Chaotic Time Series Analysis of Near-Fault Ground Motions and Structural Seismic Responses

Nonlinear dynamics theory and chaotic time series analysis are suggested to investigate the nonlinear characteristic of near-fault ground motions and structural seismic responses in this paper. Based on the power spectrum analysis and principal component analysis, it is illustrated qualitatively that the acceleration time series of ground motions have chaotic property. Then, the chaotic time series analysis is applied to calculate quantitatively the nonlinear characteristic parameters of 30 acceleration time histories of near-fault ground motions. Numerical results show that the correlation dimension of these ground motions is fractal dimension with the value 1.0–4.0, and their maximal Lyapunov exponent is in the interval 0-2.0. The average maximum Lyapunov exponents between the ground motions with rupture forward directivity and fling-step effect are close, while those values of non-pulse ground motions are smaller. Moreover, the earthquake ground motions present the chaotic characteristic rather than the pure random signal. Finally, the chaotic feature of seismic responses of single degree of freedom systems subjected to ground motions is revealed by using chaotic time series analysis.