## 2 Development of an Advanced SR-JOINT (SR-II)
### Optimal SR-Joint Shape Design
#### 2.2.4 Results  
The degree of influence of the data normalization was analyzed when the optimal design was implemented to minimize the objective function load. The actual test value (Max Load), maximum normalization using the maximum value (Load-max, \(Load_{\text{max}}\)), maximum-minimum normalization (Load-minmax, \(Load_{\text{minmax}}\)), and the z-score method using standard deviation and average value (Load-zscore, \(Load_{\text{zscore}}\)) were applied to the maximum load applied to the pressure jig. Each normalization method is expressed in Equation (5), and the predicted results for six data items through the SVM and statistical regression are shown in Figure 12, where, \(y_{r}\) denotes the test value, \(y_{r-\text{max}}\) denotes the maximum test value, \(y_{r-\text{min}}\) denotes the minimum test value, \(\overline{y_{r}}\) denotes the average test value, and \(\sigma(y_{r})\) denotes the standard deviation of the test value. \[Load_{\text{max}}=\frac{y_{r}}{y_{r-\text{max}}},Load_{\text{minmax}}=\frac{y_ {r}-y_{r-\text{min}}}{y_{r-\text{max}}-y_{r-\text{min}}},Load_{\text{zscore}}= \frac{y_{r}-\overline{y}_{r}}{\sigma(y_{r})} \tag{5}\]  
The SVM and statistical regression analysis results are shown in blue and red, respectively. The smaller data with respect to the data ratio are shown in a lighter color, and the coefficient of determination (R\({}^{2}\)) was used to compare the prediction accuracy. R\({}^{2}\) was used as a measure of goodness-of-fit in the regression and calculated as shown in Equation (6), where \(y_{p}\) denotes the predicted value. It was discovered in both the statistical regression and SVM that the larger data resulted a smaller R\({}^{2}\), and that R\({}^{2}\) was the highest when the maximum normalization was applied. The statistical regression analysis had a smaller R\({}^{2}\) than the SVM regardless of the amount of data, and the maximum difference was 0.0212 when the data ratio was 100% and the maximum normalization was applied. The R\({}^{2}\) based on the data ratio when the maximum normalization was applied is shown in Table 5. When the data ratio was 100%, the difference in R\({}^{2}\) was the greatest at 0.0212. The mean based on the data ratio was 0.9739 and 0.9875 for the statistical regression and SVM, respectively, and the difference was 0.0136, indicating that the SVM was more suitable. Although the R\({}^{2}\) was lower when the number of datasets was larger, the range was 0.0346 and 0.0225 for the statistical regression and SVM, respectively. This indicates that the relationship between the dependent and independent variables was not two-dimensional as the data ratio increased, and that the statistical regression predicted a quadratic polynomial regression equation as  
Figure 12: Comparison of prediction accuracy for support vector machine (SVM) and statistical regression data based on data normalization (R\({}^{2}\)). well as demonstrated the relationship between the dependent and independent variables considering only two dimensions. However, because SVM approaches involve not only two dimensions but also higher dimensions for learning the most appropriate prediction weight, they are more accurate than statistical regression analysis regardless of the amount of data. The results of training and prediction using 61 datasets are shown in Figure 13. The R\({}^{2}\) of the SVM statistical regression is shown in blue and red, respectively; it was discovered that the SVM predicted more accurately than the statistical regression. \[\text{R}^{2}=1-\frac{\sum(y_{r}-y_{p})^{2}}{\sum(y_{r}-\overline{y}_{r})^{2}} \tag{6}\]  
The test was conducted using the test dataset for each design variable listed in Table 4 based on the training and prediction results for each data ratio through regression analysis and the SVM. The data were compared by applying test values, maximum normalization, minimum-maximum normalization, and z-score normalization, as shown in Figure 14, based on the amount of data.