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Spectral representation-based efficient simulation method for fully non-stationary spatially varying ground motions
Abstract As one of the most commonly-used simulation methods, the spectral representation method (SRM) has been utilized to generate fully non-stationary spatially varying ground motions. However, this method usually fails to simulate these ground motions at a large number of interesting locations because of the heavy computational cost of the decomposition of spectral matrices and the superposition of harmonic functions, especially for simulations with time-frequency coupled modulation functions. To address this issue, this study develops an efficient SRM-based method based on a simple interpolation strategy and a quadratic regularization projected Barzilai–Borwein assisted non-negative matrix factorization (QRPBB-NMF). Concretely, the distribution of interpolation nodes is predetermined via spectral feature analysis and only the spectral matrix decomposition at these nodes is required. Then, QRPBB-NMF is introduced to decouple the decomposed spectra into the sum of the products of various time and frequency expressions. Finally, a simple spline interpolation is carried out for these expressions, thereby approximately achieving the SRM-required matrix decomposition in a decoupled manner. The developed method can decrease the operand of the matrix decomposition and invoke the Fast Fourier Transform to speed up the harmonic superposition. A case study in which the fully non-stationary spatially varying ground motions of a tunnel are simulated proves the effectiveness of the developed method in terms of accuracy and efficiency.
Highlights A fast simulation method for spatially varying ground motions is developed. A new interpolation strategy is proposed to accelerate spectral decomposition. A novel matrix factorization method is used to invoke FFT.
Spectral representation-based efficient simulation method for fully non-stationary spatially varying ground motions
Abstract As one of the most commonly-used simulation methods, the spectral representation method (SRM) has been utilized to generate fully non-stationary spatially varying ground motions. However, this method usually fails to simulate these ground motions at a large number of interesting locations because of the heavy computational cost of the decomposition of spectral matrices and the superposition of harmonic functions, especially for simulations with time-frequency coupled modulation functions. To address this issue, this study develops an efficient SRM-based method based on a simple interpolation strategy and a quadratic regularization projected Barzilai–Borwein assisted non-negative matrix factorization (QRPBB-NMF). Concretely, the distribution of interpolation nodes is predetermined via spectral feature analysis and only the spectral matrix decomposition at these nodes is required. Then, QRPBB-NMF is introduced to decouple the decomposed spectra into the sum of the products of various time and frequency expressions. Finally, a simple spline interpolation is carried out for these expressions, thereby approximately achieving the SRM-required matrix decomposition in a decoupled manner. The developed method can decrease the operand of the matrix decomposition and invoke the Fast Fourier Transform to speed up the harmonic superposition. A case study in which the fully non-stationary spatially varying ground motions of a tunnel are simulated proves the effectiveness of the developed method in terms of accuracy and efficiency.
Highlights A fast simulation method for spatially varying ground motions is developed. A new interpolation strategy is proposed to accelerate spectral decomposition. A novel matrix factorization method is used to invoke FFT.
Spectral representation-based efficient simulation method for fully non-stationary spatially varying ground motions
Liu, Shuoyu (author) / Peng, Liuliu (author) / Liu, Jun (author) / Zhao, Shuang (author) / Jiang, Zhongming (author)
2022-07-08
Article (Journal)
Electronic Resource
English
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