Multi-pulse decomposition for nonlinear seismic analysis of structural systems

Large sympathetic, resonance-like, structural behaviour to earthquake excitations with analogous frequency content often plays a critical role in determining its maximum seismic response. Earthquake excitation typically contains a broad spectrum of non-stationary frequency content, wave packets, which are difficult to observe from the recorded time series. Therefore, identifying the root cause of large responses (which act sympathically with the input but do not achieve full-resonance) of a structure is problematic. Hence, this paper proposes a new multi-pulse decomposition method of ground motions, through which components of a ground motion within a specific period range are determined. In this method, a ground motion is approximated with a Gauss-Fourier wave packet series. The decomposed components, wave packets, contain information about its time-position, frequency, amplitude, pulse width and phase angle. Unlike the Ricker (Morlet) wavelet the Gauss-Fourier wave packet is not limited to symmetrical pulses. One ensemble of 40 near-fault ground motions and one ensemble of 44 far-fault ground motions are used to demonstrate the application and efficiency of the proposed method. The method is shown to be precise in reconstructing the original ground motion using its decomposed components. It is also concluded that the method is accurate in replication of elastic and inelastic response spectra of ground motions within a specific period range. It is demonstrated that for some structure/ground motion combinations, only a few Gauss-Fourier components are required to faithfully describe response behaviour. This highlights that, for these systems, most of the recorded earthquake time series acts like noise on a much simpler wave-packet signal.