The statistical distribution of the time series generated by three simulation algorithms of Gaussian stochastic processes are derived and compared. In all three methods, the time histories are modeled as weighted linear combinations of terms of the form cos(ωkt +φk) where the phases φk are independent random variables uniformly distributed in [0, 2π]. The frequencies ωk, however, are either deterministic parameters (the spectral representation algorithm), or independent random variables either uniformly distributed in a very small interval (the randomized spectral representation scheme) or distributed according to the specified power spectral density (the random frequencies algorithm). The results of the present investigation show that, from the standpoint of normality of the generated time series and irrespectively of computational aspects, the random frequencies algorithm performs always (considering first-order distributions) and generally (considering second-order distributions) better than or as well as the spectral representation technique and its randomized version, which yield almost identical probability density functions. Finally, if the spectral representation algorithm or its randomized version is used, it is recommended that the frequencies ωk be selected so that the energy associated with each term cos(ωkt +φk) be the same.
|Original language||English (US)|
|Number of pages||5|
|Journal||Journal of Engineering Mechanics|
|State||Published - Feb 1 1996|
ASJC Scopus subject areas
- Mechanics of Materials
- Mechanical Engineering