Abstract

Due to the depletion of fossil fuel reserves, the significant pollution produced during their combustion and the increasing costs, biodiesel sources have gained recognition as an attractive alternative energy source. The integration of carbon nanotubes (CNTs) as a catalyst with biofuels such as biodiesel and bioethanol has the potential to optimize engine performance and reduce emissions when used in conjunction with diesel fuel. An emissions and performance prediction model for diesel engines is introduced in this research, utilizing biodiesel and CNTs in conjunction with machine learning. Due to its proficiency in forecasting systems with limited data, the emotional artificial neural network (EANN) model of machine learning was implemented. As an innovative approach, this study considers the following variables: fuel calorific value, fuel speed, engine density, viscosity, fuel consumption, exhaust gas temperature, oil temperature, oxygen output from exhaust gas, humidity, ambient temperature and ambient air pressure. The model was informed of every effective technical and functional environment parameter. This study additionally assessed the pollution and engine performance forecasts generated by the EANN model. Adding 5% biodiesel to gasoline fuel decreased carbon monoxide emissions while increasing torque and braking power, according to the findings. The fuel’s specific consumption increased. These findings were consistent with previous investigations. Moreover, as the concentration of CNTs in the fuel mixture increased, NOx, NO, CO2 and CO emissions decreased. The addition of 120 ppm of CNT to biodiesel–diesel fuel decreased emissions of CO, NO, NO2 and NO by 12.90%, 14.53%, 18.80% and 47.68%, respectively. The performance of the EANN model was found to be optimal when trained with the rectified linear unit activation function, as demonstrated by the evaluation results using various neurons.

1 Introduction

The recent surge in population, excessive consumption of fossil fuels and rapid technological advancements have resulted in environmental pollution as a byproduct of industrial development [1–4]. The use of fossil fuels significantly reduces the emissions of these harmful pollutants [5–7]. The future of global energy depends on sustainable renewable energy sources [8–10]. The renewable nature of biofuels has prompted extensive research into their potential replacement for fossil fuels [11]. Biodiesel and bioethanol are the most common liquid biofuels globally. Biodiesel is a diesel fuel substitute made from animal or plant fatty acids, typically in the form of methyl or ethyl ester [12–14]. Bioethanol, or bioethanol, is an alcohol compound with two carbon atoms and the chemical formula C2H5OH [15, 16]. This fuel has a higher octane rating than gasoline and contains an oxygen atom in its molecular structure, which increases combustion efficiency [17].

The inclusion of nanoparticles or nanocatalysts in the diesel–biodiesel fuel blend enhances the fuel’s performance, reduces engine pollution and improves its physical and thermal properties [18–20]. This includes augmenting the surface-to-volume ratio and thermal conductivity, among other factors. Multiple studies indicate that the inclusion of nanomaterials in diesel fuel, biodiesel and diesel–biodiesel fuel blends has resulted in higher ignition points, kinematic gravity and other properties [21–23]. The combustion process in the engine can directly affect the durability and wear of engine parts through mechanical vibrations. The parameters that have an impact on engine body vibration in compression ignition and spark ignition engines include injector injection, injection time, fuel quantity, fuel type and combustion dynamics [24, 25]. Adding biodiesel to the diesel–biodiesel fuel mixture induces alterations in engine body vibration resulting from combustion and pressure fluctuations within the cylinder [26].

Carbon nanotubes (CNTs) have sparked widespread interest as a catalyst support in heterogeneous catalytic processes due to their unique electrical properties, resistance and exceptional thermal conductivity [27]. CNTs, with their tubular network structure and meso-cavities, help to transport reactants and products. In addition, these bases are resistant to acidic and alkaline environments, as well as coke formation. However, due to their hydrophobic nature, CNTs are used in polar solvents to improve base dispersion [28]. The formation of oxygenated functional groups on the nanotube surface is critical in achieving a uniform distribution of the active phase on the base surfaces, as well as providing sites for the nucleation and growth of active phase particles during catalyst production [29]. CNTs are functionalized as part of the chemical purification process. Nanotube functionalization can be divided into two categories: covalent and noncovalent approaches [30]. The most common method for producing oxygenated functional groups is chemical oxidation. Temperature, duration, type and concentration of oxidants and oxidation method all have an impact on functional group formation [31].

Intelligent systems, including machine learning models, have gained increasing attention in addressing complex problems that lack specific and definitive solutions in recent years. These models derive the hidden relationships in the information [32–34]. The utilization of machine learning techniques offers distinct benefits compared to the application of traditional and deterministic statistical methods [35, 36]. In the linear regression model, the values need to be centered around a mean value, whereas this requirement does not apply to the neural network [37]. As a result, it maintains the integrity of the data modifications. Due to the multitude of factors influencing engine performance and emissions, and the impracticality of conducting tests in every scenario, machine learning models are employed. Studies have been conducted on engine performance and emissions utilizing neural networks, with minimal input provided to the neural network. Nevertheless, it is evident that factors such as density, viscosity, calorific value of fuel, inlet duct pressure, exhaust gas temperatures and oxygen levels in exhaust gases have an impact on the engine’s performance and emissions. Fortunately, these issues can be addressed by employing neural network technology. Artificial neural networks and time series are employed for the purpose of simulating and monitoring the condition of the system [38]. Artificial neural networks have proven effective in addressing diverse engineering challenges, particularly those that conventional modeling approaches cannot adequately address [39]. The predictive capability of an artificial neural network is achieved through training on experimental data and subsequent validation using additional data [40]. Machine learning possesses the capability to discern connections between inputs and outputs of a process, without necessitating intricate physical conditions [41, 42]. It possesses the capability to establish a connection between two multidimensional spaces, despite the presence of incomplete and erroneous information. The aforementioned attributes have rendered it appropriate for addressing estimation and forecasting challenges in the domains of agriculture and industry. Additionally, the neural network demonstrates efficacy in scenarios involving non-linear relationships [43].

The effect of incorporating cerium oxide nanoparticles into biodiesel fuel on the emission reduction of a diesel engine was examined by Ganesh and Gowrishankar [44]. The findings indicated that the incorporation of this nanoparticle into biodiesel led to an elevation in its ignition point, serving as an indicator of its volatility. Biodiesel’s gravity is proportional to the quantity of cerium oxide nanoparticles present. The degree of diffusion and variations are intrinsically linked to the concentration of nanoparticles. The range analyzed was between 20 to 80 ppm. Additionally, it was observed that the thermal efficiency of braking generally improves as the dose level of nanoparticles increases.

Canakci et al. [45] examined the effects of combining diesel and biodiesel fuel mixtures with an artificial neural network on diesel engine performance and emissions. The target network incorporated the following output parameters for each fuel, including average molecular weight, net heat of combustion, specific gravity, kinematic viscosity and carbon to hydrogen ratio. The performance R value was 0.99, and the mean error rate of the training data was below 2.4%. The R value for the evaluation data was computed to be 0.99, with an average error rate below 5.5%. Soufi et al. [46] utilized an artificial neural network to assess the performance and emissions of a two-stroke spark ignition engine operating in bioreactors. Type of lubricant and engine speed constituted the input parameters for the engine. The model in use incorporated engine braking power, torque, fuel consumption via viscosity and exhaust gases as output parameters. A multilayer perceptrons (MLPs) was designed to address the issues of performance and pollution. Its architecture comprised 25 hidden layers, 8 output layers and 3 input layers. Kapusuz et al. [47] predicted torque, braking power and specific fuel consumption in spark ignition engines using neural networks. The findings indicated that the corresponding values of R for specific fuel consumption, braking power and torque were 0.9312, 0.997 and 0.9906, respectively.

The purpose of this study is to present a machine learning-based model for predicting performance variables and emissions of a diesel engine powered by biodiesel and CNTs. The emotional artificial neural network (EANN) machine learning model was chosen because it performs well in predicting systems with limited data. In this study, the input variables for the EANN model are engine speed, fuel density, viscosity and calorific value, fuel consumption, exhaust gas temperature, oil temperature, oxygen output from exhaust gas, humidity, ambient temperature and ambient air pressure, as part of a novel strategy. Previous studies commonly used fuel type, load and engine speed as input variables, which are limited; however, in this study, all effective parameters of the technical and functional environment were considered as input to the model. In addition, the EANN model’s ability to predict pollution levels and engine performance data was tested.

2 Materials and methods

2.1 Laboratory instrument

A single-cylinder, four-stroke, air-conditioned diesel engine was used in this study (Lombardini Model 3LD510). The engine was launched at a pressure of 878 mbar and a temperature of 20°C. Motor load and torque were measured using an eddy current dynamometer. An AVL DITEST GAS 1000 emission analyzer was used to measure engine pollution.

2.2 Test fuel sample

The fuel’s compatibility with diesel fuel does not necessitate any modifications to the diesel engine infrastructure; however, all systems and components associated with diesel fuel storage and distribution can be adapted to accommodate biodiesel. Biodiesel is a fatty acid monoalkyl esters mixture [48]. The transesterification process, which involves the reaction of triglycerides (the primary components of oil and fat) with short chain alcohols like ethanol and methanol, is the typical method used to produce biodiesel. Biodiesel is derived from renewable and natural sources, including animal fats and vegetable oils [49].

According to the American Society for Testing and Materials (ASTM), the definition of biodiesel is as follows: monoalkyl esters of long chain fatty acids generated from renewable lipids such as vegetable oils or animal fats [50]. In the presence of a catalyst, biodiesel can be made by transesterifying a natural triglyceride (such as animal fat or vegetable oil) with a short chain alcohol. The production of biodiesel yields an important and useful byproduct known as glycerin. The fuel product that is formed from the reaction of alcohol with triglyceride is recognized as biodiesel. This reaction is known as the transesterification reaction or alcoholysis. The standards EN 14214-12 and ASTM D6751-12 are utilized in order to measure this. The transesterification process was utilized in this investigation to facilitate the production of biodiesel from waste sunflower vegetable oil (Table 1). CNT was combined with B5 fuel (composed of 5% biodiesel and 95% diesel) at concentrations of 30, 60, 90 and 120 ppm, respectively. The characteristics of the CNT that was employed are illustrated in Figure 1.

Table 1

Biodiesel and diesel fuel characteristics and standards

PropertiesDieselBiodiesel (tested)Standard (biodiesel)
Flashpoint (°C)165176>130
Kinematic viscosity (mm2/s)2.664.391.9 to 6
Density (g/cm3)0.8230.8930.87 to 0.9
Cloud point (°C)+9−3 to 12
PropertiesDieselBiodiesel (tested)Standard (biodiesel)
Flashpoint (°C)165176>130
Kinematic viscosity (mm2/s)2.664.391.9 to 6
Density (g/cm3)0.8230.8930.87 to 0.9
Cloud point (°C)+9−3 to 12
Table 1

Biodiesel and diesel fuel characteristics and standards

PropertiesDieselBiodiesel (tested)Standard (biodiesel)
Flashpoint (°C)165176>130
Kinematic viscosity (mm2/s)2.664.391.9 to 6
Density (g/cm3)0.8230.8930.87 to 0.9
Cloud point (°C)+9−3 to 12
PropertiesDieselBiodiesel (tested)Standard (biodiesel)
Flashpoint (°C)165176>130
Kinematic viscosity (mm2/s)2.664.391.9 to 6
Density (g/cm3)0.8230.8930.87 to 0.9
Cloud point (°C)+9−3 to 12
(a) TEM, (b) scanning electron microscope (SEM) additive carbon nanotubes (CNTs) to the biodiesel fuel.
Figure 1

(a) TEM, (b) scanning electron microscope (SEM) additive carbon nanotubes (CNTs) to the biodiesel fuel.

The addition of CNTs to biodiesel, as shown in Table 1, alters various fuel characteristics such as flashpoint, kinematic viscosity, density and cloud point. These changes can affect fuel combustion behavior, engine operation and subsequent emissions profiles.

The biodiesel–CNT blends exhibit elevated flashpoint and density in comparison to pure biodiesel. These characteristics suggest possible enhancements in fuel stability and energy content, which could have an impact on emissions formation and combustion efficiency. Furthermore, alterations in the observed kinematic viscosity and cloud point indicate potential adjustments in the atomization of fuel, spray properties and cold-start efficiency. These modifications could have an impact on the kinetics of combustion and emissions.

The combustion characteristics of biodiesel–CNT blends were discernibly different when compared to those of pure biodiesel or conventional diesel. The combustion stability and efficiency are impacted by the modifications in fuel–air mixing dynamics, flame propagation mechanisms and heat release profiles that occur in the presence of CNTs.

2.3 Emotional artificial neural network

ANNs are computational models inspired by the structure of the human nervous system. These networks consist of a number of computational units known as neurons or nodes, and weighted connections between these units. Each neuron receives specific inputs from previous neurons, combines them with designated weights and produces an output. In the context of materials and methods, ANNs are utilized as a computational tool for various applications, leveraging their ability to learn and generalize patterns from data through a training process. The weights in the network are adjusted during training to optimize the model’s performance in tasks such as classification, regression or pattern recognition. This methodology allows ANNs to adapt and make predictions based on input data, making them valuable tools in diverse scientific and engineering fields. EANN models represent a sophisticated progression from conventional ANN models. They are equipped with a synthetic sensing device that is capable of secreting hormones in order to regulate the activity of neurons, or nodes [51–53].

The value of the hormone’s weight can change depending on the input and output values of the nodes in the network. Every node in the EANN is able to generate the dynamic hormones Ha, Hb and Hc, in addition to supporting the continuous transmission and reception of information between its input and output components. This is accomplished through the use of a mechanism known as a dynamic hormone generator. In the beginning of the phase where the model is being trained, the coefficients are aligned depending on the correlation that exists between the input and the output. After that, the alignment is improved by repeatedly going through the iteration process [54, 55].

Node components are affected by hormonal coefficients, such as the activation function, net function and weight. The output of the EANN model incorporating the three hormones Ha, Hb and Hc is demonstrated in Equation (1).

(1)

where the h, i and j correspond to the input neurons, hidden layers and output layers, respectively. The f denotes an activation function. Equation (2) represents the quantification of artificial hormones. The statistical neural weight |${\gamma}_i$| and the harmonic weight |$\sum_h{\partial}_{i,h}{H}_h$| are utilized to apply to the f. The second and third components are correspondingly associated with the applied weights. The net function and the input value |${\chi}_{i,h}$| are determined by neuron j in the preceding layer. The fourth component consists of the bias of the network function, which encompasses neuronal and hormonal weights |${\alpha}_i$|⁠, |${\Phi}_{i,j,k}\sum_h\kern0.20em {\chi}_{i,h}{H}_h$|⁠, |${\chi}_{i,h}$|⁠, |${\Phi}_{i,j,k}$|⁠,|${\partial}_{i,h}$|⁠. The parameters regulate the hormone level (Hh) in each hormone. The neuron output (⁠|${Y}_i$|⁠) provides hormonal feedback |${H}_{i,h}$| to the system, as described in Equation (3). The calibration of the EANN’s glandity is crucial throughout the training phase to guarantee the gland receives the appropriate hormone level [56].

(2)
(3)

In this particular investigation, the process of network training makes use of the emotional back propagation (EmBP) algorithm. EmBP connects the learning parameters (learning factor (η) and movement rate (α)) with the sensitivity parameters (disturbance coefficient (μ) and confidence coefficient (k)) to minimize the amount of time spent on computation and the amount of error that occurs during calculation. The values of μ are dependent not only on the pattern of inputs but also on the total inaccuracy in the output of each iteration. When it comes to updating weights, EANN uses the same law as the BP algorithm. While only complex computations are carried out in the network convergence layer, the output layer is responsible for classifying the networks. The error value in the output neuron (Δ), is back-propagated during each iteration of the EmBP training process. This allows for the normal weights (wjh) and bias (wjb) of the hidden layer to be adjusted in accordance with Equations (4) and (5).

(4)
(5)

where |${\delta}_{\mathrm{wih}}\left(\mathrm{old}\right)$| is the last value of the alternating weight, |${\delta}_{\mathrm{wjb}}\ \left(\mathrm{old}\right)$| is the last value of the alternating bias and |${\mathrm{YH}}_{\mathrm{h}}$| is the output of the hidden neuron. The sentiment weight (wjm) is updated (Equation 6).

(6)

The term |$\delta{w}_{jm}\left(\mathrm{old}\right)$| represents the previous alternating emotional weight, whereas Yavg denotes the average value of the input pattern on the EANN model in each iteration. The values of μ and k are represented by Equations (7) and (8) in this equation [57].

(7)
(8)

where μ0 is the value of the disturbance factor at the end of the first repetition period. In a similar way, the adjustment of the input layer to the displacement and weight of a hidden layer is done.

The proposed model’s performance was evaluated using mean average error (MAE), mean standard error (MSE), root mean square error (RMSE) and correlation coefficient (R). In Equations (9) to (12), Xi represents the predicted value, Yi represents the actual value, |$\overline{X},\overline{Y}$| represent the data’s mean value and N is number of data.

(9)
(10)
(11)
(12)

Before training the model, the input and output parameters were placed in the data set. The inputs in the data set were normalized with the equation that lies between 0 and 1 domains (Equation (1)).

(13)

3 Results and discussion

According to Table 2, the addition of 5% biodiesel to gasoil fuel reduced the amount of CO pollutant while increasing torque and braking power. The specific fuel consumption has also been improved. These findings are consistent with the findings of Atadashi et al. [58], who found that while biodiesel in diesel engines reduces CO, suspended particles and SO2, the presence of O2 in the molecular structure of biodiesel increases NO in combustion products. It was discovered that increasing the concentration of CNT in different ratios of 30, 60, 90 and 120 reduces the amount of NOx, NO, CO2 and CO pollutants.

Table 2

Engine technical and environmental performance

FuelDensity (g/cm3)Heat valueTorque (N·m)Brake power (W)Specific fuel consumption (g/kWh)O2 (%)CO (ppm)CO2 (%V)NO (ppm)NOx (ppm)
B5CNT300.8410 60529.14479240.1212.79315.9333355
B5CNT600.8510 62329.584485245.0913.09055.8325342
B5CNT900.8510 63529.164489251.1113.28885.8312330
B5CNT1200.8610 63829.224502252.6913.88805.6300315
B50.8410 64029.44491238.0812.59695.9342351
Diesel0.8310 80129.164478261.7912.216826.9351362
FuelDensity (g/cm3)Heat valueTorque (N·m)Brake power (W)Specific fuel consumption (g/kWh)O2 (%)CO (ppm)CO2 (%V)NO (ppm)NOx (ppm)
B5CNT300.8410 60529.14479240.1212.79315.9333355
B5CNT600.8510 62329.584485245.0913.09055.8325342
B5CNT900.8510 63529.164489251.1113.28885.8312330
B5CNT1200.8610 63829.224502252.6913.88805.6300315
B50.8410 64029.44491238.0812.59695.9342351
Diesel0.8310 80129.164478261.7912.216826.9351362
Table 2

Engine technical and environmental performance

FuelDensity (g/cm3)Heat valueTorque (N·m)Brake power (W)Specific fuel consumption (g/kWh)O2 (%)CO (ppm)CO2 (%V)NO (ppm)NOx (ppm)
B5CNT300.8410 60529.14479240.1212.79315.9333355
B5CNT600.8510 62329.584485245.0913.09055.8325342
B5CNT900.8510 63529.164489251.1113.28885.8312330
B5CNT1200.8610 63829.224502252.6913.88805.6300315
B50.8410 64029.44491238.0812.59695.9342351
Diesel0.8310 80129.164478261.7912.216826.9351362
FuelDensity (g/cm3)Heat valueTorque (N·m)Brake power (W)Specific fuel consumption (g/kWh)O2 (%)CO (ppm)CO2 (%V)NO (ppm)NOx (ppm)
B5CNT300.8410 60529.14479240.1212.79315.9333355
B5CNT600.8510 62329.584485245.0913.09055.8325342
B5CNT900.8510 63529.164489251.1113.28885.8312330
B5CNT1200.8610 63829.224502252.6913.88805.6300315
B50.8410 64029.44491238.0812.59695.9342351
Diesel0.8310 80129.164478261.7912.216826.9351362

Although there was no discernible trend in terms of power, torque or fuel consumption, adding 120 ppm of CNT to biodiesel–diesel fuel reduced NOx, NO, CO2 and CO by 12.90%, 14.53%, 18.80% and 47.68%, respectively. In comparison to diesel fuel, specific fuel consumption occurred in biodiesel, and 2.04% more O2 was added to the exhaust output. However, there was no discernible trend in terms of power, torque or fuel consumption. Although no significant improvement in power or torque was observed, there was a 0.82% increase in torque and a 0.29% decrease in braking power when compared to diesel fuel. It is understood that the significant reduction in pollutants casts a shadow on the minor reduction in power and torque. CNTs generally led to greater enhancements in diesel engine performance and achieved satisfactory results in reducing pollutants. By adding CNT into a diesel–biodiesel fuel mixture, the heat value of the fuel rises, its cost falls and its density rises [59]. The decrease in gravity improves the spraying and atomization of the fuel inside the cylinder, which increases the engine’s power [60]. CNT catalyst, according to previous research, reduces ignition delay, resulting in higher peak pressure inside the cylinder and a faster heat release rate [61].

The results of EANN model with various neurons are shown in Table 3. This table displays the obtained values for MAE, MSE, RMSE and R for network training and testing. According to the results, the network trained with rectified linear unit (ReLU) activation function had the lowest MSE and the RMSE for engine performance, and this was done in two hidden layers where the values MSE, MAE, RMSE and R were 2.44, 2.71, 3.12 and 0.91, respectively, for the test phase. The best values performance for CO were in networks with the same number of layers and ReLU activation function, and the MSE, MAE, RMSE and R were 13.50, 11.29, 7.40 and 0.99, respectively, for the test phase.

Table 3

EANN model performance results

Activation functionStatisticTorqueNOxNOCO2COBrake power
TrainTestTrainTestTrainTestTrainTestTrainTestTrainTest
ReLUMSE2.392.443.505.515.146.150.150.2111.4113.500.570.61
Tanh3.713.814.645.646.256.290.180.2212.4913.551.631.69
ReLUMAE2.622.716.666.827.388.440.300.3310.2111.290.450.46
Tanh2.662.618.558.717.398.440.330.3911.3312.360.450.47
ReLURMSE3.183.1210.1211.179.1110.090.170.198.019.020.400.43
Tanh3.463.5211.1713.2310.1411.150.240.299.319.440.490.55
ReLUR0.990.910.990.960.990.990.980.970.990.990.990.99
Tanh0.990.890.980.970.990.950.980.890.990.900.970.92
Activation functionStatisticTorqueNOxNOCO2COBrake power
TrainTestTrainTestTrainTestTrainTestTrainTestTrainTest
ReLUMSE2.392.443.505.515.146.150.150.2111.4113.500.570.61
Tanh3.713.814.645.646.256.290.180.2212.4913.551.631.69
ReLUMAE2.622.716.666.827.388.440.300.3310.2111.290.450.46
Tanh2.662.618.558.717.398.440.330.3911.3312.360.450.47
ReLURMSE3.183.1210.1211.179.1110.090.170.198.019.020.400.43
Tanh3.463.5211.1713.2310.1411.150.240.299.319.440.490.55
ReLUR0.990.910.990.960.990.990.980.970.990.990.990.99
Tanh0.990.890.980.970.990.950.980.890.990.900.970.92
Table 3

EANN model performance results

Activation functionStatisticTorqueNOxNOCO2COBrake power
TrainTestTrainTestTrainTestTrainTestTrainTestTrainTest
ReLUMSE2.392.443.505.515.146.150.150.2111.4113.500.570.61
Tanh3.713.814.645.646.256.290.180.2212.4913.551.631.69
ReLUMAE2.622.716.666.827.388.440.300.3310.2111.290.450.46
Tanh2.662.618.558.717.398.440.330.3911.3312.360.450.47
ReLURMSE3.183.1210.1211.179.1110.090.170.198.019.020.400.43
Tanh3.463.5211.1713.2310.1411.150.240.299.319.440.490.55
ReLUR0.990.910.990.960.990.990.980.970.990.990.990.99
Tanh0.990.890.980.970.990.950.980.890.990.900.970.92
Activation functionStatisticTorqueNOxNOCO2COBrake power
TrainTestTrainTestTrainTestTrainTestTrainTestTrainTest
ReLUMSE2.392.443.505.515.146.150.150.2111.4113.500.570.61
Tanh3.713.814.645.646.256.290.180.2212.4913.551.631.69
ReLUMAE2.622.716.666.827.388.440.300.3310.2111.290.450.46
Tanh2.662.618.558.717.398.440.330.3911.3312.360.450.47
ReLURMSE3.183.1210.1211.179.1110.090.170.198.019.020.400.43
Tanh3.463.5211.1713.2310.1411.150.240.299.319.440.490.55
ReLUR0.990.910.990.960.990.990.980.970.990.990.990.99
Tanh0.990.890.980.970.990.950.980.890.990.900.970.92

Based on the analysis of various functional characteristics and engine pollution emissions, it is clear that the ReLU activation function with two hidden layers produces better results.

Table 4 shows the optimal execution rate and learning cycle for each number of neurons in the hidden layer. The results show that the neurons achieved the highest training rate in the double-layer implementation. The low performance number suggests that the network adapts quickly to these loads. Table 4 shows that the hyperbolic tangent (Tanh) activation function facilitated network formation at a lower execution rate. However, the results in Table 3 show that the ReLU activation function is the best topology. Indeed, when establishing a network, it is critical to consider both the speed and the topology. During network evaluation, it was discovered that the hyperbolic tangent activation function produced a faster network. Furthermore, using the ReLU activation function in a network with multiple layers resulted in a higher training rate.

Table 4

EANN topologies for various activation function

Activation functionTrainTest
ReLU-2 Execution35
Iteration15739
ReLU-3 Execution36
Iteration17149
Tanh-2 Execution35
Iteration9831
Tanh-3 Execution35
Iteration8825
Activation functionTrainTest
ReLU-2 Execution35
Iteration15739
ReLU-3 Execution36
Iteration17149
Tanh-2 Execution35
Iteration9831
Tanh-3 Execution35
Iteration8825
Table 4

EANN topologies for various activation function

Activation functionTrainTest
ReLU-2 Execution35
Iteration15739
ReLU-3 Execution36
Iteration17149
Tanh-2 Execution35
Iteration9831
Tanh-3 Execution35
Iteration8825
Activation functionTrainTest
ReLU-2 Execution35
Iteration15739
ReLU-3 Execution36
Iteration17149
Tanh-2 Execution35
Iteration9831
Tanh-3 Execution35
Iteration8825

Figures 2 to 7 display the regression coefficients for braking power, NOx, CO2, CO and torque over various networks. The most optimal regression coefficient for braking power was achieved in a network utilizing a ReLU activation function. On the other hand, the Tanh activation function failed to yield the desired values for the regression coefficient. In models with ReLU activation function, the regression coefficient for CO and CO2 was found to be the most optimal. However, the Tanh activation function failed to yield suitable regression coefficient values. The regression coefficient values for NOx and NO were found to be highest in networks utilizing a ReLU activation function. Specifically, the regression coefficient values for these two components exceeded 0.90 in networks employing the ReLU activation function. The Tanh activation function did not accurately predict the desired result. The model utilizing the ReLU activation function successfully achieved the desired regression coefficient for torque, but the network employing the hyperbolic tangent activation function failed to achieve the desired values.

A comparison between measured and predicted values obtained for torque. (a) ReLU and (b) Tanh activation function.
Figure 2

A comparison between measured and predicted values obtained for torque. (a) ReLU and (b) Tanh activation function.

A comparison between measured and predicted values obtained for brake power. (a) ReLU and (b) Tanh activation function.
Figure 3

A comparison between measured and predicted values obtained for brake power. (a) ReLU and (b) Tanh activation function.

A comparison between measured and predicted values obtained for CO emission. (a) ReLU and (b) Tanh activation function.
Figure 4

A comparison between measured and predicted values obtained for CO emission. (a) ReLU and (b) Tanh activation function.

A comparison between measured and predicted values obtained for CO2 emission. (a) ReLU and (b) Tanh activation function.
Figure 5

A comparison between measured and predicted values obtained for CO2 emission. (a) ReLU and (b) Tanh activation function.

A comparison between measured and predicted values obtained for NO emission. (a) ReLU and (b) Tanh activation function.
Figure 6

A comparison between measured and predicted values obtained for NO emission. (a) ReLU and (b) Tanh activation function.

A comparison between measured and predicted values obtained for NOx emission. (a) ReLU and (b) Tanh activation function.
Figure 7

A comparison between measured and predicted values obtained for NOx emission. (a) ReLU and (b) Tanh activation function.

Both ReLU and Tanh activation functions exhibit similar patterns of prediction for torque objective function. Data points cluster around the line of perfect prediction, indicating a good level of accuracy. However, there is noticeable dispersion of points around the line, suggesting some prediction error. This dispersion is expected in real-world scenarios due to various factors such as noise, measurement inaccuracies and system variability. The ReLU function (Figure 2a) shows slightly tighter clustering of points compared to the Tanh function (Figure 2b). This suggests that ReLU may offer higher predictive accuracy. The dispersion in the Tanh plot is slightly wider, indicating that the Tanh function might be more sensitive to outliers or nonlinearities. Both activation functions can be considered effective in predicting torque.

In Figure 3, for both activation function, data points cluster around the 45° line, indicating accuracy of the machine learning model. The ReLU function (Figure 3a) clusters points tighter than the Tanh function (Figure 3b). This suggests ReLU has better predictive accuracy. Tanh plot dispersion is wider, suggesting the Tanh function is more sensitive to outliers and nonlinearities. Both activation functions predict brake power well.

As shown in Figures 4 and 5, the prediction results of the model in the ReLU activation function are more closely aligned with the 45° bisector line for CO and CO2 emissions, respectively. Nevertheless, the model’s performance in the Tanh activator function is satisfactory for both outputs as well.

Observed and predicted NO emissions from a diesel engine powered by biodiesel containing CNTs are depicted in Figure 6. Two distinct activation functions were used to generate the predictions. Across the entire dataset, the predicted values for the ReLU activation function tend to underestimate the observed emissions by a small margin, with a few instances in which the predicted values are lower than the observed ones. This suggests that although the ReLU activation function is generally accurate, it might not consistently account for the complete variability of the observed emissions. For Tanh activation function results, similar to the ReLU activation function, the predicted values generally show a tendency to overestimate the observed emissions. However, in some instances, particularly at lower observed emission levels, the Tanh activation function appears to provide more accurate predictions compared to ReLU, as it tends to produce slightly lower predicted values.

Figure 7 contains observed and predicted NOx emissions from a diesel engine fueled with biodiesel containing CNTs, using two different machine learning techniques with different activation functions. Based on Figure 7a, it seems that the predicted values appear to slightly overestimate the observed values, with some exceptions where the predicted values are lower than the observed ones. The prediction performance seems relatively consistent across the range of observed values. Similarly, for the Tanh activation function (Figure 7b), the predicted values generally show a slight overestimation compared to the observed values, with some instances of underestimation. The overall prediction performance seems consistent across the observed range.

4 Conclusion

The study aimed to develop a machine learning model, specifically the EANN, for predicting performance variables and emissions of a diesel engine using biodiesel and CNTs. Unlike previous studies that focused on limited input variables such as fuel type, load and engine speed, this research considered all significant parameters of the technical and functional environment as inputs to the model. The EANN model’s ability to predict pollution levels and engine performance data was investigated.

The results showed that the addition of 5% biodiesel to gasoil fuel reduced CO emissions while increasing torque and braking power. It also improved specific fuel consumption. These findings were consistent with previous research. Furthermore, increasing the concentration of CNT in the fuel mixture resulted in reduced levels of NOx, NO, CO2 and CO pollutants. Adding 120 ppm of CNT to biodiesel–diesel fuel led to a significant reduction in NOx, NO, CO2 and CO emissions by 12.90%, 14.53%, 18.80% and 47.68%, respectively.

Although no discernible pattern was observed with regard to power, torque or fuel consumption, the incorporation of CNT had a negligible effect on these parameters in comparison to diesel fuel. Nevertheless, the marginal decline in power and torque was eclipsed by the substantial reduction in pollutants. CNTs demonstrated potential for improving diesel engine performance and reducing emissions. The incorporation of CNT improved the fuel’s density, decreased its cost and increased its heat value. Additionally, it enhanced fuel atomization and spraying within the cylinder, which resulted in increased engine output. Moreover, CNTs minimize the duration of ignition, leading to increased peak pressure and accelerated heat dissipation.

The performance of the EANN model was assessed using various neurons, and the findings indicated that the network that underwent training using the ReLU activation function and two hidden layers achieved the highest level of effectiveness. In every instance, the ReLU activation function comprising two hidden layers produced enhanced results in terms of engine performance and CO emissions. In addition, the optimal learning cycle and execution rate for each particular quantity of neurons in the hidden layers were ascertained. The implementation consisting of two layers was found to have the highest training rate. In network topology, the selection of the activation function was critical, and in terms of speed and performance, the ReLU activation function exhibited superiority over the Tanh activation function. It was determined that the ReLU activation function consistently generated optimal regression coefficients for braking power, CO, CO2, NOx and NO when regression coefficients for various networks were analyzed. The performance of the Tanh activation function in forecasting these variables was deemed unsatisfactory.

The addition of biodiesel and CNTs showed promising results in reducing pollutants while maintaining satisfactory engine performance. The ReLU activation function and a two-hidden-layer-network configuration were found to be optimal for the EANN model. Furthermore, our utilization of machine learning techniques underscores the importance of data-driven approaches in engineering research, particularly in the optimization of complex systems and processes. The integration of advanced computational tools with experimental methodologies enables a holistic assessment of fuel–engine interactions, facilitating informed decision-making and innovation in clean energy technologies.

It is critical to recognize the constraints of this investigation and propose possible directions for subsequent scholarly inquiry. The impact of CNT addition on biodiesel combustion and emissions is significantly enhanced by our research. However, it is important to note that the observed results could be influenced by various factors, including engine operating conditions, CNT dispersion characteristics and combustion chamber geometry.

Author Contributions

Ali Asghar Moslemi Beirami (Conceptualization [equal], Formal analysis [equal], Investigation [equal], Methodology [equal], Resources [equal]), Ebrahim Maghsoudlou (Data curation [equal], Investigation [equal], Software [equal], Validation [equal]), Mohammadali Nasrabadi (Conceptualization [equal], Investigation [equal], Methodology [equal], Validation [equal], Writing—original draft [equal]), Klunko Natalia Sergeevna (Conceptualization [equal], Formal analysis [equal], Methodology [equal], Writing—review & editing [equal]), Sherzod Abdullaev (Investigation [equal], Resources [equal], Software [equal], Writing—original draft [equal]) and Wubshet Ibrahim (Data curation [equal], Formal analysis [equal], Investigation [equal], Methodology [equal], Software [equal]).

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