## 4 Conclusions  
In this paper, the energy-flow method was adopted to establish a mixed FE-SEA model with three-coupled systems and a multi-system coupling model to solve the intermediate-frequency solving accuracy problem of the existing mixed FE-SEA model. The parameter identification of effective coupling loss factors in the mixed FE-SEA model was studied. The system response of deterministic components and the energy response of stochastic subsystems in three-coupled systems were derived. Based on the three-coupled system models, the multi-system coupling system response solution method was extended. Aiming at the ill-posed matrix problem for the solution of energy-specific density in the hybrid FE-SEA model with the existing technology, an improved principal-component-weighted correction method was applied by introducing intermediate variables and error transfer. The inverse matrix of energy density was modified to solve the singular-value problem of the ill-posed matrix. In order to further verify the effectiveness of the improved hybrid FE-SEA model parameter identification method, the calculation results of the effective coupling loss factors of each plate were compared. The results showed that the effective coupling loss factor calculated by the mixed FE-SEA method had a singular solution at some frequency points, which was an invalid coupling matrix. In this paper, the principal-element correction method was used to correct the inverse matrix of the ratio of subsystem energy to modal density in the coupling matrix. The effective coupling loss factors calculated were all effective coupling matrices. The effective coupling loss factors calculated by the improved mixed FE-SEA method at the frequency of 400-2000 Hz had a high degree of fit with the test results, which verifies the effectiveness of the proposed method. Compared with the existing literature, the cumulative error caused by the application of the theoretical analytical solution to the effective coupling loss factors in complex structures is avoided. In the calculation frequency range of 1000-2000 Hz, the calculation accuracy of the frequency band was also improved, and the overall calculation error of the whole frequency band was less than 10%, which has a certain engineering-application significance. An effective solution for calculating coupling loss factors via the mixed FE-SEA model has been provided.  
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Figure 14: Effective coupling loss factors of plates 1–4. (**a**) Comparison of several calculation methods of coupling loss factors. (**b**) Test results. (**c**) FE-SEA method. (**d**) The present method.  
**Funding:** The research was financially supported by the Hubei Superior and Distinctive Discipline Group of \"New Energy Vehicle and Smart Transportation\".  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** All data are true and valid.  
**Conflicts of Interest:** The authors declare no conflict of interest.