## 2 Materials and Methods
### Parameter Optimization by the Cuckoo Search Algorithm  
Sound absorption performance of the composite structure is mainly determined by its structural parameters, which can be judged from the constructed theoretical model in the Section 2.1. For the given porous metal sample, the influencing factors were its thickness and length of the rear cavity. With regard to the microperforated panel absorber, the influencing factors were diameter of the hole, distance between the neighboring holes, thickness of the panel, and length of the rear cavity. A simple investigation on influence of the structural parameters to the sound absorption performance was conducted by selecting a series of varied parameters for the composite structure of PCMC in the Figure 1a with the same total thickness of 40 mm, as shown in the Figure 2, and the corresponding selected parameters are summarized in the Table 1. It can be observed that the changes of structural parameter led to notable variety of sound absorption coefficient, which indicated that optimization of structural parameters of the composite structure was not only an essential, but also an effective method to develop the desired sound absorber. Total thickness of the composite sound absorbing structure is an important factor that affects its practical application, which consists of thickness of the porous metal, thickness of the panel, and length of each rear cavity. Total thickness \(T\) of the five composite structures in the Figure 1 can be calculated using Equation (22). \[T= \begin{cases}d_{p}+D_{p}+t+D_{a}&for&structure&in&Figure&1a\\ d_{p}+D_{p}&for&structure&in&Figure&1b\\ t+D_{a}+d_{p}+D_{p}&for&structure&in&Figure&1c\\ t+D_{a}&for&structure&in&Figure&1d\\ d_{f}+D_{f}+t+D_{a}+d_{b}+D_{b}&for&structure&in&Figure&1e\\ \end{cases} . \tag{22}\]  
Supposing the limit for total thickness of the sound absorber is \(T_{0}\), it is determined by the available space for installing the sound absorber. The normal range \(T_{0}\) in a common workshop is 10-100 mm, so the selected constraint conditions of \(T_{0}=30\) mm, \(T_{0}=\)50 mm, and \(T_{0}=100\) mm were investigated in this research. In addition to the total thickness, each structure parameter also has the constraint condition for the practical application. Thickness of the porous metal \(d_{p}\) and that of the microperforated panel \(t\) shall be not too small, otherwise strength and stiffness of the formed composite structure will be too low. Meanwhile, according to the definition of the microperforated panel and process capability of the used precise machine tool, the diameter of the hole \(d\) and distance of the neighboring holes \(b\) should be in a reasonable range. Therefore, constraint conditions for the parameter optimization of the composite structure are summarized in Equation (23). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Serial**} & \multicolumn{2}{c}{**Porous Metal**} & \multicolumn{2}{c}{**Microperforated Panel**} & \multicolumn{2}{c}{**Average Sound Absorption**} \\ \cline{2-7}  & \(d_{p}\) **(mm)** & \(D_{p}\) **(mm)** & \(d\) **(mm)** & \(b\) **(mm)** & \(t\) **(mm)** & \(D_{a}\) **(mm)** & **Coefficient in Frequency Range** \\ \hline
0001 & 12 & 15 & 0.1 & 1 & 0.1 & 12.9 & 82.61\% \\
0002 & 14 & 12 & 0.2 & 1.5 & 0.3 & 13.7 & 88.91\% \\
0003 & 16 & 9 & 0.3 & 2 & 0.5 & 14.5 & 86.39\% \\
0004 & 18 & 6 & 0.4 & 2.5 & 0.7 & 15.3 & 82.78\% \\
0005 & 20 & 3 & 0.5 & 3 & 0.9 & 16.1 & 79.87\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The selected parameters for studying their influence on the sound absorption performance. Figure 2: Qualitative comparisons of sound absorption coefficient of the composite sound absorbing structures with the varied structural parameters. \[\left\{ \begin{array}{l}T\leq T_{0}\\ d_{p},d_{b},d_{f}\geq 1\cdot 10^{-4}m\\ t\geq 1\cdot 10^{-4}m\\ d\geq 1\cdot 10^{-4}m\\ b\geq 1\cdot 10^{-3}m\\ D_{a},D_{p},D_{f},D_{b}\geq 0\end{array}