Extrema Prediction and Fatigue Assessment of Highly Non-Gaussian Random Processes Using a Homogenous Reproduction Method

Abstract

Given a limited number of time histories of a non-Gaussian random process, it is of interest to reproduce a much greater number of samples while retaining homogenous statistical characteristics. In structural engineering, this matters to extrema prediction and fatigue assessment. Particularly when the given data exhibit strong non-Gaussianity, the issue of how to capture such stochastic characteristics while retaining the original spectral profile of the underlying process needs to be resolved. This study is an extension of the translation method that employs Hermite models to establish the relationship between the non-Gaussian process and underlying Gaussian process. Thus, unlike many other works, no information regarding a probability density function (PDF) is mandated for the translation in the present study; only central and linear moments are required. Specifically, for highly non-Gaussian processes, quartic and quintic Hermite models are discussed because the commonly used cubic Hermite model cannot yield an accurate approximation. For spectral restoration, the explicit relationship between the autocorrelation of the transformed process and that of the underlying Gaussian process is presented to retain homogeneity in the non-Gaussian characteristics. This explicit relationship also allows for more straightforward implementation of the proposed method in the time domain than the conventional PDF-based translation method. Furthermore, to remove negative power spectral contents incurred by incompatible and numerical errors, a correction procedure inspired by the iteration algorithm is used. Through comprehensive analyses of three offshore engineering problems (Morison drag force, total wave load on a jack-up platform, and stress response of a typical offshore wind turbine), the robustness and accuracy of the proposed homogeneous reproduction method in capturing both extrema and fatigue damage are affirmed.