Generation of partially coherent stationary time histories with non-Gaussian distributions

In a previous paper Smallwood and Paez (1991) showed how to generate realizations of partially coherent stationary normal time histories with a specified cross-spectral density matrix. This procedure is generalized for the case of multiple inputs with a specified cross-spectral density function and a specified marginal probability density function (pdf) for each of the inputs. The specified pdfs are not required to be Gaussian. A zero memory nonlinear (ZMNL) function is developed for each input to transform a Gaussian or normal time history into a time history with a specified non-Gaussian distribution. The transformation functions have the property that a transformed time history will have nearly the same auto spectral density as the original time history. A vector of Gaussian time histories are then generated with the specified cross-spectral density matrix. These waveforms are then transformed into the required time history realizations using the ZMNL function.

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