## 5 Test Verification
### Identification Results and Discussion  
The measured acceleration response signal of the seven-story frame structure in a healthy state is shown in Figure 11, the proposed hybrid method of IEMD and ARMA was used for modal parameter identification, and the detailed identification process was shown as follows:  
First, the acceleration signal was measured by means of IEMD for preprocessing; namely, choosing two groups of the acceleration response in a structural healthy condition. Then, a FFT process was performed, followed by picking up the peak frequency of the Fourier spectrum as the central frequency of the band-pass filter. Two sets of acceleration response signals separately passed through the band-pass filter with a specified frequency band, and frequency range can be expressed as \(j_{L}<j<j_{R}\), in this paper, while the frequency range was no more than 5%. Finally, a two-time cluster analysis was used to determine the real IMFs. Second, the cross-correlation function was obtained using the NExT method. Obviously, two sets of acceleration response signals can obtain two groups of IMFs (The first seven order IMFs are shown in Figure 11). With one set of IMFs as the reference signal, the corresponding cross-spectral density function of each IMF was solved, and the inverse Fourier transform was carried out to obtain the cross-correlation function, as the free vibration response of the structure (as shown in Figure 12). Figure 11: Acceleration signal and IMF1\(-\)7 using IEMD. Figure 10: Testing of a seven\(-\)story steel frame structure. Finally, by using an ARMA(\(2,2\)) model to simulate the free vibration response (cross-correlation function), the sixth IMF was taken as an example, as shown in Figure 13, for identifying the modal frequency of the structures (as shown in Table 2). As mentioned above, ARMA-based modal identification is one of the most popular methods, since it offers a high accuracy of modal parameters, with the main obstacle in ARMA-based modal identification being the determination of proper system order. This defect has attracted a large number of scholars to complete a lot of related research [13; 14; 15], but the problem of model order determination is still very difficult. However, in this paper, since the components of the IMFs are all single-order modes after disposing of the IEMD, the order of the model is two, which is twice the order of the mode. In order to identify the mode shape, the vibration response signals of all freedom degrees should be measured. For different measuring points, the coefficients of the vibration mode are obtained using the residue and normalized to obtain the mode shape. Figure 12: Free vibration curves of IMF6 obtained using the NExT method. Figure 13: Corresponding to Figure 11, the fitting curve used in the ARMA model. In order to further illustrate the effect of the IEMD method, the IMFs obtained by classical EMD decomposition are shown in Figure 14. From Figures 11 and 14, it can be seen that mode mixing occurred for the six and seventh IMFs obtained by EMD locally, i.e., some data with the same, or nearly the same, frequency are decomposed into more than one IMF (labeled by the red dotted rectangle), while in Figure 11 the modes are well separated from original signal. A Hilbert spectrum analysis and cluster analysis of IMFs obtained using IEMD are shown in Figures 15 and 16, respectively. It can be seen from these two figures that the IEMD resolved the problems of modal mixing, and the identified IMFs were all single independent components. Therefore, the IEMD/ARMA methods could obtain more accurate recognition results (as shown in Table 2). It can also be concluded that EEMD cannot completely improve the mode mixing problem of classical EMD based on the frequency identification results. However, EEMD can obtain more accurate frequency identification results than classic EMD in the low frequency domain.