A modified straightforward spectral representation method for accurate and efficient simulation of the stationary non-Gaussian stochastic wave

2020 ◽  
Vol 205 ◽  
pp. 107308
Author(s):  
Xiancang Song ◽  
Yonggang Jia ◽  
Shuqing Wang ◽  
Liwei Yu
Keyword(s):  
Spectral Representation ◽  
Efficient Simulation ◽  
Spectral Representation Method ◽  
Representation Method ◽  
Non Gaussian

scholarly journals Generating fractal rough surfaces with the spectral representation method

2021 ◽  
pp. 135065012110496
Author(s):  
Yuechang Wang ◽  
Abdullah Azam ◽  
Mark CT Wilson ◽  
Anne Neville ◽  
Ardian Morina
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Spectral Representation ◽  
Rough Surfaces ◽  
Filtering Method ◽  
Fractal Surfaces ◽  
Spectral Representation Method ◽  
Power Spectral ◽  
Representation Method ◽  
Non Gaussian

The application of the spectral representation method in generating Gaussian and non-Gaussian fractal rough surfaces is studied in this work. The characteristics of fractal rough surfaces simulated by the spectral representation method and the conventional Fast Fourier transform filtering method are compared. Furthermore, the fractal rough surfaces simulated by these two methods are compared in the simulation of contact and lubrication problems. Next, the influence of low and high cutoff frequencies on the normality of the simulated Gaussian fractal rough surfaces is investigated with roll-off power spectral density and single power-law power spectral density. Finally, a simple approximation method to generate non-Gaussian fractal rough surfaces is proposed by combining the spectral representation method and the Johnson translator system. Based on the simulation results, the current work gives recommendations on using the spectral representation method and the Fast Fourier transform filtering method to generate fractal surfaces and suggestions on selecting the low cutoff frequency of the power-law power spectral density. Furthermore, the results show that the proposed approximation method can be a choice to generate non-Gaussian fractal surfaces when the accuracy requirements are not high. The MATLAB codes for generating Gaussian and non-Gaussian fractal rough surfaces are provided.

Simulation of Stochastic Processes and Fields for Monte Carlo Simulation Applications: Some Recent Developments

1995 ◽  
Author(s):  
George Deodatis ◽  
Radu Popescu ◽  
Jean H. Prevost
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Stochastic Processes ◽  
Spectral Representation ◽  
Distribution Functions ◽  
Spectral Density Matrix ◽  
Spectral Representation Method ◽  
Cross Spectral Density ◽  
Representation Method ◽  
Non Gaussian

Abstract Two of the latest developments concerning the spectral representation method (used to simulate stochastic processes and fields) are presented in this paper. The first one introduces an extension of the spectral representation method to simulate non-stationary stochastic vector processes with evolutionary power. The proposed simulation formula is simple and straightforward and generates sample functions of the vector process according to a prescribed non-stationary cross-spectral density matrix. The second development introduces another extension of the spectral representation method to simulate multi-dimensional, multi-variate, non-Gaussian stochastic fields. In this case, sample functions are generated according to a prescribed cross-spectral density matrix and prescribed (non-Gaussian) probability distribution functions. Numerical examples are provided for both developments.

An efficient Cholesky decomposition and applications for the simulation of large-scale random wind velocity fields

2018 ◽  
Vol 22 (6) ◽  
pp. 1255-1265 ◽  
Author(s):  
Yongle Li ◽  
Chuanjin Yu ◽  
Xingyu Chen ◽  
Xinyu Xu ◽  
Koffi Togbenou ◽  
...  
Keyword(s):  
Wind Velocity ◽  
Large Scale ◽  
Spectral Representation ◽  
Cholesky Decomposition ◽  
Velocity Fields ◽  
Data Driven ◽  
Long Span Bridges ◽  
Long Span ◽  
Spectral Representation Method ◽  
Representation Method

A growing number of long-span bridges are under construction across straits or through valleys, where the wind characteristics are complex and inhomogeneous. The simulation of inhomogeneous random wind velocity fields on such long-span bridges with the spectral representation method will require significant computation resources due to the time-consuming issues associated with the Cholesky decomposition of the power spectrum density matrixes. In order to improve the efficiency of the decomposition, a novel and efficient formulation of the Cholesky decomposition, called “Band-Limited Cholesky decomposition,” is proposed and corresponding simulation schemes are suggested. The key idea is to convert the coherence matrixes into band matrixes whose decomposition requires less computational cost and storage. Subsequently, each decomposed coherence matrix is also a band matrix with high sparsity. As the zero-valued elements have no contribution to the simulation calculation, the proposed method is further expedited by limiting the calculation to the non-zero elements only. The proposed methods are data-driven ones, which can be applicable broadly for simulating many complicated large-scale random wind velocity fields, especially for the inhomogeneous ones. Through the data-driven strategies presented in the study, a numerical example involving inhomogeneous random wind velocity field simulation on a long-span bridge is performed. Compared to the traditional spectral representation method, the simulation results are with high accuracy and the entire simulation procedure is about 2.5 times faster by the proposed method for the simulation of one hundred wind velocity processes.

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