## 3 Hybrid FE-SEA Modeling Parameter Identification Algorithm
### The Algorithm of a Case Analysis
#### 3.6.3 Coupling Loss-Factor Analysis of the System  
In order to further verify the effectiveness of the improved mixed FE-SEA method, the effective coupling loss factors of each plate were compared. Figure 12 shows the results of the effective coupling loss factor transferred from plate 1 to plate 2. It can be seen from Figure 12a that plate 1 is the excitation surface, and the effective coupling loss factors calculated by the mixed FE-SEA method appear as singular solutions at individual frequency points, which are regarded as the invalid coupling matrix. In the method presented in this paper, the application of the principal-component correction method to  
Figure 9: The inverse matrix of the energy density of plate 1. (**a**) The inverse matrix of the energy density of plate 1. (**b**) The inverse matrix distribution of the reference solution. (**c**) The inverse matrix distribution of the present method. (**d**) The inverse matrix distribution of the FE-SEA method. determine the coupling matrix subsystem energy density was used to obtain the ratio of the inverse matrix and calculate the effective coupling loss factor of the effective matrix in order to effectively calculate the mixed FE--SEA model, the effective coupling loss factor of the feasible method providing a theory and the calculation results tallying with the test results. The improved hybrid FE-SEA method in the frequency range of 400-2000 Hz had a high degree of fit with the test results, which verified the effectiveness of the proposed method. Compared with the existing literature, the cumulative errors caused by the application of theoretical analytical solutions to solve the effective coupling loss factors in complex structures is avoided, and the calculation accuracy in the frequency band of 1000-2000 Hz is improved, which is more suitable for the solution of the effective coupling loss factors in complex structures [22]. Figure 12b-d are the distribution diagrams of effective coupling loss factors obtained by the test method, the mixed FE-SEA method, and the proposed method, respectively. It can be seen from the figures that the distribution of the effective coupling loss factors obtained by the proposed method is reasonable and that no invalid coupling matrix appears. Figure 10: The inverse matrix of the energy density of plate 2. (**a**) The inverse matrix of the energy density of plate 2. (**b**) The inverse matrix distribution of the reference solution. (**c**) The inverse matrix distribution of the present method. (**d**) The inverse matrix distribution of the FE-SEA method. Figure 13 shows the results of the effective coupling loss factor transferred from plate 1 to plate 3. It can be seen from Figure 13a that plate 1 is the excitation surface, and the effective coupling loss factor calculated by the mixed FE-SEA method presents an invalid coupling matrix region at such frequency points as 400 Hz, 1000 Hz, and 1800 Hz. In this paper, the principal-element correction method was used to correct the inverse matrix of the ratio between the subsystem energy and the modal system, and the effective coupling loss factors calculated were all effective coupling matrices, which were in good agreement with the test results. In the frequency ranges of 0-1000 Hz and 1400-2000 Hz, the improved hybrid FE-SEA method had a high degree of fit with the test results, which verified the effectiveness of the proposed method. Figure 13b-d are the distribution diagrams of the effective coupling loss factors obtained by the test method, the mixed FE-SEA method, and the proposed method, respectively. It can be seen from the figures that the distribution of the effective coupling loss factors obtained by the proposed method is reasonable. Figure 11: The inverse matrix of the energy ratio density of plate 3. (**a**) The inverse matrix of the energy density of plate 3. (**b**) The inverse matrix distribution of the reference solution. (**c**) The inverse matrix distribution of the present method. (**d**) The inverse matrix distribution of the FE-SEA method.