Extremes of Nonlinear Vibration: Comparing Models Based on Moments, L Moments, and Maximum Entropy

Abstract

Wind and wave loads on offshore structures show nonlinear effects, which require nonGaussian statistical models. Here we critically review the behavior of various nonGaussian models. We first survey momentbased models; in particular, the fourmoment “Hermiteâ€‌ model, a cubic transformation often used in wind and wave applications. We then derive an “LHermiteâ€‌ model, an alternative cubic transformation calibrated by the response “Lmomentsâ€‌ rather than its ordinary statistical moments. These Lmoments have recently found increasing use, in part because they show less sensitivity to distribution tails than ordinary moments. We find here, however, that these Lmoments may not convey sufficient information to accurately estimate extreme response statistics. Finally, we show that fourmoment maximum entropy models, also applied in the literature, may be inappropriate to model broaderthanGaussian cases (e.g., responses to wind and wave loads).