Engine performance and emission optimization with waste cooking oil biodiesel/diesel blend using ANN and RSM techniques coupled with ACKTR-DE and HHO algorithms

Abstract

In this experimental investigation, Artificial Neural Network (ANN) and Response Surface Methodology (RSM) model structures were constructed to predict and optimize the performance and exhaust emissions of a diesel engine operating on a blend of diesel fuel and waste oil biodiesel. The test engine was operated with 0%, 50%, and 100% biodiesel content under varying injection pressures and loads. The RSM model was used to derive regression equations from the experimental results. The correlation coefficient (R²) for all responses of the constructed model ranged from 0.9785 to 0.9997. By applying the developed model, the brake thermal efficiency (BTE) response was optimized to its maximum value, while all other responses were minimized. All responses were predicted using an ANN model with R > 0.99 and a maximum mean absolute error (MAAE) of 1.723%. RSM-based optimization analysis was applied to the design of experiments (DOE). At an injection pressure of 180 bar, an engine torque of 3.846 Nm, and a 100 percent biodiesel ratio, optimal diesel engine performance characteristics, the lowest exhaust emissions, and the lowest specific fuel consumption values were achieved. In addition, the RSM approach performed satisfactorily, with a desirability value of 0.750. The RSM regression equations were assessed using the Actor Critic with Kronecker-Factored Trust Region-Differential Evolution (ACKTR-DE) and Harris Hawks Optimization (HHO) algorithms. The outcomes derived from the ACKTR-DE and HHO algorithms corroborated the results obtained from the RSM. Furthermore, verification experiments were conducted to confirm the optimal results, thus demonstrating that the combined use of RSM, ANN, and advanced algorithms offers a robust and accurate framework for optimizing biodiesel engine performance.

Graphical Abstract

Introduction

Diesel engines are extensively employed across the global transportation sector, particularly in commercial and public transit, owing to their superior durability and operational efficiency [1]. Additionally, diesel engines play a crucial role in power generation and serve as a primary source of propulsion in a wide range of powertrain applications [2, 3]. However, the increasing global energy demand, coupled with the depletion of fossil fuel reserves and the associated environmental degradation, has accelerated the search for sustainable and eco-friendly fuel alternatives [4–6].

Among various renewable options, biodiesel has emerged as a viable substitute due to its biodegradability, reduced emission profile, and compatibility with existing diesel engines without major modifications [7, 8]. The substitution of conventional diesel with biodiesel effectively diminishes HC, CO, and smoke emissions, yet induces a slight increment in NOx emissions and specific fuel consumption [9–11]. The production of biodiesel can be produced using diverse feedstock sources, including edible vegetable oil (such as soybean, rapeseed, palm, sunflower, coconut, and corn oils), non-edible vegetable oils (including jatropha, karanja, neem, stillingia, Sylbum marianum, and rubber seed), animal fats (tallow, yellow grease, chicken fat, and by-products from fish oil), waste cooking oils, and microalgae [12–16]. The choice of suitable feedstock for biodiesel production depends on regional agricultural capacities, economic considerations, and sustainability criteria, including land-use efficiency and greenhouse gas emission reduction potential [7].

In recent years, the use of waste cooking oil (WCO) as a second-generation feedstock source has attracted considerable attention in biodiesel production, particularly due to its cost-effective and sustainable properties [17, 18]. Utilizing WCO for biodiesel production not only reduces the environmental burden associated with improper disposal of used oils but also contributes [8]. Compared to edible oils, WCO eliminates the food-fuel dilemma associated with edible oils and provides a sustainable waste management solution. However, the primary drawback of WCO lies in its typically high free fatty acid (FFA) and moisture content, which significantly hinder the efficiency of the transesterification process [19]. Therefore, WCO generally requires a pretreatment step, commonly acid-catalyzed esterification, to reduce FFA levels before undergoing base-catalyzed transesterification for biodiesel production [20].

Recent advancements in modeling and optimization techniques have further enabled researchers to explore and optimize the performance and emission characteristics of biodiesel/diesel blends. Techniques such as Response Surface Methodology (RSM) and Artificial Neural Networks (ANN) have been widely adopted to predict and optimize engine parameters across various operating conditions, including injection pressure, load, and fuel blend ratio [21–23]. More recently, advanced metaheuristic algorithms such as Kronecker-Factored Trust Region-Differential Evolution (ACKTR-DE) and Harris Hawks Optimization (HHO) have been introduced to further enhance optimization efficiency and solution quality [24, 25]. ACKTR-DE synergistically combines the global search capability of differential evolution with the rapid convergence properties of trust region methods, making it particularly effective for high-dimensional, multi-modal optimization problems encountered in engine studies [26]. Similarly, HHO, inspired by the cooperative hunting strategy of Harris hawks, offers robust exploration and exploitation abilities, which have demonstrated superior performance in optimizing engine operating conditions for reduced emissions and improved fuel efficiency [27].

This study aims to address significant gaps in the literature by integrating advanced modeling techniques with novel optimization algorithms to enhance diesel engine performance using waste cooking oil biodiesel. While many previous studies have focused on biodiesel applications, the systematic combination of ANN and RSM with ACKTR-DE and HHO algorithms represents a novel approach in this field. The integration of these four methods within a comprehensive Neuroevolution Optimization with Reinforcement Learning (NEORL) framework is applied systematically for the first time to engine performance and emission optimization (Figure 1).

Fig. 1.

Graphical abstract

Another innovative aspect of this research is the validation of optimization results through physical experiments. Unlike most studies, where model predictions are limited to experimental data, this work experimentally verifies the optimized parameters, thereby clearly demonstrating the practical applicability of the proposed methodology. The outputs of RSM, HHO, and ACKTR-DE were compared, and a high degree of agreement among the results was experimentally confirmed. With outstanding predictive accuracy (R² > 0.97) and a desirability score of 0.75, the model utilizes practical engine parameters such as biodiesel ratio, injection pressure, and torque to maximize performance while minimizing environmental impacts. This demonstrates that improvements can be achieved in existing systems without the need for entirely new engine designs. Furthermore, the study provides a comprehensive analysis of varying biodiesel concentrations (0%, 50%, and 100%) and uniquely identifies the optimal operating parameters (180 bar injection pressure, 3,846 Nm engine torque, and 100% biodiesel

ratio) that maximize brake thermal efficiency while minimizing emissions and fuel consumption. The experimental validation of these optimized parameters further highlights the practical feasibility of the proposed methodology. In summary, this research offers a robust and innovative framework for the utilization of waste cooking oil biodiesel in diesel engines, making a significant contribution to sustainable energy solutions by addressing both environmental concerns and the performance optimization challenges that have not been sufficiently resolved in previous studies.

Materials and methodology

Fuel specifications and experimental procedure

In the studies, diesel fuel and biodiesel fuel derived from waste oils were utilized as fuel. At Kocaeli University, biodiesel fuel derived from waste oils was manufactured and studied. The characteristics of the experimental fuels, determined according to ASTM D6751 standards, are presented in Table 1.

Table 1.

Specifications of Fuel

No	Property	Diesel	Biodiesel	ASTM D6751 Requirements
1	Density at 15 °C (kg/m3)	820–860	875–880	860–900
2	Kinematic Viscosity (40 °C, mm2/s)	2.50–3.50	4.3	1.9–6.0
3	Flash Point (°C)	> 55	> 100	≥ 93 °C
5	Cetane Number	49–55	> 55	≥ 47
6	Ash Content (% mass)	< 0.01	< 0.01	≤ 0.02 (% mass)
7	Water Content (mg/kg)	< 200	< 300	≤ 500

The WCO used in this study was collected from local restaurants and was first filtered to remove food residues and impurities. The oil was then pretreated to reduce FFA content to below 1% using an acid-catalyzed esterification process, as suggested by previous studies [28, 29]. Subsequently, the biodiesel was produced through a transesterification reaction using methanol and sodium hydroxide (NaOH) as a catalyst, following ASTM D6751 standards. The reaction was conducted at 60 °C for 60 minutes under continuous stirring at 600 rpm. After phase separation, the biodiesel layer was purified by successive washing with warm distilled water and dried at 110 °C to eliminate residual moisture [30, 31].

In the studies, a Katana brand single-cylinder, four-stroke, compression-ignition research engine was utilized. Table 2 lists the technical specifications of the test engine. Experiments were conducted in two phases. In the first stage, the engine was operated with diesel fuel and varying biodiesel ratios (0, 50, and 100%) under standard injection pressure (200 bar), and fuel consumption, exhaust temperature, and exhaust emission values were measured.

Table 2.

Technical characteristics of the test engine

Brand	Katana 178
Engine general characteristics	4-stroke, Compression ignition (CI)
Diameter x Strok	78 × 62 mm
Volume	296 cm3
Number of cylinders	1
Compression ratio	18.5/1
Fuel system and type	Direct injection and Diesel
Cooling system	Reinforced air cooled
Engine speed	300 rpm
Maximum output power	hp

These tests were performed at a constant speed (2800 rpm) with four distinct loads (3.06, 6.13, 9.2, and 12.26 Nm). In the second stage, the engine was tested with different biodiesel ratios (0, 50, and 100 percent biodiesel) at constant load and variable injection pressures. Since the standard injection pressure of the engine is 200 bar, one lower and two higher injection pressure values were determined. The test setup diagrams illustrate the layout of the experimental installation (Figure 2). Injection pressures of 180, 200, 220, and 240 bar were used to assess their effect on performance and emissions, consistent with the methods employed by Suresh et al. [11] and Samuel et al. [32].

Fig. 2.

Schematic view of the test installation

(1. Engine, 2. Electric dynamometer, 3. Load cell, 4. Speed sensor, 5. Force indicator, 6. Exhaust pipe, 7. Smoke meter, 8. Exhaust emission gas analyzer, 9. Fuel flow meter, 10. Fuel gauge, 11. Control panel, 12. Speedometer, 13. Loading switch, 14. Starter switch)

In the experiments, diesel fuel and biodiesel mix performance (BTE, EGT, SFC) and exhaust emissions (NOX, HC, CO, Smoke) were measured when the engine speed and torque stabilized in each step and the force and thermometer indicators stabilized. Gas analyzers and a smoke meter were used for emission measurements, complying with ISO 8178 standards. The sampling procedures and calibration steps followed the protocols described by Khan et al. [33] and Garg et al. [34].

RSM based optimization techniques with regression model

RSM was utilized to examine the impact of diesel and biodiesel fuel blends on performance and exhaust pollutants. Using the multiple regression model, analyses were performed. Equation 1 demonstrates the general relationship between dependent and independent variables. Where Y is the estimation dependent on the response, X₁, X₂,..., X_n are independent factors for the regression coefficients, and ɛ is the regression error.

$$Y=y_o+y_1{X}_1+y_2{X}_2+\cdots +y_n{X}_n+\epsilon$$ 1

Table 3 displays the experimental design framework for RSM. The outcome of a variance analysis (ANOVA). Table 4 demonstrates that the regression model for BTE, SFC, NOx, HC, CO, EGT, and Smoke is significant for each response. Since the correlation coefficient R² is fairly high, a strong correlation between fuel performance and emission characteristics and input parameters has been discovered (injection pressure, engine torque and biodiesel ratio).

Table 3.

Design of experiment (DOE)

Factors				Respones
Injection Pressure (bar)	Engine Torque (Nm)	Biodiesel Ratio (%)	NOx (ppm)		HC (ppm)	CO (%)	Smoke (%)	EGT (oC)	BTE (%)	SFC (g/kWh)
240	12.26	100	908.449		49	1.01	10	659.4	24.6	412.4
210	7.66	50	601.299		32	0.36	32	456.3	23.8	383.7
210	7.66	50	601.299		32	0.36	32	456.3	23.8	383.7
210	3.06	50	465.419		22	0.06	28	309.9	22.2	393.4
210	12.26	50	752.179		85	0.92	42	602.7	23.4	373.9
210	7.66	50	601.299		32	0.36	32	465.3	23.8	383.7
240	12.26	0	800.449		105	1.21	45	622.4	22	372.1
210	7.66	0	547.299		38	0.39	35	437.8	22.5	353.6
240	3.06	100	606.689		10	0.3	15	366.6	23.5	431.9
180	3.06	0	294.149		30	0.5	18	253.2	23	354.9
210	7.66	50	601.299		32	0.36	32	456.3	23.8	383.7
180	12.26	100	703.909		45	1.35	22	583	27.1	375.7
180	12.26	0	595.909		98	1.48	40	546	24.2	335.4
210	7.66	50	601.299		32	0.36	32	456.3	23.8	383.7
180	7.66	50	499.029		28	0.75	25	418.1	25	365.3
240	7.66	50	703.569		42	0.54	32	494.5	23.8	402
240	3.06	0	498.689		40	0.4	34	329.6	21	391.6
210	7.66	50	601.299		32	0.36	32	456.3	23.8	383.7
180	3.06	100	402.149		15	0.28	20	290.2	25.7	395.2
210	7.66	100	655.299		18	0.34	15	474.8	25.2	403.8

Table 4.

Summary of variance analysis (ANOVA) of the model for responses

Model	NOx	HC	CO	Smoke	EGT	BTE	SFC
Degree	Q	Q	Q	Q	Q	Q	Q
Standart deviation	3.38	5.13	0.0334	1.90	2.67	0.2252	2.26
Mean	602.5	40.85	0.5845	28.65	456.78	23.85	383.22
R2	0.9997	0.9793	0.9963	0.9785	0.9997	0.9855	0.9943
Adjusted R2	0.9994	0.9606	0.9929	0.9592	0.9994	0.9724	0.9891
Predicted R2	0.9978	0.8184	0.9483	0.8158	0.9996	0.8982	0.9599
F-value	3462.69	52.49	297.50	50.66	3613.71	75.50	198.42
p-Value	< 0.0001	< 0.0001	< 0.0001	< 0.0001	< 0.0001	< 0.0001	< 0.0001

In addition, when the regreeration model's p-value was investigated, it was determined to be quite significant with a value of 0.0001. Table 5 provides regression equations for all responses based on input variables for the diesel-biodiesel mixture.

Table 5.

RSM regression model equations

	Regression equation
NOx	602.39 + 102.27 A + 149.38B + 54 C-1.42142e-13 AB −8.91966e-14 AC −1.25176e-13BC + −2.72727 A2 + 4.77273B2 + −2.72727C2
HC	32.5091 + 3 A + 26.5B −17.4C + 0.75 AB −2.25AC −8BC + 1.72727 A2 + 20.2273B2 −5.27273C2
CO	0.354727 −0.09A + 0.443B −0.07C + −0.06625AB + 0.00625 AC −0.00125BC + 0.298182 A2 + 0.143182B2 + 0.0181818 C2
Smoke	31.8545 + 1.1 A + 4.4B −9C −2.25AB −4.75AC −4.5BC −3.13636A2 + 3.36364B2 −6.63636C2
EGT	457.397 + 38.19 A + 146.39B + 18.5 C −6.2343e-14 AB + 1.60311e-14 AC-3.23047e-14BC −0.409098A2 −0.409098B2 −0.409098C2
BTE	23.7823 −0.999831A + 0.58788B + 1.35701 C −0.0578229AB −0.0764531AC + 0.038927BC + 0.737421 A2 −0.805552B2 + 0.198009 C2
SFC	382.992 + 18.33 A −9.7566B + 21.15 C + 9.26967e-15 AB −5.15616e-15 AC −3.06168e-15BC + 1.81821 A2 + 1.81821B2 −3.18186C2

A-Injection pressure, B-Engine Torque, C-Biodiesel ratio

Neuroevolution optimization with reinforcement learning (NEORL) utilizing ACKTR-DE and HHO optimization techniques

NEORL provides a global optimization interface for advanced neural network techniques utilizing evolutionary computation, hybrid neuroevolution algorithms, and reinforcement learning. NEORL encompasses a diverse array of optimization challenges, including high-dimensional, expensive, constrained engineering optimization, as well as combinatorial, continuous, and mixed discrete/continuous problems [35]. This work employed NEORL algorithms, namely Actor Critic with Kronecker-Factored Trust Region-Differential Evolution (ACKTR-DE) and Harris Hawks Optimization (HHO).

Q = Quadratic.

We employ the ACKTR-DE method, which is based on the actor-critic framework of deep reinforcement learning, to ascertain the optimal course of action [24]. Upon receiving a fitness function within a reinforcement learning environment, the Actor Critic utilizing the Kronecker-Factored Trust Region (ACKTR) algorithm initiates the search to acquire some of them. The second step's derivation entails employing the most proficient ACKTR individuals to guide Differential Evolution (DE), whereby the least effective DE individuals are supplanted by Reinforcement Learning (RL) individuals, who are randomly integrated into the DE population to enhance its diversity. The optimal results from both phases are delivered to the user following the execution of an ACKTR search and a DE [36].

Harris Hawks Optimization (HHO) is a population-based, gradient-free optimization method inspired by natural phenomena. These algorithms utilize a population of individuals to initiate the optimization process, with each individual representing a potential solution to the optimization problem. The optimization procedure continues until a stopping criterion or the maximum number of iterations is met [36]. The flow process of HHO and ACKTR-DE algorithms is shown in Figure 3.

Fig. 3.

Application of the HHO and ACKTR-DE algorithms

Results and discussion

RSM results

As shown in Figure 4, brake thermal efficiency (BTE) demonstrated a significant enhancement with increasing biodiesel ratio. The superior oxygen content inherent in biodiesel facilitated more complete combustion, leading to improved energy conversion efficiency. Notably, BTE increased with engine torque due to higher mechanical work output per cycle, in agreement with previous studies [2, 30]. Injection pressure also exhibited a non-linear relationship with BTE: efficiency improved from 180 bar to 220 bar, dropped slightly at 220 bar due to over-atomization reducing penetration, and rose again beyond 230 bar. These results align with observations by Samuel et al. [32] and Uslu et al. [37], where optimal injection pressure significantly influenced combustion characteristics. The improved BTE also demonstrates the effectiveness of biodiesel blends in promoting better air-fuel mixing and atomization under the selected operating conditions, as reported by Samuel et al. [38].

Fig. 4.

The effect of injection pressure, engine torque, and biodiesel ratio on BTE

Specific fuel consumption (SFC) trends, depicted in Figure 5, indicated a marginal increase with rising biodiesel content, attributed to the lower calorific value of biodiesel compared to diesel [23]. This phenomenon is characteristic of oxygenated fuels, which, despite burning more cleanly, require greater volumes to achieve equivalent power output. Furthermore, elevated injection pressures exacerbated SFC due to increased atomization energy requirements, confirming trends noted by Kumar et al. [21]. Conversely, as engine torque increased, SFC decreased, highlighting improved combustion stability under load. These findings align with the thermodynamic principles outlined in Ma et al. [39], reinforcing the relationship between load, fuel energy density, and combustion efficiency.

Fig. 5.

The effect of injection pressure, engine torque, and biodiesel ratio on SFC

Exhaust gas temperature (EGT) consistently increased with higher biodiesel ratios and elevated engine loads (Figure 6). This phenomenon is attributed to biodiesel's higher oxygen content facilitating prolonged combustion and higher cylinder peak temperatures [40]. The influence of injection pressure was evident but less pronounced, consistent with findings by Mondal and Mandal [41]. Increased EGT can be advantageous for after-treatment systems such as diesel particulate filters (DPF), as reported by Kumar and Sharma [16], although it also requires careful management to avoid excessive thermal loads.

Fig. 6.

The effect of injection pressure, engine torque, and biodiesel ratio on EGT

NOx emissions escalated with an increase in biodiesel concentration, engine load, and injection pressure (Figure 7). The higher in-cylinder temperatures and abundant oxygen content of biodiesel promoted thermal NOx formation through the Zeldovich mechanism [42, 43]. Similar findings were reported by Kumar et al. [21], emphasizing biodiesel's dual impact on combustion enhancement and NOx intensification. Strategies such as exhaust gas recirculation (EGR) or water injection have been suggested in the literature to mitigate this side effect without compromising the environmental benefits of biodiesel usage [44]. CO emissions exhibited a decreasing trend with higher biodiesel proportions (Figure 8), corroborating the oxygenated nature of biodiesel promoting complete oxidation of carbonaceous species [44]. However, a rise in CO emissions was observed beyond 220 bar injection pressure, suggesting incomplete combustion due to fuel over-penetration, aligning with observations by Youn and Jeon [45]. This highlights the delicate balance between atomization quality and combustion completeness at elevated injection pressures.

Fig. 7.

The effect of injection pressure, engine torque, and biodiesel ratio on NOx

Fig. 8.

The effect of injection pressure, engine torque, and biodiesel ratio on CO

HC emissions were significantly reduced with increasing biodiesel ratio (Fig. 9), attributed to the oxygen enrichment improving combustion completeness [3, 46]. However, increments in injection pressure and torque showed mild increases in HC emissions, indicating suboptimal atomization dynamics at extreme operating conditions [47]. Further investigation into spray breakup phenomena could provide more insights into this behavior.

Fig. 9.

The effect of injection pressure, engine torque, and biodiesel ratio on HC

Smoke emissions decreased sharply with higher biodiesel content (Fig. 10). This behavior stems from the lower aromatic content and higher oxygen availability in biodiesel, which restricts soot precursor formation [48]. These results echo the findings of Dey et al. [49] and Samuel and Okwu [38], reinforcing biodiesel's environmental advantages. Additionally, the interplay between injection pressure and smoke emission trends suggests that fuel-jet dynamics and local air–fuel ratios critically impact soot formation tendencies.

Fig. 10.

The effect of injection pressure, engine torque, and biodiesel ratio on Smoke

ANN results

This section describes the Artificial Neural Network's outcomes. As depicted in Figure 11, an ANN structure was developed to predict responses using experimental data in the current investigation. For the prediction of responses, the experimental data were examined with the neural fitting tool, and the ANN model was trained using a backpropagation algorithm with Levenberg–Marquardt optimization, ensuring high prediction accuracy, following approaches outlined by Kumar et al. [50] and Bano et al. [51].

Fig. 11.

Schematized structure of the ANN model

As shown in Table 6, the training function TRAINLM and the transfer function TANSIG were employed. MSE was utilized to analyze the network's performance (minimum square error). The network consists of three inputs (injection pressure, engine torque, and biodiesel ratio), a hidden layer with fifteen neurons, and an output layer monitoring seven dependent variables (BTE, SFC, EGT, NOx, HC, CO, Smoke). 70% of the data was randomly allocated to training, while 30% was allocated to testing.

Table 6.

Specifications of ANN

Specifications
Network Type	Feed-forward back propagation
Data	70% trainnig, 30%testing, Number of neuron-15
Function type	TRAINLM
Adaption learning function	LEARNGDM
Performance function	MSE
Transfer function	TRANSIG
Shape of network	Input layer 1, hidden layer 1, output layer 1

The ANN model was subjected to many training and testing iterations in succession, and the estimates obtained for each response were evaluated using Table 7's RMSE and R values.

Table 7.

Summary of result ANN

Predicted Responses	RMSE	R2	Training data (R)	Testing data (R)	All data (R)
BTE	0.497%	0.896	0.9999	0.9595	0.9470
SFC	2.290 g/kWh	0.992	0.9999	0.9821	0.9967
EGT	15.483 °C	0.984	0.9980	0.9805	0.9926
NOx	18.228 ppm	0.984	0.9958	0.9818	0.9920
HC	10.948 ppm	0.885	0.9937	0.9847	0.9412
CO	0.157%	0.981	0.9999	0.9892	0.9905
Smoke	2.83%	0.910	0.9683	0.9470	0.9543

Anticipated values for BTE, SFC, and EGT are shown in Figure 12, along with R² values of 0.896, 0.992, and 0.984, and RMSE values of 0.497%, 2.290 g/kWh, and 15.483 degrees Celsius. Figure 13 presents the predicted values for NOx, HC, CO, and Smoke emissions, with R² values of 0.984, 0.885, 0.883, and 0.910 with RMSE values of 18.228 ppm, 10.948 ppm, 0.157%, and 2.83%. The constructed ANN model demonstrated good prediction ability, notably with a high correlation coefficient. As a result, and as stressed by numerous research, ANN was found to be quite beneficial and effective for predicting responses [2, 52–56].

Fig. 12.

Comparison of measured engine performance values and ANN-predicted results

Fig. 13.

Comparison of measured exhaust emission values and ANN-predicted results

Optimization Results for Fuel Mixture

In this work, RSM was used to estimate the optimal diesel and biodiesel fuel mixture for engine performance and exhaust emissions. Figure 14 depicts the selected ideal results and the desirability value. The highest value of the desirability surface graph was calculated to be 0.750 at a biodiesel concentration of 100 percent. Therefore, it has been determined that the appropriate biodiesel concentration is extremely effective.

Fig. 14.

Selection of optimal values

Table 8 contains the optimal value constraints that have been determined. While maximum BTE is necessary, EGT, SFC, and exhaust emissions should be reduced. Consequently, upper and lower limits are specified based on experimental results.

Table 8.

Constraints of optimization

Name	Goal	Lower Limit	Upper Limit	Lower Weight	Upper Weight	Importance
A:Injection pressure	is in range	180	240	1	1	5
B:Engine torque	is in range	3.06	12.26	1	1	5
C:Biodiesel ratio	is in range	0	100	1	1	5
NOx	minimize	294.149	908.449	1	1	5
HC	minimize	10	105	1	1	5
CO	minimize	0.06	1.48	1	1	5
SMOKE	minimize	10	45	1	1	5
EGT	minimize	253.253	659.414	1	1	5
BTE	maximize	21.0587	27.1661	1	1	5
SFC	minimize	335.483	431.956	1	1	5

In Table 9, a comparative presentation of the ACKTR-DE and HHO optimization algorithms, applied to motor performance and emission parameters optimized using ANN and RSM models, was provided. The comparison was performed based on the best fitness values obtained for each parameter. The results were comprehensively evaluated in terms of both motor performance (BTE, SFC, and EGT) and emission characteristics (CO, HC, NOx, and Smoke). The comparative analysis of the ACKTR-DE and HHO algorithms employed for the optimization of engine performance and exhaust emissions revealed that the HHO algorithm generally exhibited superior performance. Under both ANN and RSM modeling approaches, the HHO algorithm achieved higher efficiency in terms of BTE while attaining lower values for SFC, CO, HC, and Smoke emissions. These results indicate that the HHO algorithm is more effective than ACKTR-DE in reducing fuel consumption and mitigating environmental impacts. However, variability was observed in EGT and NOx emissions depending on the modeling framework, where HHO performed better under ANN modeling, whereas ACKTR-DE produced lower emission outputs under RSM modeling.

Table 9.

Best fitness values for ACKTR-DE and HHO

	Coupled with ANN		Coupled with RSM
Parameter	ACKTR-DE	HHO	ACKTR-DE	HHO
BTE (%)	27.2141	27.2183	26.95	26.99
SFC (g/kWh)	335.68	335.29	339.01	338.49
EGT (0C)	246.64	244.91	267.59	271.96
CO (%)	0.0877	0.0822	0.0243	0.0205
HC (ppm)	13.87	13.44	6.42	5.7
NOx (ppm)	298.38	295.91	331.61	341.52
Smoke (%)	11.22	11.09	11.37	9.42

These findings suggest that the selection of an optimization algorithm should depend on the nature of the targeted parameters and the modeling approach adopted. Nevertheless, when the overall trend is considered, the HHO algorithm appears to offer broader advantages in enhancing engine efficiency and minimizing emissions. In particular, when the aim is to improve fuel economy alongside reducing CO, HC, and Smoke emissions, HHO can be regarded as the primary choice. Conversely, when more precise control over parameters such as EGT and NOx is required, the ACKTR-DE algorithm should also be considered as an alternative solution depending on the modeling strategy.

The ANN and RSM findings were evaluated using the HHO and ACKTR-DE algorithms. Figures 15 and 16 illustrate the convergence behavior of the HHO and ACKTR-DE algorithms in terms of optimizing engine performance and reducing exhaust emissions.

Fig. 15.

Convergence curves of the ACKTR-DE and HHO algorithms based on ANN and RSM engine performance findings

Fig. 16.

Convergence curves of the ACKTR-DE and HHO algorithms based on ANN and RSM exhaust emission findings

The high R² values (ranging between 97% and 99%) obtained for engine performance and exhaust emissions indicate the strong predictive capability of the developed RSM models. However, to fully validate the reliability of the model, a series of validation experiments were conducted under optimum conditions, and the results were compared with the model predictions. Accordingly, a set of validation experiments was carried out for the optimum values presented in Figure 14, and the results are summarized in Table 10.

Table 10.

Validation experiment results based on optimum RSM results

Parameters	RSM (R2) (%)	RSM Results	Validation experiments	Accuracy (%)
BTE (%)	0.9855	26.030	25.783	99.05
SFC (g/kWh)	0.9943	393.786	395.471	99.57
EGT (0C)	0.9997	315.250	305.628	96.95
NOx (ppm)	0.9997	428.109	419.356	97.96
HC (ppm)	0.9793	10.000	10.145	98.55
CO (%)	0.9963	0.362	0.359	99.17
SMOKE (%)	0.9785	17.261	17.995	95.75

Validation experiments were conducted in triplicate

As a result of the validation tests, the measured values for engine performance parameters, namely BTE (%), SFC (g/kWh), and EGT (°C), were 25.783, 395.471, and 305.628, respectively. For the exhaust emissions, the validation test results yielded NOx (ppm), HC (ppm), CO (%), and Smoke (%) values of 419.356, 10.145, 0.359, and 17.995, respectively. When comparing the RSM predictions with the validation results, it was observed that the accuracy rates ranged between 95.75% and 99.57% across all parameters, indicating a high level of agreement between predicted and experimental values. These findings confirm the precision of the optimization process and validate the safe applicability of the developed mathematical model for optimizing both engine performance and exhaust emissions.

Conclusion

In this study, the effects of adding 0%, 50%, and 100% biodiesel to diesel fuel on engine performance and exhaust emissions were investigated. Simultaneously, an experimental design was developed, and optimization and prediction studies were conducted using Response Surface Methodology (RSM) and Artificial Neural Networks (ANN) based on experimental data.

The R² values obtained from the regression models developed through the RSM approach ranged between 0.9785 and 0.9997, while those for the ANN models ranged between 0.88 and 0.990, indicating exceptionally strong correlations for both methods. These results demonstrate that both models are applicable and reliable for predicting engine performance and emission outcomes. Optimization was carried out using the RSM approach, achieving a desirability score of 0.750, thereby confirming the accuracy and suitability of the optimization process. RSM was preferred over ANN for optimization purposes, as the fluctuating weights and biases inherent to ANN models across retrials render it unsuitable for stable optimization. Nonetheless, the ANN model still provided highly accurate predictions with individual R values ranging between 0.94 and 0.99, predicting all responses with R > 0.99 and a maximum mean absolute error (MAAE) of 1.723%.

As a result of RSM-based optimization, the optimum engine performance and emission values were achieved at an injection pressure of 180 bar, an engine torque of 3.846 Nm, and a biodiesel ratio of 100%. The ideal values obtained were NOx = 428.111 ppm, HC = 9.999 ppm, CO = 0.362%, Smoke = 17.261%, EGT = 315.252 °C, BTE = 26.029%, and SFC = 393.786 g/kWh.

To validate the optimization process, a series of experimental tests were performed under optimum conditions. The validation results for BTE, SFC, EGT, NOx, HC, CO, and Smoke exhibited a high degree of agreement with the RSM predictions, achieving accuracy rates between 95.75% and 99.57%. These findings confirm the robustness and safe applicability of the developed mathematical models for optimizing engine performance and exhaust emissions.

Moreover, the comparative analysis of the ACKTR-DE and HHO optimization algorithms revealed that the HHO algorithm generally exhibited superior performance in optimizing both engine efficiency and emission characteristics. HHO achieved higher BTE and lower SFC, CO, HC, and Smoke emissions across both ANN and RSM models. Although minor variations in EGT and NOx emissions were observed depending on the modeling approach, the overall findings suggest that HHO is more effective in improving fuel economy and reducing harmful emissions, while ACKTR-DE remains a viable alternative when precise control of EGT and NOx is required.

In summary, the addition of biodiesel to diesel fuel was found to enhance engine performance while reducing exhaust emissions. Among the parameters studied, although injection pressure and engine torque influenced combustion and performance characteristics, the biodiesel ratio had the most significant impact. Future studies could further enhance optimization and prediction outcomes by increasing the number of evaluated parameters or by incorporating additional combustion-related factors.

Abbreviations

ACKTR-DE

Actor Critic with Kronecker-Factored Trust Region-Differential Evolution

ANN

Artificial Neural Network

ANOVA

Analysis of Variance

BTE

Brake Thermal Efficiency

CCD

Central Composite Design

CO

Carbon Monoxide

DOE

Design of Experiments

EGT

Exhaust Gas Temperature

HC

Hydrocarbon

HHO

Harris Hawks Optimization

MAAE

Maximum Mean Absolute Error

MSE

Mean Square Error

NEORL

Neuroevolution Optimization with Reinforcement Learning

RMSE

Root Mean Square Error

RSM

Response Surface Methodology

SFC

Specific Fuel Consumption

Author contributions

M.A.B.: Investigation and Writing—Original Draft, Methodology, Conceptualization, Optimization of Experimental data, Formal analysis and Writing Visualization and Review and Editing. M.B. C.: Investigation and Writing—Original Draft, Methodology, Validation, Conceptualization, Review and Editing. E. O.: Investigation and Writing—Original Draft, Methodology, Validation, Conceptualization, Review and Editing.

Funding

An organization or institution has not offered funding support.

Data availability

Data will be made available on request.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.