Principal Component Ananalysis Of Seismic Ground Motion Nonstationarity And Nonlinear Response Of Mdof Systems

The nonstationary nature of ground motions can affect the nonlinear response of engineering structures,potentially increasing the risk of structural damage and collapse.The seismic analysis and design of structures in high seismic intensity areas need to consider the nonstationarity of ground motions.Based on this,this paper adopts the principal component analysis method to analyze the correlation between the nonstationary characteristics of the ground motion and the nonlinear response of the multi-degree-of-freedom system,and study the influence of the nonstationary ground motion on the structural response.Specific research contents include:First,the ground motion time history is selected and the nonstationary characteristic quantities are calculated.Select 530 measured ground motion time histories as seismic input.Based on the generalized harmonic wavelet,the evolution power spectrum of ground motion is estimated,and four nonstationary characteristic quantities of instantaneous frequency,instantaneous bandwidth,instantaneous skewness coefficient and instantaneous kurtosis coefficient of the selected ground motion time history are calculated from the evolution power spectrum.The cross-correlation between the four nonstationary characteristic quantities of ground motion and the peak time of ground motion peak acceleration,spectral acceleration and duration is analyzed.After that,a nonlinear model of an eight-layer multi-degree-of-freedom system is established,and the Bouc-Wen hysteresis relationship,which can simulate the degradation of strength and stiffness,is used to reflect the force-deformation relationship between layers.The maximum interstory displacement angle and the top relative displacement of the multi-degree-of-freedom system under earthquake are calculated,and the occurrence time and location of the maximum interstory displacement angle are obtained.Finally,based on the principal component analysis method,the nonstationary feature quantity of ground motion is dimensionally reduced and three principal components are obtained.Taking the three principal components as the comprehensive index,and the nonstationary characteristic of vibrations as the single index,the correlation between the two indexes and the nonlinear response of the structure was analyzed by using the Pearson correlation coefficient method.The study shows that when the single index is calculated,the occurrence time of the maximum interlayer displacement angle has a high correlation with the four nonstationary characteristic quantities obtained based on the evolution power spectrum,and has a strong negative correlation with the ground motion duration.The maximum interstory displacement angle and the relative displacement of the top layer only show a good correlation with the spectral acceleration;when the comprehensive index is calculated,the three comprehensive indexes all show a high correlation with the occurrence time of the maximum interstory displacement angle.The comprehensive index represented by the peak time of the ground motion peak acceleration,the spectral acceleration and the duration showed a high correlation with the occurrence time of the maximum interlayer displacement angle.