工程力学 ›› 2019, Vol. 36 ›› Issue (1): 23-31.doi: 10.6052/j.issn.1000-4750.2018.10.0855

• 基本方法 • 上一篇    下一篇

非高斯随机过程的短期极值估计:复合Hermite模型

高山1, 郑向远2, 黄一1   

  1. 1. 大连理工大学船舶工程学院, 大连 116024;
    2. 清华大学深圳研究生院海洋科学与技术学部, 深圳 518055
  • 收稿日期:2017-11-13 修回日期:2018-10-23 出版日期:2019-01-29 发布日期:2019-01-10
  • 通讯作者: 郑向远(1975-),男,福建人,教授,博士,博导,主要从事非线性随机动力学等研究(E-mail:zheng.xiangyuan@sz.tsinghua.edu.cn). E-mail:zheng.xiangyuan@sz.tsinghua.edu.cn
  • 作者简介:高山(1992-),男,安徽人,博士生,主要从事海洋结构物随机响应的极值与疲劳研究(E-mail:476734040@qq.com);黄一(1964-),男,辽宁人,教授,博士,博导,主要从事船舶与海洋结构物结构分析与环境强度研究(E-mail:huangyi@dlut.edu.cn).
  • 基金资助:
    国家重点研发计划项目(2016YFC0303706);深圳市发改委公共服务平台项目([2015]-75);国家自然科学基金项目(51379035)

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

GAO Shan1, ZHENG Xiang-yuan2, HUANG Yi1   

  1. 1. School of Naval Architecture and Ocean Engineering, Dalian University of Technology, Dalian 116024, China;
    2. Division of Ocean Science and Technology, Tsinghua University, Shenzhen Graduate School, Shenzhen 518055, China
  • Received:2017-11-13 Revised:2018-10-23 Online:2019-01-29 Published:2019-01-10

摘要: 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。

关键词: 复合Hermite模型, 短期极值估计, 中心矩, 线性矩, 强非高斯过程

Abstract: The Hermite model has been widely used in estimating the short term extrema of non-Gaussian processes since late 1980s. 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.

Key words: hybrid Hermite model, short term extrema estimation, Central moment, Linear moment, strongly non-Gaussian process

中图分类号: 

  • TP391.9
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