Article,
Simulation of Multivariate and Multidimensional Random Processes
The Journal of the Acoustical Society of America, (1970)
Abstract
Efficient and practical methods of simulating multivariate and multidimensional
processes with specified cross-spectral density are presented. When
the cross-spectral density -matrix of an n-variate process is specified,
its component processes can be simulated as the sum of cosine functions
with random frequencies and random phase angles. Typical examples
of this type are the simulation, for the purpose of shaker test,
of a multivariate process representing six components of the acceleration
(due to, for example, a booster engine cutoff) measured at the base
of a spacecraft and the simulation of horizontal and vertical components
of earthquake acceleration. A homogeneous multidimensional process
can also be simulated in terms of the sum of cosine functions with
random frequencies and random phase angles. Examples of multidimensional
processes considered here include the horizontal component f_o (t,x)
of the wind velocity perpendicular to the axis (x axis) of a slender
structure, the vertical gust velocity field f_o(x,y) frozen in space,
and the boundary layer pressur field f_o(x,y,t). Also, a convenient
use of the present method of simulation in a class of non-linear
structural vibration analysis is described with a numerical example.
