## 4 Conclusions  
Sound absorption performance of the composite structure of microperforated panel and porous metal was modeled, optimized, simulated, measured, and analyzed in this study. A feasible method to develop the desired sound absorber for the effective reduction of industrial noise was proposed and the following conclusions were obtained from the research results.  
1. Theoretical models of the sound absorption performance of the composite sound absorbing structures were derived by the transfer matrix method, and the sound absorption coefficients were calculated by a series of equations, which provided an objective function for the structural parameter optimization process and the contrast accordance for the further finite element simulation and the following experimental validation.  
Figure 10: Evolutions of the experimental data of sound absorption coefficients of the PCMC in the 10 standing wave tube measurements.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Limited Total** & **PCMC (mm)** & **PC (mm)** & **MCPC (mm)** & **MC (mm)** & **PCMCPC (mm)** \\ \hline
30.00 & 30.00 & 30.00 & 12.20 & 12.48 & 30.00 \\
50.00 & 37.04 & 50.00 & 50.00 & 12.48 & 36.80 \\
100.00 & 95.24 & 100.00 & 100.00 & 12.48 & 98.60 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Summarized actual total thickness with the different presupposed limited total thickness.  
2. Structural parameters of the composite structure were optimized through the cuckoo search algorithm when the desired frequency range was (2000 Hz, 6000 Hz) and the limited total thickness was 30 mm, 50 mm, and 100 mm, respectively. The distributions and optimal averages of the sound absorption coefficients indicated that the proposed composite structures with the optimal structural parameters were excellent sound absorbers.
3. Simulation models of the composite structure with optimal structural parameters were built based on the finite element method. Detailed comparative analysis of the theoretical result and the simulation result was conducted, and the calculated absolute deviation of corresponding optimal average sound absorption coefficient was smaller than 1%, which gave a preliminarily verification to the optimization results.
4. Experimental validations of the optimal composite structures were conducted through the AWA6128A detector based on the standing wave tube method. The sandwich structure of porous metal 26.21 + cavity 0 + microperforated panel 0.1 + cavity 0 + porous metal 10.49 + cavity 0 with an actual total thickness 36.8 mm obtained the average sound absorption coefficient of 97.65% in the frequency range (2000 Hz, 6000 Hz), which indicated that the optimization of structural parameters was an effective way to develop the desired acoustic absorber and would be favorable to promote the application of the composite structures in the field of industrial noise reduction.  
conceptualization, X.S. and P.B.; software, X.L.; validation, H.D., X.S., and F.Y.; formal analysis, F.Y. and X.S.; investigation, Z.L.; data curation, H.D.; Writing--Original draft preparation, H.D. and P.B.; Writing--Review and editing, X.S. and Z.L.; supervision, X.S.; funding acquisition, X.S. and Z.L.  
This research was funded by the National Natural Science Foundation of China, grant number 51505498; Natural Science Foundation of Jiangsu Province, grant number BK20150714; National Key R&D Program of China, grant number 2016 YFC0802900; Hong Kong Scholars Program, grant number XJ2017025.  
The authors wish to express their sincere thanks to Hangzhou Aihong Instruments Co., Ltd., China for the support of the AWA6128A detector.  
The authors declare no conflict of interest.