Simulation of Improved Gaussian Time History

Abstract

An approach is presented for simulating a time history that has time-average moments in exact agreement with those for a perfect Gaussian process. A nonlinear transformation is used to obtain the improved Gaussian simulation from an approximately Gaussian time history simulated by a conventional technique. The primary improvement obtained from the new technique is in the higher order moments, since the conventional technique usually gives satisfactory values of the mean and variance. This improvement in the higher moments can remove undesirable uncertainties in estimating failure probabilities, which are often quite sensitive to the tails of the probability distribution. The technique provides the improved time history as a result of iteratively using a Hermite polynomial transformation. Any desired accuracy in any specified moments can be obtained. In addition to ordinary time-average moments, it is shown that the nonlinear transformation also improves joint moments, moments of extrema, and moments of rainflow fatigue ranges for the time history.