Performance and Emission Optimization of Palm Biodiesel Fuels with Dual Nanoparticle Additives Using Gaussian Process Regression and Multi-Criteria Decision Analysis

Abstract

This study employed a Gaussian Process Regression model combined with the Combinative Distance-Based Assessment method to analyze and optimize the performance and emission characteristics of a diesel engine operating with different fuel blends under various load conditions. The results indicated that increasing engine load generally improved brake thermal efficiency while reducing fuel consumption. Compared with conventional diesel fuel, palm biodiesel blends exhibited relatively higher fuel consumption and increased exhaust emissions under certain operating conditions. The incorporation of nanoparticle additives enhanced the combustion process, resulting in improved engine performance and reduced emissions. Among the tested fuels, the blend containing magnesium oxide nanoparticles exhibited the best overall performance across the investigated load range and showed greater potential for reducing incomplete-combustion emissions. The developed machine learning model accurately predicted engine performance and emission parameters and demonstrated strong generalization capability. Furthermore, the multi-criteria decision-making analysis enabled the identification of promising fuel–operating condition combinations based on multiple performance and emission indicators. Experimental validation demonstrated good agreement between the predicted and measured results, confirming the reliability of the proposed approach. The findings suggest that integrating machine learning techniques with multi-criteria decision-making methods provides an effective framework for fuel formulation optimization, engine performance enhancement, and emission reduction.

1. Introduction

Against the backdrop of the accelerating global energy transition and increasingly stringent emission regulations [1], the internal combustion engine sector is facing dual challenges of improving energy utilization efficiency and reducing pollutant emissions [2]. Conventional fossil diesel possesses advantages such as high energy density and well-established infrastructure; however, its combustion process generates substantial amounts of carbon dioxide (CO₂), nitrogen oxides (NOx), carbon monoxide (CO), and unburned hydrocarbons (UHC), which pose significant threats to the environment and human health [3,4]. Therefore, the development of clean alternative fuels, combined with advanced optimization approaches to enhance overall engine performance, has become one of the major research focuses in recent years.

Among the various alternative fuels, biodiesel derived from feedstocks such as animal fats and vegetable oils has been regarded as one of the most promising substitutes for conventional diesel owing to its renewability, biodegradability, and inherent oxygen-containing molecular structure [5,6]. In particular, palm biodiesel offers advantages including abundant feedstock availability and relatively low production cost [7], making it highly feasible for practical engineering applications [8]. With the increasing application of biodiesel in engine systems, the accurate measurement and evaluation of engine performance, as well as regulated emissions including CO, HC, NOx, and CO₂, have become increasingly important. Such assessments not only facilitate the evaluation of its environmental benefits but also provide essential support for compliance with increasingly stringent emission regulations. Milojević et al. [9] conducted a systematic analysis of the thermal efficiency and emission characteristics of diesel- and biodiesel-fueled engines and reported that fuel composition and engine operating conditions exert significant influences on energy utilization efficiency and pollutant formation. Their study further highlighted the importance of emission monitoring and environmental assessment in achieving sustainable engine operation. Despite its considerable potential, biodiesel still exhibits certain limitations in further improving overall engine performance due to its relatively high viscosity [10] and poor low-temperature flow properties [11].

To further enhance the combustion process and strengthen emission control, various metal oxide nanoparticles, including aluminum oxide (Al₂O₃), magnesium oxide (MgO), titanium dioxide (TiO₂), cerium oxide (CeO₂), and zinc oxide (ZnO), have attracted considerable attention due to their excellent catalytic activity, oxygen donation capability, high thermal conductivity, and large specific surface area. These nanoparticles can improve fuel atomization, accelerate oxidation reactions, and promote more complete combustion, thereby influencing engine performance and emission characteristics. Modi et al. [12] conducted a comprehensive review on nanoparticle-enhanced biodiesel fuels and reported that additives such as Al₂O₃, TiO₂, CeO₂, RuO₂, graphene oxide, and multi-walled carbon nanotubes can influence fuel properties including viscosity, cetane number, calorific value, and flash point. These nanoparticles were also found to reduce certain pollutant emissions by improving ignition characteristics, evaporation behavior, and combustion efficiency. The review further emphasized that the effectiveness of nanoparticles is strongly dependent on particle type, particle size, additive concentration, and base fuel composition. Therefore, different nanoparticle additive systems still require experimental validation under specific fuel compositions and engine operating conditions. Prabakaran et al. [13] experimentally investigated the addition of ZnO nanoparticles into a diesel–biodiesel–ethanol ternary fuel blend. The results demonstrated that the incorporation of nanoparticles improved fuel atomization and combustion characteristics, thereby enhancing brake thermal efficiency and reducing brake-specific fuel consumption. Meanwhile, CO and HC emissions were significantly reduced. However, due to the increase in combustion temperature, NOx emissions exhibited a certain upward trend. This study indicated that metal oxide nanoparticles can effectively improve overall engine performance through combustion enhancement, although trade-offs still exist in emission control. Dey et al. [14] investigated the addition of CeO₂ nanoparticles to a palm biodiesel fuel system through engine experiments. The results revealed that the nanoparticles promoted more complete combustion through their oxygen storage capability, leading to significant reductions in CO and HC emissions and simultaneous NOx reduction under high load conditions. In addition, brake thermal efficiency (BTE) was noticeably improved, indicating the synergistic effect of nanoparticles in enhancing combustion efficiency and emission characteristics. This study further confirmed the effectiveness of nanoparticles in biodiesel fuel systems, although their mechanisms remain highly dependent on specific fuel compositions and operating conditions. Similar findings regarding the effects of metal nanoparticles on combustion and emissions were also reported by Kumar et al. [15] and Ismael et al. [16]. To provide a clearer overview of nanoparticle applications in biodiesel-fueled engines, representative nanoparticle additives and their reported effects on engine performance and emissions are summarized in

Table 1. Nanoparticle additives and their effects on biodiesel engine performance and emissions.

Fuel Type	Nanoparticle	Main Effects	Ref.
B30 Cottonseed biodiesel	MgO (70 ppm)	Compared with diesel, BTE increased by up to 2.2%, BSFC decreased by up to 6.8%, while CO, HC, NOx, and smoke emissions were reduced (maximum reduction: 28%).	[17]
B20 Butea monosperma biodiesel	MgO (150 ppm)	Compared with B20, B20MgO100 increased BTE by 9.12% and reduced BSFC by 7.98%, while B20MgO150 decreased CO, UHC, and NOx emissions by 14.28%, 17.30%, and 5.08%, respectively.	[18]
Diesel	Al2O3 (150 ppm)	Compared with diesel, DA150 improved combustion and engine performance, while reducing HC, CO, and NOx emissions by up to 38%, 25%, and 23%, respectively.	[19]
B20 Sesame seed biodiesel	CeO2 (50 ppm)	Compared with diesel, CeO2 nanoparticle-enhanced sesame biodiesel increased BTE by up to 3.3% and reduced HC, CO, and NOx emissions by 30.4%, 20.2%, and 31.6%, respectively.	[20]
B20 Waste cooking oil biodiesel	SiO2 (100 ppm)	Compared with diesel, SiO2 and TiO2 nanoparticles improved combustion and fuel economy while reducing CO, HC, and PM emissions; however, both additives resulted in increased NOx emissions.	[21]
	TiO2 (100 ppm)
B25 Microalgae biodiesel	Graphene oxide (75 ppm)	Compared with diesel, graphene oxide nanoparticle-enhanced B25 microalgal biodiesel improved BTE and reduced CO, HC, NOx, smoke, and particulate matter emissions.	[22]

.

The aforementioned studies indicate that metal oxide nanoparticles can promote fuel oxidation reactions during combustion, enhance combustion rates, and improve fuel atomization quality through enhanced heat transfer and micro disturbance effects, thereby increasing BTE and reducing incomplete combustion products such as CO and HC [23,24]. In addition, different types of nanoparticles exhibit distinct catalytic mechanisms and thermophysical properties, and their effects on combustion and emission characteristics still require systematic comparative investigation. Therefore, constructing multiple fuel systems and conducting comparative experimental studies are of significant importance for revealing their synergistic interaction mechanisms.

However, significant nonlinear coupling relationships exist between multicomponent fuel systems and engine operating parameters, making it difficult for conventional experimental approaches alone to comprehensively reveal the underlying mechanisms while also increasing experimental costs [25]. Consequently, machine learning techniques have been increasingly applied to engine performance and emission prediction due to their ability to model complex nonlinear relationships [26,27]. Among these techniques, Gaussian Process Regression (GPR), a Bayesian-based nonparametric model, offers high prediction accuracy together with uncertainty quantification [28], making it particularly suitable for small-sample datasets [29]. Meanwhile, achieving an effective balance between engine performance enhancement and emission reduction remains a critical challenge in multi-objective optimization [30]. As a distance-based multi-criteria decision-making method, the Combinative Distance-Based Assessment (CODAS) approach utilizes both Euclidean and Manhattan distances to effectively discriminate among alternative solutions and identify favorable fuel–operating condition combinations [31]. Therefore, the integration of GPR-based prediction and CODAS-based decision analysis provides a promising framework for simultaneously evaluating, predicting, and optimizing engine performance and emission characteristics [32].

Although previous studies have demonstrated the benefits of nanoparticle-enhanced biodiesel fuels and the application of machine learning techniques in engine research, several important research gaps remain. Most existing investigations have focused on a single nanoparticle additive, while systematic comparisons between Al₂O₃ and MgO nanoparticles under identical palm biodiesel operating conditions are still scarce. Furthermore, the predictive capability of Gaussian Process Regression for nanoparticle-enhanced biodiesel fuels under limited experimental datasets has not been sufficiently explored. In addition, the integration of machine learning prediction models with multi-criteria decision-making approaches for fuel–operating condition optimization has received relatively limited attention. To address these gaps, the present study employed diesel fuel and a palm biodiesel blend (B20) as base fuels, while 100 ppm of Al₂O₃ and MgO nanoparticles were separately added to prepare four fuel samples, namely Diesel, B20, B20A100, and B20M100. Engine experiments were conducted under 25%, 50%, 75%, and 100% load conditions, with each test repeated three times to ensure data reliability. Based on the experimental results, a Gaussian Process Regression model was developed to predict key performance and emission parameters, and the Combinative Distance-Based Assessment method was subsequently applied to rank different fuel–operating condition combinations and identify the most favorable operating strategy. Compared with existing studies, the originality and major innovations of the present work can be summarized as follows:

(1)

A systematic comparative framework involving Al₂O₃- and MgO-enhanced palm biodiesel fuels was established to elucidate the distinct combustion and emission mechanisms associated with different nanoparticle additives.

(2)

A Gaussian Process Regression model was developed for small-sample engine datasets to achieve high prediction accuracy while simultaneously quantifying prediction uncertainty.

(3)

An integrated Gaussian Process Regression–Combinative Distance-Based Assessment framework was developed to enable simultaneous prediction, ranking, and optimization of fuel–operating condition combinations.

(4)

The proposed framework was experimentally validated, demonstrating its capability to support synergistic optimization of engine performance and emission characteristics.

2. Experimental Materials and Methods

2.1. Biodiesel Production

The diesel fuel used in this study was obtained from a local commercial fuel station, whereas the biodiesel was produced in the university laboratory through an alkali-catalyzed transesterification process. Palm oil was used as the feedstock, methanol as the alcohol reagent, and sodium hydroxide (NaOH) as the homogeneous alkaline catalyst. Initially, NaOH was completely dissolved in methanol under sealed conditions to form a sodium methoxide active intermediate solution. Subsequently, the palm oil was preheated to 50–55 °C to reduce its dynamic viscosity and improve mass transfer efficiency between the reactants. Under constant temperature conditions, the sodium methoxide solution was gradually added to the preheated palm oil while continuous stirring was maintained to enhance the interfacial contact between the oil and alcohol phases. The transesterification reaction was conducted at 50–55 °C for 60 min. This temperature range is close to the lower limit of the methanol boiling point, which is beneficial for maintaining a sufficient reaction rate while minimizing excessive methanol evaporation. After completion of the reaction, the reaction mixture was transferred into a separating device and allowed to settle for phase separation, where the crude biodiesel and glycerol phases were effectively separated based on density differences.

To further improve fuel purity, the upper crude biodiesel layer was repeatedly washed with warm water to remove residual catalyst, unreacted methanol, and saponification by products. The washing process was continued until the washing water became neutral and free of visible turbidity. Subsequently, the residual moisture in the biodiesel was removed through heating and drying treatment, and stable palm biodiesel with suitable physicochemical properties was finally obtained.

2.2. Preparation of Fuel Blends

Al₂O₃ and MgO nanoparticles at a concentration of 100 ppm were separately added into the B20 base fuel to prepare nanoparticle-enhanced blended fuels. The fuel preparation process was carried out using a two-step dispersion method. Initially, the weighed nanoparticles were gradually introduced into the B20 fuel, followed by preliminary dispersion using a magnetic stirrer under ambient temperature conditions. The stirring speed was maintained at approximately 700–800 rpm for 30 min to overcome particle agglomeration and achieve preliminary homogeneous mixing. Subsequently, the premixed fuel was subjected to further dispersion treatment in an ultrasonic cleaner at an ultrasonic frequency of approximately 40 kHz for 45 min. The ultrasonic cavitation effect effectively disrupted nanoparticle agglomerates and enhanced the dispersion uniformity and stability of the nanoparticles within the fuel.

To evaluate the dispersion stability of the prepared fuels, the nanoparticle blended fuels were stored in transparent sealed containers and observed under room-temperature conditions. No obvious sedimentation or phase separation was observed within 5 days, indicating that the prepared nano-fuels possessed satisfactory dispersion stability and were suitable for subsequent engine experiments. The properties of the experimental fuels are presented in

Table 2. Properties of experimental fuel.

Parameters	Density (kg/m3) at 15 °C	Calorific Value (MJ/kg)	Kinematic Viscosity (mm2/s) at 40 °C
Diesel	835.62	43.32	3.06
B20	843.56	42.13	3.41
B20M100	843.73	42.42	3.47
B20A100	843.81	42.33	3.52

.

2.3. Experimental Setup

The experiments in this study were conducted on a water-cooled single cylinder four stroke direct injection diesel engine, and the main engine specifications are listed in

Table 3. Engine parameters.

Parameters	Description
Engine Type	Single cylinder–water cooled–4 stroke
Manufacture	Daedong Ltd., Daegu City, Republic of Korea
Type	ND10DE
Rated Power Output (kW)	7.4
Injection Pressure (kg cm−2)	200
Displacement (cc)	673
Compression Ratio	21
Bore (mm)	95
Stroke Length (mm)	95

. As illustrated in the schematic diagram of the experimental setup shown in Figure 1, an eddy current dynamometer was employed to regulate the engine load, ensuring accurate loading and stable operation under different operating conditions. The engine speed was maintained constant throughout the experiments, while the water-cooling system was used to ensure stable thermal operating conditions. Key performance parameters were recorded in real time using a data acquisition system. Brake power was calculated based on the torque and rotational speed obtained from the dynamometer, from which BTE and brake-specific fuel consumption (BSFC) were determined to evaluate the energy utilization efficiency and fuel economy characteristics of the tested fuels. Fuel consumption was measured using a graduated burette combined with an electronic timer by recording the fuel volume variation over a specific time interval and subsequently converting it into mass flow rate according to the fuel density.

An exhaust gas analyzer was used to monitor the concentrations of CO, HC, and NOx emissions. Prior to each experiment, the gas analyzer was calibrated to ensure measurement accuracy. To minimize random experimental errors, each operating condition was repeated three times. All experimental data were collected only after the engine operating parameters had reached stable conditions to ensure that the measured results accurately reflected the steady state operating characteristics of the engine.

2.4. Gaussian Process Regression

To establish the nonlinear mapping relationship between fuel composition and engine performance and emission characteristics, a GPR model was employed in this study for experimental data modeling and prediction. GPR is a Bayesian-based nonparametric regression approach capable of achieving high fitting accuracy under small sample conditions while simultaneously providing uncertainty estimation for prediction results [33].

In the GPR model, the output variable can be expressed as:

$$y=f(x)+\epsilon$$

(1)

where $x$ denotes the input variables, $y$ represents the target output, $f(x)$ is the latent nonlinear function, and $\epsilon$ denotes the random error term.

The Gaussian process can be further expressed as:

$$f(x)\sim GP(m(x),k(x,x^{\mathrm{\prime }}))$$

(2)

where $m(x)$ denotes the mean function, and $k(x,x^{\mathrm{\prime }})$ represents the kernel function used to describe the correlation between different input samples.

2.5. Combinative Distance-Based Assessment

To achieve comprehensive evaluation of different fuels and operating conditions under multiple performance criteria, the CODAS method was employed in this study to rank and analyze the GPR prediction results. CODAS is a multi-criteria decision-making approach that evaluates the performance of alternatives by calculating their distances from the negative ideal solution, where a larger distance indicates superior overall performance [34].

First, all evaluation criteria were normalized to eliminate the influence of dimensional differences. Subsequently, a weighted normalized decision matrix was established, and the negative ideal solution was determined [35]. In the CODAS method, alternatives are mainly evaluated based on Euclidean distance and Manhattan distance, which can be expressed as follows:

$$E_i=\sqrt{{\displaystyle {\sum }_{j=1}^n}(x_{ij}-x_j^{-}{)}^2}$$

(3)

$$T_i={\displaystyle {\sum }_{j=1}^n}\mid x_{ij}-x_j^{-}\mid$$

(4)

where $E_i$ and $T_i$ denote the Euclidean distance and Manhattan distance of the $i$-th alternative from the negative ideal solution, respectively, and $x_j^{-}$ represents the negative ideal value of the $j$-th criterion.

Based on these distances, a relative assessment function was established to conduct pairwise comparisons among different alternatives and obtain the comprehensive assessment scores. Finally, all fuel and operating condition combinations were ranked according to the obtained assessment values, and the optimal alternative was selected.

3. Experimental Results and Model Analysis

3.1. Correlation Analysis

To analyze the relationships between the input variables and the engine performance and emission parameters, Pearson correlation coefficient analysis was conducted, and the results are presented in Figure 2.

It can be observed that engine load has a significant influence on both performance and emission characteristics. Load exhibited a strong positive correlation with BTE (r = 0.90) and a strong negative correlation with BSFC (r = −0.90), indicating that the combustion process was enhanced with increasing load, thereby improving thermal efficiency and reducing fuel consumption. Meanwhile, load showed positive correlations with CO, HC, and NOx emissions, with the highest correlation observed for NOx (r = 0.97), suggesting that the elevated combustion temperature under high load conditions significantly promoted NOx formation. Among the performance parameters, BTE exhibited a strong negative correlation with BSFC (r = −0.99), indicating a pronounced inverse relationship between the two parameters. In addition, CO and HC displayed a very strong positive correlation (r = 0.97), implying that both emissions were mainly governed by incomplete combustion processes.

In comparison, the regulatory effects of nanoparticles on engine performance and emissions were also evident to a certain extent. MgO exhibited a positive correlation with BTE and negative correlation trends with CO and HC, indicating its beneficial role in promoting combustion and suppressing incomplete combustion products. Although Al₂O₃ showed relatively weaker linear correlations with the investigated parameters, it generally exhibited negative correlation trends with emission parameters, suggesting its involvement in combustion process regulation as well. Overall, nanoparticles contributed to the improvement of combustion characteristics and emission performance; however, their influence was less significant than that of engine load.

3.2. Brake Thermal Efficiency

As shown in Figure 3, the variation trends of BTE for different fuels under various load conditions were generally consistent, with BTE increasing significantly as engine load increased. Within the load range of 25% to 75%, BTE exhibited a continuous upward trend, while a slight decrease or stabilization was observed at 100% load. This behavior can mainly be attributed to the increase in cylinder temperature and pressure under medium and high load conditions, which facilitates more complete fuel evaporation and combustion, thereby improving thermal efficiency [36]. Under full load conditions, however, excessive fuel injection and localized oxygen deficiency may lead to incomplete combustion, resulting in a slight reduction in efficiency.

From the comparison among different fuels, nanoparticle blended fuels generally exhibited higher BTE values. Among them, B20M100 demonstrated the best or near best thermal efficiency under all load conditions and achieved the maximum BTE at 75% load. This indicates that MgO nanoparticles can promote combustion reactions through their high specific surface area and catalytic activity, thereby enhancing combustion rate and combustion completeness. In comparison, the improvement achieved by B20A100 was slightly lower than that of B20M100, although it still outperformed the baseline fuels, suggesting that Al₂O₃ also contributes positively to the combustion process. Meanwhile, compared with pure diesel fuel, the B20 blend exhibited slightly lower BTE under certain load conditions, which is mainly associated with the higher viscosity and lower volatility of biodiesel [37]. However, this disadvantage was significantly alleviated after the addition of nanoparticles, indicating the positive role of nanoparticle additives in optimizing combustion characteristics [38].

The right side of Figure 3 presents the comparison between the GPR predicted values and the experimental values. It can be observed that all data points are closely distributed around the 45° reference line, indicating a high degree of agreement between the predicted and experimental results.

3.3. Brake-Specific Fuel Consumption

As illustrated in Figure 4, the BSFC of all tested fuels decreased with increasing engine load, indicating that the engine achieved higher fuel utilization efficiency under high load conditions. This behavior is mainly attributed to the more complete combustion process at elevated loads, resulting in lower fuel consumption per unit effective power output. In addition, BSFC had already decreased to relatively low levels at approximately 75% load, while only minor variations were observed when the load was further increased to full load, suggesting that the combustion efficiency had approached a relatively stable condition.

The differences among fuels indicate that the addition of nanoparticles exerted a positive effect on fuel consumption characteristics [39]. Compared with the baseline fuels, B20M100 exhibited lower BSFC values under most operating conditions, indicating that MgO nanoparticles enhanced combustion reactivity and improved energy release efficiency. B20A100 also demonstrated a certain degree of improvement; however, the overall enhancement was slightly lower than that of B20M100. In contrast, the B20 fuel without nanoparticle additives generally exhibited higher fuel consumption at all load conditions because of its relatively lower calorific value [40]. It should also be noted that a slight increase in BSFC was observed for some fuels under full load conditions, which may be associated with excessive fuel injection leading to locally rich mixtures and consequently affecting combustion completeness.

From the prediction results, the BSFC values predicted by the GPR model showed excellent agreement with the experimental results, with most data points distributed close to the diagonal reference line.

3.4. Hydrocarbons

As shown in Figure 5, HC emissions exhibited distinct stage-dependent characteristics with increasing engine load. From low to high load conditions, HC emissions gradually increased, which can mainly be attributed to the increase in fuel injection quantity leading to locally rich mixtures and consequently suppressing the complete oxidation of the fuel. However, under full load conditions, HC emissions showed a certain degree of reduction, indicating that the high temperature environment promoted the subsequent oxidation of unburned hydrocarbons.

B20M100 exhibited lower HC emission levels under all operating conditions, indicating that MgO nanoparticles enhanced combustion completeness by increasing reaction activity and promoting free radical generation [41]. In comparison, B20A100 also demonstrated certain improvements, although its effect was slightly weaker than that of B20M100. Meanwhile, fuels without nanoparticle additives tended to produce higher HC emissions under medium and high load conditions.

From the prediction results, the GPR model successfully reproduced the variation trends observed in the experimental data. Most scatter points were distributed close to the diagonal direction, and no obvious stratification or systematic deviation among different fuel datasets was observed.

3.5. Carbon Monoxide

As shown in Figure 6, CO emissions exhibited a trend of initially increasing and subsequently decreasing with increasing engine load. Under low, medium, and high load conditions, the increase in fuel injection quantity led to the formation of locally rich fuel mixtures, which suppressed the further oxidation of CO into CO₂, resulting in a gradual increase in CO emissions [42]. However, under full load conditions, CO emissions decreased to some extent, indicating that the elevated combustion temperature promoted the subsequent oxidation of CO and facilitated the conversion of incomplete combustion products.

From the perspective of fuel type, the introduction of nanoparticles significantly influenced CO emission characteristics. B20M100 exhibited the lowest CO emissions under all operating conditions, indicating that MgO nanoparticles promoted oxidation reactions and enhanced combustion completeness, thereby effectively reducing CO formation [43]. B20A100 also demonstrated favorable emission reduction performance, although its overall CO emissions were slightly higher than those of B20M100. In contrast, diesel and B20 fuels exhibited relatively higher CO emissions under medium and high load conditions, reflecting the comparatively less complete combustion process in the absence of nanoparticle additives.

Compared with the experimental results, the GPR model demonstrated strong predictive capability for CO emissions. The data points corresponding to different fuels were uniformly distributed along the diagonal reference line without obvious separation among fuel types, indicating that the model maintained consistent prediction performance under various operating conditions and fuel compositions. In addition, the fitting accuracy in the low CO emission region was slightly better than that in the high CO emission region, which may be associated with increased combustion instability under high load conditions. Nevertheless, the overall prediction error remained small, demonstrating the good applicability of the proposed model.

3.6. Nitrogen Oxides

As shown in Figure 7, NOx emissions exhibited a pronounced increasing trend with increasing engine load. Throughout the entire load range, NOx emissions increased almost monotonically, with a more significant rise observed under medium and high load conditions. This phenomenon is mainly attributed to the increase in cylinder temperature and pressure caused by higher engine loads, which intensified the thermal NOx formation pathway and consequently promoted NOx generation.

From the comparison among different fuels, the B20 fuel exhibited the highest NOx emission levels under all load conditions. This behavior is associated with the oxygenated nature of biodiesel, where the higher oxygen content contributes to elevated combustion temperatures, thereby intensifying NOx formation [44]. After the addition of nanoparticles, however, the overall NOx emissions were reduced. Among the tested fuels, B20M100 demonstrated relatively lower NOx levels under most operating conditions, indicating that MgO nanoparticles may suppress NOx formation to a certain extent by improving combustion uniformity or modifying local temperature distributions. B20A100 also exhibited a certain emission reduction effect, although its overall performance was slightly weaker than that of the MgO nanoparticle blended system [45].

From the model prediction results, all data points were linearly distributed along the diagonal reference line, indicating that the GPR model successfully captured the dominant variation trend of NOx emissions with increasing engine load.

3.7. Evaluation of the GPR Model

A GPR model was developed using the Scikit-learn machine learning library in Python 3.13.9. The model implementation and analysis were conducted in Jupyter Notebook within the Anaconda platform. Fuel type and engine load were selected as input variables, while BTE, BSFC, and emissions of CO, HC, and NOx were considered as output variables.

To improve model stability and numerical convergence, all input and output variables were normalized using the Min–Max scaling method to eliminate the influence of differences in data magnitude during model training. The experimental dataset consisted of 48 samples (4 fuel types × 4 load conditions × 3 repeated experiments for each condition). The dataset was randomly divided into training, validation, and testing subsets at a ratio of 70%, 15%, and 15%, respectively. In addition, four-fold cross-validation was employed during the training process to improve model robustness and reduce the risk of overfitting.

Independent GPR sub-models were established for each output parameter. A composite kernel function consisting of a Constant Kernel and a Radial Basis Function (RBF) kernel was adopted to capture the complex nonlinear relationships between operating conditions and response variables. Furthermore, a White Kernel was incorporated into the kernel structure to account for experimental uncertainty. Model hyperparameters were optimized using maximum marginal likelihood estimation, and multiple restart iterations were performed to avoid convergence to local optima, thereby enhancing the global fitting capability and prediction accuracy of the model.

Table 4. Test performance of the GPR model.

	BTE	BSFC	CO	HC	NOx
R2	0.9880	0.9865	0.9872	0.9761	0.9951
MAE	0.2880	3.0875	0.0034	1.5726	19.7049
RMSE	0.3297	3.5741	0.0040	1.7770	24.0801

presents the predictive performance of the GPR model on the test dataset. The coefficients of determination (R²) for BTE, BSFC, CO, HC, and NOx reached 0.9880, 0.9865, 0.9872, 0.9761, and 0.9951, respectively, indicating excellent agreement between the predicted and experimental values. In addition, the low values of mean absolute error (MAE) and root mean square error (RMSE) further demonstrate the high prediction accuracy and stability of the developed model.

3.8. EWM–CODAS Decision Analysis

In this study, the Entropy Weight Method (EWM) and CODAS method were jointly employed to perform comprehensive ranking and optimization of the multi-response performance and emission results under different fuel type and engine load combinations. First, all performance and emission indicators were normalized to eliminate the influence of different dimensions and magnitudes. To avoid subjective bias associated with equal-weight or expert-assigned weighting methods, the Entropy Weight Method (EWM) was employed to objectively determine the relative importance of each evaluation indicator according to the information contained in the dataset. Subsequently, the objective weights of each indicator were calculated based on entropy values and degrees of diversification, and the obtained results are presented in

Table 5. EWM weights.

	BTE	BSFC	CO	HC	NOx
Target weight (%)	21.616	17.215	20.102	15.985	25.082

.

After determining the indicator weights, the CODAS method was employed to evaluate and rank all operating conditions based on their distances from the negative ideal solution. By simultaneously considering indicator importance and performance–emission trade-offs, the EWM–CODAS framework facilitates the identification of the optimal operating strategy. The ranking results were subsequently compared with the GPR predictions.

According to the EWM–CODAS ranking results presented in

Table 6. CODAS scores and ranking.

Fuel	Load	BTE (%)	BSFC (g/kWh)	CO (%)	HC (ppm)	NOx (ppm)	CODAS	Rank
Diesel	25	25.47	326.59	0.072	45.85	380.28	1.79176	3
	50	28.07	296.09	0.115	56.63	613.70	−0.07296	7
	75	32.41	256.45	0.184	82.32	991.53	−0.92883	13
	100	31.40	264.78	0.150	70.35	1236.51	−1.01928	15
B20	25	24.34	350.67	0.064	41.45	547.60	0.91425	4
	50	27.49	310.90	0.101	49.95	775.12	−0.46610	8
	75	32.02	266.93	0.173	73.76	1230.83	−1.05264	16
	100	31.68	269.47	0.137	66.22	1397.56	−1.00447	14
B20M100	25	25.74	330.00	0.044	32.57	445.97	2.47173	1
	50	29.07	291.91	0.078	40.39	679.55	0.44487	5
	75	33.15	255.80	0.148	61.77	1024.27	−0.77458	10
	100	32.34	262.72	0.107	54.86	1282.06	−0.68247	9
B20A100	25	25.15	337.91	0.048	34.00	481.05	2.06818	2
	50	28.13	302.49	0.086	43.19	719.91	0.10118	6
	75	32.42	262.39	0.154	64.81	1131.65	−0.92303	12
	100	31.46	270.13	0.117	59.00	1281.79	−0.86762	11

, B20M100 under the 25% load condition achieved the highest assessment score, indicating that this operating condition provided the optimal overall balance between engine performance and emission characteristics.

3.9. Integrated Analysis of CODAS Optimization and GPR Prediction

Figure 8 illustrates the percentage errors between the experimental measurements and the GPR-predicted values under different fuel types and engine load conditions. Overall, the developed GPR model exhibited excellent predictive performance, with the errors of all performance and emission parameters remaining within ±5%. The prediction errors of BTE and BSFC were relatively small and closely distributed around zero, indicating high prediction accuracy for engine performance parameters. Similarly, the predicted NOx values showed good agreement with the experimental data, with only minor deviations observed under certain operating conditions. In comparison, the prediction errors of CO and HC exhibited relatively larger fluctuations; however, most error values remained within ±2.5%. The relatively low prediction errors across all fuel–load combinations further demonstrate the robustness and generalization capability of the proposed GPR model.

Table 7. Comparison of experimental and predicted values at optimal operating conditions.

	BTE (%)	BSFC (g/kWh)	CO (%)	HC (ppm)	NOx (ppm)
Experiment	25.87	327.98	0.043	31.67	433.33
Prediction	25.74	330	0.044	32.57	445.97
Error (%)	↓ 0.5	↑ 0.62	↑ 2.649	↑ 2.85	↑ 2.92

compares the differences between the experimental values and the GPR predicted values under the optimal operating condition. The prediction errors for all investigated parameters were maintained within 3%. Among them, BTE and BSFC exhibited relatively smaller errors of 0.5% and 0.62%, respectively. In terms of emission characteristics, the prediction errors for CO, HC, and NOx were 2.649%, 2.85%, and 2.92%, respectively, which were slightly higher but still remained at relatively low levels. Overall, the small prediction errors demonstrate that the GPR model possesses strong predictive capability and can accurately reflect the engine performance and emission characteristics under the optimal operating condition.

4. Limitations and Future Research Directions

This study primarily investigated the performance and emission characteristics of palm biodiesel enhanced with Al₂O₃ and MgO nanoparticles and integrated GPR with the CODAS method to predict and evaluate different fuel–operating condition combinations. Although the proposed framework achieved satisfactory prediction accuracy and optimization performance, several limitations should be acknowledged. First, this study mainly focused on the variation trends of BTE, CO, HC, NOx, and CO₂, while further expansion of emission measurement methodologies and systematic comparisons with current emission regulatory limits were beyond the scope of the present work. Second, although nanoparticle additives were found to improve combustion and emission characteristics, their effects on fuel viscosity, low-temperature flow properties, and diesel engine cold-start performance were not comprehensively evaluated. In addition, GPR was employed for prediction and CODAS was used for comprehensive decision-making analysis; however, the applicability of other machine learning algorithms and statistical optimization approaches was not comparatively investigated.

Future studies may further expand the experimental dataset by incorporating additional fuel blending ratios and operating conditions to improve the robustness of model training and validation. Furthermore, emission characteristics should be evaluated more systematically in relation to relevant emission regulations, and additional indicators such as particulate matter emissions may be included to provide a more comprehensive assessment of environmental impacts. Greater attention should also be given to the effects of nanoparticle additives on low-temperature fuel properties and long-term fuel stability to verify their practical applicability. Moreover, other machine learning algorithms and optimization approaches, such as Artificial Neural Networks (ANN), Random Forests (RF), Support Vector Machines (SVM), and alternative multi-criteria decision-making methods, may be employed and compared to further enhance the reliability and effectiveness of fuel optimization and decision-making processes.

5. Conclusions

Based on nanoparticle-enhanced biodiesel fuel systems, this study systematically investigated the engine performance and emission characteristics of a diesel engine under different fuel types and load conditions by integrating the GPR model with the CODAS multi-criteria decision-making method. The main conclusions are summarized as follows:

(1)

Engine load exerted a dominant influence on engine performance and emission characteristics. With increasing engine load, BTE increased significantly, while BSFC gradually decreased. Meanwhile, CO, HC, and NOx emissions generally exhibited increasing trends.

(2)

The introduction of nanoparticles effectively improved combustion characteristics. Compared with the B20 fuel, the addition of MgO and Al₂O₃ nanoparticles resulted in more complete combustion and significantly reduced CO and HC emissions. Among the tested fuels, B20M100 demonstrated superior overall performance under most operating conditions, indicating that MgO possessed greater advantages in promoting combustion reactions.

(3)

The developed GPR model accurately predicted engine performance and emission parameters. The test-set R² values for BTE, BSFC, CO, HC, and NOx reached 0.9880, 0.9865, 0.9872, 0.9761, and 0.9951, respectively, indicating excellent predictive performance.

(4)

CODAS analysis based on the GPR prediction results effectively achieved comprehensive multi-response evaluation. B20M100 under the 25% load condition obtained the highest overall assessment score and was identified as the optimal operating condition. Under this condition, the relative errors between the GPR predicted values and the experimental average values were all maintained within 3%, thereby validating the reliability and effectiveness of the proposed approach.

The results obtained in this study are in good agreement with previous findings demonstrating the effectiveness of metal oxide nanoparticles in improving biodiesel combustion and mitigating pollutant emissions. Moreover, MgO exhibited superior overall performance compared with Al₂O₃ under the investigated operating conditions. Overall, the proposed GPR–CODAS framework provides an effective tool for the prediction, evaluation, and optimization of engine performance and emission characteristics, offering a promising data-driven strategy for the development and application of nanoparticle-enhanced biodiesel fuels.