## 6 Verification with Modified Noises
### Modified Noise
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Modified Noise** & **Roughness (asper)** & **Fluctuation Strength (vacil)** & **Tonality (tu)** \\ \hline Modified Noises (\(-9\) dB) & 0 & 0.0044 & 0.0041 \\ Modified Noises (\(-6\) dB) & 0 & 0.0046 & 0.0014 \\ Modified Noises (\(-3\) dB) & 0.0335 & 0.0047 & 0.0334 \\ Modified Noises (\(0\) dB) & 0.1130 & 0.0050 & 0.0341 \\ Modified Noises (\(+3\) dB) & 0. 1730 & 0.0051 & 0.0346 \\ Modified Noises (\(+6\) dB) & 0.2020 & 0.0052 & 0.0356 \\ Modified Noises (\(+9\) dB) & 0.2362 & 0.0053 & 0.0358 \\ Modified Noise (Frequency \(\times\) 0.8) & 0.0397 & 0.0054 & 0.0401 \\ Modified Noise (Frequency \(\times\) 0.9) & 0.0903 & 0.0056 & 0.0381 \\ Modified Noise (Frequency \(\times\) 1.0) & 0.1130 & 0.0050 & 0.0341 \\ Modified Noise (Frequency \(\times\) 1.1) & 0.0980 & 0.0057 & 0.0337 \\ Modified Noise (Frequency \(\times\) 1.2) & 0.0721 & 0.0056 & 0.0334 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Roughness of modified churn noises. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Modified Noise** & **Roughness (asper)** & **Fluctuation Strength (vacil)** & **Roughness (asper)** \\ \hline Modified Noises (\(-9\) dB) & 0 & 0.0044 & 0.0041 \\ Modified Noises (\(-6\) dB) & 0 & 0.0046 & 0.0014 \\ Modified Noises (\(-3\) dB) & 0.0335 & 0.0047 & 0.0334 \\ Modified Noises (\(0\) dB) & 0.1130 & 0.0050 & 0.0341 \\ Modified Noises (\(+3\) dB) & 0.1730 & 0.0051 & 0.0346 \\ Modified Noises (\(+6\) dB) & 0.2020 & 0.0052 & 0.0356 \\ Modified Noises (\(+9\) dB) & 0.2362 & 0.0053 & 0.0358 \\ Modified Noise (Frequency \(\times\) 0.8) & 0.0397 & 0.0054 & 0.0401 \\ Modified Noise (Frequency \(\times\) 0.9) & 0.0903 & 0.0056 & 0.0381 \\ Modified Noise (Frequency \(\times\) 1.0) & 0.1130 & 0.0050 & 0.0341 \\ Modified Noise (Frequency \(\times\) 1.1) & 0.0980 & 0.0057 & 0.0337 \\ Modified Noise (Frequency \(\times\) 1.2) & 0.0721 & 0.0056 & 0.0334 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Tonality of modified annular noises. where \(z\) denotes critical band rate [20]. The modified noises of the churn flow were produced by changes in the amplitude and frequency of the signal for 2100-2300 Hz. The roughness was used to determine whether the modified noises were characterized as the churn noise because the value of roughness changes a lot compared to other values (Table 8). Roughness is one of the Zwicker parameters, representing the subjective perception of rapid amplitude modulation of a sound. The unit of measure for roughness is the asper. One asper is defined as the roughness produced by a 1000 Hz tone of 60 dB which is 100% amplitude modulated at 70 Hz [20]. \[R(z)=0.0003\cdot f_{mod}(z)\cdot\Delta L_{E}(z)\cdot\Delta z \tag{8}\]  
where \(f_{\text{mod}}\) is the frequency of modulation and \(\Delta L_{E}\) is the perceived masking depth and \(z\) denotes critical band rate. The modified noises of the annular flow were produced by changes in the amplitude and frequency of the signal for 1056-1356 Hz and 2085-2385 Hz. It is assumed that the annular flow noise can be expressed as tonality because the value of tonality changes a lot compared to the other two (Table 9). Therefore, the tonality was used to determine whether the modified noises were characterized as the annular noise. The equation of tonality is as follows:  
\[t_{b}=-0.4343\log\left(\frac{\sqrt{\left[r\cos\theta-\hat{r}\cos\theta\right] ^{2}+\left[r\sin\theta-\hat{r}\sin\theta\right]^{2}}}{r+\hat{r}}\right)-0.30103 \tag{9}\]  
\[\hat{r}(t,\omega)=r(t-1,\omega)+\left\{r(t-1,\omega)-r(t-2,\omega)\right\} \tag{10}\]  
\[\hat{\theta}(t,\omega)=\theta(t-1,\omega)+\left\{\theta(t-1,\omega)-\theta(t -2,\omega)\right\} \tag{11}\]  
where \(r\) denotes magnitude at time \(t\) and frequency \(\omega\) and \(\theta\) is phase at \(t\) and frequency \(\omega\)[21]. Modified noises were generated based on slug, churn, annular and any interval where no refrigerant noise occurred. A total of 48 sound sources was generated. All three kinds of modified sounds show that the corresponding Zwicker parameter changes.