Power spectral representation of nonstationary random processes defined over semi-infinite intervals

1976 ◽  
Vol 59 (5) ◽  
pp. 1184 ◽  
Author(s):  
William D. Mark
Keyword(s):  
Spectral Representation ◽  
Random Processes ◽  
Power Spectral ◽  
Infinite Intervals

On the Characterization of Dynamic Properties of Random Processes by Spectral Parameters

2000 ◽  
Vol 67 (3) ◽  
pp. 519-526 ◽  
Author(s):  
G. Petrucci ◽  
M. Di Paola ◽  
B. Zuccarello
Keyword(s):  
Dynamic Properties ◽  
Time Derivative ◽  
Wide Band ◽  
Random Processes ◽  
Spectral Parameters ◽  
Unambiguous Determination ◽  
Power Spectral ◽  
Bandwidth Parameter

This paper deals with the general problem of directly relating the distribution of ranges of wide band random processes to the power spectral density (PSD) by means of closed-form expressions. Various attempts to relate the statistical distribution of ranges to the PSD by means of the irregularity factor or similar parameters have been done by several authors but, unfortunately, they have not been fully successful. In the present study, introducing the so-called analytic processes, the reasons for which these parameters are insufficient to an unambiguous determination of the range distribution and the fact that parameters regarding the time-derivative processes are needed have been explained. Furthermore, numerical simulations have shown that the range distributions depend on the irregularity factor and bandwidth parameter of both the process and its derivative. These observations are the basis for the determination of accurate relationships between range distributions and PSDs. [S0021-8936(00)02903-2]

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.

Random Process Model of Rough Surfaces

1971 ◽  
Vol 93 (3) ◽  
pp. 398-407 ◽  
Author(s):  
P. Ranganath Nayak
Keyword(s):  
Random Process ◽  
Process Model ◽  
Rough Surfaces ◽  
Detailed Comparison ◽  
Random Processes ◽  
Surface Gradient ◽  
Power Spectral ◽  
Random Process Theory ◽  
The Mean ◽  
Surface Statistics

Rough surfaces are modeled as two-dimensional, isotropic, Gaussian random processes, and analyzed with the techniques of random process theory. Such surface statistics as the distribution of summit heights, the density of summits, the mean surface gradient, and the mean curvature of summits are related to the power spectral density of a profile of the surface. A detailed comparison is made of the statistics of the surface and those of the profile, and serious differences are found in the distributions of heights of maxima and in the mean gradients. Techniques for analyzing profiles of random surfaces to obtain the parameters necessary for the analysis of the surface are discussed. Extensions of the theory to nonisotropic Gaussian surfaces are indicated.

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 Generating Stationary Gaussian Processes Using The Spectral Representation Theorem

2015 ◽  
Vol 11 (2) ◽  
pp. 19-37
Author(s):  
Luciana Majercsik ◽  
Ion Simulescu
Keyword(s):  
Representation Theorem ◽  
Spectral Representation ◽  
Fourier Spectrum ◽  
Strong Motion ◽  
Simulation Methods ◽  
Power Spectral ◽  
The Mean ◽  
Stationary Gaussian Processes ◽  
Specific Barrier Model ◽  
Barrier Model

Abstract The paper presents the Spectral Representation Theorem of a stationary process and two simulation methods derived from it. In order to test the accuracy of the two simulation methods two numerical applications are employed. First, using a theoretical power spectral density (PSD), two sets of sample functions, corresponding to each method, are generated and a comparison of the obtained numerical results with the analytical PSD is carried out. The second example is more complex and consists in using the stationary zone of the strong motion of the recorded NS acceleration registered at INCERC during the 1977 Vrancea earthquake. The corresponding Fourier Spectrum is calculated. In order to obtain a smoother PSD representation for the real Fourier spectrum, a specific barrier model spectrum (SBM) is fitted to it and the corresponding PSD calculated. This PSD is used to generate two sets of samples. The mean PSD obtained using both methods of simulation is compared with that characterizing the registered acceleration. The paper shows that the generated time series possess all the theoretical probabilistic characteristics discussed below, when the number of terms used in the simulation formulas is large. Three types of estimators are employed in the numerical evaluation of both simulation methods

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