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.

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.

Correlation between Superhydrophobicity and the Power Spectral Density of Randomly Rough Surfaces

Langmuir ◽  
2010 ◽  
Vol 26 (23) ◽  
pp. 17798-17803 ◽  
Author(s):  
Houssein Awada ◽  
Bruno Grignard ◽  
Christine Jérôme ◽  
Alexandre Vaillant ◽  
Joël De Coninck ◽  
...  
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Rough Surfaces ◽  
Power Spectral ◽  
Randomly Rough Surfaces

A time-domain procedure for non-Gaussian stationary environmental testing using zero-memory nonlinear transformation

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1197-1213 ◽  
Author(s):  
Song Cui ◽  
Enlai Zheng ◽  
Min Kang
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Time Domain ◽  
Finite Impulse Response ◽  
Numerical Test ◽  
Nonlinear Transformation ◽  
Spectral Densities ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Non Gaussian

This article proposes a time-domain procedure for a non-Gaussian stationary random vibration test with prescribed power spectral densities. Previous procedures for generating non-Gaussianity suffered from certain defects. For example, zero-memory nonlinear transformation, an algorithm frequently applied to transform Gaussian signals into non-Gaussian signals, often produces changes in both auto-power spectral densities and cross-power spectral densities, which might result in control instability under certain circumstances. In this article, the authors propose a different approach for the zero-memory nonlinear function. First, a time-domain procedure for a non-Gaussian random test is introduced. Second, a rescaling method is applied to correct the magnitude amplification on the auto-power spectral density because of zero-memory nonlinear transformation. We offer experience formulas in this method to adjust the auto-power spectral density of both super-Gaussian and sub-Gaussian responses. Third, a control strategy using a finite impulse response filter is proposed to further improve the auto-power spectral density if the shape of the auto-power spectral density is distorted. The kurtosis loss induced by the filtering process is also analysed and a corresponding solution is put forward to ease the reduction. Numerical test and a biaxial shaker table test are conducted to validate the availability and superiority of the proposed procedure.

Simulation of Multi-Dimensional Gaussian Stochastic Fields by Spectral Representation

1996 ◽  
Vol 49 (1) ◽  
pp. 29-53 ◽  
Author(s):  
Masanobu Shinozuka ◽  
George Deodatis
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Autocorrelation Function ◽  
Structural Engineering ◽  
Spectral Representation ◽  
Target Function ◽  
Stochastic Field ◽  
Cosine Series ◽  
Stochastic Fields ◽  
Power Spectral

The subject of this paper is the simulation of multi-dimensional, homogeneous, Gaussian stochastic fields using the spectral representation method. Following this methodology, sample functions of the stochastic field can be generated using a cosine series formula. These sample functions accurately reflect the prescribed probabilistic characteristics of the stochastic field when the number of terms in the cosine series is large. The ensemble-averaged power spectral density or autocorrelation function approaches the corresponding target function as the sample size increases. In addition, the generated sample functions possess ergodic characteristics in the sense that the spatially-averaged mean value, autocorrelation function and power spectral density function are identical with the corresponding targets, when the averaging takes place over the multi-dimensional domain associated with the fundamental period of the cosine series. Another property of the simulated stochastic field is that it is asymptotically Gaussian as the number of terms in the cosine series approaches infinity. The most important feature of the method is that the cosine series formula can be numerically computed very efficiently using the Fast Fourier Transform technique. The main area of application of this method is the Monte Carlo solution of stochastic problems in structural engineering, engineering mechanics and physics. Specifically, the method has been applied to problems involving random loading (random vibration theory) and random material and geometric properties (response variability due to system stochasticity).

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