*2.8. Sensitivity Analysis*

The importance of the studied variables (coconut oil to ethanol molar ratio, reaction time, and microwave power) was explored through conducting the sensitivity analysis. In this analysis, Equation (18) is used with the "sum of squares" values obtained from the ANOVA table generated from response surface methodology (RSM).

$$
exists \psi \forall \psi \forall \stackrel{\circ}{\circ} = \frac{S\_x}{S\_y} \times 100\tag{18}$$

where *Sx* and *Sy* indicate the sum of square of the individual variable and total sum of squares of all the variables, correspondingly.

The significance input variables for ANN, were calculated based on Equation (19) [37]:

$$F\_k = \frac{\sum\_{j=1}^{j=M\_\sigma} \left( \left( \frac{|\mathcal{W}\_{kj}^{ag}|}{\sum\_{h=1}^{M\_\sigma} |\mathcal{W}\_{hj}^{ac}|} \right) \times \left| \mathcal{W}\_{jm}^{\mathcal{S}I} \right| \right)}{\sum\_{h=1}^{h=M\_\sigma} \left\{ \sum\_{j=1}^{j=M\_\sigma} \left( \left( \left| \mathcal{W}\_{qr}^{an} \right| \frac{|\mathcal{W}\_{hj}^{ag}|}{\sum\_{l=1}^{M\_\sigma} |\mathcal{W}\_{hj}^{ag}|} \right) \times \left| \mathcal{W}\_{jm}^{\mathcal{S}I} \right| \right) \right\}} \tag{19}$$

where, *Fk* is the relative significance of the *k*th input variable on the output variable. *Mo* is the number of input neurons and *My* is the number of hidden neurons. *W* is the connection weight. The superscript *a*, *g*, and *l* represent the input, output, and hidden layer, respectively, whereas the subscript *h*, *j*, and *m* represent the input, output, and hidden neuron, respectively.

### *2.9. Optimization of Transesterification Process Variables*

RSM and ANN-ACO were used to evaluate the optimal value of the three respective studied parameters in order to obtain the highest bio-jet fuel yield. The bio-jet fuel yield and the studied parameters were set at "maximum" and "in the range" individually in the case of RSM. ACO was used to determine the optimal values with the maximum bio-jet fuel yield for ANN. By conducting triplicate experiments, the optimal values determined by each approach were validated and the average values obtained were compared with the expected values.

### *2.10. Bio-Jet Fuel Properties*

The bio-jet fuel isolated from biodiesel (FAEE) was then analyzed and compared with the standard requirements for aviation turbine fuels (ASTM D1655) of the American Society for Testing and Materials. In this work, according to the respective ASTM test process, physicochemical properties including density at 15 ◦C, kinetic viscosity at −20 ◦C, flash point, and freezing point were calculated. Using a bomb calorimeter, the lower heating factor, also known as calorific value, was calculated as well.

#### **3. Results**

#### *3.1. RSM*

Based on this result, a fit summary table was generated to evaluate the suitable model for the optimization study. The fit summary table is shown in Table 3, and the outcomes indicate that the quadratic model is adequate to model the studied response (bio-jet fuel yield). This finding is based on the sequential *p*-value of the quadratic model, which is less than 0.05. In other words, the quadratic model consists of more than 95% confidence in modeling the experiments. Besides that, inclusion of cubic model terms might cause the model to be aliased and hence, the quadratic model is the best with the highest polynomial order.

The model used in this quadratic equation using a notation such as F1 for the coconut oil ethanol molar ratio, F2 for the reaction time, and F3 for microwave power. The experimental and predicted results in this work are summarized in Table 4 and the uncoded quadratic equation is shown in the following equation:

Bio − jet fuel yield (%) = 21.84F1 + 2.419F2 + 0.0416F3 − 0.00717F1F2 + 0.00227F1F3 − 0.000165F2F3 <sup>−</sup>1.18644F2 <sup>1</sup> <sup>−</sup> 0.082917F2 <sup>2</sup> <sup>−</sup> 0.00016F<sup>2</sup> <sup>3</sup> <sup>−</sup> 50.84552 (20)

**Table 4.** Experimental runs in RSM design with the different operating conditions and their respective experimental and predicted bio-jet fuel yield.



**Table 4.** *Cont.*

\* The center points of the experiments are replicated for 3 times.

The effect of the studied parameters as linear, quadratic, and interaction coefficients on the studied responses was determined for their significance through analysis of variance (ANOVA). The ANOVA results of this work are reported in Table 5. The studied parameters coconut oil to ethanol molar ratio, reaction time and microwave power represent as F1, F2, and F3 terms particularly. It is noted that the model used was statistically significant with a confidence level of 95%. From the table, it observed that parameters F1, F2, and F3 have a significant influence on bio-jet fuel production (*p*-values < 0.0500). Furthermore, note that the "lack of fit" of the model consists of a *p*-value of 0.4227 (not significant as >0.05). In the other words, the model is fit to be used for further analysis.


**Table 5.** Analysis of Variance for the modeling of bio-jet fuel production.

\* The F value for a term shows the test in order to compare the variance of that particular term with the residual variance.
