Nonlinear effects beset virtually all aspects of offshore structural loading and response. These nonlinearities cause non-Gaussian statistical effects, which are often most consequential in the extreme events—e.g., 100- to 10,000-year conditions—that govern structural reliability. Thus there is engineering interest in forming accurate non-Gaussian models of time-varying loads and responses, and calibrating them from the limited data at hand. We compare here a variety of non-Gaussian models. We first survey moment-based models; in particular, the 4-moment “Hermite” model, a cubic transformation often used in wind and wave applications. We then derive an “L-Hermite” model, an alternative cubic transformation calibrated by the response “L-moments” rather than its ordinary statistical moments. These L-moments have recently found increasing use, in part because they show less sensitivity to distribution tails than ordinary moments. We find here, however, that these L-moments may not convey sufficient information to accurately estimate extreme response statistics. Finally, we show that 4-moment maximum entropy models, also applied in the literature, may be inappropriate to model broader-than-Gaussian cases (e.g., responses to wind and wave loads).
Extremes of Nonlinear Vibration: Models Based on Moments, L-Moments, and Maximum Entropy
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Winterstein, SR, & MacKenzie, CA. "Extremes of Nonlinear Vibration: Models Based on Moments, L-Moments, and Maximum Entropy." Proceedings of the ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. Volume 2: Structures, Safety and Reliability. Rotterdam, The Netherlands. June 19–24, 2011. pp. 617-626. ASME. https://doi.org/10.1115/OMAE2011-49867
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