A Spectral Representation Model for Simulation of Multivariate Random Processes

2011 ◽  
Vol 368-373 ◽  
pp. 1253-1258
Author(s):  
Jun Jie Luo ◽  
Cheng Su ◽  
Da Jian Han
Keyword(s):  
Spectral Density ◽  
Stochastic Processes ◽  
Power Spectral Density ◽  
Spectral Representation ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Recursive Algorithm ◽  
Spectral Density Function ◽  
Cholesky Factorization ◽  
Power Spectral

A model is proposed to simulate multivariate weakly stationary Gaussian stochastic processes based on the spectral representation theorem. In this model, the amplitude, phase angle, and frequency involved in the harmonic function are random so that the generated samples are real stochastic processes. Three algorithms are then adopted to improve the simulation efficiency. A uniform cubic B-spline interpolation method is employed to fit the target factorized power spectral density function curves. A recursive algorithm for the Cholesky factorization is utilized to decompose the cross-power spectral density matrices. Some redundant cosine terms are cut off to decrease the computation quantity of superposition. Finally, an example involving simulation of turbulent wind velocity fluctuations is given to validate the capability and accuracy of the proposed model as well as the efficiency of the optimal algorithms.

scholarly journals Spline-Interpolation-Based FFT Approach to Fast Simulation of Multivariate Stochastic Processes

2011 ◽  
Vol 2011 ◽  
pp. 1-24 ◽  
Author(s):  
Jinhua Li ◽  
Chunxiang Li ◽  
Shuisheng Chen
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Stochastic Processes ◽  
Power Spectral Density ◽  
Spline Interpolation ◽  
Spectral Density Matrix ◽  
Power Spectral ◽  
Computational Speed ◽  
Interpolation Technique ◽  
Spline Interpolation Technique

The spline-interpolation-based fast Fourier transform (FFT) algorithm, designated as the SFFT algorithm, is proposed in the present paper to further enhance the computational speed of simulating the multivariate stochastic processes. The proposed SFFT algorithm first introduces the spline interpolation technique to reduce the number of the Cholesky decomposition of a spectral density matrix and subsequently uses the FFT algorithm to further enhance the computational speed. In order to highlight the superiority of the SFFT algorithm, the simulations of the multivariate stationary longitudinal wind velocity fluctuations have been carried out, respectively, with resorting to the SFFT-based and FFT-based spectral representation SR methods, taking into consideration that the elements of cross-power spectral density matrix are the complex values. The numerical simulation results show that though introducing the spline interpolation approximation in decomposing the cross-power spectral density matrix, the SFFT algorithm can achieve the results without a loss of precision with reference to the FFT algorithm. In comparison with the FFT algorithm, the SFFT algorithm provides much higher computational efficiency. Likewise, the superiority of the SFFT algorithm is becoming more remarkable with the dividing number of frequency, the number of samples, and the time length of samples going up.

Analysis of power spectral density of random Landau-Lifshitz-Slonczewski dynamics by using stochastic processes on graphs

2008 ◽  
Vol 103 (7) ◽  
pp. 07B120 ◽  
Author(s):  
Isaak D. Mayergoyz ◽  
Claudio Serpico ◽  
Giorgio Bertotti ◽  
Roberto Bonin ◽  
Massimiliano d’Aquino
Keyword(s):  
Spectral Density ◽  
Stochastic Processes ◽  
Power Spectral Density ◽  
Power Spectral

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.

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