## 5 Simulations and Discussion
### Simulation Results and Discussion
The total sound pressure levels of different structures are also calculated in Table 4. Figure 8 illustrates the power spectrum densities (PSDs) of noise attenuation in different structures when the gain factor was equal to 0.5. The primary noise signal included the line-spectrum noise signal and the Gaussian random noise signal. From Figures 7 and 8, it can be seen that the two modified structures for the hybrid active sound quality control systems could not only control sound quality of line-spectrum noise by decreasing the noise amplitude, but they could also reduce the Gaussian random noise. The different gain factors could also be selected to retain and amplify the noise amplitude to achieve the goal of control sound quality. Meanwhile, the noise reductions of the two modified structures were equivalent to that of the traditional structure because of the influence of the gain factor on the coupling effect. The noise reductions in the different structures were about 6.0 dB between 10 Hz and 100 Hz, and the simulation results were in accordance with the theoretical calculations in Reference [10]. Figure 7: Spectra of noise attenuation in different structures (\(\beta=0.5\)): (**a**) traditional hybrid structure; (**b**) simplified hybrid structure using new leaky FxLMS algorithm in the feedback controller; (**c**) modified hybrid structure; (**d**) simplified hybrid structure using leaky FxLMS algorithm in the feedback controller (\(\gamma=0.8\)). Figure 9 describes the waveforms of output signals for feedback control filters using different algorithms when the step size of the feedback control filter was 0.005 and the gain factor was 0.5. Figure 9 indicates the waveforms of output signals for the feedback control filters using the FxLMS algorithm, the new leaky FxLMS algorithm, and the leaky FxLMS algorithms with different leakage factors. It can be seen that the output signals for the feedback control filters using the leaky class FxLMS algorithms were more stable compared to the one using the FxLMS algorithm because some iterations of the feedback control filter were unstable. Meanwhile, it is indicated in Figure 9-d that the feedback control filter with the new leaky FxLMS algorithm had better constraint performance, avoiding the excessive output signal of the feedback control filter. However, the output signal of the feedback control filter with the new leaky FxLMS algorithm fluctuated remarkably because the constraint term was updated in real time, as presented in Equation (17). Furthermore, the fluctuation slightly enabled the amplitude of the output signal to maintain a high level, which resulted in a higher noise reduction compared to the leaky FxLMS algorithm with a constant leakage factor. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Structure** & **ANCoff** & \begin{tabular}{c} **Tra Structure** \\ **[10]** \\ \end{tabular} & \begin{tabular}{c} **Tsim Structure** \\ **[19]** \\ \end{tabular} & \
\begin{tabular}{c} **Nsim** \\ **Structure** \\ \end{tabular} &
\begin{tabular}{c} **Mod** \\ **Structure** \\ \end{tabular} \\ \hline SPL (dB) & 92.1 & 86.2 & 86.2 & 86.1 & 86.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Noise reductions of the different structures (\(\beta\) = 0.5). Figure 8: PSDs of noise attenuation in different structures \(\beta\) = 0.5): (**a**) traditional hybrid structure; (**b**) simplified hybrid structure using new leaky FxLMS algorithm in the feedback controller; (**c**) modified hybrid structure; (**d**) simplified hybrid structure using new leaky FxLMS algorithm in the feedback controller (\(\gamma\) = 0.8). It is shown in Figures 10 and 11 that noise reductions of the new leaky FxLMS algorithm and the leaky FxLMS algorithm with a constant leakage factor (\(\gamma=0.8\)) were correlated when the gain factor was set to zero.