The aim of this paper is to extend a stochastic model for simulation of highly nonstationary ground motions (GMs). In this model, the dual-tree complex discrete wavelet transform (DT-CDWT) is applied to a recorded ground motion to extract its wavelet coefficients and then the Smooth Transition Generalized Autoregressive Conditional Heteroscedastic (ST-GARCH) model is used to simulate these coefficients. This model simulates nonstationary features of real GMs greatly, because the conditional variance estimated by this model changes compatibly with the amplitude nonstationary features of real GMs. Because of having asymmetric structure, this model also estimates sudden changes in the amplitude of ground motions. Some of the special capabilities of this model are the simulation of multiple increasing–decreasing cycles in the temporal amplitude of GMs, prediction of several peaks in the frequency spectrum of GMs, estimation of steps of their energy curve, and simultaneous simulation of all shocks of a GM sequence. Also, this model simulates the time–frequency energy distribution of both wide-frequency and narrow-frequency bandwidth GMs.

中文翻译：

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用于模拟高度非平稳地震地面运动的平滑过渡 GARCH 模型

本文的目的是扩展用于模拟高度非平稳地面运动 (GM) 的随机模型。在该模型中，对记录的地面运动应用双树复离散小波变换 (DT-CDWT) 以提取其小波系数，然后使用平滑过渡广义自回归条件异方差 (ST-GARCH) 模型来模拟这些系数. 该模型极大地模拟了真实 GM 的非平稳特征，因为该模型估计的条件方差与真实 GM 的幅度非平稳特征相适应地变化。由于具有非对称结构，该模型还估计了地震动幅度的突然变化。该模型的一些特殊功能是模拟 GM 时间幅度的多个增减周期，预测 GM 频谱中的几个峰值，估计其能量曲线的阶跃，以及同时模拟 GM 序列的所有冲击。此外，该模型模拟了宽频和窄频带宽 GM 的时频能量分布。