Digital simulation of random processes and its applications

Efficient methods are presented for digital simulation of a general homogeneous process (multidimensional or multivariate or multivariate-multidimensional) as a series of cosine functions with weighted amplitudes, almost evenly spaced frequencies, and random phase angles. The approach is also extended to the simulation of a general non-homogeneous oscillatory process characterized by an evolutionary power spectrum. Generalized forces involved in the modal analysis of linear or non-linear structures can be efficiently simulated as a multivariate process using the cross-spectral density matrix computed from the spectral density function of the multidimensional excitation process. Possible applications include simulation of (i) wind-induced ocean wave elevation, (ii) spatial random variation of material properties, (iii) the fluctuating part of atmospheric wind velocities and (iv) random surface roughness of highways and airport runways.