## 4 Preliminary Verification by Finite Element Simulation  
According to the theoretical optimal structural parameters obtained by Cuckoo search algorithm, the finite element simulation models for the four investigated sound absorbers were constructed in the virtual acoustic laboratory, and schematic diagrams of the simulation models when the total thickness was 50 mm are shown in Figure 3. The plane wave was introduced in the acoustic source inlet, which was treated as the incident sound source. Two microphones were utilized to measure the incident sound wave and the reflected sound wave in the standing wave tube, which were used to calculate the sound absorption coefficient. In the model, porous metal was characterized by setting its structural parameters, which included the static flow resistivity, porosity, bulk density, specific heat ratio, and so on. Meanwhile, the microperforated panel was represented by the acoustic transfer relation admittance loading at the inner surface and outer surface of the panel. Dimensional parameters of the porous metal, microperforated panel, and the cavity were coincident with the obtained optimal parameters in Table 2. In this way, the real part and imaginary part of the sound pressure at microphone 1 and those at microphone 2 could be obtained from the simulation process and exported as the original data, and the sound absorption coefficient could be calculated. Similarly, the finite element simulation models of the four investigated sound absorbers with limited total thicknesses of 30 mm and 100 mm were constructed according to the theoretical optimal structural parameters in Tables 1 and 3, respectively. Comparisons of the theoretical results and the simulation results are summarized in Figure 4. It can be observed that simulation data of the microperforated panel + cavity sound absorber agreed well with its theoretical data, and that there were notable differences between simulation data of the porous metal and its theoretical data, especially when the limited total thickness was 30 mm. One important reason for this phenomenon is that [PERSON]'s theory is widely recognized as an accurate model to describe the sound absorption process of the microperforated panel [8, 16, 23], so it was easy to represent its characteristics by the acoustic transfer relation admittance in the finite element simulation model. However, many theoretical models have been developed to describe the sound absorption mechanism of porous material, such as the Johnson-Champoux-Allard model [7, 13, 22, 28], the Delany-Bazley-Miki model [29, 30], the Craggs model [31, 32], and so on. Meanwhile, there were two frame types for the porous material, rigid and lim, which made it difficult to select the appropriate models and parameters for the porous metal in the finite element simulation model. Therefore, the differences between the simulation data and theoretical data of the porous metal were larger than those of the microperforated panel. It was also found that the differences between the simulation data and the theoretical data of the porous  
Figure 2: Distributions of sound absorption coefficients for the theoretical optimal sound absorbers in the frequency range of 100–1800 Hz with different limited total thicknesses. (**a**) 30 mm; (**b**) 50 mm; (**c**) 100 mm. metal + cavity + microperforated panel + cavity sound absorber and those of the microperforated panel + cavity + porous metal + cavity sound absorber were larger than those of the microperforated panel and smaller than those of the porous metal, which were well accordant with the causal analysis because the combination structures consisted of porous material and microperforated panel. With an increase in the limited total thickness from 30 mm to 100 mm, the differences between simulation data and theoretical data of each sound absorber were gradually reduced because the sound absorption coefficients were close to their limits in this low frequency range of 100-1800 Hz.