## 3 Parameter Optimization for Better Sound Absorption Performance  
According to the constructed theoretical models, the structural parameters of the investigated sound absorbers were optimized by a Cuckoo search algorithm, which aimed to achieve satisfactory sound absorption performance in the low frequency range of 100-1800 Hz when the total thickness of the sound absorber was limited. The average sound absorption coefficient of the sound absorber in the frequency range of 100-1800 Hz was treated as the judging index and the aim of the parameter optimization was to obtain its maximal value, as shown in Equation (22). \[\max(average(\alpha(f)),f\in[100,1800]) \tag{22}\]There were two major constraint conditions for the investigated sound absorber. First was the limit for the total thickness of the sound absorber, \(L_{0}\), which represented the space available in which to install the sound absorber. The total thickness of the sound absorber \(L\) included the thickness of the porous metal \(D\), the length of the cavity backing the porous metal \(D_{1}\), the thickness of the microperforated panel \(t\), and the length of the cavity backing the microperforated panel \(D_{2}\), as shown in Equation (23). \[L=D+D_{1}+t+D_{2}L\leq L_{0},D\geq 0,D_{1}\geq 0,t\geq 0,D_{2}\geq 0 \tag{23}\]  
According to the definition of the microperforated panel, the diameter of the microhole \(d\) should be smaller than 2 mm. Meanwhile, taking the manufacturing cost and practical application into account, the thickness of the panel should be larger than 0.1 mm, the diameter of the microhole should be larger than 0.1 mm, and the distance to the neighboring microholes should be larger than 1 mm. This second constraint condition, regarding the microperforated panel, is summarized in Equation (24). \[\left\{ \begin{array}{c}t\geq 1{\cdot}10^{-4}m\\ 2{\cdot}10^{-3}m\geq d\geq 1{\cdot}10^{-4}m\\ b\geq 1{\cdot}10^{-3}m\end{array} \right. \tag{24}\]  
Based on the optimization target in Equation (22) and the constraint conditions in Equations (23) and (24), the structural parameters of the investigated sound absorbers were optimized by a Cuckoo search algorithm [16; 24; 25]. The limited total thicknesses investigated were 30 mm, 50 mm, and 100 mm, and the optimal structural parameters obtained for these investigated sound absorbers are summarized in Tables 1-3, respectively. Values of the optimal parameters are shown to four significant digits after the decimal point. It can be seen from the theoretical results that the sound absorber consisting of a microperforated panel + cavity + porous metal + cavity achieved the best sound absorption performance. Its average sound absorption coefficients reached 71.4354%, 80.2518%, and 90.3554% when the limited total thicknesses were 30 mm, 50 mm, and 100 mm, respectively. Meanwhile, it should be noted that the optimal length of the cavities backing the porous metal and the microperforated panel were all 0, no matter what the limited total thickness was, which indicates that the sound absorber simply consisted of the microperforated panel and the porous metal. Besides the satisfactory sound absorption performance, this sound absorber also had the additional advantage of a high mechanical strength, great convenience for transportation, installation, application, and maintenance, and good machinability, because there were no gaps among the microperforated panel, the porous metal, and the installed surface. With respect to the sound absorber consisting of porous metal + cavity + microperforated panel + cavity, it was found that its average sound absorption coefficients improved from 65.0575% to 88.8120% when the limited total thickness increased from 30 mm to 100 mm, a slightly smaller improvement than that found for the sound absorber consisting of microperforated panel + cavity + porous metal + cavity.