scholarly journals Generation of Two Correlated Stationary Gaussian Processes

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2687
Author(s):  
Guo-Qiang Cai ◽  
Ronghua Huan ◽  
Weiqiu Zhu
Keyword(s):  
Spectral Density ◽  
Stochastic Processes ◽  
Power Spectral Density ◽  
Series Expansion ◽  
Gaussian Processes ◽  
Linear Filters ◽  
Advantages And Disadvantages ◽  
Power Spectral ◽  
Stationary Gaussian Processes ◽  
Different Levels

Since correlated stochastic processes are often presented in practical problems, feasible methods to model and generate correlated processes appropriately are needed for analysis and simulation. The present paper systematically presents three methods to generate two correlated stationary Gaussian processes. They are (1) the method of linear filters, (2) the method of series expansion with random amplitudes, and (3) the method of series expansion with random phases. All three methods intend to match the power spectral density for each process but use information of different levels of correlation. The advantages and disadvantages of each method are discussed.

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

Optimization of linear filters under power-spectral-density stabilization

2001 ◽  
Vol 49 (10) ◽  
pp. 2292-2300 ◽  
Author(s):  
A.M. Grigoryan ◽  
E.R. Doughelly
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Linear Filters ◽  
Power Spectral

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.

scholarly journals Fretting Fatigue Damage Nucleation and Propagation Lifetime Using a Central Point Movement of Power Spectral Density

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Thanh Q. Nguyen ◽  
Hieu C. Doan ◽  
Luan C. Vuong ◽  
H. Nguyen-Xuan ◽  
Nhi K. Ngo
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Fatigue Damage ◽  
Fretting Fatigue ◽  
Central Point ◽  
Reference Source ◽  
Forced Circulation ◽  
New Approach ◽  
Power Spectral ◽  
Different Levels

This paper presents a new perception in evaluating fretting fatigue damage nucleation and propagation lifetime under periodically forced circulation. A new approach, which is proposed in this paper, is to measure the change of the central point of power spectral density (CP-PSD) in different structural stiffness degradation stages. A notable aspect of this study lies in the combination between vibration amplitude and forced frequency of the fatigue-causing factors in beam structures. Additionally, it is found that randomization of the first phase from 0 to 2π yields more accurate modelling of the fatigue phenomenon. Results show that the CP-PSD parameter is significantly more sensitive compared to the regularly damage-evaluating parameters such as natural frequency, eigenvalues, or stress value. This reflects different levels of fatigue cycle effect on the structure in the experiment. At the same time, CP-PSD also categorizes the degradation level on different points on the structure under the periodically forced circulation. In addition, this paper also quantifies the relation between the changes of CP-PSD and each fatigue state. Results of this research will be a reference source to evaluate the lifespan of the structure by experimental methods.

Life Prediction and Damage Acceleration Based on the Power Spectral Density of Random Vibration

1995 ◽  
Vol 38 (1) ◽  
pp. 34-40
Author(s):  
Jimmy Hu
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Gaussian Processes ◽  
Life Prediction ◽  
Random Vibration ◽  
Wide Band ◽  
Accelerated Testing ◽  
Test Time ◽  
Element Analysis ◽  
Power Spectral

Fatigue life prediction and accelerated verification tests under a random vibration environment are important tasks for evaluating product reliability. This paper reviews the characteristics of random stress processes, discusses the methodology of life prediction and accelerated testing under various random loadings by using the stress power spectral density (PSD) function obtained from finite element analysis (FEA), and develops an engineering method to determine the acceleration level and test time in reliability verification tests. The discussions cover the narrow-band Gaussian processes, the wide-band Gaussian processes, and the nonGaussian processes. To illustrate the practical procedure of life prediction and accelerated testing based on the damage equivalent technique, the application example of an automotive component is presented.

Fuzzy Modeling of Multi-Degree-of-Freedom Power Spectral Density Systems

2009 ◽  
Vol 2 (1) ◽  
pp. 40-47
Author(s):  
Montasser Tahat ◽  
Hussien Al-Wedyan ◽  
Kudret Demirli ◽  
Saad Mutasher
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Fuzzy Modeling ◽  
Degree Of Freedom ◽  
Power Spectral

Power spectral density of on-off sources

1997 ◽  
Vol 33 (7) ◽  
pp. 559 ◽  
Author(s):  
K. Laevens
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Power Spectral
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