## 3 Results and Discussion  
### Acoustic Characteristic Parameters of the Polyurethane Foam  
Judging from the Johnson-Champoux-Allard model in the Equations (1)-(7), it could be found that it was impossible to identify the accurate porosity \(\phi\) and the accurate static flow resistivity \(\sigma\) simultaneously, because they always appeared in the form of product \(\sigma\phi\) in Equations (6) and (7). It indicated that so long as the product of porosity and static flow resistivity was equal, the calculated sound absorption coefficient would be same, although the corresponding porosity and static flow resistivity might be different. Therefore, the obtained identification result would be the product of porosity and static flow resistivity, the evolutions of which and those of the residual error along with the increase of the function evaluation time from 1 to 1000 are shown in Figure 6. It could be observed that when the function evaluation time reached 115, the identified product of porosity and static flow resistivity was steady around 12500, and the final accurate identified value was 12503 with a final residual error of 0.021. Nominal porosity of the utilized polyurethane foam sample was 0.97, which was provided by the supplier of the GreenCARE International (Guangzhou) Ltd., Guangzhou, Guangdong, China, and the static flow resistivity was not supplied. The actual porosity was tested and calculated according to the drainage method in this research [41], and the obtained data was 0.956, which was very close to the nominal porosity of 0.97. Meanwhile, according to the identified product 12503 of porosity and static flow resistivity in Figure 6, it could be derived that the corresponding static flow resistivity was 13078 Pa*s/m\({}^{2}\). At present, measurement of static flow resistivity of the polyurethane foam sample according to the ISO 9053: 1991 Acoustics--Materials for acoustical applications--Determination of airflow resistance was not conducted in this study, because the measuring process was complex and  
Figure 6: Evolutions of the identified product of porosity and static flow resistivity and those of the residual error along with the increase of the function evaluation times. difficult to realize [42; 43]. Although check of the static flow resistivity was difficult to realize through the direct testing [42; 43], the accuracy of the identification could be examined indirectly through comparing sound absorption coefficients of the theoretical data with those of the experimental data, as shown in Figure 7. It could be observed that for each thickness of the polyurethane foam, its theoretical sound absorption coefficients were exactly consistent with the corresponding actual data. Meanwhile, comparisons of the theoretical and actual sound absorption coefficients of the studied polyurethane foams with the thicknesses of 10 mm and 60 mm were conducted respectively, which are shown in Figure 8. Identification of the acoustic characteristic parameters was achieved through using the experimental data of sound absorption coefficients of the polyurethane foam samples with thicknesses of 20 mm, 30 mm, 40 mm, and 50 mm, hence it was unsurprising that the calculated theoretical data and those experimental data were consistent in Figure 7. The further verification in Figure 8 certified effectiveness and accuracy of the identified acoustic characteristic parameters for the polyurethane foam with various thicknesses. However, for the polyurethane foams with thicknesses from 10 mm to 60 mm, the corresponding actual average sound absorption coefficients in the frequency range 100-1000 Hz were 0.0866, 0.1885, 0.2689, 0.4077, 0.5239, and 0.6362 respectively, which indicated that the achievement of the excellent low-frequency sound absorption performance required the polyurethane foam with large thickness. Therefore, it limited practical application of the polyurethane foam in the low-frequency noise reduction. Figure 7: Comparisons of theoretical and actual sound absorption coefficients of polyurethane foam.