非高斯随机过程的短期极值估计:复合Hermite模型

Hermite模型自20世纪80年代后期开始被广泛应用于非高斯随机过程的短期极值估计。当随机过程的非高斯性很强时，尤其是偏度很大时，常用的3阶Hermite模型不足以表征出极值分布的尾端特征。工程中，样本统计矩的不确定性使得更高阶的Hermite模型不宜使用。基于此，该文提出了同时基于中心矩与线性矩的复合Hermite模型，有效地将Hermite模型由3阶拓展到4阶。该文以对数正态模型作为非线性系统的研究对象，对比分析了在解析条件下和在使用蒙特卡洛模拟获得样本数据条件下，各类Hermite模型与传统的Gumbel法以及平均条件穿越率（ACER）法用于极值分析的表现。结果表明，对于大偏度强非高斯随机过程的极值预测，复合Hermite模型具有更好的精确度和鲁棒性。

HYBRID HERMITE MODELS FOR SHORT TERM EXTREMA ESTIMATION OF NON-GAUSSIAN PROCESSES

The Hermite model has been widely used in estimating the short term extrema of non-Gaussian processes since late1980s.When the non-Gaussianity of a process is very strong,especially with a large skewness,the commonly used cubic Hermite model has its limited capacity to capture the characteristics of the tail distribution of the extreme value.However,higher-order models are not recommended for engineering use due to the uncertainty in moments.In this paper,a hybrid use of ordinary central moments(C-moments)and linear moments(L-moments)is proposed to construct Hermite models up to quartic order.A lognormal function is chosen as the original nonlinear system for validating the performance of hybrid Hermite models.Both analytical solutions and numerical solutions using Monte-Carlo simulations are investigated.The comparative study involves the conventional Gumbel method and the averaged conditional exceedance rate(ACER)method.The results show that the proposed hybrid Hermite models render better accuracy and higher robustness in estimating the extreme value.