# Technology Identification, Evaluation, Selection, and Optimization of a HALE Solar Aircraft
## 4 General Methodology
### Design Space Exploration
#### 4.4.1 Screening Test  
A screening test is an experiment-designing method utilized to find variables with the greatest effect on the design objective parameters. In this study, with respect to the levels of factors, 2 factors were utilized, so that there were only max and min values. Input variable combinations, as shown in Figure 10, are generated using the JMP program. The table on the left in the figure was used to form an experimental design using fractional factorial design. As explained above, \(-1\) and \(1\) indicate 2 factor level. The table on the right shows values converted to the actual scales. In the fractional factorial design, \(-1\) represents the actual min; and \(1\), the actual max values.  
These design variable combinations created using the fractional factorial design and their performance indicators were used to perform regression analysis. The resulting graph is shown in Figure 11. In the graph, the \(x\)-axis and \(y\)-axis represent the predicted value and the actual value respectively. The actual value is the output variables calculated using the HALE solar framework. Regression equations are derived by modeling the relationship between the input variables and the calculated output variables. The predicted value is the value calculated using the regression equations. Each small dot in the graph means 128 cases; the red-colored dotted line shows how well the model was estimated. The red line represents a perfect model. The closer the dotted line is to this red line, the better the fitting is. However, since the screening test, using a linear DOE, is performed to find variables with the largest effect on the performance, the distances between two dotted lines seem large. In addition, the determination coefficient, (\(R^{2}\)), is one of the indicators that can be used to evaluate the optimized response surface equations (RSE) and represents the data variance ratio as an indicator showing how well the regression function model fits the estimations. Determination coefficient values are always  
Figure 9: Design of experiment in HALE framework.  
between 0 and 1; the closer to 1, the better the explanation of the relationship between the design objective parameters and the independent variables will be. As shown in Table 9, the determination coefficient is also unsatisfactory. This is compared with the results of regression analysis performed using the response surface method after selecting independent variables with the largest effect on the design objective variables through pareto plot and \(p\)-value.  
Figure 11: Actual predicted plots of design target variables.  
Figure 10: Conversion of actual design variable values by fractional factorial design.  
After this, to determine the independent design variables with the largest influence on the design objective parameters, a pareto graph was analyzed. Pareto graphs express responses to individual independent design variables. The lines in each graph show the accumulated effect of the independent design variables [25]. As can be seen in Figure 12, the airframe weight adjustment factor and the battery-specific energy density are the two primary contributors to the wing loading, while the solar cell fill factor and the battery energy hardly contribute at all. The pareto plot is a means to visually determine the most significant contributors to a response, and a parameter estimate can be used to numerically determine the important variables.  
In Figure 13, looking at \"Prob > \(|t|\)\" in the second column, if this value is less than 0.05, the parameter estimate significantly influences the response. As shown in Table 10, the most influential independent design variables can be selected by comparing the pareto plot and the independent design variables with a parameter estimate of less than 0.05.