# Sound Quality Estimation of Electric Vehicles Based on GA-BP Artificial Neural Networks
## 3 SQ Evaluation Model of EVs  
### Multiple Linear Regression Model  
Most of the prediction models of SQ are based on theories of multiple linear regression (MLR). Before the MLR analysis, a correlation analysis between the subjective SQ evaluation results and the objective physical-psychoacoustical parameters should be carried out so as to better study the relationship between the subjective SQ evaluation scores and the objective evaluation parameters to determine which objective evaluation parameters have a significant influence on the subjective SQ evaluation of EVs. According to the subjective and objective evaluation results, the SPSS software was used to analyze the relationship between the objective physical-psychoacoustical evaluation parameters and the subjective evaluation scores.  
Table 3 shows the correlation coefficient between the objective evaluation parameters and the subjective evaluation scores. It can be seen from the table that the correlation coefficients of the loudness, AI, SPL, roughness, sharpness, and FS are all above 0.7, while the correlation coefficient of the tonality is much lower. Thus, the independent variables were the loudness, AI, SPL, roughness, sharpness, and FS, which had a better correlation with the subjective scores, and the dependent variable was the subjective evaluation score of the SQ. Through the MLR analysis of the subjective evaluation scores and the objective parameters, an objective quantitative SQ model for EVs can be established.  
After the MLR analysis, there were three models, as shown in Table 4. All the regression coefficients of the models were significant, as the accompanied probability sig values corresponding to the t-statistic of the three models were less than 0.01. This indicates that the three models are reasonable. Moreover, it seems that model 3 is the most suitable model, as the value of the determination coefficient R\({}^{2}\) is larger than that of any other model. It also contains a constant term, the loudness, sharpness, and FS variables. In addition, this model had higher correlation and determination coefficients. Consequently,  
Figure 11: Interior noise articulation index (AI) in the EV as a function of the vehicle’s speed.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline  & **SPL** & **Loudness** & **Sharpness** & **Roughness** & **AI** & **FS** & **Tonality** \\ \hline Correlation coefficient & \(-0.908\)** & \(-0.928\)** & \(-0.821\)** & \(-0.879\)** & \(0.917\)** & \(-0.794\)** & \(0.272\)** \\ Two-tailed test & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.017 \\ \hline \end{tabular}  
* indicates significant correlation at the 0.01 level (bilateral).  
\end{table}
Table 3: Correlation coefficients between the sound quality (SQ) scores and the physical-psychoacoustical parameters. SPL, sound pressure level; AI, articulation index; FS, fluctuation strength.  
it was selected as a prediction model. On the basis of the unstandardized coefficient in Table 4, the MLR model of the SQ can be described as  
\[SQ=11.575-0.078\times L-1.023\times S-20.92\times F, \tag{1}\]  
where \(SQ\) is the subjective sound quality score, \(L\) is the loudness, \(S\) is the sharpness, and \(F\) is the fluctuation strength. It can be seen from Equation (1) that the loudness, sharpness, and FS are negatively correlated with the subjective evaluation score of the SQ. As seen from Table 4, the absolute loudness value of the standard coefficient 0.517 is greater than that of the others, which indicates that the loudness contributes more to the subjective evaluation score of the SQ.