Synthesis of the time-frequency non-stationary stochastic near-fault fling-step ground motion based on time-frequency non-stationary ground motion model and stochastic pulse model

Near-fault fling-step ground motions (NFFS-GMs) are known to cause significant permanent ground displacements, resulting in greater structural damage for long-period flexible structures compared to far-field ground motions. Furthermore, even during the same seismic event, the pulse parameters—such as permanent ground displacements $D_{site}$ and pulse period $T_p$—can vary considerably. Despite their importance, research on stochastic NFFS-GMs remains limited. To address this gap, this paper proposes a method for synthesizing the time-frequency non-stationary stochastic near-fault fling-step ground motion for a specific seismic scenario. Firstly, we employ the discrete wavelet transform (DWT) method, utilizing five mother wavelet functions (MWFs) to analyze 210 Chi-Chi ground motions. This analysis identifies 41 valid NFFS-GMs. The effectiveness of the identification method is validated by comparing the displacement time histories of the original ground motion. Pulse parameters are subsequently derived using the fling-step (FS) pulse model proposed by Abrahamson, in conjunction with the nonlinear least-squares method. A regression model correlating pulse parameters with the seismological parameter of the fault distance R is then developed through Pearson correlation analysis and the nonlinear least-squares method. The residuals of the regression model ${\sigma }_{\ln D_{site}}$ and $T_p$ are treated as random variables, and their probability distributions are determined. After that, a new stochastic pulse model is introduced to simulate low-frequency ground motions, while a time-frequency non-stationary model is used to simulate high-frequency ground motions. These components are synthesized in the frequency domain to obtain the time-frequency non-stationary stochastic near-fault fling-step ground motion (TFNS-SNFFS-GM) via inverse Fourier transform. Finally, the effectiveness of the proposed method is confirmed by comparing the response spectrum of the synthesized ground motion with that of actual NFFS-GMs.