硬化非高斯模型及其在首次穿越中的应用

Hardening non-Gaussian models and its application to first passage

提出了一个硬化非高斯过程的首次穿越概率计算方法.对比研究了Winterstein硬化模型、正交展开模型以及四阶矩标准化函数在硬化反应阶段的适用范围与精度.结果表明：四阶矩标准化函数精度最高,适用于峰度系数不小于2.333的应用场合;正交展开模型精度高于Winterstein硬化模型,适用范围分别为峰度系数不小于1.25和1.0的应用场合.基于硬化非高斯过程的峰度系数取值,以四阶矩标准化函数、正交展开模型以及Winterstein硬化模型为体系建立了首次穿越概率计算方法.最后,以硬化非高斯风压为例,验证了本文方法在首次穿越中的应用的可行性.

A method for calculating the first passage probability of hardening non-Gaussian response processes was developed. Firstly,the application range and the accuracy of Winterstein hardening model,orthogonal expansion model and the fourth-moment standardization function in the hardening stage were compared and analyzed. Research results show that the accuracy of the fourth-order moment normalization function is the highest and applicable to kurtosis no less than 2.333;the accuracy of the orthogonal expansion model is higher than that of the Winterstein hardening model,and the applicable range is no less than 1.25 and 1.0,respectively.Then,based on the kurtosis value of hardening non-Gaussian processes,the method for calculating first-passage probability was established by using the fourth-moment standardization function,orthogonal expansion model and Winterstein hardening model.Finally,the hardening non-Gaussian wind pressure was used as an example to illustrate the application to the first passage of the developed method.