## 3 Results and Discussion
### Sound Absorption Performance of the Composite Sound Absorbing Structure
#### 3.2.2 Comparative Analysis of Theoretical Data, Simulation Data, and Experimental Data  
Comparisons of theoretical data, simulation data, and experimental data of the sound absorption coefficients of the composite sound-absorbing structure are shown in Figures 9 and 10 respectively. It could be observed that consistencies among the theoretical data, simulation data, and experimental data were good, and effectiveness of the utilized cuckoo search identification/optimization algorithm, the constructed theoretical sound absorption model, and the used finite element simulation method were validated. Meanwhile, comparisons of theoretical data, simulation data, and experimental data of average sound absorption coefficients of the optimal composite sound-absorbing structures are summarized in Table 3. When the original thicknesses of the polyurethane foam were 10 mm, 20 mm, 30 mm, and 40 mm, actual average sound absorption coefficients of the composite sound-absorbing structure for the investigated frequency range of 100-1000 Hz were 0.4015, 0.5296, 0.6184, and 0.6803 respectively, and those for the investigated frequency range of 100-2000 Hz were 0.5254, 0.6482, 0.7251, and 0.7778 respectively, which exhibited excellent sound absorption efficiency with a smaller total thickness of the sound absorber. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Thickness of Original** & **Investigated** & \multicolumn{2}{c}{**Theoretical Average Sound**} & \multicolumn{2}{c}{**Improvement**} \\ \cline{3-6}
**Polyurethane** & **Range (Hz)** & **Polyurethane** & **Composite** & **Absolute** & **Relative** \\
**Foam (mm)** & **Foam** & **Structure** & **Value** & **Percentage** \\ \hline
10 & 100–1000 & 0.0694 & 0.3969 & 0.3275 & 471.59\% \\
10 & 100–2000 & 0.1489 & 0.5179 & 0.3690 & 247.76\% \\ \hline
20 & 100–1000 & 0.1673 & 0.5409 & 0.3736 & 223.24\% \\
20 & 100–2000 & 0.3422 & 0.6611 & 0.3189 & 93.21\% \\ \hline
30 & 100–1000 & 0.2966 & 0.6283 & 0.3317 & 111.83\% \\
30 & 100–2000 & 0.5369 & 0.7374 & 0.2005 & 37.35\% \\ \hline
40 & 100–1000 & 0.4331 & 0.6884 & 0.2553 & 58.95\% \\
40 & 100–2000 & 0.6799 & 0.7849 & 0.1050 & 15.44\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparisons of the theoretical sound absorption coefficients before and after optimization. Figure 9: Contrasts of sound absorption coefficients of composite structure for 100–1000 Hz. **(a)** For polyurethane foam with thickness of 10 mm; **(b)** For polyurethane foam with thickness of 20 mm; **(c)** For polyurethane foam with thickness of 30 mm; **(d)** For polyurethane foam with thickness of 40 mm. It could be observed that when thickness of the composite structure was 10 mm, its actual sound absorption coefficients in the 100-500 Hz range were slightly larger than those obtained in theory and those achieved in simulation, as shown in Figures 9a and 10a. Similar phenomenon also existed for the composite structures with other thicknesses, which demonstrated that the theoretical and simulation data tended to slightly underestimate the experimental data in the low-frequency range. The different testing mechanism was the major reason. The theoretical data was derived by the transfer matrix method, and the simulation data was achieved by the transfer function method. The experimental data was obtained by the standing wave tube method, which was realized by measuring the peak and valley values of the incident and reflected waves [32; 33; 34; 35]. There existed a superposition between the incident and reflected waves, and this superposition in the low-frequency range was more effective than that in the high-frequency range, which resulted in the different deviations for different frequency ranges.