Artificial neural network, Adaptive Neuro-Fuzzy prediction and sensitivity analysis of Hura crepitans seed oil-based biodiesel production

1 Introduction

The cravings of national energy independence and the pursuit of alternatives to fossil fuels introduced bioenergy that uses renewable, agricultural, and low-cost materials as feedstock (Haas et al., 2006). Major research efforts have been devoted to using these cheap raw materials for producing fuel substitutes for petroleum and natural gas, whose global market prices are forever on the increase with concerns about their swift depletion (Sai et al., 2018). Moreover, the urgent necessity to combat global warming and minimize emissions of carbon dioxide (CO₂) and carbon monoxide (CO) has greatly accelerated global efforts in advancing bioenergy development (Oyelade et al., 2017). It has been reported by Sebayang A. et al. (2023) that burning fossil fuel contributes about 62% of the greenhouse gases in the world. In this regard, emission of CO and CO₂ is greatly influenced by fuel type and quality, combustion efficiency, and engine conditions (Oniya et al., 2014). Biodiesel is gaining widespread recognition as a prominent substitute for fossil diesel because of the close resemblance in their physical and chemical characteristics (Adewuyi et al., 2014; Ogundele et al., 2021). Samuel et al. (2020a) noted that its appeal lies in features such as a high flash point and octane rating. According to Sai et al. (2018), Oyelade et al. (2017) and Sebayang A. H. et al. (2023), biodiesel is a renewable, biodegradable, non-toxic, and environmentally sustainable fuel that performs efficiently in internal combustion engines, particularly in transportation. It is generally produced through the transesterification process involving either culinary or non-culinary oils or animal fats such as tallow or lard, with ethanol or methanol in the presence of a basic catalyst (Kassem et al., 2018; Oke et al., 2022).

Switching from fossil (diesel) fuel to biodiesel in a diesel engine causes clogging and degrading of some engine parts (Samuel et al., 2020a). Therefore, to combat the effects of clogging and degradation in hoses and pipes of engines, a more efficient method called transesterification is required for the production of fuel with most biodiesel standards. Samuel et al. (2020b) defined transesterification process as an essential method for the production of biodiesel which entails the reaction between the oil and alcohol with a catalyst. The virgin vegetable oil is seen as the best feedstock for biodiesel production considering that its chemical reaction is the shortest and the most complete (Samuel et al., 2020b). Globally, biodiesel production has increased significantly, with growth rate ringing from 20% to 100% in countries such as Germany, United State and Brazil (Sebayang A. et al., 2023). According to Sebayang A. et al. (2023), this growth is due to various initiatives taken by these nations in minimizing national carbon emissions. The viability of biodiesel from the commercial point of view is jeopardized primarily by the price and supply constraints of feedstock which contribute to the high cost of biodiesel production. More than 70%, of biodiesel production costs is spent to procure feedstock (Omilakin et al., 2023). It is in this line that research into the feedstock that are not edible and those under-utilized would serve as a focus in biodiesel studies in order to mitigate the food-versus-fuel debate and ensure sustainability. One of such promising candidates is Hura crepitans, popularly called the sandbox tree, which is found in tropical geographical locations and is known to produce high oil yields, which are inedible and not considered a food item (Ajala et al., 2023a; Oyelade et al. (2017)).

Hura crepitans (H. crepitans) seed oil can be extracted from H. crepitans seed using different extraction methods, such as solvent extraction that allows about 99% recovery of the oil (Omilakin et al., 2023). It offers an appreciable amount of extractable oil (30%–35% by weight) with high unsaturation that makes it good for biodiesel synthesis (Oyelade et al., 2017). Since it is regarded as a non-edible species, the oil derived from it poses minimal competition within the food chain. Hence, it becomes a sustainable and economically viable alternative to the commonly used edible oils such as soybean, palm, and sunflower oils. Furthermore, H. crepitans can be grown and harvested on a continuous basis throughout the year under controlled cultural conditions, thereby making it a sustainable renewable energy source of oil that could meet the global energy demand (Owhor et al., 2021).

Oyelade et al. (2017) reported that H. crepitans seed oil has some notable physicochemical properties relevant to biodiesel production, such as a characteristic golden-yellow colour kinematic viscosity of 4.55 mm²/s, specific gravity of 0.91, pour point of −1.0 °C, and cloud point of 5.9 °C. They also measured the refractive index of H. crepitans seed oil to be 1.4683 (30 °C), with an acid value of 2.771 mg KOH/g. Although, little variations were observed in some of these values across different studies, this is attributable to variation in extraction conditions and growing environments, these values are broadly consistent with earlier values reported by Oniya et al. (2017), and also fall within the ASTM D671 specification limits. In Nigeria, this species occurs naturally across several states, including Edo, Kogi, Osun and Benue (Owhor et al., 2021), where local communities have traditionally grown it for shade and structural purposes. Since the seed oil currently lacks a defined commercial use, the seeds are typically discarded as wastes. Several earlier studies such as Oyelade et al. (2017), Sebayang A. et al. (2023) and Adewuyi et al. (2014) have documented the use of H. crepitans seed oil in biodiesel generation through transesterification process. However, converting H. crepitans oil to biodiesel via transesterification is influenced by some set of parameters-such as temperature, reaction time, catalyst concentration, and catalyst type-with each contributing uniquely to the biodiesel yield (Samuel et al., 2020a). The inherent nonlinear interactions among these parameters make conventional modeling techniques insufficient for accurate prediction and optimization.

Recently, artificial intelligence (AI) tools such as adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network (ANN) have been used to model parameters of the transeseterification process in the literature (Azhar et al., 2025). This is attributed to their capability to manage nonlinear and complex stochastic data sets effectively. ANN is a machine learning tool which proffers solution to difficult problems that cannot be handled by statistical or human standard (Ajala et al., 2023b) and was originally designed on the basis of the human brain scheme. It is a framework where various algorithms work together for processing complex data input to simulate the data processing ability of the human brain (Jasni et al., 2020). According to Saghouri et al. (2020), ANN is a computational technique with several advantages, such as direct learning via real data without any need for statistical parameters and statistical assumptions. ANN as a black-box modelling technique can handle a system’s complexity, non-linearity, and uncertainty as well as multivariate systems. Samuel et al. (2020b) highlighted a key limitation in using ANN for modeling, noting its inability to effectively establish a direct connection between input variables and the output (response). This shortcoming arises from the ANN model’s lack of capacity to process linguistic information accurately (Ajala et al., 2023b). ANFIS handles the limitation by embedding fuzzy logic within the neural network framework to retain the adaptive learning power of the former while enabling the latter’s interpretable, language-like rule structure (Omilakin et al., 2023). According to Sada and Ikpeseni (2021), ANFIS learns directly from data involving complex mathematical relationships and represent the output as a set of human-readable fuzzy inference rules. Salih et al. (2019) reported that the most essential choices when developing an ANFIS-based model including characterizing the input-output mapping accurately, selection of membership function types which reflect the data distribution and formulation of a rule base that is both concise and representative.

The modeling and prediction of biodiesel production from various feedstock, particularly non-edible oils, using ANN and ANFIS techniques have been widely reported. Biodiesel production from transesterification of castor oil was modeled and predicted by Yue et al. (2018) using ANFIS modeling technique. Najafi et al. (2018) developed RSM- ANN- ANFIS-based models to predict biodiesel yield from waste cooking oil. Kinematic viscosity and density of biodiesel blends under different ratios and temperatures were predicted using ANN and ANFIS techniques by Kassem et al. (2018). Transesterification process of biodiesel production from tobacco seed oil was modeled and predicted using ANN and ANFIS techniques by Samuel et al. (2020b). Patnaik et al. (2024) developed ANN models to predict biodiesel performance and emission characteristics of compression ignition engines powered by blends of diesel produced from waste cooking oil. Zhu et al. (2025) developed ANN and ANFIS models for predicting yield of heterogeneous composite biodiesel from neem and castor oil, and emissions of biodiesel blend. Annal et al. (2025) integrated ultrasound technique and RSM and ANFIS methodologies to optimize biodiesel production from Peltophorum pterocarpum oil. Performance evaluation of ANFIS and RSM models for predicting biodiesel yield from soybean oil through transesterification process was carried out by Kumar and Bansal (2023). All these previous studies found in literature demonstrated high predictive ability for both ANN and ANFIS models, and other machine learning models.

Although, ANN and ANFIS techniques have been widely applied for biodiesel yield prediction from various feedstock. However, literature search shows that direct application of ANN or ANFIS for predicting biodiesel yield from H. crepitans seed oil is scarcely reported, with only few studies (Omilakin et al., 2023; Oraegbunam et al., 2023) have explored and reported this pathway to date. The present work builds on the earlier contribution of Oyelade et al. (2017), who used RSM-based model to predict biodiesel yield from H. crepitans seed oil. Therefore, this study is novel by developing a comparative predictive framework through ANN- and ANFIS-based models for this under-investigated feedstock, integrated with sensitivity analysis, which goes beyond simple yield prediction, to systematically determine which of the process parameters influences and provides information directly relevant to experimental planning and process control. This study offers a more complete picture of the transesterification process behaviour than modelling or empirical observation could deliver in isolation.

The outcome of this study provides empirical data that can contribute to assist the relevant stakeholders mitigate financial risk, meet statutory mandates reduce environmental impacts of biodiesel production. It can also assist in the identification of major process factors that influence biodiesel production and keep them within their optimal range for improved viability of the process.

2 Methods

The comprehensive description of the data collection procedures and the underlying principles of the ANN and ANFIS modeling techniques used for predictive analysis are given in this section. The flowchart illustrating the overall methodology is shown in Figure 1.

2.1 Input-output data collection

This study is computational in nature and draws entirely on published experimental data from Oyelade et al. (2017). A total of 24 data points were available for model development and evaluation, distributed across training, validation, and test subsets in proportions described in Section 2.2. The dataset contained four process inputs: reaction time, catalyst concentration, reaction temperature, and catalyst type, with measured biodiesel yield as the output variable. Table 1 shows the datasets used in this study.

TABLE 1. Actual and predicted values of biodiesel yield.

KOH: potassium hydroxide; CSS: calcined snail shell.

2.2 Development of ANN-based model for biodiesel yield prediction

In this section, ANN technique was used to model and predict biodiesel yield obtained from transesterification of H. crepitans seed oil. The model was built via the ANN toolbox in MATLAB 2020a, a built-in feature which is suitable for capturing complex and nonlinear relationships that are difficult to handle by traditional or conventional modeling techniques. The development process for the ANN model is illustrated in the flowchart presented in Figure 2. The model was developed using the input/output dataset (Table 1) sourced from the study of Oyelade et al. (2017). The input variables considered included reaction time (min), temperature (°C), catalyst concentration (%), and catalyst type, while the output variable was the biodiesel yield (%). Multilayer feedforward neural network architecture was adopted for the modeling. The training of the neural network was done by Levenberg-Marquardt (L-M) backpropagation algorithm. This algorithm was chosen due to its fast convergence (Ajala et al., 2026), and its ability to handle small datasets such as the 24 experimental datasets being considered in this study. The 24 datasets used were partition into 70% training, 15% testing and 15% validation by dividerand.

A series of neural network (NN) architectures was evaluated to obtain the best NN architecture in estimating biodiesel yield. The best NN architecture was determined through systematic trial-and-error technique by varying the number of hidden neurons and assessing model performance using statistical metrics such as coefficient of determination (R ²) and root mean square error (RMSE). A single hidden layer was selected based on its proven capability to approximate nonlinear functions with minimal complexity. The selected configurations for the neural network (NN) model architecture are presented in Table 2. The best NN architecture (Figure 3) consisted of 10 neurons in the hidden layer, which provided the best trade-off between accuracy and generalization, four input nodes corresponding to the input variables, and one output node representing the output variable. A simple architecture was intentionally adopted to avoid over-parameterization and reduce the risk of over fitting given relatively small dataset size.

TABLE 2. Summary of neural network configuration.

2.3 Development of ANFIS-based model for biodiesel yield prediction

ANFIS serves as a hybrid modeling technique that combines the learning capability of Artificial Neural Networks with Fuzzy Logic systems (Sebayang A. H. et al., 2023). In this study, the ANFIS model was developed using experimental input-output data obtained from the study of Oyelade et al. (2017). A portion of the dataset was partitioned for training and checking (validation) subsets. A checking dataset was used to monitor performance of the model and minimize overfitting during training. Figure 4 illustrates the structure of the ANFIS model, including its input (independent) and output (dependent) variables. To enhance model interpretability and facilitate efficient analysis, the crisp numerical values for inputs and outputs were translated into linguistic variables, which allowed for the generation of segmented membership function plots. The model was implemented in MATLAB and configured to predict biodiesel yield based on four input factors: residence time (60–120 min), reaction temperature (55 °C–65 °C), catalyst concentration (1–3 wt%), and catalyst type (KOH/CSS). Gaussian membership functions (gaussmf) were adopted for training the model. The ANFIS architecture was based on 1^st -order Takagi-Sugeno fuzzy inference system, in which fuzzy rules are generally expressed as follows:

If j is C and k is D then , p = f j , k

Here, C and D represent fuzzy sets associated with the input variables, and p = f (j, k) denotes a linear or nonlinear function describing the relationship between the inputs and the output.

The structural and training parameters of the developed ANFIS model are presented in Table 3. The model was configured with a maximum of 100 training epochs and comprised 193 nodes, 81 linear parameters, 24 nonlinear parameters, 105 total parameters, and 81 fuzzy rules. These parameters define the structure and computational configuration of the ANFIS model used for biodiesel yield prediction.

TABLE 3. The parameters/configurations for ANFIS-based model for biodiesel yield prediction.

2.4 Statistical evaluation of ANN and ANFIS models

Predictive performance of the ANN and ANFIS-based models in biodiesel production was assessed using various statistical performance indicators expressed in Equations 1–5. These indicators include Mean Absolute Error (MAE), Root Mean Square Error (RMSE); Standard Error of Prediction (SEP); Mean Squared Error (MSE), Average Deviation (AD), and Coefficient of Determination (R ²). Low MSE, RMSE, MAE, SEP, and AD values closer to zero indicate a highly precise and dependable model performance, while an R ² value close to unity indicates good model performance. Finally, the comparative analysis of predictive capabilities has been carried out based on statistical metrics to find out which is better fitted to the biodiesel production dataset. The evaluation and interpretation of these statistical metrics follow the methodologies outlined in Samuel et al. (2020b) and Okwu et al. (2023). where Y_{i, actual}, Y_{actual, ave},Y_{i, pred} are the actual value, average value of the experimental outputs and predicted value, respectively, while n represents total number of actual data points.

R 2 = 1 − ∑ i = 1 n Y i , p r e d − Y i , a c t u a l 2 ∑ i = 1 n Y i , p r e d − Y exp ⁡ , a v e 2 (1)

R M S E = ∑ i = 1 n Y i , a c t u a l − Y i , p r e d 2 n (2)

S E P = R M S E Y a c t u a l , a v e (3)

M A E = ∑ i = 1 n Y i , a c t u a l − Y i , p r e d n (4)

A D = 100 n ∑ i = 1 n Y i , a c t u a l − Y i , p r e d Y i , a c t u a l (5)

2.5 Sensitivity analysis of process input variables

The sensitivity analysis was tested via various combinations of input variables. The approach adopted by Ajala et al. (2023a) was utilized, where each input variable was systematically excluded from the input set one at a time to observe the resulting impact on the model’s performance using RMSE and R ² values. The degree of variance in RMSE and R ² values depicts how highly influenced the individual input variable is in biodiesel production.

3 Results and discussion

3.1 Predicted biodiesel yield from Hura crepitans oil

This section reports the biodiesel predictions generated by ANN and ANFIS models for each experimental run, utilizing either CSS or KOH as a catalyst.

3.2 Predicted biodiesel yield by ANN model

The ANN model for biodiesel yield prediction was built in MATLAB R2020a; Table 4 summarizes how the dataset was divided across training, validation, and testing phases. The model returned MSE values of 4.477, 11.774, and 24.049 for training, validation, and testing respectively, with corresponding correlation coefficients (R) of 0.979, 0.938, and 0.996 (shown in Figure 5). Low MSE values combined with R values approaching unity across all three subsets indicate that the network generalized well beyond the training data (Ajala et al., 2023b). The training correlation coefficient of 0.979 indicates a strong fit to the data used for model development, while the validation coefficient of 0.938 demonstrates that the model maintained good predictive performance for data not directly used in training. Notably, the testing dataset yielded the highest correlation coefficient (R = 0.996), indicating excellent agreement between the actual and predicted values for the independent test observations. All the high values of R indicate a strong positive linear relationship between the actual and model-predicted biodiesel yields, demonstrating that the ANN was able to adequately capture the underlying relationship between the input process variables and biodiesel yield. The consistently high correlation coefficients across the three datasets suggest good predictive capability and generalization of the developed ANN model. Additionally, the overall R value of 0.964 also confirms that the trained ANN closely tracked the actual biodiesel yields, with residuals small enough to be considered acceptable for this type of process modelling study.

TABLE 4. Values of MSE and R for ANN prediction.

Furthermore, in each plot of the regression plots of ANN model (Figure 5) across all data subsets, predicted values are tightly clustered around the 45-degree ideal line. This confirms a strong linear agreement between model output and the actual output (target). Figure 6 presents the training, validation, and testing performance of the developed ANN model as a function of the training epochs. The training error decreased progressively with increasing epochs, indicating continuous improvement in the model’s fit to the training data. The validation error also decreased during the initial training stage and reached its minimum at epoch 2, which represents the best validation performance (11.7743) of the ANN model. Beyond this point, the validation error showed a slight increase and subsequently remained relatively stable, whereas the training error continued to decrease. This divergence between the training and validation performances suggests that further training beyond the optimum validation point did not improve the model’s generalization capability and could lead to overfitting. The test error exhibited a similar trend, with its lowest value occurring during the early training stage before increasing and subsequently stabilizing. Overall, the plot indicates that the ANN model achieved its best generalization performance at approximately epoch 2, as determined from the minimum validation error.

Figure 7 presents the error histogram of the developed ANN model for the training, validation, and testing datasets. The orange vertical line represents zero error, corresponding to an exact agreement between the ANN-predicted and target values. The prediction errors were distributed on both sides of the zero-error line, indicating that the model produced both over-predictions and under-predictions rather than exhibiting a pronounced systematic bias. The training dataset showed the largest number of observations across the error intervals, reflecting the greater number of samples used for model development. The validation and testing datasets contained fewer observations, but their errors were distributed across the error range and included observations close to the zero-error region. Overall, the distribution indicates reasonable agreement between the predicted and target values, although some observations exhibited relatively larger deviations from zero. A concentration of errors closer to the zero-error line would indicate better predictive performance; therefore, the histogram complements the regression and performance metrics by providing a visual assessment of the magnitude and distribution of the ANN prediction errors.

3.3 Biodiesel yield prediction using ANFIS model

The developed ANFIS model based on the Takagi-Sugeno fuzzy inference system (FIS) is shown in Figure 8. The model comprises of three membership functions for each input variable, representing low, medium, and high values, thereby enabling the developed model to capture the nonlinear relationships between the input variables and biodiesel yield. The use of Gaussian membership functions provided smooth transitions between the defined fuzzy regions, while the grid-partitioning structure generated the corresponding fuzzy rule combinations. The fuzzy logic rule viewer contains 81 rules, each connected by the logical operator AND, as shown in Figure 9. The rules specified input variables-temperature, residence time, catalyst concentration, and type of catalyst -as rulers on either side of the rule viewer, with associated output on the right as predicted biodiesel yields. The ANFIS rule viewer (Figure 9) shows the influence of the input variables on the predicted biodiesel yield. For the selected operating conditions of 60 °C temperature, 90 min reaction time, 2% (w/w) catalyst concentration, and catalyst type 1 (KOH), the corresponding membership functions are activated and processed through the 81 fuzzy rules embedded in the ANFIS model. The highlighted regions represent the membership functions activated by the specified input values, while the output section shows the contributions of the activated rules to the final prediction. Under these conditions, the ANFIS model predicted a biodiesel yield of approximately 85%. The figure therefore demonstrates the inference mechanism of the developed ANFIS model, whereby multiple input conditions are simultaneously evaluated through fuzzy rules to generate the predicted biodiesel yield.

The effectiveness of the ANFIS-based model in estimating biodiesel yield was assessed by the coefficient of determination (R ²). With an R ² value of 0.961, the model explains 96.1% of the variation between actual and predicted biodiesel yields, demonstrating its high predictive accuracy. This shows that ANFIS-based model gave accurate prediction of biodiesel yield as shown in Figure 10. According to Figure 10, the predicted values of predicted biodiesel yield showed little variation to actual biodiesel yield.

3.4 Evaluation of ANN and ANFIS-based model for predictive accuracy

Table 5 shows that across all five metrics, ANFIS returned a higher R ² and lower RMSE, MSE, SEP, MAE, and AD than ANN, confirming it as the more accurate of the two models for this dataset. On that basis, the ANFIS model is regarded as the preferred tool for predicting H. crepitans seed oil biodiesel yield within the studied operating range. The very small ANFIS errors: MAE of 0.0001 and AD of 0.00012, deserve particular attention. Values this close to zero are partly a consequence of the modest scale of the dataset, the restricted spread of input conditions, and the relatively smooth nonlinear behaviour of the system within input-output bounds. They do not necessarily mean the model would perform equally well under wider or different conditions. The possibility of overfitting cannot be rule out entirely dues to limited number of data points. The models should therefore be regarded as reliable within the parameter ranges represented in the training data, and any extrapolation beyond those ranges should be accompanied by experimental verification.

TABLE 5. Statistical performance comparison of ANN and ANFIS-based models.

Additionally, Figure 11 presents a comparative graph showing actual versus predicted biodiesel yield values obtained from both the ANFIS and ANN models across various experimental runs. The ANFIS model’s predictions closely matched the actual yields, achieving an R ² value of 0.961, which means it accounted for 96.1% of the variability in the data. In comparison, the ANN model achieved an R ² value of 0.925, reflecting 92.5% data explanation. Further statistical metrics also supported the conclusion that the ANFIS model delivered slightly superior predictive performance compared to the ANN model.

3.5 Sensitivity analysis

In the comparison of ANN-based and ANFIS-based model performances discussed in Section 3.4, ANFIS model was found to slightly outperform the ANN model. Additionally, due to its hybrid nature—combining the advantages of both fuzzy logic and neural networks—the ANFIS model is well-suited for designing adaptive controllers for complex systems. As a result, it was selected for conducting a sensitivity analysis to evaluate the relative influence of each input parameter on model performance. As presented in Table 6, the greatest changes in R ² and RMSE values occurred when residence time (t)was excluded from the input set. This indicates that residence time (t) is the most critical (or sensitive) parameter impacting the accuracy of biodiesel yield predictions using the ANFIS model. Catalyst type C t emerged as the second most influential variable, while temperature (T) showed the least impact. These findings highlight the significant role of residence time in accurately modeling biodiesel production from H. crepitans seed oil.

TABLE 6. Relative importance of process input variables on biodiesel yield.

T: Temperature; t: Time; C c: Catalyst concentration; C t: Catalyst type.

3.6 Comparative analysis of developed artificial intelligent models with previous studies

The ANN and ANFIS models’ effectiveness in prediction, based on R ² values in this study, was compared with the biodiesel yield prediction by AI model in previous studies. As shown in Table 7, the results indicate that the accuracy and reliability of the AI models in this study align closely with those from previous studies, as all models exhibit R ² values near unity. Nonetheless, the ANFIS models in the present and previous studies stand out as the most suitable model, owing to its capacity for adaptive controller design, making it more versatile for complex system applications. With these results, this present study is in agreement with the results of the previous studies.

TABLE 7. Comparison between previous research and the current study.

KOH: potassium hydroxide; CSS: calcined snail shell; NaOH: sodium hydroxide; CaO: calcium oxide; ECHC: Eggshell-cow bones heterogeneous catalyst.

4 Conclusion

Currently, this study very novel in exploration of AI application for the prediction of biodiesel yield from H. crepitans seed oil and sensitivity of different process variables. ANN and integrated ANN- models with fuzzy logic would enable to predict effectively the complex, nonlinear interrelationships between key input parameters such as catalyst type, catalyst concentration, reaction temperature, and reaction time. The results showed that the ANFIS model slightly outperformed the ANN model, achieving a higher coefficient of determination (R ² = 0.961) and lower prediction errors than the ANN model (R ² = 0.925), indicating that the integration of neural-network learning with fuzzy-logic reasoning provided improved representation of the nonlinear relationships governing biodiesel yield. Sensitivity analysis further identified reaction time as the most influential process variable, followed by catalyst type, whereas temperature exhibited the least influence within the investigated operating range. This demonstrated interesting trends in terms of the contribution of individual process variables to biodiesel yield.

This study’s findings have practical implications for experimental planning and process development, as the developed models can provide rapid estimates of biodiesel yield and help identify process variables that warrant greater attention during experimental optimization. Additionally, the sensitivity analysis results may also assist in prioritizing process variables for further experimentation, potentially reducing unnecessary experimental trials, material consumption, and associated costs. However, the predictive models should be regarded primarily as data-driven predictive tools rather than direct substitutes for experimental validation or process optimization, particularly when applied outside the range of conditions represented in the training dataset.

A major limitation of the present study is the relatively small dataset of 24 experimental observations, which was obtained from previously published experimental work. The limited dataset restricts the ability to fully assess model generalization and may increase the risk of overfitting, particularly for flexible machine-learning models. Furthermore, the computational nature of the study means that the predictions were not independently verified through new laboratory experiments. Consequently, the reported model performance should be interpreted within the range and characteristics of the available dataset rather than assumed to represent universal predictive performance for H. crepitans biodiesel production. Therefore, future studies should incorporate larger, more diverse and independently generated datasets as well as external or cross-validation techniques, to provide a more rigorous assessment of model generalization. Experimental validation of the ANN and ANFIS-based predictions within the investigated operating range is also recommended. Additionally, future works should investigate additional machine-learning or hybrid modelling techniques as well as focusing on scale-up and techno-economic assessments, to determine the feasibility of implementing the developed predictive framework under real-life conditions. These would strengthen the connection between data-driven biodiesel prediction, experimental process optimization and industrial application.

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Footnotes

Edited by: Mariefel V. Olarte, Pacific Northwest National Laboratory (DOE), United States

Reviewed by: Kevin Tochukwu Dibia, University of Delta, Nigeria

Mandeep Singh, University of Engineering and Management (UEM) Jaipur, India

Footnotes

AI, Artificial intelligence; ANN, Artificial neural network; ANFIS, Adaptive neuro-fuzzy inference system; R, Correlation coefficient; R², Coefficient of determination; RMSE, Root mean square error; MAE, Mean absolute error; AD, Average deviation; SEP, Standard error of prediction; CO, carbon monoxide; CO_2, Carbon dioxide; KOH, potassium hydroxide; NaOH, sodium hydroxide; CaO, Calcium oxide; ECHC, Eggshell-cow bone heterogeneous catalyst; ASTM, American society for testing and materials; RSM, Response surface methodology; CSS, Calcined snail shell; NN, Neural network; L-M, Levenberg-Marquardt; MSE, Mean square error; FIS, Fuzzy inference system; C_t, Catalyst type; C_c, Catalyst concentration; T, Temperature; t, Reaction/residence time.