## 4 Predictive Modelling of Sound Design Elements and User's Emotional Evaluation
### Comparative Analysis of Linear and Non-Linear Prediction Models  
The experimental samples were simulated by QTTI, GRNN, BPNN, and GA-BPNN models to obtain their respective predicted values. Then, they were tested by paired sample \(t\)-test with the user emotional evaluation values and the predicted values, and the results showed that their \(p\)-values were all greater than 0.05. It shows no significant difference between the predicted and the assessed values, indicating the reliability of the application  
Figure 12: (a) GA iterative process, (b) GA-BPNN training completion chart.  
Figure 13: Predicted results for (a) “Annovance-Comfortable”, (b) “Inexpensive-Premium”, and (c) “Weak-Powerful” of Kansei words.  
of QTTI multiple linear regression analysis, GRNN, BPNN, and GA-BPNN non-linear analysis predictions.  
The four validation samples were put into each of the four prediction models for prediction, the prediction results were compared and analyzed with emotional evaluation values of users, and the error comparison method was used to make a comparison of the three prediction accuracies. The relative error rate for each sample was calculated as ((! users' evaluation value--predicted value | /users' evaluation value] \(\times\) 100%) [24], which was used to determine a better prediction model, as shown in Table 6.  
The comparison shows that the average error values for GA-BPNN are 6.23%, 8.08%, and 8.43%; the average error values for QTTI are 4.10%, 5.40%, and 7.40%; the average error values for GRNN are 6.23%, 8.08%, and 8.43%; the average error values for BPNN are 15.87%, 6.89%, and 8.65%.  
The results showed that GA-BPNN has a better prediction accuracy, followed by QTTI. The four prediction models were ranked in order of accuracy: 1. GA-BPNN, 2. QTTI, 3. GRNN, 4. BPNN.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{**Sample\(\times\)**} & \multicolumn{1}{c}{**Adj**} & \multicolumn{2}{c}{\(Y_{1}\)**Annoyance-**} & \multicolumn{1}{c}{\(Y_{2}\)**Inexpensive-**} & \multicolumn{1}{c}{\(Y_{3}\)**Weak-**} \\  & & & **Comfortable** & **Premium** & **Powerful** \\ \hline \multirow{8}{*}{Test1} & QTTI & AEV * & 0.240 & 0.400 & 0.200 \\  & & REV * & 5.15\% & 9.01\% & 4.57\% \\  & BPNN & AEV & 0.529 & 0.264 & 0.347 \\  & & REV & 11.4\% & 5.94\% & 7.92\% \\  & GA-BPNN & AEV & 0.181 & 0.179 & 0.523 \\  & & REV & 3.89\% & 4.04\% & 11.9\% \\  & & AEV & 0.203 & 0.373 & 0.269 \\  & GRNN & REV & 4.37\% & 8.42\% & 6.15\% \\ \hline \multirow{8}{*}{Test2} & QTTI & AEV & 0.210 & 0.030 & 0.400 \\  & & REV & 5.50\% & 0.85\% & 8.66\% \\  & BPNN & AEV & 0.819 & 0.360 & 0.131 \\  & & REV & 21.5\% & 10.2\% & 2.84\% \\  & & AEV & 0.145 & 0.094 & 0.117 \\  & GA-BPNN & REV & 3.80\% & 2.65\% & 2.54\% \\  & & AEV & 0.243 & 0.163 & 0.092 \\  & GRNN & REV & 6.39\% & 4.64\% & 2.01\% \\ \hline \multirow{8}{*}{Test3} & QTTI & AEV & 0.110 & 0.000 & 0.300 \\  & & REV & 3.49\% & 2.71\% & 7.25\% \\  & BPNN & AEV & 0.799 & 0.357 & 0.340 \\  & & REV & 25.3\% & 10.8\% & 8.22\% \\  & GA-BPNN & AEV & 0.089 & 0.172 & 0.167 \\  & & REV & 2.83\% & 5.19\% & 4.03\% \\  & GRNN & AEV & 0.081 & 0.068 & 0.336 \\  & & REV & 2.56\% & 2.06\% & 8.14\% \\ \hline \multirow{8}{*}{Test4} & QTTI & AEV & 0.100 & 0.400 & 0.300 \\  & & REV & 2.24\% & 9.03\% & 9.10\% \\ \cline{1-1}  & BPNN & AEV & 0.240 & 0.030 & 0.515 \\ \cline{1-1}  & & REV & 5.38\% & 0.68\% & 15.6\% \\ \cline{1-1}  & GA-BPNN & AEV & 0.154 & 0.407 & 0.361 \\ \cline{1-1}  & & REV & 3.46\% & 9.18\% & 10.9\% \\ \cline{1-1}  & & AEV & 0.517 & 0.761 & 0.574 \\ \cline{1-1}  & & REV & 11.6\% & 17.2\% & 17.4\% \\ \hline \multirow{8}{*}{
\begin{tabular}{c} AEV (Total) \\ \end{tabular} } & QTTI & 4.10\% & 5.40\% & 7.40\% \\  & BPNN & 15.87\% & 6.89\% & 8.65\% \\ \cline{1-1}  & GA-BPNN & 3.50\% & 5.27\% & 7.37\% \\ \cline{1-1}  & GRNN & 6.23\% & 8.08\% & 8.43\% \\ \hline \hline \end{tabular}  
* REV/Relative error value; AEV/Average error value.  
\end{table}
Table 6: Comparative analysis of prediction results of linear and non-linear prediction models.