The selection of Karanja and Algae oil for biodiesel production in this experiment is underpinned by their unique characteristics and suitability for the optimization of process parameters. Karanja oil, chosen for its non-edibility, easy availability, lower density, higher cetane number, and superior calorific value, offers a promising source for synthesis of biodiesel. The saturated fatty acid profile of Algae and Karanja oil is enlisted in Table 3. However, it is essential to note that the FFA concentration in Karanja oil is initially measured at 2%, which exceeds the permissible limit when employing a base catalyst. An FFA concentration above 1% can trigger saponification process, leading to the formation of soap during biodiesel production. Consequently, the FFA content in Karanja oil must be reduced to less than 1% to ensure a smooth transesterification process. In contrast, Algae oil presents a more favourable FFA concentration of only 0.54%. This lower FFA concentration positions it as an excellent candidate for blending with Karanja oil to achieve the desired ultimate FFA amount of under 1%. In this experiment, the oils are unified in a proportional volume of 75:25, offering the advantage of maintaining a suitable FFA level for efficient biodiesel production. This innovative blend leverages the strengths of each oil source while mitigating the challenges associated with high FFA content in Karanja oil, ultimately contributing to the optimization of the biodiesel production process. Fig. 1 shows the schematic diagram of biodiesel production methodology.

The oil blend for this experiment consisted of a 75% Karanja oil and 25% Algae oil ratio by taking 750 mL of Karanja and 250 mL of algae oil making total quantity of hybrid oil to be 1000 mL. The process was repeated thrice and thus we had 3 liters of concoction of hybrid oil. From this mixture we took 100 mL in a separate beaker of 250 mL and added 20 mL of methanol to it along with 1 gram of CaO catalyst and then positioned the beaker on the magnetic stirrer to ensure optimal homogeneity. The transesterification process unfolds on a electric hotplate endowed with a precisely modulated magnetic stirrer and a temperature sensor for meticulous control. This blended oil combination served as the feedstock for the transesterification process, aimed at producing biodiesel. The hybrid oil undergoes a meticulous preheating process at a temperature of 40°C to expunge any surplus water content. Under these process parameters the entire process involving 27 individual tests conducted within a magnetic stirrer at a constant stirring speed, facilitated by a hot plate stirrer was implemented: a)

Predetermined methanol-to-oil volumetric ratio ranging from 20% to 60% v/v,

A Fractionating funnel was utilized to separate the fatty acid methyl ester (FAME) and glycerol layers, ultimately yielding pure biodiesel. FAME was found in the upper lamina of the assorted product, while 1,2,3-propanetriol accumulated in the bottom layer. Subsequently, the bio propellant phase went through a water rinsing process to eliminate adulterants up until the wastewater attained a neutral pH level. The ultimate product was scalded to 80°C to facilitate the evaporation of any unconsumed methyl alcohol. The yield of biodiesel can be determined by employing Eq. (5). (5)Biodieselyield=(Wt.ofbiodieselproduced)/(Wt.ofhybridoilusedforthereaction)×100

To ensure the quality and compliance of the produced biodiesel with industry standards, a physicochemical characterization was carried out in compliance with ASTM D6751 specifications [40]. The analysis necessitates the entailing of transesterification process for the blend of Karanja oil and Algal oil by utilizing the meticulously engineered Response Surface Methodology (RSM) with subsequent implementation of the Box-Behnken Design (BBD) at a consistent reaction speed. The acquired data was subjected to comprehensive statistical analysis and optimization procedures, facilitated through the use of the Minitab software, to ascertain the most favourable conditions for this biodiesel synthesis.

Experimental design, often abbreviated as DOE (Design of Experiments), is an amalgamation of analytical techniques employed to create a model or systematically study a problem. The primary objective is to investigate standardized parameters concerning the enhancement of the intended reaction in relation to the process variables. Response Surface Methodology (RSM), a robust tool for commencing new processes, enhancing existing ones, designing new products, and overall process optimization, is one of the most extensively employed DOE techniques for constructing mathematical models [42]. RSM offers substantial advantages over conventional methods as it necessitates fewer experimental runs, facilitating a more rapid and cost-effective assessment of process parameters. Additionally, it allows for the exploration of interdependencies between various factors and the development of models to predict predefined responses [32].

Within RSM, the BBD is a prevalent and highly effective design method for creating experimental data suitable for quadratic modelling. BBD systematically explores the effectiveness of numerous elements spanning throughout a comprehensive range of distinct design points, while also consistently assessing curvature to accumulate a significant database for examining incongruity [33]. Response Surface Methodology is a DOE technique that constructs a framework in accordance to the correlation betwixt a response and multiple supervised independent elements, enabling multifaceted estimation and refinement. Eqs. (6) and (7) provide the fundamental frameworks grounded on primary and quadratic polynomial expressions that are often utilized in RSM, respectively. These models are invaluable for understanding and optimizing complex processes, offering a powerful tool for scientific inquiry and process improvement. (6)y=β0+∑ikβiXi+β (7)y=β0+∑ikβiXi+∑i=1k∑j≥ikβijxixj+βwhere β0 is the constant, βi is the linear and βij is interaction coefficients, and i and j are the linear and quadratic coefficients respectively. β is random test error, k is the number of components, y is the predicted response, X_i and X_j are independent variables [43].

Artificial Neural Network (ANN) is a widely recognized machine learning technique that has garnered significant attention in various engineering disciplines. It operates by transforming an input dataset into an output dataset. A prevalent type of neural network is the Multilayer Perceptron (MLP) network, which utilizes a feed-forward back-propagation (BP) approach. ANN offers a flexible simulation method that learns from the process by adjusting the network’s weight. In contrast to Response Surface Methodology (RSM), which is limited to variables within its control, ANN can accommodate a broader range of variables.

In this research, the ANN approach is employed to optimize the process variables. ANN is essentially a computer model inspired by the information processing mechanism of the human brain. Each layer of the neural network consists of a multitude of tiny entities called neurons, primarily dedicated to processing specific components. For this study, the artificial neural network analyzed 27 data points derived from independent factors, including temperature, time, catalyst concentration, and methanol-to-oil ratio. An MLP configuration, encompassing three layers comprising the input layer, hidden layer, and output layer, was utilized to facilitate the optimization process. This approach provides a powerful tool for exploring the interplay of variables and predicting optimal process conditions.

The perturbation plot in Fig. 2 illustrates the sensitivity of biodiesel yield to factors like methanol-to-oil ratio (A), temperature (B), time (C), and catalyst concentration (D). Notably, temperature (B) shows the most significant impact, particularly between 30°C and 60°C. Parameters C, D, and A also influence yield, albeit to a lesser extent. Understanding these sensitivities is crucial for optimizing biodiesel production [42].

Fig. 2 emphasizes the significant influence of factor B (reaction temperature) on biodiesel yield, supported by its pronounced slope and higher regression coefficients. The temperature range tested (30°C to 90°C) aligns with optimal yield conditions found in literature, with peak yields (>80%) observed around 55°C to 60°C. However, exceeding 60°C leads to reduced yield due to methanol evaporation.

In Fig. 2, biodiesel yield increases with catalyst concentration up to 1% (w/w), but then sharply declines [41]. Higher concentrations create a cavitation barrier, hindering transesterification, and increase soap formation. This leads to emulsification of glycerol and biodiesel, causing separation difficulties and yield decrease. These insights aid biodiesel production optimization [20,42].

The relationship between biodiesel yield (Y) and reaction time (C) is depicted in Fig. 2. It’s evident that biodiesel yield increases with the reaction time up to 100 min, after which it experiences a slight deterioration. This drop-in yield beyond 100 min could be attributed to the combination of high-temperature conditions and the potential saponification of triglycerides, which might occur over an extended reaction time [40].

Factor A, represented by the methanol-to-oil ratio, displayed a less pronounced slope compared to the other factors, indicating that this particular factor is less sensitive to all the responses. The experiment’s range for the methanol-to-oil ratio was selected to vary from a minimum of 6:1 to a maximum of 12:1 (mol/mol). An increase in biodiesel yield was observed as the methanol-to-oil ratio increased. However, beyond a certain threshold, increasing the methanol-to-oil ratio resulted in a significant decrease in density. This reduction in density suggests a decrease in the early collapse of cavitation bubbles and cavitation intensity, ultimately leading to reduced biodiesel yield [40].

Moreover, the decline in biodiesel yield with an increasing methanol-to-oil ratio can also be attributed to the solubility of methanol with glycerol, biodiesel, and other reactants. This increased solubility makes the separation of the products more challenging and contributes to emulsification [40]. Additionally, a larger amount of excess methanol at the end of the reaction can increase the cost associated with methanol separation [20]. These findings highlight the complex interplay of factors influencing biodiesel yield and underscore the importance of optimizing these variables for efficient production.

ANOVA, i.e., Analysis of variance was incorporated to evaluate the applicability and computational significance of the mathematical model. As depicted in Table 5, ANOVA helps identify the independent influences of each trait and their associations with biodiesel yield [44]. The importance of each independent variable is determined through the collected data, and the Fisher’s F-test (F-value) and probability value (p-value) play a crucial role in this assessment. A higher F-value and a lower p-value indicate the substantial effectiveness of an autonomous factors [45,46]. These constants are instrumental in gauging the meaningfulness of individual regression coefficients and the likelihood of anomaly.

The regression model’s F-value of 11.87 and a p-value less than 0.0001 affirm the model’s reliability within the experimental design.

Fig. 3 depicts the actual (experimental) data vs. the predicted data of biodiesel yield. As can be seen, the actual data were constantly distributed around a straight line (y = x), with a decent correlation (R² = 95%) between such values.

In ANN modeling, the configuration of network size, hidden layers, and neurons is vital for forecasting experimental results. Additionally, ANN can be employed in second-order polynomial regression, based on the RSM model. This study investigates an ANN model with one output, ten hidden, and four input neuron layers (1-10-4), representing variables like reaction time, temperature, methanol-to-oil ratio, and catalyst concentration, with biodiesel yield as the output.

The experimental yield dataset is split into training (70%), testing (15%), and validation (15%) sets to prevent overfitting and enhance model reliability. Regression coefficients for training, validation, and test networks are 0.99, 0.94, and 0.95, respectively, indicating high modeling accuracy. Linear regression of target plots vs. validation outputs yields a strong correlation (Output = 0.95 * Target + 3.9). Notably, the data distribution around a 45° angle signifies promising agreement between ANN predictions and experimental results.

Fig. 4 illustrates the ANN regression findings for general, validation, test, and training data, showing reasonable correlation coefficients across all datasets. Overall, the study concludes that the ANN model effectively optimizes significant parameters for biodiesel production.

Table 6 presents the iterations and allied reaction data points of produced biodiesel from RSM and ANN, respectively. The empirical statistics was fit with a quadratic polynomial model, and the resultant quadratic function was employed to illustrate the bio fuel productivity rooted in the categorical variables, as highlighted in Eq. (8).

(8)Biodieselyield(%)=−203.9+16.32×A+2.679×B+2.304×C+88.6×D+0.0025×A×B−0.0075×A×C−0.12×A×D−0.00027×B×C−0.008×B×D−0.162×C×D−0.923A2−0.02423B2−0.01112C2−33.40D2where A, B, C, and D represent the coded forms of molar ratio, reaction temperature, time and catalyst concentration. The occurrence of a positive symbol in front of the terms implies a collaborative ramification, whereas the negative symbol suggests an inconsistence implication [21].

The study investigated the significant effects of various working factors on biodiesel yield, employing a homogenous transesterification technique to derive biodiesel from a novel oil amalgamation of C. vulgaris and Karanja. The examination of alterations in reactions with each criterion variation, while clutching onto other components consistent at zero level values, shed light on the primary effects of the reaction parameters. Notably, all linear and quadratic terms were determined to be significant (p < 0.05) by ANOVA analysis, prompting an exploration of the main effects of all parameters to understand their influence on biodiesel yield.

The ideal values of each of the variables influencing the reaction were found using the regression equation generated from RSM followed by BBD model to optimize the effectiveness production of biodiesel during the transesterification reaction. The ideal reaction conditions were found by modifying the independent variables in the experimental range and maximizing the efficiency of biodiesel yield with the greatest degree of relevance (+5), simultaneously reducing the standard deviation in the optimization portion of the program with a moderate level of significance (+3).

The most favorable indicators confirmed from the RSM for the transesterification of blends of C. vulgaris oil and Karanja oil to engender bio propellant are displayed in Fig. 5. The maximum 98% yield of biodiesel was achieved with desirability 94% at the ideal operational temperature of 56.86°C, amount of catalyst being at 1% (w/w), with timespan of reaction being at 91.47 min, and Methyl alcohol to oil molar ratio of 8.46:1 as indicated in the Fig. 6.