Predictive Models for Biodiesel Performance and Emission Characteristics in Diesel Engines: A Review

Abstract

With the increasing global demand for renewable energy, biodiesel has become a promising alternative to fossil fuels with significant environmental benefits. This article systematically reviews the latest advances in predictive modeling techniques for estimating the characteristics of biodiesel and its impact on diesel engine performance. Various methods for predicting the key performance of biodiesel and the performance and emissions of diesel engines have been summarized. According to the categories of parameters, research cases in recent years have been listed and discussed separately. This review provides a comprehensive overview and serves as a reference for future research and development of biodiesel.

1. Introduction

With the increasing global demand for renewable energy, biodiesel as a clean energy source is being applied in an increasing number of fields. It can directly replace or be mixed with petroleum diesel and is widely used in transportation, agricultural machinery, power generation equipment, and other fields. In recent years, many countries and regions have promoted the production and use of biodiesel through policy incentives and regulatory requirements to reduce dependence on fossil fuels and reduce greenhouse gas emissions [1,2,3].

Among various alternative energy sources, biodiesel has become a highly promising alternative fuel due to its renewability, environmental friendliness, and compatibility with existing diesel engines [4]. Biodiesel is a fuel obtained through the transesterification reaction of vegetable oil, animal fat, or waste oil with alcohols (such as methanol or ethanol), and its main component is fatty acid methyl esters (FAMEs). Compared with traditional petroleum diesel, biodiesel can not only reduce greenhouse gas emissions but also effectively reduce the emissions of carbon monoxide (CO), hydrocarbons (HC), and particulate matter (PM), thereby reducing air pollution and improving environmental quality [5].

On a global scale, the application of biodiesel not only promotes the development of agriculture and industry but also effectively reduces dependence on petrochemical fuels [6]. However, despite the advantages demonstrated by biodiesel in the fields of environment and energy, there are still many problems in its practical application. For example, the physicochemical properties of biodiesel vary significantly due to differences in raw materials and production processes, which directly affect its performance in diesel engines [7]. In addition, the combustion characteristics, emission characteristics, and engine performance impact of biodiesel in engines also vary depending on the fuel composition. Thus, accurately predicting biodiesel properties and its performance in diesel engines is a key focus of current research [8].

The properties of biodiesel directly affect its performance in diesel engines. The physicochemical properties of biodiesel, such as viscosity, density, heating value, and oxidation stability, not only determine the combustion efficiency of the fuel in the engine but also affect the engine’s starting performance, fuel consumption, emission characteristics, and long-term reliability. In diesel engine systems, the combustion process of biodiesel directly affects the thermal efficiency, power output, and emission generation of the engine. For example, the high oxygen content of biodiesel can promote the completeness of the combustion process and reduce the emissions of HC and CO [9]. However, this characteristic may also lead to an increase in nitrogen oxide (NO_x) emissions. Therefore, during engine optimization design, it is crucial to consider both the physicochemical properties and combustion characteristics of the fuel. Accurate prediction models must be established to evaluate the overall performance of biodiesel.

In traditional research methods, the properties of biodiesel are mainly obtained through experimental measurements, but this method is not only time-consuming and costly but also has certain experimental errors [10]. As computing technology and data science advance, predictive methods based on mathematical models and machine learning (ML) have emerged as prominent areas of research. These methods can rapidly predict biodiesel properties by leveraging existing experimental data, providing a robust scientific basis for fuel development and application.

The establishment of predictive models can not only save a lot of experimental time and costs but also explore the impact of different raw materials and production processes on fuel performance, thereby optimizing the production process and improving fuel quality [11]. For example, prediction models based on linear regression, support vector machines (SVMs), and artificial neural networks (ANNs) can accurately predict key attributes such as heating value, viscosity, and oxidation stability of biodiesel [12]. The application of these models enables researchers to better understand the characteristics of different biodiesel fuels, providing effective tools for fuel optimization design. At the same time, an increasing number of researchers are adopting data-driven methods to predict the performance of biodiesel in engines. By analyzing a large amount of experimental data and training models, ML methods can capture the complex nonlinear relationships between fuel properties and engine performance, thereby achieving high-precision predictions. These methods provide new perspectives for studying biodiesel–engine interactions. They also offer robust support for optimizing fuel blends and engine design.

Due to its renewability, lower carbon dioxide emissions, and good biodegradability, biodiesel, as an important renewable energy source, offers significant environmental benefits and application prospects. Research related to biodiesel has rapidly developed, with researchers continually expanding the raw material sources, fuel blend formulations, and application scenarios for biodiesel [13,14]. The performance of biodiesel varies depending on the type of raw materials used [15]. Additionally, biodiesel is typically blended with diesel using additives for practical use. Therefore, the properties of biodiesel blends and their performance in diesel engines are more complex compared to other alternative fuels.

This article aims to systematically organize and review the research progress in predicting the properties of biodiesel and its performance in diesel engines in recent years. Starting from the key attributes and performance parameters of biodiesel, specific research cases were cited, covering application examples of different prediction models and experimental methods. This review highlights the advantages and limitations of these methods in practical research. These cases help identify best practices and potential improvements in current methods, provide guidance for future research, and promote further development of biodiesel applications.

2. Biodiesel

2.1. Production and Main Components of Biodiesel

Biodiesel is a renewable fuel obtained through the transesterification process from vegetable oils or waste edible oils. Compared with traditional petroleum diesel, biodiesel is a more environmentally friendly alternative fuel, mainly composed of FAMEs. The production of biodiesel is primarily achieved through transesterification reactions using raw materials such as edible oils, inedible oils, waste oils, and algae [16,17,18]. This process requires mixing the raw oil and fat with methanol or ethanol under the action of a catalyst, heating, and reacting to produce FAMEs and glycerol. Common catalysts include NaOH, KOH, and acidic catalysts such as H₂SO₄. The efficiency of the transesterification reaction is influenced by various factors, including reaction temperature, reaction time, molar ratio of alcohol to oil, and catalyst amount.

The composition of FAMEs varies depending on different raw oils and fats and usually includes the following main components [19,20,21]:

Saturated FAMEs, such as palmitic acid methyl ester (C16:0) and stearic acid methyl ester (C18:0), typically have high melting points and viscosities. Unsaturated FAMEs, such as oleic acid methyl ester (C18:1) and linoleic acid methyl ester (C18:2), have lower melting points and better fluidity. Linolenic acid methyl ester (C18:3) has a lower melting point and poorer oxidation stability.

The physical and chemical properties of biodiesel, such as density, viscosity, combustion characteristics, etc., are mainly determined by its fatty acid composition [22]. The structure of fatty acid components, including carbon chain length, saturation, number, and position of branched or double bonds, plays a decisive role in the final performance of fuels [23]. The composition of biodiesel results in distinct physical and chemical properties compared to petroleum-based diesel [24]. The advantages of biodiesel include high oxygen content, high cetane number, high flash point, and excellent lubricity [25]. Biodiesel molecules contain higher oxygen content than petroleum diesel, allowing for more complete combustion and reduced emissions of HC and CO [26]. The sulfur content of biodiesel is extremely low, which greatly reduces the emission of SO₂ and helps alleviate the formation of acid rain [27].

In addition to the aforementioned advantages, the drawbacks of biodiesel are also evident. The long fatty acid chains in biodiesel contribute to its high viscosity and low fluidity, particularly at low temperatures [28]. This characteristic is particularly evident in low-temperature environments and may cause clogging in fuel injection systems, which may be mitigated by using additives or blending with petroleum diesel. Meanwhile, unsaturated FAMEs are prone to oxidation, leading to the deterioration of biodiesel during storage [29]. Depending on the storage environment and the composition of biodiesel itself, this oxidative deterioration may accelerate [30]. To enhance its stability, it is typically necessary to add antioxidants and implement an appropriate storage strategy [31].

2.2. Main Properties Affecting the Performance of Biodiesel in Diesel Engines

2.2.1. Density and Kinematic Viscosity

The density of biodiesel is higher than that of diesel. The density increases as the fatty acid chain length decreases and the degree of unsaturation increases.

The density of biodiesel has a significant impact on its combustion characteristics and performance in diesel engines [32]. High-density biodiesel can lead to increased injection volume, poor fuel atomization quality, and thus affect the mixing efficiency and combustion completeness of air and fuel [33]. This phenomenon usually manifests as prolonged ignition delay and combustion duration. Ultimately, it will lead to a decrease in combustion efficiency and an increase in the generation of incomplete combustion products, affecting the overall performance and emission characteristics of the engine.

Kinematic viscosity significantly affects the spray characteristics and combustion quality of the fuel [34]. If the viscosity is too high, it may result in poor flow of the fluid between certain components, causing energy loss and reduced engine efficiency. At the same time, high viscosity often leads to the formation of larger droplets during injection, resulting in poor atomization [35].

2.2.2. Cetane Number

The cetane number (CN) is the key indicator for measuring the spontaneous combustion quality of fuel. The CN of biodiesel is affected by the chain length and degree of unsaturation of the FAMEs. Biodiesel usually has a higher CN than diesel fuel. A high CN helps reduce the formation of white smoke and improves cold start performance. A low CN will increase ignition delay, thereby increasing the likelihood of knocking in diesel engines [36].

2.2.3. Thermophysical Properties

The thermophysical properties of biodiesel, including heating value, thermal conductivity, specific heat capacity, and coefficient of thermal expansion (CTE), are the key factors affecting its combustion characteristics, heat transfer efficiency, and overall engine performance. These thermal properties are not only important for the energy output of fuel but also affect the temperature distribution and combustion efficiency in the combustion process.

Heating value is the energy released during fuel combustion, and it is an important index to measure the energy density of biodiesel. Biodiesel with a high heating value usually has a higher energy density and can provide greater power output [37]. Thermal conductivity determines the heat transfer efficiency of biodiesel in the combustion process and has a direct impact on the temperature distribution and combustion stability of the combustion chamber [38]. Specific heat capacity is an index describing the ability of fuel to absorb or release heat during heating, which directly affects the heating rate and combustion efficiency of fuel. The CTE, which measures the volume change of fuel when the temperature changes, has an important impact on the design and safety of fuel systems [39].

3. Classification of Prediction and Optimization Techniques for Biodiesel Properties and Engine Performance

3.1. Statistical Modeling and Regression Methods

Statistical modeling and regression methods are traditional analytical tools used to reveal and quantify relationships between variables. These methods describe patterns in data by establishing mathematical models that provide a basis for prediction. The following will introduce several commonly used statistical modeling and regression methods and their specific applications in biodiesel research.

Response surface methodology (RSM) is a method that combines experimental design, regression modeling, and optimization techniques, particularly suitable for handling multivariate problems in complex systems. In biodiesel research, RSM is commonly used to optimize fuel formulations, evaluate the effects of different production processes on biodiesel properties, and predict the performance and emission characteristics of diesel engines [40]. The construction of RSM models typically involves conducting quadratic regression analysis on experimental data to generate a mathematical equation that describes the relationship between input variables and output response. By analyzing these models, researchers can identify the factors that have the greatest impact on the properties of biodiesel and determine the optimal production conditions [41]. RSM has also demonstrated strong application potential in predicting diesel engine performance. The performance and emission characteristics of diesel engines are influenced by multiple factors, including fuel composition and engine operating conditions (such as speed and load), injection timing, and injection pressure [42,43]. RSM can systematically study the interaction of these factors and predict their impact on engine performance by designing a reasonable experimental plan.

Table 1. Comparison of predicted results from the RSM model and experimental validation results [44].

	NOx (g/kWh)	Smoke Opacity	CO2 (kg/kWh)	BTE (%)	BSFC (kg/kWh)
Predicted	16.918	10.228	0.624	35.874	0.253
Actual	17.178	10.55	0.646	35.5	0.2572
% Error	1.51	3.05	3.41	1.05	1.63

shows the comparison between the predicted results and experimental validation results after optimizing the three parameters: injection pressure, injection timing, and exhaust gas recirculation using the RSM model by Saravanan, S et al. [44].

Regression analysis methods are used to quantify the linear relationship between one or more independent variables and the dependent variable. The most basic linear regression can be used to estimate the production of biodiesel [45]. However, the limitation of linear regression is that it assumes that the relationship between variables is linear, while actual combustion processes often have complex nonlinear characteristics. Nonlinear regression is suitable for modeling complex relationships between variables using nonlinear functions [46]. In the research of biodiesel and engines, nonlinear regression can be used to predict complex dynamic changes during engine operation. For example, Figure 1 shows the variation of braking thermal efficiency with power output [47]. This enables researchers to describe engine performance under different conditions more accurately. Multiple regression is an extension of linear regression that allows for simultaneous analysis of the effects of multiple independent variables on a single dependent variable. In the study of biodiesel and engine performance, multiple regression is widely used to simultaneously consider the comprehensive impact of multiple factors (such as fuel composition, engine operating conditions, and environmental conditions) on the output results. For example, predicting the physical properties such as viscosity, density, and flash point of biodiesel based on raw materials [48]; predicting biodiesel performance based on fatty acid composition [49]; When predicting engine emissions (such as CO, NO_x, and HC), multiple regression models can integrate multiple input variables to establish a comprehensive prediction model [50].

Statistical modeling and regression methods have significant application value in the study of biodiesel and engine performance. They can provide clear explanations of variable relationships, which are easy to understand and implement. However, these methods typically assume that the model structure is known and there are no significant nonlinear or interactive effects in the data, which may limit their accuracy and applicability in practical applications. Therefore, when researchers use these methods, they usually need to perform sufficient preprocessing and exploratory analysis on the data to ensure the rationality and reliability of the model.

3.2. Machine Learning and Artificial Intelligence Methods

ML and artificial intelligence methods are increasingly important tools for predicting biodiesel properties and engine performance. This is due to their powerful nonlinear modeling capabilities, automatic feature learning capabilities, and advantages in processing high-dimensional data [51,52]. These methods can not only significantly improve prediction accuracy but also reduce the number of experiments and optimize the design process. The following are several common ML and artificial intelligence methods and their applications in predicting biodiesel properties and engine performance.

An ANN is a computational model that simulates biological neural networks and can learn complex nonlinear relationships between inputs and outputs through a large amount of training data. An ANN is particularly suitable for processing high-dimensional data and nonlinear systems, demonstrating extremely high accuracy in predicting the performance, such as brake thermal efficiency (BTE), brake-specific fuel consumption (BSFC), and emission characteristics of biodiesel blends [53,54,55]. Figure 2 shows the structure of the ANN used to study biodiesel performance and its performance in diesel engines. Research has shown that ANNs can accurately predict the performance and emissions of engines using different biodiesel blends by capturing the subtle impact of fuel composition changes on engine behavior. For example, when studying the effects of certain biodiesel additives on engine performance, ANN models can accurately predict how changes in additive concentration affect the combustion efficiency and emission levels of the engine by learning experimental data [56]. This high-precision predictive ability makes an ANN a valuable tool in biodiesel research.

SVM is a supervised learning model based on statistical learning theory, commonly used for classification and regression problems. The advantage of SVM in predicting the properties and engine performance of biodiesel lies in its powerful nonlinear processing capability and efficiency in processing high-dimensional data. SVM maps input data to a high-dimensional space through kernel functions, enabling it to identify and capture hidden patterns and relationships in complex biodiesel-blended fuel datasets [57,58]. Figure 3 illustrates the application of SVM in predicting biodiesel yield. The SVM has shown significant performance in optimizing the production process and composition of biodiesel [59,60]. When studying engine emission characteristics, SVM can handle complex combinations of input variables, such as different biodiesel components, engine operating conditions, etc., to provide accurate emission predictions [61].

A decision tree is a predictive model that establishes relationships between input variables and target outputs by recursively splitting the data [62]. Random forest is an ensemble method of decision trees that enhances the stability and accuracy of the model by constructing multiple decision trees and combining their prediction results. In the prediction of biodiesel properties and engine performance, random forest can automatically identify and select the most important feature variables, thereby improving prediction performance. For example, when predicting engine combustion efficiency or emissions, random forests can identify the factors that have the greatest impact on target output from multiple fuel components and engine operating variables, thereby improving the accuracy and reliability of predictions [63,64].

ML and artificial intelligence methods offer significant advantages in predicting the properties and engine performance of biodiesel. They are capable of handling complex nonlinear relationships, automatically extracting data features, and providing high-precision prediction results [65]. However, these methods also face challenges, such as the large amount of data required for model training, high data quality requirements, and the opacity of the models that may limit interpretability. To overcome these challenges, researchers are exploring hybrid models that combine ML with other methods to improve model interpretability while ensuring high-precision predictions [66,67].

3.3. Evolutionary Algorithms and Optimization Methods

Evolutionary algorithms and optimization methods are powerful tools developed based on the principles of natural selection and genetics and are widely used in solving complex problems and multi-objective optimization [68]. These methods are suitable for the prediction and optimization of biodiesel properties and engine performance because they can search for the optimal solution in a wide range of search spaces, deal with complex multi-objective optimization problems, and do not depend on the specific mathematical model of the problem. The following are some common evolutionary algorithms and optimization methods in recent years and their applications in biodiesel and engine research.

A genetic algorithm (GA) is an evolutionary algorithm that simulates the process of natural selection. It optimizes candidate solutions in the search space through selection, crossover, mutation, and other operations [69]. GA is widely used in biodiesel research, such as predicting the properties of biodiesel or optimizing the biodiesel production process [70,71]. In the prediction of biodiesel properties and engine performance, GA is used to find the best fuel ratio to optimize combustion efficiency and reduce emissions [72]. GA’s adaptability enables it to handle multi-objective optimization problems with complex nonlinear relationships and find the optimal fuel combinations and engine operating parameters.

Particle swarm optimization (PSO) is an optimization algorithm based on swarm intelligence that simulates the collective behavior of organisms, such as birds or fish, during foraging. PSO gradually approaches the global optimal solution through information sharing and cooperation among individuals. In biodiesel and engine research, PSO can be used to optimize multivariable systems, including fuel composition, engine tuning parameters. PSO is characterized by its fast convergence speed and simple calculation, which is especially suitable for continuous optimization problems [73]. Researchers can use PSO to find the optimal ratio of biodiesel-blended fuel to achieve the best combustion performance and the lowest emission level [74]. In addition, PSO can also be used to optimize the multi-objective performance of the engine, such as fuel economy and power output.

Genetic programming (GP) is an evolutionary computation method based on GA that is used to automatically generate computer programs. GP can be used to model complex nonlinear systems, predict the physical and chemical properties of biodiesel, and optimize the production process [75]. Figure 4 shows the GP tree model used for predicting kinematic viscosity [76]. In the prediction of biodiesel properties and engine performance, GP can generate nonlinear regression models or classifiers to predict engine performance and emissions under different fuel conditions. This method does not rely on the pre-defined model structure but automatically generates the optimal model through the evolution process. Researchers can use GP to generate a prediction model for simulating and optimizing engine operating parameters and fuel ratio to improve overall performance [77].

The application of evolutionary algorithms and optimization methods in biodiesel and engine research demonstrates great potential and flexibility. These methods can deal with complex multi-objective optimization problems and do not depend on the specific mathematical model of the problem, so they are widely applicable. However, these methods may face the problems of computational complexity and convergence speed when dealing with high-dimensional problems. In addition, the randomness and multiplicity of evolutionary algorithms may lead to the uncertainty of the results, which need to be addressed.

3.4. Scientific Modeling and Simulation Methods

Scientific modeling and simulation are key tools for studying complex physical and chemical processes. In the prediction and analysis of biodiesel and engine performance, these methods can simulate the actual combustion process and engine working state and provide in-depth theoretical support for optimizing design and improving performance [78]. Scientific modeling and simulation are not only limited to the analysis of experimental results but also can explore system behaviors under different conditions through virtual experiments so as to reduce the number and cost of actual experiments.

Computational fluid dynamics (CFD) is a scientific method that uses numerical analysis and data structures to simulate fluid flow. In biodiesel and engine research, CFD is widely used to simulate fluid flow, fuel injection, and combustion processes, as well as their impact on emissions in the combustion chamber [79]. CFD models can describe in detail the atomization, mixing, ignition, and combustion processes of fuel in the combustion chamber and predict engine performance and emission characteristics [80,81,82]. CFD simulation can provide the detailed distribution of temperature field, pressure field, and chemical reaction in the combustion process, which is very important for understanding the combustion behavior of biodiesel under different working conditions. For example, Gowrishankar, S. et al. [83] used CFD tools to compare and analyze the differences between conventional injection mode and premixed mode based on delayed injection. As shown in

Table 2. CFD simulation results of two injection strategies [83].

Combustion Mode	Cylinder Pressure (Error %)	Heat Release Rate (Error %)	Fuel Distribution	Temperature Distribution
Conventional	1.50%	13%	Near piston bowl	Higher overall
Late injection	10%	15%	Throughout the combustion chamber	Lower temperatures

.

The chemical kinetic model is used to simulate the chemical reactions in the combustion process, including reaction rate, product distribution, heat release, etc. In biodiesel combustion, chemical kinetic models can help to study the decomposition, oxidation, and product formation processes of fuel molecules under high temperature and high pressure [84,85]. At present, the study of chemical kinetic models often involves the simplification of reaction mechanisms. Reaction mechanism simplification is a technique used to accelerate the calculation by simplifying the complex chemical reaction network, which is suitable for large-scale combustion simulation. In the combustion simulation of biodiesel, the chemical reaction network is usually very complex, including a large number of chemical substances and reaction steps. By simplifying the reaction mechanism, the reactions and substances that have little impact on the combustion behavior can be removed, so as to reduce the computational complexity and shorten the simulation time [86,87].

Scientific modeling and simulation methods offer powerful tools for the study of biodiesel combustion characteristics and engine performance. These methods can deeply reveal complex physical, chemical, and thermodynamic processes and provide high-fidelity simulation results. However, scientific modeling and simulation methods also face some challenges, such as the high demand for computing resources, the fact that the accuracy of the model depends on the accuracy of input parameters, and the high dependence on experimental data in some cases. To overcome these challenges, researchers usually combine experimental verification and optimization techniques to ensure the reliability and applicability of simulation results.

4. Recent Research Case Analysis

4.1. Properties of Biodiesel

As an alternative fuel, the physical and chemical properties of biodiesel have a direct impact on its performance in the engine. Understanding and predicting these properties not only helps optimize the production process of biodiesel but also improves engine combustion efficiency and reduces emissions. Related studies are shown in

Table 3. Summary of research on predicting the properties of biodiesel.

Ref.	Algorithm/Model Type	Input Parameters	Output Parameters	Fuel Composition
[75]	GP	Fatty acid composition	Kinematic viscosity, flash point, cold flow properties, CN and iodine numbers	Various biodiesel compositions
[88]	RSM	Ethanol, diesel, biodiesel blend ratios	Density, viscosity	Ethanol–diesel–biodiesel blends
[89]	Empirical Correlations	Biodiesel blend ratios	Density, viscosity	Ternary biodiesel blends
[90]	ANN, LSSVM	Intermolecular interactions, temperature	Density	Various biofuels
[91]	GPR	Molecular weight, carbon number, double bonds, fatty acid types	Kinematic viscosity, cloud point, pour point, iodine value	Various biodiesel compositions
[92]	ANN, Random Tree	Biodiesel composition, fatty acid profile	Kinematic viscosity, density, flash point, oxidation stability, acid value, and calorific values	Hybrid biodiesel fuels
[93]	Empirical Correlation	Fatty acid composition	CN	Various biodiesel compositions
[94]	LSSVM, GA, PSO, HGAPSO	FAME composition	CN	Various biodiesel compositions
[95]	ANN, SVM	FAME composition	CN	Various biodiesel compositions
[96]	ANN	FAME composition	CN	Various biodiesel compositions
[97]	ANFIS, PSO	Fatty acid composition	CN	Various biodiesel and diesel oils
[98]	Grey Wolf Optimizer, Experimental	Fuel Composition, Temperature	Calorific value	Nicotiana Tabacum L. oil methyl ester
[38]	Experimental Analysis	Temperature, Pressure, Fuel Composition	Thermal conductivity	Methyl pentanoate, methyl octanoate, methyl decanoate
[99]	Experimental Analysis	Temperature, Pressure, Fuel Blend Ratio	Density, viscosity, specific heat	Rapeseed and soybean oil methyl ester blends
[100]	Empirical Correlation, PC-SAFT	Temperature, Pressure, Fuel Blend Ratio	Density, viscosity, specific heat, isothermal compress-ibility	Waste cooking oil biodiesel, 1-butanol
[101]	ANN	Temperature, Composition	Solid fraction, cold flow properties	Ethylic biodiesel blends
[49]	Multiple Regression	Fatty acid composition	CN, density, kinematic viscosity, Heating value	Various biodiesel compositions
[102]	Regression Model	Storage time, antioxidant concentration, saponification value, acid value	Viscosity	Jatropha and Pongamia biodiesel
[103]	Empirical Models	Chemical structure, composition	Flash point	HC, biodiesel, petroleum fractions
[104]	Multivariate Regression	Near-infrared spectroscopy data	Cold filter plugging point, kinematic viscosity	Biodiesel and blends
[105]	ML	Temperature, pressure, composition	Density, viscosity	Biodiesel and diesel blends
[106]	ANN, Empirical Models	Temperature, blend ratio	Viscosity	Various biodiesel blends
[107]	Multiple Regression	Fatty acid composition	Iodine value, saponification value	Various biodiesel compositions
[108]	Experimental, Modeling	Temperature, Pressure	Thermal conductivity	Methyl butyrate, methyl caproate

. This paper selects several key properties related to biodiesel combustion: density, viscosity, CN, and thermophysical properties. In the following chapters, we will discuss these properties in detail and analyze their impact on the performance of biodiesel.

4.1.1. Density and Kinematic Viscosity

The density and kinematic viscosity of biodiesel are important physical parameters that determine its combustion characteristics and engine performance. These properties directly affect the fuel injection, atomization, and combustion processes. Therefore, accurate prediction of these physical properties is very important for optimizing the formulation of biodiesel. In the research of this field, the traditional empirical formula can estimate these attributes to a certain extent, but with the progress of technology, researchers are increasingly turning to computational modeling and data analysis technology.

Existing models usually use the FAMEs component of biodiesel as input to predict multiple physical or chemical properties, including density and kinematic viscosity.

Researchers are increasingly focusing on predicting the properties of mixed fuels rather than studying single categories of biodiesel. For example, Razzaq et al. [88] studied the density and viscosity model of ethanol–diesel–biodiesel ternary mixture. It is pointed out that the physical properties of these mixtures can be effectively predicted by combining experimental data with regression analysis. This method shows the importance of combining experimental data with modeling technology.

Mujtaba et al. [89] evaluated the performance of three regression methods (linear regression, polynomial regression, and exponential regression) in predicting the density and viscosity of biodiesel–diesel mixtures containing additives. The study found that the exponential regression model performed well under specific conditions, but its versatility and accuracy still need to be further improved in the face of different biodiesel mixtures. This finding highlights the applicability differences of different regression methods in specific application scenarios.

In the application of ANN/ML, Nabipour et al. [90] tested four models to estimate the density of biofuels based on intermolecular interactions and the van der Waals radius of atoms, a least squares support vector machine (LSSVM), a radial basis function artificial neural network, a multilayer perceptron artificial neural network, and an adaptive neuro-fuzzy inference system (ANFIS). Among them, LSSVM performs best. This method provides a highly accurate density estimation model than the traditional method by analyzing the interaction of different fatty acids in biodiesel. By comparing various models, this study shows the superior performance of LSSVM in dealing with complex biofuel attribute prediction.

Pustokhina [91] successfully predicted the viscosity and other properties of biodiesel using a Gaussian process regression (GPR) model combined with a variety of kernel functions. The results show that the Matérn kernel function performs best in viscosity prediction, the determination coefficient R² reaches 0.992, and the root mean square error (RMSE) is 0.157, which indicates that the GPR model has high robustness and accuracy in dealing with nonlinear problems. This shows that nonlinear modeling technology has a wide application potential in predicting the complex properties of biodiesel. Giwa et al. [92] used ANN and a random tree algorithm to predict the density and viscosity of two or more kinds of oil–synthetic biodiesel blends. The research shows that the two kinds of prediction models based on FAME components have high prediction accuracy and perform well in processing complex data.

Additionally, Alviso et al. [75] used a GP model to predict the physical and chemical properties of biodiesel, including density and viscosity. The results show that GP can effectively capture the complex relationship between fatty acid composition and density, viscosity, and is also a reliable prediction tool. The introduction of GP technology provides a new solution for dealing with complex nonlinear relationships.

4.1.2. CN

CN of biodiesel is the key index to measure its ignition performance. High CN means that the ignition delay time of fuel is short, and the combustion is more complete, thereby improving the engine performance and reducing pollution emissions. With the increasingly important role of biodiesel in replacing traditional diesel fuel, accurate prediction of its CN is very important for optimizing fuel performance.

Some researchers used a linear regression model and multivariate analysis to estimate CN. For example, Lin et al. [93] used the composition information of fatty acid methyl ester (FAME) to predict the CN through a regression analysis model. The results showed that there was a significant correlation between different fatty acid compositions and CN, and the regression model could effectively estimate the CN of different biodiesel.

With the development of ML and artificial intelligence technology, more complex models are gradually applied in this field to improve the accuracy of prediction.

Bemani et al. [94] used LSSVM combined with GA, PSO, and hybrid genetic particle swarm optimization to predict CN, showing the potential of these evolutionary algorithms in optimizing models. The author believes that the combination of the LSSVM algorithm and GA, PSO, or hybrid genetic particle swarm optimization can be used as an accurate estimation model of the CN of biodiesel fuel. These methods show the advantages of the combination of evolutionary algorithms and ML technology and can achieve better prediction results on complex data sets.

Ghiasi et al. [95] compared the prediction performance of LSSVM and extra tree (ET). The results show that ET has higher reliability and stability in predicting CN.

Rahaju et al. [96] used a cascade neural network to predict the CN of 63 kinds of biodiesel. After training with 10 different algorithms, the study found that the Levenberg-Marquardt algorithm has the highest prediction accuracy, with a determination coefficient (R²) of 0.9245 and a RMSE of 3.1541.

In addition, Noushabadi et al. [97] studied the prediction performance of the hybrid model based on PSO and ANFIS for the CN of biodiesel. The model can effectively integrate FAMEs data and optimize model parameters through an evolutionary algorithm so as to improve the prediction accuracy.

4.1.3. Thermophysical Properties

The interaction between thermophysical properties has complex effects on the overall performance of biodiesel. Research has shown that biodiesel blends exhibit higher instability compared to pure diesel [3]. Therefore, when developing biodiesel formulations, not only these thermal properties should be considered separately, but also their synergy should be comprehensively analyzed to optimize fuel performance and ensure long-term stable operation of the engine. This overall analysis method can help researchers more comprehensively understand the performance of biodiesel in practical applications.

Samuel et al. [98] used the grey wolf optimizer (GWO) to predict the heating value of biodiesel. GWO is an optimization algorithm based on swarm intelligence, which optimizes the solution of the problem by simulating the hunting behavior of gray wolves. This algorithm is applied to the heating value prediction of tobacco oil methyl ester, and the effectiveness of the model is verified by experimental data. The results show that the GWO model can accurately predict the heating value of biodiesel, showing high prediction accuracy. This research highlights the potential of the GWO in predicting complex fuel attributes.

Zheng et al. [38] measured the thermal conductivity of three biodiesel compounds (methyl valerate, methyl octanoate, and methyl decanoate) by experimental method. Using the transient hot wire method, the researchers obtained the thermal conductivity data of these compounds at different temperatures and pressures and used these data to verify and improve the existing prediction model.

Giuliano Albo et al. [99] proposed a formula for indirectly calculating the specific heat capacity of biodiesel through sound velocity and density. However, the accuracy of the results, especially, depends on the accuracy of density. This method can be used as an alternative method when the specific heat capacity cannot be measured directly.

Ait Belale et al. [100] studied the thermophysical properties of the binary liquid mixture of waste edible oil biodiesel and 1-butanol and predicted and correlated these thermophysical properties through experimental data and models (Tait equation and PC-SAFT model). The Tait equation fits the experimental data well, but due to its empirical nature, it cannot explain the interaction between fluid molecules. In contrast, the PC-SAFT model has many parameters, but it can better explain the intermolecular interaction and shows good prediction ability in the whole concentration range.

A neural network also shows great potential in the prediction of complex thermophysical properties, especially when dealing with multivariable nonlinear relationships.

Magalhães et al. [101] used the multilayer perceptron feed-forward neural network to predict the CTE and solid fraction of ethyl–biodiesel mixture. The ANN model can effectively predict the thermal expansion behavior of fuel at different temperatures by learning the nonlinear relationship in the experimental data, and the results show good prediction accuracy.

4.2. Performance and Emissions of Biodiesel in Diesel Engines

The performance and emission characteristics of diesel engines are significantly affected by fuel types and properties. As an alternative fuel, biodiesel has unique advantages in diesel engine performance due to its high oxygen content and excellent combustion characteristics. However, the disadvantages of biodiesel, such as high viscosity, poor low-temperature fluidity, and poor oxidation stability, may lead to engine performance degradation or emissions increasing under specific operating conditions. Therefore, accurately predicting the performance of biodiesel in diesel engines is of great significance for promoting the widespread application of biodiesel. Related studies are shown in

Table 4. Summary of research on the performance of biodiesel in diesel engines.

Ref.	Theme	Algorithm/Model Type	Input Parameters	Output Parameters	Fuel Composition
[54]	Engine performance and emissions	ANN, RSM	Engine load, biodiesel ratio, injection pressure	BTE, BSFC, EGT, NOx, CO, HC, smoke	Biodiesel–diesel blends
[77]	Engine performance and emissions	GP	Fuel blend ratio, engine load	BTE, BSFC, NOx, CO, smoke	Biodiesel–diesel blends with nanoparticles
[109]	Engine performance and emissions	ANN	Injection timing, fuel blend ratio, engine speed	BTE, BSFC, NOx, CO, HC	Waste cooking oil biodiesel
[110]	Engine performance and emissions	ANN	Engine load, fuel type	BTE, CO, HC, NOx, smoke	Waste cooking oil biodiesel blends
[111]	Engine performance and emissions	ANN, RSM	Engine load, biodiesel ratio	BTE, BSFC, NOx, CO, smoke	Animal fat-derived biodiesel
[112]	Engine performance and emissions	ANN, GEP	Engine load, fuel injection parameters, blending ratio	BTE, BSFC, CO, NOx, UHC	Linseed oil biodiesel blends
[113]	Engine performance and emissions	ANN	Engine load, fuel, additive, CN	BTE, HC, CO, NOx, smoke	Palm biodiesel–diesel blends with nanoparticles and ethanol
[114]	Engine performance and emissions	Random Forest, SVM, ANN	Additive concentration, fuel blend, engine load	BTE, NOx, CO, HC, Smoke	Biodiesel with diphenylamine and ceria nanoparticles
[115]	Engine performance and emissions	ANN, RSM	Engine load, fuel blend ratio, DMC additive concentration	BTE, BSFC, NOx, CO, exergy efficiency	Diesel–Bael biodiesel with DMC additive
[116]	Engine performance and emissions	ANN	Engine load, quantum dot concentration, fuel blend ratio	BTE, BSFC, NOx, CO, HC	Biodiesel–diesel blends with carbon-doped quantum dots
[117]	Engine performance and emissions	RSM	Engine load, fuel blend ratio	BTE, BSFC, NOx, CO	Algal biodiesel–diesel blends
[118]	Engine performance and emissions	ANN, GA	Engine load, biodiesel blend ratio, injection pressure	BTE, BSFC, NOx, CO, Smoke	Castor oil biodiesel blends
[119]	Engine performance and emissions	ANN	Engine load, alumina nano-catalyst concentration, fuel blend ratio	BTE, NOx, CO, UHC, vibration	Diesel–biodiesel with alumina nano-catalyst
[120]	Engine performance and emissions	ANN, RSM	Engine load, producer gas flow rate, biodiesel ratio	BTE, BSFC, NOx, CO, smoke	Biodiesel-producer gas dual-fuel
[121]	Engine performance and emissions	ANN, Multiple Regression, Taguchi	Engine load, biodiesel–alcohol blend ratio	BTE, BSFC, NOx, CO, smoke	Biodiesel–alcohol blends
[122]	Engine performance and emissions	ANN, RSM	Engine load, decanol proportion, fuel blend ratio	BTE, BSFC, NOx, CO, smoke	Palm biodiesel–decanol blends
[123]	Engine performance and emissions	ANFIS, GA, PSO	Engine load, fuel injection timing, fuel injection pressure, biodiesel blend	BTE, UHC, NOx	Jojoba biodiesel blends
[57]	Combustion characteristics	ANN, SVM	Engine load, fuel type, injection timing	Ignition delay (ID)	Diesel and biodiesel blends
[124]	Combustion characteristics	Chemical kinetic model	Hydrogen concentration, biogas–air ratio	Ignition delay, combustion duration, flame speed	Biogas–hydrogen–air mixtures
[125]	Combustion characteristics	CFD	Engine load, fuel type, heat loss parameters	Heat release rate, cylinder pressure, exhaust gas temperature	Various biodiesel blends
[126]	Combustion characteristics, Emission	Chemical kinetic model	Engine load, air–fuel ratio, fuel type	Heat release rate, NOx, CO	Diesel–natural gas dual fuel
[127]	Combustion characteristics	ANN, CFD	Engine load, fuel blend ratio, engine speed	Heat release rate, cylinder pressure, ignition delay	Diesel–tomato seed oil biodiesel blends
[128]	Combustion characteristics	ANN	Engine load, fuel type	cylinder pressure, heat release rate, ignition delay	Diesel–safflower biodiesel blends

.

When studying the performance and emission characteristics of compression ignition engines, selecting appropriate parameters is the key. The selected parameters need to be able to fully reflect the operating efficiency, fuel economy, and environmental impact of the engine. In this paper, the key parameters such as combustion characteristics, BTE, BSFC, torque, and emission (such as NO_x, CO, HC, and particulate emissions) are selected for discussion.

4.2.1. Combustion Characteristics

The combustion characteristics of biodiesel in diesel engines have an important impact on its dynamic performance and emission performance. Combustion characteristics include combustion rate, ignition delay, heat release rate, and cylinder pressure, which directly determine engine efficiency and emissions.

Combustion rate refers to the speed at which fuel is burned in unit time, which is usually expressed by the mass or volume change rate of fuel.

Ignition delay refers to the time between fuel injection into the combustion chamber and fuel combustion, which is an important performance of the fuel injection system and fuel spontaneous combustion characteristics. Heat release rate is the heat released from the fuel per unit time, which reflects the energy release rate of the combustion process. In-cylinder pressure refers to the pressure measured inside the engine cylinder, which is usually measured at different stages of the combustion process. The cylinder pressure reflects the gas state in the cylinder and has a direct impact on the working process and performance of the engine.

In previous research, many mature thermal mathematical models have been widely used in the field of combustion research. They are used to simulate combustion characteristics and heat loss in compression ignition engines. In some papers focusing on the analysis of experimental data, the existing models will be combined to support their conclusions [124]. For example, Alhikami et al. [129] studied the spray ignition characteristics of biodiesel and other fuels through constant volume combustion chamber experiments. They made a comparative analysis with the prediction results of the model in the literature to help explain the relationship between the difference in ignition delay and fuel characteristics.

With the wide application of biodiesel as an alternative fuel, based on the existing theoretical framework, improving the accuracy of biodiesel combustion characteristics prediction through experimental verification and model adjustment has become the focus of research. Kamta Legue et al. [125] analyzed the effect of heat loss model changes on biodiesel combustion characteristics in combination with experiments and simulations. Through model prediction, the fuel ratio can be optimized, the heat loss can be reduced, and the combustion efficiency can be improved.

Another idea is to simplify the complex chemical mechanism model and analyze the interaction and influence of various components in the chemical reaction through the chemical reaction kinetics analysis technology. This method is also common in predicting the combustion characteristics of other fuels. For example, Liu [126] developed a simplified multi-component combustion mechanism for predicting the combustion characteristics of diesel natural gas dual fuel engines. In this study, several simplified steps and methods were introduced into the mechanism model, such as direct relationship graph, error propagation extended direct relationship graph, and species-wide sensitivity analysis. Through cross-reaction analysis, the model can accurately predict the combustion rate of fuel mixture, and the main emissions generated. This method not only reduces computational cost but also provides reliable prediction results. It is a direction worthy of further exploration in the future of biodiesel-related research.

In addition, some researchers choose to combine ANN/ML technology with other technologies to predict the combustion characteristics of biodiesel.

Karami et al. [127] used ANN and CFD models to predict the combustion characteristics of diesel engines using a tomato seed oil–biodiesel mixture. The results show that the ANN model can effectively predict the ignition delay, combustion duration (CD), heat release rate (HRR), and cylinder pressure (CP) under different biodiesel mixing ratios, and it is highly consistent with the experimental data.

Tuan et al. [57] compared the performance of ANN and SVM models in predicting the ignition delay of diesel and biodiesel blends. The results show that SVM has better prediction ability and accuracy than the ANN model. The authors suggest that SVM can be used to predict the ignition delay of diesel and biodiesel engines to improve combustion efficiency.

Dharmalingam et al. [109] used the Bayesian regularization neural network model to optimize the stratified injection strategy of waste edible oil biodiesel in diesel engines to improve combustion performance. The model successfully predicted the combustion characteristics under different injection conditions and reduced the generation of emissions through optimization.

4.2.2. BTE and BSFC

The performance of biodiesel in diesel engines, especially BTE and BSFC, is an important index to evaluate fuel economy and engine performance. BTE reflects the efficiency of the engine in converting the chemical energy of fuel into mechanical energy, while BSFC measures the amount of fuel consumed by the engine in generating unit power. Biodiesel usually has high oxygen content, which can improve combustion efficiency, but its low energy density may lead to the increase of BSFC. Therefore, how to accurately predict and optimize the BTE and BSFC of biodiesel has become a research hotspot in the academic community.

Although the traditional experimental methods can obtain accurate data, due to their high cost and time consumption, more and more researchers turn to the modeling method based on ML. These methods can deal with the complex nonlinear relationship and accurately predict the BTE and BSFC of biodiesel under different operating conditions.

Many researchers have introduced ANN, ML, and other models in the study of biodiesel engine performance.

Patnaik et al. [110] used the ANN model to predict the BTE and BSFC of biodiesel-blended fuel made from waste edible oil. The researchers trained the ANN model through a large number of experimental data and obtained the engine performance under different loads and different fuel ratios. This study shows the advantages of an ANN model in complex nonlinear data processing, especially when dealing with fuel mixtures under transformation conditions it can provide high-precision prediction results. Similarly, Simsek et al. [111] explored the effect of ANNs and RSMs to predict the BTE and BSFC of animal fat biodiesel in diesel engines. Moreover, the fuel ratio was adjusted according to the predicted results, optimizing the fuel economy of the engine.

Sharma et al. [130] compared the performance of enhanced regression tree (BRT) and ANN in predicting BTE and BSFC of biogas biodiesel dual fuel engines. The use of the BRT model shows its powerful ability in small samples and high-dimensional data. Especially in practical engineering applications, the robustness of BRT makes it an effective alternative to ANN. However, due to the complexity and high computational requirements of BRT models, their application may be limited to some extent.

In addition, some authors chose to use the gene expression programming (GEP) model and compared it with ANN. Sharma et al. [112] compared the performance of GEP and ANN in predicting the performance of biodiesel engines (including BTE and BSFC). The GEP model generates prediction models through an evolutionary algorithm, showing high prediction accuracy. The GEP model can generate accurate and explanatory prediction models through its unique evolutionary algorithm. Although its computational complexity is high, it has significant advantages in finding the optimal prediction formula and processing complex nonlinear data.

With the development of biodiesel research, more and more researchers have begun to explore the performance of biodiesel in the presence of different additives. At the same time, the prediction of diesel engine performance when using biodiesel with additives has become a hot research field. At present, many models can achieve this prediction goal more accurately.

Sule et al. [113] discussed the effect of adding nano particles and ethanol to biodiesel diesel blend fuel on engine BTE and BSFC. Through the ANN model, the researchers predicted and optimized the effect of additives on fuel performance. This study shows the advantages of combining experiment and modeling, especially when predicting and optimizing complex fuel formulations containing multiple additives.

Similarly, Kumar et al. [114] used ML methods to predict the BTE and BSFC of biodiesel-blended fuel with diphenylamine antioxidant and ceria nanoparticles in diesel engines. The ML algorithm effectively captures the performance changes of different additives and fuel ratios.

Ghanbari et al. [77] used the GP model to predict the BTE of biodiesel diesel blended fuel with nanoparticles. The GP model also has certain interpretability, which can generate accurate predictions of different fuel ratios and provide detailed performance analysis. By simulating the natural selection process, the model generates and optimizes the fuel performance prediction formula, which provides data support for the addition of different nanoparticles. This study shows the potential of evolutionary computation in fuel performance prediction.

Some researchers choose to combine ANNs and RSMs to make full use of their advantages: an ANN is good at processing complex data, while an RSM is outstanding in optimization. This method can provide a more comprehensive optimization scheme and has high practical application value. Aydın [54] and others combined ANNs and RSMs to predict and optimize the BTE and BSFC of biodiesel diesel blend fuel. The ANN model is used to predict the fuel performance, and RSM is used to optimize the fuel ratio to improve BTE and reduce BSFC.

In the face of biodiesel containing additives, the optimization method combining ANN and RSM also performs well. Pitchaiah [115] and others predicted and optimized BTE and BSFC of diesel engines using Bael biodiesel and DMC additives through ANN and RSM models. The study combines energy and exergy analysis to comprehensively evaluate the fuel performance.

4.2.3. Torque

In a diesel engine, the torque performance of biodiesel is an important index to measure its power output capacity. The torque directly affects the acceleration performance and traction of the engine. Accurately predicting the torque output of biodiesel under different operating conditions is very important for optimizing engine performance.

Some researchers also mentioned the attribute of torque when studying the prediction model of engine performance. In the following research cases, the torque is predicted by ANN, RSM, and a multi-objective optimization algorithm.

Taheri Garavand et al. [116] applied ANN to predict the torque performance of a carbon-based biodiesel mixture doped with quantum dots in internal combustion engines. The research shows that the ANN model can well predict the torque output of the engine under different load and speed conditions, indicating that this model has significant advantages in capturing complex fuel combustion characteristics.

Umeuzuegbu et al. [117] used RSM to model and predict the torque of seaweed biodiesel diesel blend fuel under different engine loads and speeds. The results show that with the increase in load, the torque also increases, while the increase in biodiesel proportion slightly reduces the torque output. This result proves the effectiveness of RSM in capturing torque changes.

Khoobbakht et al. [118] used computational modeling and multi-objective optimization technology to predict the torque of biodiesel made from castor oil in the engine. The results show that castor oil biodiesel can provide higher torque output under high load conditions, and the model optimization results show that the torque performance can be further optimized by adjusting the fuel ratio and engine operating parameters.

4.2.4. Emissions

Co, NO_x, HC, PM, smoke opacity, and other parameters are often considered when studying the emissions of biodiesel [131,132]. Among them, NO_x is one of the main pollutants emitted by diesel engines, which is formed at high temperatures. The use of biodiesel usually leads to an increase in NO_x emissions, which is due to the high oxygen content in biodiesel, resulting in an increase in combustion temperature. Therefore, the generation and control of NO_x has become an important research focus in the study of biodiesel emissions [133]. The mixing ratio of the biofuel mixture needs to be optimized according to engine operating conditions to balance the amount of NO_x and other exhaust emissions [134].

CO and HC emissions are usually related to incomplete combustion. Since the combustion efficiency of biodiesel is typically higher than that of traditional diesel, these emissions are often lower [135]. Researchers often track these pollutants to assess the environmental benefits of biodiesel.

In actual biodiesel diesel engine experiments, researchers can usually obtain information including BTE, BSFC, and various emissions parameters at the same time. Therefore, while training models to predict BTE and BSFC, many studies also predict emission characteristics (such as CO and NO_x), as shown in Table 4. This comprehensive data acquisition makes the prediction model more comprehensive and effective in application. However, although the prediction of CO and NO_x has received extensive attention in the research, the research on HC emissions and smoke opacity is relatively less mentioned. This difference may be related to the low emission of HC in biodiesel combustion, but it is still necessary to further explore the prediction of HC in order to improve the accuracy of the overall emission model.

ANN and RSM are considered to be accurate and reliable ways to predict HC emissions and smoke opacity [54,111,113]. For example, Hosseini [119] and others used experimental data to train multilayer perceptron feedforward neural networks through a back propagation algorithm. In the prediction of emissions, the model shows high accuracy. When predicting HC emissions, the model achieved a correlation coefficient of 0.98, indicating a strong relationship between the predicted and actual values.

Singh et al. [136] proposed a hybrid model combining ANFIS and GA to predict diesel engine performance and emission parameters, including HC emissions. This method significantly improves the prediction accuracy of engine performance and emission parameters. Compared with the ANFIS model alone, the hybrid model shows higher prediction accuracy.

In addition, some researchers have trained models specifically on the data of emissions. For example, Zhang et al. [137] use supervised ML tools to handle complex emission prediction tasks. The specific models used include multi-output least squares support vector regression and two types of ANN models (cascaded feedforward neural network and multilayer perceptron neural network). The results show that mls-svr model performs best in predicting CO₂, CO, and NO_x emissions.

5. Conclusions

Biodiesel is increasingly becoming an important alternative to fossil fuels due to its environmental and economic benefits. The development of predictive models and optimization techniques is crucial for the widespread application of biodiesel.

This article reviews the prediction models and optimization techniques for the characteristics and engine performance of biodiesel in recent years, analyzes statistical modeling, ML, and evolutionary algorithms, and emphasizes their effectiveness in predicting biodiesel characteristics (such as viscosity, density, and CN) and their impact on engine performance indicators (such as BTE and BSFC).

These studies indicate that combining experimental data with advanced computing techniques to improve prediction accuracy can provide important reference opinions for optimizing biodiesel formulations and engine tuning. Although significant progress has been made in this type of research, there are still challenges, such as relying on the data quality and interpretability of complex models. Future research can focus on improving these models and exploring hybrid methods to enhance their predictability and applicability in biodiesel engine systems. Research on the performance prediction of biodiesel can be expanded to include biodiesel derived from non-traditional biomass sources such as microalgae and waste oils. Given that many countries are promoting policies for the use of biodiesel, future studies could focus on increasing the proportion of biodiesel in fuel blends to develop comprehensive predictive models. This would broaden the applicability of these models. Additionally, research can be conducted to predict engine performance using biodiesel under specific operating conditions, further enhancing the practical relevance of these models.