Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 232 https://internationalpubls.com Artificial Neural Network Approach to Multi-Response Prediction of Transesterification Rohit Khatri1*, Om Prakash Jakhar1 Department of Mechanical Engineering, Engineering College Bikaner, India *Corresponding Author: rohit_me_mania@yahoo.co.in Article History: Received: 22-10-2024 Revised: 25-11-2024 Accepted: 26-12-2024 Abstract: This study investigates the impact of transesterification parameters on biodiesel yield and kinematic viscosity, using an Artificial Neural Network (ANN) with the Levenberg-Marquardt algorithm to predict these outcomes. Predictions are validated against experimental results using established metrics like RMSE, MAPE, and R2. The experiments follow a Design of Experiment (DOE) approach, enabling accurate yield and viscosity measurements for each biodiesel sample. Results show that the ANN model strongly aligns with experimental results, showing lower RMSE and MAPE and higher R², outperforming RSM. Consequently, the ANN model is recommended for reliable biodiesel yield and viscosity prediction. Keywords: ANN, Regression, Optimization, Prediction. 1. Introduction The transportation sector has been utilizing about three-fourths of the total petroleum consumption in the country [1]. Transport contributes 12% of India’s energy-related CO2 emissions. To address these challenges, sustainable and renewable fuel alternatives like biodiesel must be explored [2], [3], [4]. The environmentally friendly fuel known as biodiesel stands out as a very promising substitute because of its biodegradability and lack of sulphur oxides in the exhaust [5] [6], [7]. Biodiesel can be obtained from edible and non-edible crops, algae, etc. WCO is obtained after frying or cooking, and this is a third-generation feedstock to produce biodiesel [8]. Transesterification is the most suitable and cost- effective method to manufacture high-quality biodiesel, which has qualities similar to diesel. The process aims to reduce oil viscosity and mimic petrochemical diesel's physical properties [9], [10], [11]. Furthermore, the existing literature has shown that biodiesel meets the ASTM D6751 and EN 14214 fuel specifications [12]. ANNs are widely used for predicting and optimizing parameters and responses in biodiesel production, often outperforming traditional methods. Studies have shown ANN models yield higher accuracy, with better R² values and lower MSE than RSM models [13], [14] [15]. [16] ANN provided more accurate predictions than RSM based on RMSE and R² metrics. This study optimizes transesterification variables to maximize biodiesel yield and minimize viscosity. It performs multi-response optimization, predicts outcomes, and compares results with ANN. 2. Materials and Methods 2.1 Feedstock and chemicals Waste cooking oil was collected from a vendor in Bikaner, Rajasthan, filtered with sieves to remove microparticles and heated to 110°C approx. for 30 minutes to eliminate moisture. The methanol and ethanol are used as alcohols, and KOH as catalysts. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 233 https://internationalpubls.com 2.2 Design of Experiment & Transesterification The design of the experiment is done using RSM, Design Expert 13 software using the BBD approach[17]. Five process parameters were selected: reaction temperature (A), reaction duration (B), oil: alcohol ratio (C), catalyst amount (D), and methanol to ethanol Ratio (E). The number of trials (NT) with different conditions is determined using the Box-Behnken design (BBD) as described in Equation (1). 𝑁𝑇 = 2𝑘(𝑘 − 1) + 𝑁𝐶 (1) where k represents the number of variables studied and Nc denotes the number of replicas for central points. Biodiesel was generated utilizing WCO as feedstock, methanol, ethanol as alcohol, and KOH as a catalyst by Hot plate mode of heating the reactants. The speed of hot plate stirrer was constant. Following a specific time, the reaction mixture was dumped into a separating funnel and left for one day to separate biodiesel and glycerol via gravity. After separating glycerol, the WCO-derived biodiesel is water-washed to remove any pollutants. The yield conversion and kinematic viscosity was evaluated based on eq. (1) & (2) respectively. Yield(%) = 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑏𝑖𝑜𝑑𝑖𝑒𝑠𝑒𝑙 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑤𝑎𝑠𝑡𝑒 𝑐𝑜𝑜𝑘𝑖𝑛𝑔 𝑜𝑖𝑙 𝑠𝑎𝑚𝑝𝑙𝑒 ∗ 100 (2) Kinematic viscosity (ν) = (𝐶1 ∗ t) − 𝐶2 𝑡 (3) Where, 𝜈 represents Kinematic viscosity in centi-stokes, C1 shows the Viscometer constant, which can be determined by equipment and C2 denotes the Coefficient of kinetic energy, and t in equation represents Time of flow in seconds[18]. 2.3 Modelling of ANN network Artificial Neural Networks (ANNs) have become a pivotal tool in research, offering significant advancements in prediction and optimization. ANN models have shown superior performance in predicting and optimizing biodiesel yields & kinematic viscosity compared to traditional method [19], [20]. MATLAB 2023 MathWorks was used for modelling of ANN. Levenberg-Marquardt (trainlm) algorithm was used to train model. The network was created by dividing 80% of the data for training and validation, and 20% was used for testing [21]. 5–10–2 architecture was framed as it contains 5 inputs, 2 outputs, and 10 neurons. The metrics employed for assessing the performance of the employed models include RMSE, MAPE, and R2 [22]. 3. Results and Discussion 3.1 RSM analysis Signification of model was evaluated by lack of fit, analysis of variance and coefficient of determination (R2). 2FI model was suggested by model due to high F-value & lesser p value (Table1)[13]. ANOVA also helps to recognize the most influential parameter[23][24]. According to ANOVA, the amount of catalyst (D) has the most significant effect, and the reaction time (B) has the least effect on biodiesel yield, whereas for kinematic viscosity, oil to alcohol ratio(C) has the most significant effect, and the reaction temperature (A) has the least effect. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 234 https://internationalpubls.com 3.2 Artificial Neural Network (ANN): The study utilized an artificial neural network to forecast biodiesel yield and kinematic viscosity, demonstrating its superior effectiveness to other statistical tools. Model was trained for minimum mean square error and maximum coefficient of determination. Model validation used R2, root mean square error (RMSE), and MAPE. Figures 1 & 2 illustrate the performance evaluation of an ANN model used to predict the kinematic viscosity & yield of biodiesel. High value of R and data trend near the mean line show the adequacy of model training and model can predict a new data set. Table 1 ANOVA analysis Biodiesel Yield Kinematic Viscosity Source Sum of Squares df Mean Square F-value p- value Source Sum of Squares df Mean Square F- value p- value Model 498.49 11 45.32 117.39 < 0.0001 Model 17.72 8 2.22 67.19 < 0.0001 significant A-Temp 39.31 1 39.31 101.84 < 0.0001 A-Temp 0.1406 1 0.1406 4.27 0.046 B-Time 4.04 1 4.04 10.47 0.0027 B-Time 6.48 1 6.48 196.53 < 0.0001 C- O:M/E 8.24 1 8.24 21.34 < 0.0001 C- O:M/E 8.17 1 8.17 247.66 < 0.0001 D- catalyst 389.37 1 389.37 1008.65 < 0.0001 D- catalyst 1.01 1 1.01 30.66 < 0.0001 E-M:E 10.91 1 10.91 28.25 < 0.0001 E-M:E 0.1914 1 0.1914 5.81 0.0211 AB 1.12 1 1.12 2.91 0.0971 AC 0.648 1 0.648 19.65 < 0.0001 AC 5.22 1 5.22 13.53 0.0008 BD 0.2314 1 0.2314 7.02 0.0118 AE 30.47 1 30.47 78.93 < 0.0001 BE 0.8556 1 0.8556 25.95 < 0.0001 BD 2.81 1 2.81 7.27 0.0108 BE 5.09 1 5.09 13.17 0.0009 CE 1.92 1 1.92 4.97 0.0325 Residual 13.13 34 0.386 Residual 1.22 37 0.033 Lack of Fit 12.34 29 0.4255 2.7 0.1349 Lack of Fit 1.06 32 0.0331 1.03 0.5513 not significant Pure Error 0.7865 5 0.1573 Pure Error 0.1611 5 0.0322 Cor Total 511.62 45 Cor Total 18.94 45 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 235 https://internationalpubls.com Figure1 Regression curves for biodiesel yield Figure2 Regression curves for biodiesel Kinematic viscosity In training phase, high value of correlation coefficient (R) 0.99874 & 0.9976 and alignment of Regression line with data for yield and kinematic viscosity respectively, indicates model’s capability to establish relationship between predicted and actual values. Similarly, for validation, plot R-values of 0.99069 & 0.95889 for yield and kinematic viscosity, respectively, signifying the predictive capability of the trained model and trend of the curve showing that the model predicted well without overfitting. This high overall correlation for Figures 5 and 6 indicates that the ANN model is highly effective in predicting biodiesel's kinematic viscosity and yield, with minimal deviation from the experimental values. This highlights the capability of ANN models in complex nonlinear regression tasks. Further prediction is made for the complete data set and compared with RSM based on evaluation metrics RMSE, MAPE & R2. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 236 https://internationalpubls.com 3.3 Comparative Analysis: In this section, ANN and RSM results were compared with experimental results. Comparison was made in two separate phases: In first phase, ANN and RSM results were compared with experimental results for the complete data set as shown in Figure (3-4). In second phase, a comparison of ANN and RSM model results was made based on RMSE, MAPE & R2 to find the most accurate model (Figure 5). Figure 3&4 shows the comparative illustration of experimental, ANN & RSM values for yield and kinematic viscosity, respectively. The data shows that the values predicted by the ANN closely match the experimental results. Metrics for biodiesel yield and kinematic viscosity supports this. Predictions were also compared with experimental results and RSM. (Fig3). Figure 3 comparative chart of Experimental, ANN & RSM yield values for testing data Figure 4 comparative chart of Experimental, ANN & RSM kinematic viscosity values for Testing data The figure 4 compares experimental data with predictions from an Artificial Neural Network (ANN) and a Response Surface Methodology (RSM) model for the kinematic viscosity and yield of biodiesel. It presents forty-six data points, with the experimental results shown as a green line, ANN predictions in blue, and RSM predictions in yellow. 1 2 3 4 5 6 Exp. 86.75 96.65 93.01 92.97 90.52 84.73 ANN 86.8595 96.4852 93.0258 92.6898 90.2568 84.6405 RSM 87.627912 96.493522 92.337222 92.850712 90.473212 84.581417 80 85 90 95 100 Exp. ANN RSM 1 2 3 4 5 6 Exp 8.01 6.3 7.67 6.61 7.24 7.03 ANN 7.92 6.29 7.61 6.57 7.29 6.96 RSM 7.79 6.3 7.76 6.56 7.37 6.91 6 6.5 7 7.5 8 8.5 Exp ANN RSM Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 237 https://internationalpubls.com The experimental data serve as a reference, and error bars indicate measurement uncertainty. Both ANN and RSM models closely track the experimental results and demonstrate their effectiveness in capturing the non-linear trend. The slight deviations between the models and experimental data indicate minimal discrepancies, with the ANN model consistently aligning more closely to experimental values than the RSM model. This suggests that the ANN model better handles the complexities of predicting biodiesel yield and kinematic viscosity. This comparison underscores the ANN model’s suitability for capturing complex non-linear relationships. Meanwhile, the RSM model also performs satisfactorily, but its predictive accuracy slightly lags compared to the ANN model, particularly in regions with higher variance. Figure5: R2, MAPE & RMSE comparison for ANN & RSM The graph shows that the ANN significantly outperforms the RSM. The ANN's root mean square error (RMSE) for yield is 0.30, 47% lower than the RSM's 0.57. The ANN's mean absolute percentage error (MAPE) for viscosity is 0.09, 95% lower than the RSM's 1.95. Additionally, the ANN achieves higher R² values for yield (0.99 vs. 0.97) and viscosity (0.98 vs. 0.94), indicating superior predictive accuracy. 4. Conclusion The study demonstrates that implementing response surface methodology and an artificial neural network approach can significantly reduce experimental work in finding the combination of process parameters for a desirable response. The experimental and predicted results can be summarized as follows: 0. 30 0. 57 0. 99 0. 97 0. 17 0. 53 0. 09 0. 16 0. 98 0. 94 0. 62 1. 95 AN N R SM RMSE Yield R2 Yield MAPE Yield RMSE Kinematic Viscosity R2 Kinematic Viscosity MAPE Kinematic Viscosity Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 8s (2025) 238 https://internationalpubls.com a) A maximum biodiesel yield of 96.65% and a kinematic viscosity of 5.467cSt were observed for an oil-to-alcohol ratio (WCO Molar ratio) of 9.99876:1 mol/mol, a catalyst dosage of 0.751004, a reaction time of 68.7703, a reaction temperature of 59.9689, and a methanol-to-ethanol ratio of 95.0148± 0.5. b) The Levenberg-Marquardt algorithm was more accurate, and the optimized architecture and hidden layers were (5-10-2) and 10, respectively. c) Finally, the root mean square error for yield and kinematic viscosity was 47% and 43.75% lower, respectively, and the value of R2 for yield and kinematic viscosity was higher for the artificial neural network compared to response surface methodology. 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