Hybrid C- and L-Moment–Based Hermite Transformation Models for Non-Gaussian Processes

Abstract

The moment-based Hermite transformation models are widely used in extreme-value prediction and fatigue estimation of non-Gaussian processes. However, when only higher-order ordinary central moments (C-moments) are involved in the transformation, the Hermite model would lead to statistical uncertainty. Furthermore, the application of moment-based Hermite models to measured time series is restricted if accurate moments cannot be retrieved from data. In this paper, the respective virtues of C-moments and linear moments (L-moments) are exploited to formulate a new style of nonlinear transformation. Combinations of these two types of moments are sought with various strategies in terms of the accuracy in extreme-value prediction of non-Gaussian processes. It is found that for a process of very strong non-Gaussianity, the quartic C-moment model renders best accuracy when the sampling data are rich, while two of hybrid C- and L-moment (C/L) models work most nicely when data size is limited.