## 5 Results and Discussion
### Distinguishing between Model Configurations
Hence, this decrease in uncertainty is due to an increase in sensitivity of the model, which could be due to the larger glottal width having fewer parameter combinations that are capable of matching the data. Alternatively, the change in uncertainty could be due to the pre-stress model. The estimates computed for \(p_{\mathrm{sub}}=$1.09\,\mathrm{kPa}$\) and \(p_{\mathrm{sub}}=$1.18\,\mathrm{kPa}$\) have \(x_{0}>$8.3\,\mathrm{mm}$\), whereas the other two estimates have \(x_{0}<$8.3\,\mathrm{mm}$\); in addition, there is a marked decrease in the uncertainties in \(x_{0}\) as \(p_{\mathrm{sub}}\) increases. This could indicate that a higher level of VF compression results in a model with lower sensitivity to the parameters. That is, the dynamics may be more influenced by pre-stress at higher subglottal pressures. Overall, the consistency in the material property estimates and the reasonably low relative uncertainty in \(p_{\mathrm{sub}}\) indicates that the FE model is capable of distinguishing between operational conditions. In pairwise t-tests of the four estimates only two pairs fail to reject the hypothesis of unique data sets (95% confidence); those pairs are \(p_{\mathrm{sub}}=$0.91\,\mathrm{kPa}$\) versus \(1.00\,\mathrm{kPa}$\) and \(p_{\mathrm{sub}}=$1.00\,\mathrm{kPa}$\) versus \(1.09\,\mathrm{kPa}$\). In these two pairs there are small changes in the experimental subglottal pressures (\(0.09\,\mathrm{kPa}\)) and similar fundamental frequencies. Interestingly, there is significant difference between the two cases with the highest subglottal pressures, despite also only differing by \(0.09\,\mathrm{kPa}\) in line with the decreased uncertainty in subglottal pressure at these conditions. We note there is a more marked difference between fundamental frequencies in these cases. For further validation we compare the volumetric flow rate, \(Q\), estimated from the model with the experimentally measured values; volumetric flow rate was not included in the estimation process and thus provides an independent measure for method/model validation. Table 6 compares the estimated and experimentally measured values. The estimated flow rate is derived directly from the Bernoulli flow model embedded in the FE model (see Section 3) as \(Q(t)=$1.3A_{\mathrm{min}}(t)\sqrt{2\varrho^{-1}(p_{\mathrm{sub}}-p_{\mathrm{ sup}})}$\) where \(\varrho=Figure 6:0\) is the density of air. As can be seen in the table, the estimated values generally agree well with, but tend to slightly over-predict, the experimentally measured values. Excepting for the case of \(p_{\mathrm{sub}}=Figure 6:1\), the estimated values are all within one standard deviation of the measurements. With the FE models developed for the four cases and validated with an independent measure (\(Q\)), an additional parameter is explored that is not available experimentally. Table 7 presents the average mean and maximum contact pressures experienced during collisions for the four subglottal pressures. The contact pressures increase with increasing subglottal pressure, which qualitatively agrees with previous studies [37]. Excepting for the \(p_{\mathrm{sub}}=Figure 6:2\) case, the contact pressures are all less than the subglottal pressure. The silicone VFs employed in this study qualitatively do not appear to have vigorous contact when self-oscillating, and as such, the contact pressures may indeed be less than the subglottal pressure. The outlier in the estimated pressure data is the highest subglottal pressure, which exhibits mean and maximum contact pressures well above the subglottal pressure. This is also the case that predicted a volumetric flow rate well above the measured value, suggesting that this model is less reliable. Interestingly, \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(p_{\mathrm{sub}}\) (kPa) & \(0.91\) & \(1.00\) & \(1.09\) & \(1.18\) \\ \hline Experimental & 236 & 260 & 291 & 307 \\ Estimated & 242.5 & 272.2 & 301.4 & 361.6 \\ Uncertainty & 8.29\% & 7.02\% & \(t6.14\%\) & 4.87\% \\ \hline \hline \end{tabular}
\end{table}