Radu Popescu -
George Deodatis -
Jean H. Prevost
Department of Civil Engineering and Operations Research
Princeton University, Princeton, New Jersey 08544
February, 1996
A spectral representation-based simulation methodology is proposed to generate sample functions of a multi-variate, multi-dimensional, non-Gaussian stochastic vector field, according to a prescribed cross-spectral density matrix and prescribed (non-Gaussian) probability distribution functions. The proposed methodology starts by generating a Gaussian vector field that is then transformed into the desired non-Gaussian one using a memoryless nonlinear transformation in conjunction with an iterative scheme. The generation of the Gaussian vector field is performed taking advantage of the Fast Fourier Transform technique for great computational efficiency. The special case of simulation of non-Gaussian vector fields modeling material properties is examined, mainly from the point of view of certain simplifying assumptions that can be made for such random media. Finally, a numerical example involving a tri-variate, two-dimensional, non-Gaussian stochastic vector field is presented in order to demonstrate the capabilities and the efficiency of the proposed methodology.
Keywords
Non-Gaussian stochastic vector field, multi-variate stochastic
field,
multi-dimensional stochastic field, Monte Carlo simulation,
spectral representation,
Fast Fourier Transform, memoryless nonlinear transformation,
iterative scheme, stochastic variability of material properties
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