## 5 Results and Discussions  
The response measured from the number 6 accelerometer under damage conditions of the connecting plate 2 is used as an example to show the analysis process. The acceleration waveform in the time domain is shown in Figure 8.  
Figure 8: The measured acceleration waveform. Figure 7: Photographs of the model cable-stayed bridge: (**a**) general view of the model bridge, (**b**) damage of the connecting plate, and (**c**) damage of the stay-cable. The IMFs of the given signal can be obtained by using the IEEMD method proposed in Section 2.2, which is shown in Figure 9.  
The stationary and linear surrogate signals of each IMF can be generated by using the method in Section 3.2.2, which are shown in Figures 10 and 11. Figure 11: The linear surrogate signals of each IMF. Figure 9: The extracted IMFs and residual of the selected signal. The appropriate time delay and embedding dimension of each IMF can be obtained by using the method explained in Section 3.2.2. The mutual information, false nearest neighbors, and phase-space figures of IMF1 are shown in Figure 12. From the figure, we can see that the first local minimum of the time-delayed mutual information is 3\(\Delta\)t (\(\Delta\)t is the Sampling interval) and the false nearest neighbors equal zero when the embedding dimension is 7. The appropriate time delay and embedding dimension of other IMFs is similar to the analysis process of the IMF1. The appropriate time delay and embedding dimension parameters of all IMFs are listed in Table 1.  
[PERSON] [33] and [PERSON] [1] both have stated that the length of the diagonal lines is related to the largest positive Lyapunov exponent, which is usually taken as an indication that the system is chaotic and nonlinear. In addition, the length of vertical lines allows for the investigation of intermittency, even for rather short and non-stationary data series [1]. According to this point, in this paper, the diagonal line-based RQA measures (e.g., Lmax, ENTR, DET) are used as indicators of the nonlinear level. The vertical line-based RQA measures (e.g., Vmax, VENTR, LAM) are used as the indicators of the nonstationary level. The statistical six indicators of each IMF can be calculated by using the method described in Section 3.2.3. Due to the length of the paper, we only select the statistical RQA measures of the IMF1 and IMF7 to compare the results, which are shown in Figure 13.  
From Figures 13 and 14, it can be clearly seen that the nonstationary indicators (Vmax, VENTR, LAM) and the nonlinear indicators (Lmax, ENTR, DET) of IMF1 are all in the confidence interval, which indicates that the stationary and linear hypothesis should be accepted. However, the nonstationary indicators and nonlinear indicators of IMF7 all fall outside the confidence interval, which indicates that the stationary and linear hypothesis should be rejected. The conclusion in this case is consistent with the results shown in Figure 9 in which IMF1 mostly contains the stationary and linear white noise, and IMF7 mostly contains the non-stationary and nonlinear structural dynamic information. To further prove the effectiveness of the above nonstationary indicators, the time-frequency analysis of IMF1 and IMF7 is performed by the continuous wavelet transform algorithm [45], which is shown in Figure 15. The figure has shown that the IMF1 has a relatively uniform frequency distribution with time. Unlike the former, the frequency range 1-2 Hz of IMF7 is the major frequency components and the main frequency in IMF7 is steadily decreasing with time. The time-frequency analysis results of IMF1 and IMF7 indicate that the IMF1 is stationary and IMF7 is nonstationary, which are consistent with the results of the proposed nonstationary test indicators in this paper.