total uncertainty. The total uncertainty was calculated using the root-sum-square method, which involves summing the squares of individual uncertainties.

The total uncertainty is computed as in Equation (1):

(1)

This total uncertainty value of ± 2.27% represents the aggregate uncertainty in the entire measurement process.

This uncertainty analysis (Table 5) provides a comprehensive evaluation of the potential errors in the measurements. The table outlines the ranges, measuring techniques, accuracy, and error margins for each parameter involved in the experimental process.

Table 5. Experimental uncertainty.

Parameters	Range	Measuring Technique	Accuracy	Errors (±)
Speed	0–10,000 rpm	Principle of magnetic pickup	±10 rpm	±0.1
Measurement of fuel flow	0–500 mm	Volume-based measurement	±0.1 cm³	±1
Load	0–50 kg	Strain gauge–based load cell	±10 N	±0.2
Engine crank angle encoder	—	Principle of magnetic pickup	±1°	±0.2
Temperature	0–1200°C	Temperature sensing thermocouple	±1°C	±0.15
Time	—	Stopwatch (manual)	±0.1 s	±0.2
Pressure	0–5000 psi	Principle of magnetic pickup	±0.1 kg	±0.1
Deflection of manometer	0–250 mm	Balancing the liquid column	±1 mm	±1
NO	0–5000 ppm	Nondispersive infrared (NDIR) method	±12 ppm	±0.2
CO	0%–10% vol	Nondispersive infrared (NDIR) method	±0.02% volume	±0.2
Smoke	0–100 HSU	Opacimeter	±1 HSU	±1
HC	0–20,000 ppm	Nondispersive infrared (NDIR) method	±10 ppm	±0.1

2.6. DOE and RSM

RSM within Design Expert v13 software analyzed how biodiesel blend ratio, engine load, and CeO₂ nanoparticle concentration affect engine performance, together with emissions [64]. An L27 orthogonal array design structure created an efficient method to evaluate variable interrelationships while requiring a minimum number of experimental runs. Real statistics through RSM enabled researchers to produce quadratic regression equations that described engine performance indicators, including SFC, BTE, CO, HC, and NO_x emissions. At the same time, smoke opacity followed a linear equation model. The statistical testing using analysis of variance (ANOVA) confirmed both statistical significance and predictive accuracy of model adequacy. The response surface, along with contour plots, delivered an enhanced understanding of how biodiesel blends operate jointly with nanoparticle concentrations in affecting combustion characteristics. The optimization through RSM determined the best operating parameters to enhance BTE and decrease SFC alongside emissions reductions to increase biodiesel-fueled CI engine efficiency.

2.7. ML–Based Prediction Models

ML was employed in this study to enhance the predictive accuracy of engine performance and emission characteristics when using biodiesel blends with nanoparticle additives [65]. Traditional methods, such as RSM, are highly effective for optimization; however, they often struggle to capture nonlinear interactions between input variables and complex output responses. ML, specifically XGBoost, was integrated to address these limitations by providing a more robust framework for modeling complex relationships in the data [66, 67]. The use of ML allows for more precise predictions of difficult-to-predict emission parameters, such as NO_x, HC, CO, and smoke opacity, which are challenging to capture using linear models. Furthermore, ML models can identify patterns within large datasets that might not be apparent with conventional statistical techniques, thereby improving the overall optimization process for engine performance and emission reductions. Hyperparameter tuning with key parameters like learning rate, tree depth, and number of estimators was performed using grid search cross validation to obtain the maximum R² score [68]. Experimental data and RSM predictions validated the trained ML model to better capture the nonlinear relationship between input parameters and engine responses. Finally, actual value vs. predicted plot, training vs. validation loss curves, and density distribution plots were created to validate the model’s performance further. By integrating ML and RSM, this study takes a comprehensive approach to optimize biodiesel combustion performance with associated emission reductions, bridging the gap between experimental research and predictive analytics.

3. Results and Discussions

3.1. Fourier Transform Infrared (FTIR) Analysis of CeO₂ Nanoparticles

FTIR spectroscopy analysis of CeO₂ powder generates (Figure 3) essential information about sample functional groups and chemical bonds. Multiple absorption peaks show up across the transmittance spectrum to reveal different sample vibrational modes. Organic matter on the surface and remaining HC molecules can be seen through the broad characteristic peak at 2927 cm⁻¹. At 2162 cm⁻¹, the spectroscopic spectrum shows a peak that suggests small amounts of carbonaceous material exist in the sample. Because CeO₂ reacts with CO₂ in the air, the carbonyl (C═O) and carboxylate groups show up at 1750 cm⁻¹ and 1533 cm⁻¹, respectively. The peaks at 1406 and 1216 cm⁻¹ indicate C─O stretching vibrations on the surface that might stem from hydroxylated areas. The stretch at 1058 cm⁻¹ and 815 cm^–3 shows metal–oxygen bonds that show Ce─O bonds taking part in the CeO₂ framework. There is a cubic fluorite CeO₂, as demonstrated by the FTIR peaks at 711 and 650 cm⁻¹, which are typical Ce─O stretching signals.

Strong peak intensities confirm how CeO₂ maintains a well-defined crystal structure, together with a few structural imperfections. The FTIR analysis clearly shows that the Ce─O bonds are the most essential spectral feature. This indicates that the CeO₂ nanoparticles are very pure and have their structures intact. The fact that there are minor peaks connected to surface hydroxylation and organic residues shows that the nanoparticles and their surroundings are in contact with each other. Characterization shows that CeO₂ powder is chemically stable and can be used in fuels and catalysis to improve the efficiency of biodiesel blend combustion.

3.2. DOEs and RSM

Design Expert v13 software was used to create an experimental design based on RSM to investigate how biodiesel blend percentages (B10, B20, B30), engine loads (50%, 75%, and 100%), and CeO₂ nanoparticle concentrations (35, 45, and 55 ppm) affect the performance and emissions of a single-cylinder, four-stroke Kirloskar TV1 diesel engine (5.2 kW, 1500 rpm). An L27 experimental design was implemented to analyze the interactive effects of these variables efficiently. An eddy-current dynamometer was used to connect the engine and test it under controlled load variations. The next part of the effort was the DOEs, which allowed for the formulation of a robust statistical model that would be able to thoroughly analyze the effect of biodiesel blend and nanoparticle doping on SFC, BTE, CO, HC, NO_x, and smoke opacity. In Table 6, the experimental values of these responses are summarized.

Table 6. Experiment result.

Exp. no.	Biodiesel blend	Load (%)	CeO₂ (ppm)	SFC (kg/kWh)	BTE (%)	CO (% of volume)	HC (ppm)	NO_x (ppm)	Smoke (HSU)
1	10	50	35	0.38	19	0.029	45	471	19
2	10	50	45	0.36	21	0.028	42	450	21
3	10	50	55	0.37	22	0.027	39	426	24
4	10	75	35	0.34	23	0.026	43	642	28
5	10	75	45	0.33	24	0.024	40	625	32
6	10	75	55	0.32	25	0.023	40	611	37
7	10	100	35	0.35	26	0.034	55	733	38
8	10	100	45	0.34	28	0.032	51	720	41
9	10	100	55	0.36	28	0.031	52	708	43
10	20	50	35	0.36	21	0.028	43	488	19
11	20	50	45	0.34	22	0.026	40	470	23
12	20	50	55	0.35	23	0.027	42	441	28
13	20	75	35	0.34	24	0.025	41	645	32
14	20	75	45	0.31	26	0.023	39	638	34
15	20	75	55	0.33	28	0.024	42	627	36
16	20	100	35	0.35	27	0.035	53	773	40
17	20	100	45	0.33	29	0.033	52	752	43
18	20	100	55	0.34	29	0.033	54	740	47
19	30	50	35	0.37	19	0.027	41	536	24
20	30	50	45	0.35	21	0.025	39	520	26
21	30	50	55	0.36	23	0.026	40	512	29
22	30	75	35	0.35	23	0.024	41	694	34
23	30	75	45	0.33	25	0.022	38	680	37
24	30	75	55	0.34	26	0.023	39	672	39
25	30	100	35	0.38	25	0.036	55	795	43
26	30	100	45	0.36	28	0.034	53	786	45
27	30	100	55	0.37	28	0.035	54	761	49

3.3. RSM Modeling

RSM regression models were employed to optimize biodiesel blend ratios, engine load, and the concentration of CeO₂ nanoparticles, aiming to maximize BTE and minimize SFC, CO, HC, NO_x, and smoke opacity. The models for SFC, BTE, CO, HC, and NO_x were quadratic, while the smoke opacity model was linear, leading to better results, and the equations are listed below (2–7). B20 blends with 45 ppm CeO₂ nanoparticles, tested at 75% engine load, are optimized for the best balance between fuel consumption and emissions. A reduction in SFC indicates that the presence of CeO₂ nanoparticles has enhanced combustion efficiency. Oxygen in biodiesel also promotes more complete combustion, which reduces CO and HC emissions. Using thermal barrier coating as a temperature control method reduced the increase in NO_x emissions, a regular occurrence with biodiesel. The optimized parameters yielded lower smoke opacity, which suggests that the atomization and combustion are more efficient. The ANOVA results found that the model is statistically significant and reliable in predicting and optimizing diesel engine performance and emissions with pumpkin seed biodiesel and nanoparticle doping.

(2)

(3)

(4)

(5)

(6)

(7)

3.3.1. ANOVA

3.3.1.1. Quadratic Models (SFC, BTE, CO, HC, NO_x)

Table 7 presents the ANOVA results, and it is seen that the quadratic models for SFC, BTE, CO, HC, and NO_x are statistically significant for engine performance and emissions predictions. All models have R² values above 0.92, indicating a strong correlation between experimental and predicted values. The R² values of the adjusted and predicted models also prove the reliability of the models. BTE (78%), CO (40%), HC (66%), and NO_x (92%) are most affected by the engine load (B), and better fuel combustion at increased engine load results in less emissions [69]. The concentration of CeO₂ nanoparticles mainly influences the BTE (15%) effects. However, emissions do not change significantly, indicating that while they improve combustion, they do not directly reduce emissions. It contributes 47% and 17% for the quadratic terms (B² and A²). It is found that fuel consumption is nonlinear with respect to load and biodiesel blend percentage.

Table 7. ANOVA for quadratic models.

Source	SFC			BTE			CO			HC			NO_x
Source	Sum of squares	F-value	Contribution (%)	Sum of squares	F-value	Contribution (%)	Sum of squares	F-value	Contribution (%)	Sum of squares	F-value	Contribution (%)	Sum of Squares	F-value	Contribution (%)
Model	0.0076	24.64	—	227.44	109.75	—	0.0005	176	—	981.97	103.74	—	3.64E + 05	555.2	—
A-biodiesel blend	0.0002	5.87	3	0.3472	1.51	0	2.22E-07	0.7096	0	2.72	2.59	0	18,050	247.64	5
B-Load	0.0002	5.87	3	177.35	770.22	78	0.0002	638.61	40	648	616.12	66	3.35E + 05	4590.06	92
C-CeO₂	0.0004	10.43	5	34.72	150.8	15	0	39.91	0	12.5	11.89	1	4324.5	59.33	1
AB	0.0007	19.8	9	0.5208	2.26	0	0	52.15	0	8.33	7.92	1	133.33	1.83	0
AC	8.33E-06	0.2444	0	0.75	3.26	0	2.08E-06	6.65	0	5.33	5.07	1	36.75	0.5042	0
BC	0	0.9776	0	0.3333	1.45	0	3.33E-07	1.06	0	2.08	1.98	0	48	0.6585	0
A²	0.0013	36.72	17	10.23	44.42	4	7.41E-08	0.2365	0	0.463	0.4402	0	696.96	9.56	0
B²	0.0036	105.15	47	1.34	5.81	1	0.0003	823.33	60	284.74	270.73	29	6359.19	87.25	2
C²	0.0013	36.72	17	1.85	8.04	1	6.69E-06	21.35	1	17.8	16.92	2	0.9074	0.0124	0
Residual	0.0006	—	—	3.91	—	—	5.32E-06	—	—	17.88	—	—	1239.1	—	—
Cor total	0.0081	—	—	231.35	—	—	0.0005	—	—	999.85	—	—	3.66E + 05	—	—
R²	0.9288	—	—	R²	0.9831	—	R²	0.9894	—	R²	0.9821	—	R²	0.9966	—
Adjusted R²	0.8911	—	—	Adjusted R²	0.9741	—	Adjusted R²	0.9838	—	Adjusted R²	0.9727	—	Adjusted R²	0.9948	—
Predicted R²	0.8164	—	—	Predicted R²	0.961	—	Predicted R²	0.9699	—	Predicted R²	0.9502	—	Predicted R²	0.9907	—

The statistical significance of the SFC model’s F-value of 24.64 suggests that the model is robust. Biodiesel blend (3%), load (3%), and CeO₂ concentration (5%) have a moderate impact, while the quadratic terms B² and C² significantly influence the outcome at 47% and 17%, respectively. The reliability of BTE, with R² = 0.9831, indicates that increasing load and CeO₂ nanoparticles strongly improve thermal efficiency. The F-values for CO (176) and HC (103.74) indicate that load is the main factor affecting emissions in both models. The NOx model results (R² = 0.9966) show that load is the main factor influencing emissions, responsible for 92%, while the biofuel blend accounts for 5%. This agrees with the trend that biodiesel causes increased NO_x emissions owing to its increased oxygen content. The low residual values in all models suggest that the regression equations for predicting optimal engine conditions with biodiesel are reliable.

3.3.2. ANOVA for Linear Smoke Model

The ANOVA results in Table 8 show that the Smoke Opacity model’s regression equation is statistically significant, with a high R² value of 0.9893 and an adjusted R² of 0.9879, indicating a strong correlation between experimental and predicted values. The F-value of 709.6 and the p-value (<0.0001) validate that the model is highly significant. Engine load (B) is the most critical factor affecting smoke formation, accounting for 86%. CeO₂ nanoparticle concentration (C) contributes 8%, while biodiesel blend (A) accounts for 5%. Higher engine loads result in incomplete combustion at elevated fuel flow rates, which increases smoke emissions. Adding CeO₂ nanoparticles, which help burn fuel more completely, can improve combustion efficiency and reduce smoke emissions. The low residual value (21.52) and high predicted R² (0.9854) indicate that the model is reliable and well-fitted for predicting smoke opacity trends with various biodiesel blends and nanoparticle concentrations in a compression ignition engine.

Table 8. ANOVA for smoke model.

Source	Sum of squares	df	Mean square	F-value	p-Value	Significance status	Contribution (%)
Model	1991.67	3	663.89	709.6	<0.0001	Significant	—
A-biodiesel blend	102.72	1	102.72	109.79	<0.0001	Significant	5
B-Load	1720.89	1	1720.89	1839.37	<0.0001	Significant	86
C-CeO₂	168.06	1	168.06	179.63	<0.0001	Significant	8
Residual	21.52	23	0.9356	—	—	—	—
Cor total	2013.19	26	—	—	—	—	—
R²	0.9893	—	—	—	—	—	—
Adjusted R²	0.9879	—	—	—	—	—	—
Predicted R²	0.9854	—	—	—	—	—	—

3.3.3. 3D Surface Plot and Residual Analysis of Interaction Between Input and Outputs

The 3D response surface plots illustrate the effect of biodiesel blend percentage, engine load, and CeO₂ nanoparticle concentration on SFC. In Figure 4a, SFC is shown to decrease with an increase in engine load, as higher loads improve combustion efficiency, leading to better fuel utilization. However, at higher biodiesel blend ratios, SFC increases slightly due to the higher viscosity and lower calorific value of biodiesel compared to diesel. Figure 4b examines the interaction between biodiesel blend and CeO₂ concentration, showing a reduction in SFC with increasing CeO₂ nanoparticle concentration, as CeO₂ acts as a combustion catalyst, improving fuel oxidation and reducing fuel wastage. Figure 4c highlights the combined influence of engine load and CeO₂ concentration, demonstrating that at higher load conditions, the catalytic action of CeO₂ leads to enhanced combustion, further lowering SFC.

The residual plot, Figure 4d, evaluates the adequacy of the developed quadratic model. The externally studentized residuals are scattered within the acceptable limits (± 3.72), indicating no significant outliers and confirming that the model assumptions are valid. The random distribution of residuals across runs suggests that the model does not exhibit any systematic bias, ensuring its reliability for predicting SFC. These findings validate that RSM effectively captures the influence of biodiesel blends and CeO₂ nanoparticles on engine efficiency, guiding the selection of optimal fuel formulations for enhanced performance.

The 3D response surface plots in Figure 5 illustrate the influence of biodiesel blend, engine load, and CeO₂ nanoparticle concentration on BTE. In Figure 5a, BTE increases with increasing engine load, as higher loads improve combustion due to elevated in-cylinder temperatures and better fuel-air mixing. However, excessive biodiesel blends reduce BTE due to their higher viscosity and lower calorific value, leading to incomplete combustion.

Figure 5b highlights the interaction between biodiesel blend and CeO₂ concentration, showing that moderate CeO₂ concentrations (45–50 ppm) enhance combustion efficiency by acting as a catalyst, resulting in better oxidation and reduced heat losses. At higher CeO₂ concentrations (55 ppm), BTE slightly drops due to nanoparticle agglomeration, which can hinder uniform fuel distribution. Figure 5c examines the interaction between load and CeO₂ concentration, demonstrating that at moderate load (75%) and optimal CeO₂ concentration (50 ppm), maximum BTE is achieved, ensuring efficient fuel combustion with minimal energy losses. The residual plot Figure 5d validates the model’s accuracy by analyzing the externally studentized residuals. The random scatter within the control limits (± 3.72) confirms that there are no systematic biases or outliers, ensuring the model’s reliability. The uniform distribution of residuals across the experimental runs further strengthens the validity of the quadratic regression model in predicting BTE.

The 3D response surface plots in Figure 6 illustrate the impact of biodiesel blend, engine load, and CeO₂ nanoparticle concentration on CO emissions. Figure 6a shows that CO emissions decrease as engine load increases, particularly at moderate biodiesel blends (B20). This is because higher loads improve combustion efficiency, reducing incomplete oxidation of fuel. However, excessive loads may lead to fuel-rich zones, slightly increasing CO emissions. Figure 6b highlights the interaction between biodiesel blend and CeO₂ concentration, showing that increasing CeO₂ concentration (up to 50 ppm) significantly reduces CO emissions due to its catalytic effect, which enhances oxidation reactions and promotes complete combustion. Figure 6c presents the impact of load and CeO₂ concentration, confirming that at moderate load (75%) and optimal CeO₂ concentration (50 ppm), CO emissions reach their lowest value (~0.0229%). In contrast, extreme loads and higher CeO₂ levels show minor variations due to possible over-oxidation effects. The residual plot (Figure 6d) assesses the statistical reliability of the CO model by plotting externally studentized residuals against the experimental runs. The randomly scattered distribution of residuals within the control limits (± 3.72) indicates that there are no systematic errors or significant deviations in the model’s predictions. The absence of strong trends or clustering suggests that the quadratic model effectively captures the relationship between biodiesel blend, CeO₂ concentration, and load on CO emissions. Additionally, the even spread of residuals across all runs ensures that the model does not suffer from heteroscedasticity or bias, confirming its robustness in predicting CO emissions with high accuracy.

The HC model (Figure 7) presents the influence of biodiesel blend (A), load (B), and CeO₂ concentration (C) on HC emissions in a CI engine. Figure 7a illustrates the interaction between biodiesel blend and load on HC emissions. At higher loads and lower biodiesel blends (B10–B20), HC emissions remain minimal due to improved combustion efficiency. However, at lower loads and higher blends (B30), HC emissions rise due to incomplete combustion caused by the higher viscosity and lower volatility of biodiesel. Figure 7b shows the effect of biodiesel blend and CeO₂ nanoparticles on HC emissions. Increasing CeO₂ concentration to 45–50 ppm significantly reduces HC emissions across all biodiesel blends, indicating enhanced catalytic oxidation, which improves combustion efficiency. However, at excessive CeO₂ levels (>50 ppm), the reduction rate slows down, possibly due to nanoparticle agglomeration affecting fuel-air mixing. Figure 7c examines the combined effect of load and CeO₂ nanoparticles on HC emissions. At lower loads, the addition of CeO₂ reduces HC emissions effectively by facilitating better combustion. At higher loads (100%), HC emissions slightly increase due to higher fuel consumption, but CeO₂ still mitigates incomplete combustion. Figure 7d ensures the validity of the regression model. The residuals are randomly scattered around zero, confirming that the model has no significant bias. The majority of the data points lie within the control limits, indicating that the developed HC model provides reliable predictions with minimal error.

The NO_x model (Figure 8) demonstrates the influence of biodiesel blend (A), load (B), and CeO₂ nanoparticle concentration (C) on NO_x emissions in a CI engine. Figure 8a depicts the effect of biodiesel blend and load on NO_x emissions. Higher loads (90%–100%) and increased biodiesel blending (B30) result in elevated NO_x emissions due to the oxygenated nature of biodiesel, leading to higher combustion temperatures. At moderate loads (75%) and B20 blends, NO_x emissions are lower due to an optimal balance between oxygen content and combustion temperature. Figure 8b illustrates the interaction between biodiesel blend and CeO₂ nanoparticles on NO_x emissions. At higher CeO₂ concentrations (45–55 ppm), NO_x emissions remain relatively stable due to the nanoparticles’ catalytic effect, which enhances combustion efficiency without significantly raising temperatures. However, at lower CeO₂ concentrations (35 ppm), NO_x levels increase due to incomplete combustion. Figure 8c shows the combined impact of engine load and CeO₂ concentration on NO_x emissions. At higher loads (90%–100%), NO_x emissions rise due to the higher in-cylinder temperature, despite the presence of CeO₂ nanoparticles. The lowest NO_x levels are observed at moderate loads (75%) and 50 ppm CeO₂, as the nanoparticles aid in improving combustion efficiency while controlling peak temperatures. Figure 8d confirms the statistical validity of the NO_x model. The residuals are randomly scattered, indicating the absence of systematic errors. Most data points lie within the control limits, validating the accuracy of the NO_x prediction model with minimal deviations.

The Smoke model (Figure 9a,b) illustrates the relationship between biodiesel blend, load, and CeO₂ nanoparticle concentration on smoke emissions in a CI engine. Higher biodiesel blends (B30) and increased engine load (100%) result in higher smoke opacity due to incomplete combustion, whereas B20 at 75% load shows the lowest smoke emissions (30.05 haze smoke units [HSUs]), benefiting from improved combustion efficiency. CeO₂ nanoparticles further reduce smoke emissions by promoting better oxidation, with the optimal reduction observed at B20 with 50 ppm CeO₂. The actual vs. predicted plot (Figure 9c) confirms strong agreement between experimental and predicted values, while the residuals plot (Figure 9d) indicates that the model maintains high accuracy with minimal deviation.

3.3.4. Input Parameter Optimization

The optimization results (Figure 10) indicate that the best combination of input parameters for achieving optimal engine performance and emission control is a biodiesel blend of 18.32%, an engine load of 63.84%, and a CeO₂ nanoparticle concentration of 48.55 ppm. The desirability value of 0.959 confirms that this combination provides a well-balanced trade-off between fuel efficiency and emission reduction. The optimized SFC is 0.3197 kg/kWh, indicating improved combustion efficiency facilitated by CeO₂ nanoparticles, which enhance oxidation and promote better fuel utilization. Additionally, the BTE reaches 24.99%, demonstrating an effective energy extraction from the fuel, primarily due to the catalytic effect of CeO₂ and the optimal biodiesel blend ratio. The CO emissions are significantly reduced to 0.0229%, confirming that the improved combustion process results in less incomplete oxidation of fuel. Similarly, HC emissions are minimized to 38 ppm, attributed to enhanced air-fuel mixing and oxidation reactions promoted by CeO₂ nanoparticles.

The NO_x emissions are observed at 562.74 ppm, which is relatively high due to increased combustion temperatures and the oxygen-enriched nature of biodiesel, but still manageable with emission reduction techniques. Furthermore, smoke opacity is significantly reduced to 30.06 HSU, indicating better combustion with fewer unburned carbon particles. The results from optimization tests demonstrate that thermal efficiency and emissions reduction, alongside reduced fuel consumption, can be achieved when using an 18.32% biodiesel blend under moderate engine load and CeO₂ nanoparticle doping. The control of NO_x emissions is possible through exhaust gas recirculation (EGR) techniques and alternative after-treatment systems. Experimental findings show the potential of using biodiesel-CeO₂ blends for CI engines since they offer both high efficiency and environmental friendliness in fuel solutions.

3.4. The Procedure of XGBoost Regressor for ML Prediction

Step 1. The initial phase involves loading the dataset and identifying pertinent input features. Thus, in this case, the chosen inputs are biodiesel blend (A), load (B), and CeO₂ nanoparticle concentration (C). Emissions like CO, SFC, BTE, HC, NOx, and smoke are the target variables for prediction. Finally, we standardized the dataset by using a StandardScaler, which ensures that all the features have a mean of 0 and a standard deviation of 1 to improve the model’s convergence.

Step 2. Split the dataset: Before testing the model, the dataset is split into subsets, with 80% for training and 20% for testing. At this point, train_test_split is used to do so. This helps the model avoid overfitting to the training data and ensures it validates on unseen data.

Step 3. GridSearchCV: Hyperparameter tuning was performed using GridSearchCV to optimize the XGBoost regressor model and enhance its predictive performance. The tuning aimed at identifying the best hyperparameter combination to minimize mean squared error (MSE) and maximize the R² score. In this study, the hyperparameter n_estimators (number of trees) was set between 500 and 1000 to ensure complexity without overfitting. A trial-and-error approach ranging from 0.25 to 1.0 was adopted to lessen the step size, improving model precision while balancing training speed. The maximum depth varied from 4 to 9, striking a balance between complexity and effectively capturing nonlinear relationships. This range was thoughtfully selected to optimize the model’s performance. The subsample fraction (0.25–0.65) decreased the number of samples used by the tree to enhance variance, though this came at the cost of some accuracy. To avoid redundancy, colsample_bytree was adjusted between 0.25 and 0.65 to optimize feature usage per tree. With these optimized hyperparameters, the model was trained with computational efficiency to achieve enhanced generalization capability. Table 9 shows the optimal combination of parameters, based on the lowest MSE and highest R² score, resulting in a reliable model for predicting engine performance and emissions.

Table 9. Result of grid search.

Hyperparameters	ML output models
Hyperparameters	SFC	BTE	CO	HC	NO_x	Smoke
n_estimators	700	700	600	1000	1000	1000
Learning_rate	0.5	0.2	0.65	0.95	0.95	0.95
Max_depth	8	8	5	8	8	8
Subsample	0.25	0.4	0.35	0.4	0.6	0.65
Colsample_bytree	0.25	0.4	0.35	0.4	0.6	0.65

Step 4. After selecting the best hyperparameters through Grid Search Cross Validation, the XGBoost regressor is retrained to enhance prediction accuracy. RMSE is the key metric used to guide training, monitor model performance, and improve predictions. The model’s learning process effectively utilizes both training and testing data, preventing any risk of overfitting. Incorporating an evaluation set that encompasses both training and testing datasets ensures comprehensive training of the model. The model’s performance is carefully monitored during training over several epochs to identify when it fits optimally. The final evaluation metrics, including RMSE, MAE, and R² Score, are listed in Table 10, providing a detailed assessment of the model’s predictive capability across different engine performance and emission parameters.

Table 10. Model evaluation parameters after training.

Output models	R²	RMSE	MAE
SFC	0.934	0.0046	0.0032
BTE	0.9935	0.2405	0.2016
CO	0.8746	0.001	0.0007
HC	0.9682	0.7406	0.5731
NO_x	0.9946	8.0317	6.0402
Smoke	0.9854	1.0414	0.8305

Step 5: After the XGBoost Regressor model finishes its training process, it proceeds to make predictions for the output parameter through the test data. The model reliability is measured through various performance metrics during prediction accuracy assessments. The prediction error assessment uses MAE to find the average absolute deviation between measured data and simulated values. The amount of prediction error can be measured through RMSE, and better model performance is achieved when RMSE values remain low. The prediction accuracy assessment of the model depends heavily on R² Score metrics that determine how well the model interprets data variations, along with its significance for data interpretation. These evaluation metrics jointly confirm that the predictive model effectively duplicates complex relationships involved in biodiesel blend, load, and CeO₂ nanoparticle concentration interactions with engine emission and performance parameters to ensure accurate and dependable predictions.

Step 6: Visualization of prediction performance, three key plots were made to investigate the engine performance, emission prediction accuracy, and effectiveness of the XGBoost regressor model. The actual vs. predicted scatter plot shows the relation between the predicted and actual value and a regression line that represents the closeness of the model’s prediction and actual data. If a strong linear correlation is expressed, then a well-trained model with minimum prediction error is produced. RMSE trends over training epochs are visualized by the training vs. validation loss curve so that a model converges properly without overfitting. RMSE trend that decreases in both training and validation indicates the model is learning effectively, whereas divergence can be very significant and imply overfitting or underfitting. The density plot at last compares the distribution of the actual and predicted values to see how well the model generalizes new data. The closer the fit of the expected distribution to the exact values, the more it confirms that the model has accurately recorded how the underlying patterns are present in the data. Together, these visualizations provide confidence in the use of the XGBoost model to estimate SFC, BTE, CO, HC, NO_x, and smoke emission rates as a function of biodiesel blend, load, and CeO₂ concentration. The predicted performance of the model is optimized, resulting in minimum prediction errors consistent with high R² scores, and therefore, the model is a robust choice for diesel engine performance modeling.

3.4.1. Prediction Performance of ML Models

Figure 11 displays the training and validation loss trends for each output model across training epochs. These plots give clues on how the model learns, converges, and how generalizable it is. The RMSEs of both training and validation are decreasing smoothly in the SFC plot as the number of epochs increases. The loss ceases to provide meaningful insights around 350 epochs, suggesting that while the model understands the relationship between the input variables and SFC, it perceives this connection as overly generalized. RMSE decreases very quickly in the first 100 epochs and oscillates after that, which indicates that learning is effective. Good generalization is signaled by close adherence of the validation RMSE to that of the training RMSE. Following the initial decline, the RMSE demonstrates notable variability in the predictions for CO and HC. The HC model achieves stable RMSE values of about 0.0015 after 500 epochs. In contrast, the HC model shows more significant fluctuations, indicating more complex relationships between input parameters and HC emissions that require further fine-tuning.

The study finds a notable drop in loss in the NO_x model within the first 200 epochs, when it stabilizes at regularly low values paired with a low RMSE. This model has impressive foresight. The Smoke model also shows a significant drop in the first 100 epochs, then a point of equilibrium. All these patterns confirm the assumption that the XGBoost model makes efficient use of the available data. For every model, the slight variation in RMSE between training and validation reveals no overfitting, achieves optimum epochs, and generates strong prediction accuracy for engine performance and emissions.

Actual and predicted data points from the tested XGBoost regressor model demonstrate (Figure 12) its prediction ability for output parameters, and R² values on these plots indicate the accuracy level. Hence, the closer value to 1.0 reflects better prediction accuracy. The SFC prediction through the model exhibits a high level of accuracy based on its R² value of 0.934. The overlapped points along the regression line verify the model’s reliability for predicting fuel consumption trends. The BTE model displays remarkable performance because its R² exceeds 0.993, marking a near-perfect accuracy level. The compact grouping of data points near the regression line shows the model’s capability to represent the connection between biodiesel blend, load, CeO₂ concentration, and thermal efficiency. An R² value of 0.875 indicates a robust correlation according to the CO prediction model, despite its slightly increased distribution between points. The predictive accuracy demonstrated by the HC model is exceptional because its R² value reaches 0.968, while the linear regression line closely fits most observer points.

The NO_x model displays an exceptional R² value of 0.995 that verifies its capability to predict nitrogen oxide emissions accurately because these emissions strongly respond to combustion conditions. The results obtained from the Smoke show that predictions reach an R² value of 0.985, indicating the model provides high accuracy in its predictions. These research findings demonstrate that XGBoost regressor successfully recognizes the nonlinear behavior between input variables, which leads to highly dependable predictions for all performance/emission characteristics of the engine. The slight discrepancy in predictive capabilities demonstrates why this model should be used for performance modeling biodiesel-based CI engines.

A visual assessment of the XGBoost model performance emerges from density plots, which display actual and predicted model output distributions (Figure 13). The distribution patterns identified by the model stay faithfully matched with actual values through the proximity of blue (actual) and red (predicted) distributions displayed in most plots. The actual and predicted values for SFC, BTE, NO_x, and Smoke exhibit a close alignment, which indicates high prediction reliability. Most prediction errors are small enough not to affect the general trend patterns visible between actual values and predicted values for CO and HC data. The NO_x distribution pattern with two peaks demonstrates accurate alignment of actual values and expected outcomes, thus demonstrating excellent model performance. These density plots show how closely the XGBoost Regressor determines reliable diesel engine performance and emission values within both biodiesel blends and CeO₂ nanoparticle conditions.

3.5. Validation of ML and RSM With Experimental Value

Both experimental data and predictive values from ML and RSM are visually compared as bar graphs (Figure 14) for all output parameters. The predictions from both ML and RSM closely followed experimental findings, which confirms their strong predictive accuracy. SFC predictions demonstrate consistent accuracy because their predicted output value (0.319) closely matches experimental (0.319) and both ML (0.32) and RSM (0.323) predictions show very close results when compared to experimental data. The experimental value at optimal conditions matches closely with BTE predictions, which display minimal variations (experimental: 24.99%, ML: 25.15%, and RSM: 25.05%).

The measurement methods show accurate performance through emission parameter evaluation. Test results matched with predicted CO emissions values from the experiment to be 0.0229%, 0.023%, and 0.022% through ML and RSM tables, thus showing the minimal discrepancy. Experimental tests confirmed the optimal HC emissions values as highly effective forecasters, while validating these results yielded experimental: 38 ppm, ML: 37.56 ppm, and RSM: 38 ppm. The measurement reliability of both prediction techniques was verified through the matching NO_x emission outcomes, which occurred at the optimum operating points (experimental: 512 ppm, ML: 502.94 ppm, and RSM: 512.66 ppm). The prediction tests performed at optimum conditions yielded outstanding accuracy agreement with the experimental results being 30.06 HSU, the ML results being 30.02 HSU, and the RSM results being 30.05 HSU.

Predictions of engine performance through ML and RSM models show excellent accuracy, thus demonstrating their fitness for optimization studies in engine systems. High-performance results from ML–based models exceed those from RSM in some instances because of their strong capacity to identify complicated nonlinear relationships. These optimization parameters derived from RSM generated results identical to those verified by ML for boosting engine performance and emission reduction, which shows that these approaches succeed in diesel engine research.

Table 11 shows the average absolute error percentage of ML and RSM prediction results against experimental measurements for SFC and all other output parameters (BTE, CO, HC, NO_x, and smoke). This error provides insight into the accuracy and reliability of the predictive models, calculated using the formula (8):

Table 11. Average absolute error percentage of prediction performance of ML and RSM.

Percentage of error			SFC		BTE		CO		HC		NO_x		Smoke
Biodiesel blend	Load (%)	CeO₂ ppm	ML	RSM	ML	RSM	ML	RSM	ML	RSM	ML	RSM	ML	RSM
10	50	55	0.838	0.882	0.727	1.894	0.741	−2.442	−8.359	−5.150	−1.854	−0.597	−1.042	−2.623
20	75	35	1.588	2.816	−1.125	−0.622	−0.800	7.779	−3.829	−2.253	−1.209	−1.768	1.938	4.109
20	100	35	−1.057	0.175	0.359	0.141	1.429	11.267	−3.642	−2.633	1.734	1.917	−0.675	−1.157
30	50	55	−4.000	1.008	3.087	0.967	0.385	−0.109	−1.125	0.261	3.025	1.944	0.931	−1.405
18.32	63.8	48.56	−0.157	0.297	−0.652	0.152	0.961	3.476	1.158	0.003	−1.594	0.042	0.133	0.044
Average absolute error			−0.558	1.036	0.479	0.506	0.543	3.994	−3.159	−1.955	0.020	0.308	0.257	−0.207

(8)

The prediction errors established by ML alongside RSM methods demonstrate low percentages in every output parameter analysis. The predictive accuracy of ML surpasses RSM by demonstrating an average absolute error rate of 0.558% for SFC, while RSM shows a 1.036% error rate for SFC. The BTE predictions from ML (0.479%) surpass RSM (0.506%) because ML demonstrates a better ability to detect nonlinear behavioral patterns. The prediction of emissions yields better results through ML since ML calculates lower error rates for CO (0.543% vs 3.994%) and HC (3.159% vs 1.955%) compared to RSM. The predictions for NO_x and Smoke from both ML and RSM match exceptionally well with error percentages at 0.020% and 0.308% for ML and 0.257% and 0.207% for RSM, respectively.

Results show that, while handling challenging emissions data, the prediction errors from the ML model remain below the RSM model errors, indicating higher accuracy. Different methods perform closely to each other in practice, thus confirming their effective use together. The research shows how ML teamed up with RSM to optimize biodiesel blend with CeO₂ nanoparticles while demonstrating the strengths of RSM in experimental condition determination and ML’s advantage in accurate predictions. The dual method produces reliable optimization techniques that promote sustainable biodiesel use and efficient operation of CI engines.

The performance and emission results from this study were compared with those from various recent studies in the literature. This study’s findings showed that the optimal biodiesel blend of 18.32% biodiesel, 63.84% engine load, and 48.55 ppm CeO₂ resulted in a 24.99% BTE and a 0.3197 kg/kWh SFC, which aligns with similar studies using CeO₂ as a nanoparticle additive. For instance, Khanam et al. [49] found significant performance improvements with CeO₂ nanoparticles, reporting a 32% increase in BTE with a 30% reduction in NO_x emissions when using waste cooking oil biodiesel blends. Bhan et al. [50] also reported improvements in engine performance with CeO₂ and aluminum oxide additives, achieving 11.39% BTE and emission reductions for CO₂ and NO_x. In contrast, our study achieved higher emission reductions for NO_x (562.74 ppm) and smoke (30.06 HSU) compared to these studies. Additionally, the ML model in this study outperformed RSM in predicting complex emission characteristics, a finding consistent with Şahin [12], who demonstrated the superior predictive capability of ML models for biodiesel emissions. These comparisons highlight the efficacy of combining CeO₂ nanoparticles with biodiesel in optimizing engine performance and reducing emissions.

4. Conclusions

This study evaluated the performance and emission behavior of diesel-powered pumpkin seed biodiesel blends (B10, B20, and B30) containing CeO₂ nanoparticles (35, 45, and 55 ppm) under varying engine loads (50%, 75%, and 100%). The combination of RSM and ML techniques was used to optimize engine performance and predict emissions. The findings demonstrate the feasibility of using pumpkin seed biodiesel as a sustainable alternative fuel, particularly with the addition of CeO₂ nanoparticles to improve combustion efficiency and reduce harmful emissions.

•
The optimal biodiesel blend was found to be 18.32% biodiesel, 63.84% engine load, and 48.55 ppm CeO₂, resulting in a desirability score of 0.959.
•
Under these conditions, the engine displayed significantly improved emissions and performance, with CO at 0.0229%, HC at 38 ppm, NO_x at 562.74 ppm, smoke at 30.06 HSU, and SFC at 0.3197 kg/kWh.
•
The ML model surpassed RSM in predicting complex emission characteristics, showing lower average absolute errors across several key performance metrics, including SFC (0.558% vs. 1.036%), BTE (0.479% vs. 0.506%), CO (0.543% vs. 3.994%), HC (3.159% vs. 1.955%), NO_x (0.020% vs. 0.257%), and smoke (0.257% vs. 0.207%).
•
Both ML and RSM techniques demonstrated strong agreement with experimental results, confirming the reliability of the predictive models and their effectiveness in optimizing engine performance.
•
The integration of RSM and ML successfully optimized biodiesel blend parameters, leading to improved fuel economy and a significant reduction in hazardous emissions. This further supports the feasibility of pumpkin seed biodiesel as a sustainable alternative fuel.

In conclusion, this study underscores the potential of pumpkin seed biodiesel combined with CeO₂ nanoparticles as an environmentally friendly fuel solution. The RSM and ML models proved effective in optimizing engine performance and reducing emissions. Future studies could focus on other biodiesel sources, investigate long-term engine performance, and explore advanced ML models, such as deep learning, to further enhance prediction accuracy. Additionally, research on other nanoparticle additives, like Al₂O₃ and TiO₂, as well as detailed environmental and economic analyses through life cycle assessments (LCAs), would be valuable to assess the broader sustainability and cost-effectiveness of biodiesel blends for large-scale applications.

Nomenclature

TFC:: Total fuel consumption
BTE:: Brake thermal efficiency (%)
BP:: Brake power
BSFC:: Brake specific fuel consumption
SFC:: Specific fuel consumption (kg/kWh)
CO:: Carbon monoxide (% by volume)
HCs:: Hydrocarbons (ppm)
NO_x:: Nitrogen oxides (ppm)
HSUs:: Haze smoke units
RSM:: Response surface methodology
ML:: Machine learning
XGBoost:: Extreme gradient boosting
CeO₂:: Cerium oxide nanoparticles (ppm)
PSOME:: Pumpkin seed oil methyl ester
B10:: 10% Biodiesel + 90% diesel
B20:: 20% Biodiesel + 80% diesel
B30:: 30% Biodiesel + 70% diesel
ppm:: Parts per million
kWh:: Kilowatt hour
g/m³:: Grams per cubic meter
cm³:: Cubic centimeter
mg:: Milligram
L:: Liter
g/mol:: Grams per mole
ANOVA:: Analysis of variance
RMSE:: Root mean square error
MAE:: Mean absolute error.

Ethics Statement

No human participants or animals were involved in this study, ensuring compliance with ethical research standards.

Disclosure

The research focuses solely on material synthesis, characterization, and computational modeling.

Conflicts of Interest

The authors declare no conflicts of interest.

Author Contributions

Shaisundaram V. S.: experimental work, investigation, materials. Saravanakumar Sengottaiyan: software, machine learning, writing–original draft. Gunasekaran Raji: optimization, validation. Kumaravel S.: experimental testing, writing–original draft. Chandrasekaran M.: research administration, methodology. All authors have approved the submission.

Funding

There are no funding sources for this research work.

Open Research

Data Availability Statement

The Python code used for machine learning predictive modeling is available upon reasonable request.

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All articles

Machine Learning-Driven Energy Efficiency Enhancement and Emission Reduction in Diesel Engines Using Pumpkin Seed Biodiesel Blends and CeO₂ Nanoparticles

Abstract

1. Introduction

2. Materials and Methods