scholarly journals Appendix A: Derivation of the Jakes Power Spectral Density and the Corresponding Autocorrelation Function

2003 ◽  
pp. 321-324
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Autocorrelation Function ◽  
Power Spectral

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).

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
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