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The smooth transition GARCH model for simulation of highly nonstationary earthquake ground motions

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Abstract

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.

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Authors and Affiliations

  1. Faculty of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, 15914, Iran

    Reza Sharbati, Faramarz Khoshnoudian & Mohammadreza Koopialipoor

  2. Faculty of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, 15914, Iran

    Hamidreza Ramazi

  3. Faculty of Statistics, Amirkabir University of Technology, Tehran, 15914, Iran

    Toktam Valizadeh

  4. Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam

    Danial Jahed Armaghani

Authors
  1. Reza Sharbati
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  2. Hamidreza Ramazi
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  3. Faramarz Khoshnoudian
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  4. Toktam Valizadeh
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  5. Mohammadreza Koopialipoor
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  6. Danial Jahed Armaghani
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Correspondence to Danial Jahed Armaghani.

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Sharbati, R., Ramazi, H., Khoshnoudian, F. et al. The smooth transition GARCH model for simulation of highly nonstationary earthquake ground motions. Engineering with Computers 38, 1529–1541 (2022). https://doi.org/10.1007/s00366-020-01117-5

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