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Simulation of Multivariate Nonstationary Random Processes by FFT
Yousun Li,Ahsan Kareem +1 more
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In this paper, the fast Fourier transform (FFT) technique is utilized to simulate a multivariate nonstationary Gaussian random process with prescribed evolutionary spectral description, and a stochastic decomposition technique facilitates utilization of the FFT algorithm.Abstract:
The fast Fourier transform (FFT) technique is utilized to simulate a multivariate nonstationary Gaussian random process with prescribed evolutionary spectral description. A stochastic decomposition technique facilitates utilization of the FFT algorithm. The decomposed spectral matrix is expanded into a weighted summation of basic functions and time‐dependent weights that are simulated by the FFT algorithm. The desired evolutionary spectral characteristics of the multivariate unidimensional process may be prescribed in a closed form or a set of numerical values at discrete frequencies. The effectiveness of the proposed technique is demonstrated by means of three examples with different evolutionary spectral characteristics derived from past earthquake events. The closeness between the target and the corresponding estimated correlation structure suggests that the simulated time series reflect the prescribed probabilistic characteristics extremely well. The simulation approach is computationally efficient, p...read more
Citations
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Non-stationary stochastic vector processes: seismic ground motion applications
TL;DR: A spectral-representation-based simulation algorithm is used in this paper to generate sample functions of a non-stationary, multi-variate stochastic process with evolutionary power, according to its prescribed non- stationary cross-spectral density matrix.
Journal Article
Applications of wavelet transforms in earthquake, wind and ocean engineering
Kurtis R. Gurley,Ahsan Kareem +1 more
TL;DR: The wavelet transform is used to decompose random processes into localized orthogonal basis functions, providing a convenient format for the modeling, analysis, and simulation of non-stationary processes as discussed by the authors.
Journal ArticleDOI
Spatial variation of seismic ground motions: An overview
Aspasia Zerva,Vassilios Zervas +1 more
TL;DR: In this paper, the authors address the topic of the spatial variation of seismic ground motions as evaluated from data recorded at dense instrument arrays, focusing on spatial coherency and its interpretation.
Journal ArticleDOI
Recent research advances in the dynamic behavior of shells: 1989–2000, Part 2: Homogeneous shells
Journal ArticleDOI
Simulation of Nonstationary Stochastic Processes by Spectral Representation
Jianwen Liang,Jianwen Liang,Samit Ray Chaudhuri,Samit Ray Chaudhuri,Masanobu Shinozuka,Masanobu Shinozuka +5 more
TL;DR: In this article, a rigorous derivation of a previously known formula for simulation of one-dimensional, univariate, nonstationary stochastic processes integrating Priestly's evolutionary spectral representation theory is presented.
References
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Journal ArticleDOI
Digital simulation of random processes and its applications
Masanobu Shinozuka,C.-M. Jan +1 more
TL;DR: In this article, the authors presented an efficient method for digital simulation of general homogeneous processes as a series of cosine functions with weighted amplitudes, almost evenly spaced frequencies, and random phase angles.
Journal ArticleDOI
Simulation of Multivariate and Multidimensional Random Processes
TL;DR: In this article, the authors present efficient and practical methods of simulating multivariate and multidimensional processes with specified cross-spectral density matrix, which can be expressed as the sum of cosine functions with random frequencies and random phase angles.
Journal ArticleDOI
Monte Carlo solution of structural dynamics
TL;DR: A technique of digital simulation of multivariate and/or multidimensional Gaussian random processes (homogeneous or nonhomogeneous) which can represent physical processes germane to structural engineering is presented.
Journal ArticleDOI
Stochastic Variation of Earthquake Ground Motion in Space and Time
TL;DR: In this paper, the ground motion during a specific earthquake event is conceived as the realization of a space-time random field and accelerograms recorded by the SMART 1 seismograph array in Lotung, Taiwan are examined to determine the frequency-dependent spatial correlation of earthquake ground motions.
Journal ArticleDOI
Power spectral analysis of non-stationary random processes
TL;DR: In this article, the problem of power spectral analysis for non-stationary processes is discussed from the point of view of physical and engineering applications, with emphasis on defining a nonstationary spectrum whose physical interpretation is similar to that of a stationary spectrum.