###### Abstract  
Comparing the empirical modal decomposition (EMD) method and the modified ensemble empirical modal decomposition (MEEMD) method, a response analysis of the long-period components, with the separation and reconstruction of the two methods, and the original long-period ground vibration on high-pier bridges is carried out to verify the validity of the extracted long-period components. In addition, the response characteristics of the components extracted based on the MEEMD and the original ground vibration are studied on the bridges at different points. The results show that, through the correlation of the displacement response of the bridge piers, the long-period component of the long-period ground shaking can well reflect the response characteristics of the long-period ground shaking on the long-period structure, and the MEEMD provides better results than the EMD extraction method. The long-period structure resonates during the long-period component of the long-period ground shaking, the short-period structure resonates during the short-period component, and the structural seismic response is similar to the self-resonance of the structure. The seismic response of the structures is closely related to the self-oscillation period and the spectral parameters of the ground shaking. long-period ground shaking; long-period components; MEEMD; high-pier large-span bridge; seismic response +
Footnote †: journal: Applied  
19 April  
the ground shaking in the Mexican earthquake, and the long-period portion of the shaking (2-4 s) was reduced in this earthquake. Long-period ground shaking in the time domain can be influenced by site factors. [PERSON] et al. [8] analyzed the 1999 Jiji earthquake and the effects of the site conditions, epicentral distance, and magnitude on the long-period ground shaking response spectra; they found that the long-period ground shaking response spectra changed with the site conditions and magnitude. In summary, it is found that long-period ground shaking is susceptible to site conditions in both the time and frequency domains, and the next step is to characterize long-period ground shaking properties and define long-period ground shaking by focusing on the study of spectral parameters of long-period ground shaking. [PERSON] et al. [9] proposed the smoothing cycle parameter, they analyzed the spectral characteristics of 150 near-fault ground shocks based on the HHT, discussed the mean values, coefficients of variation, and the correlation between the three remarkable cycles and seven smoothing cycles that characterized the spectral characteristics of ground shocks, and pointed out that the smoothing cycle parameter can be used as a characterization parameter of near-fault impulsive ground shocks. [PERSON] et al. [10] proposed \(\beta_{t}\), they analyzed the energy characteristics of ground shaking with the Hilbert-Huang transform theory, put forward a method for evaluating the period characteristics of ground shaking, and proposed using the \(\beta\) spectral curve, from the spectral value of 2 to 10 s, and the square-weighted average of the periods, \(\beta_{t}\), as the defining parameters of the long-period ground shaking. [PERSON], et al. [11] proposed two parameter indexes, namely, the energy ratio and the peak ratio of the long-period component, and based on these two indexes, the definition index of the long-period ground vibration, LPGI, was proposed using logistic regression. [PERSON] [12] improved the modified ensemble empirical mode decomposition (MEEMD) method and used it to decompose the long-period ground motion. Taking the separated and reconstructed ground motions as input action, the influence of long-period components on the seismic response of the diagrid structures of high-rise buildings was studied. [PERSON] et al. [13] used the empirical mode decomposition in Hilbert-Huang transform theory to decompose and reorganize typical ordinary, near-field, and far-field long-period seismic waves.