平稳地震动过程的正交展开-随机函数模型

Simulation of Stationary Ground Motion Processes:Hybrid Orthogonal Expansion-random Function Approach

在随机过程正交展开的基础上,建议了一类随机过程的正交展开-随机函数模型.将随机过程展开为标准正交基函数与标准正交随机变量的线性组合形式.利用随机函数的思想,将展开式中的标准正交随机变量表达为基本随机变量的函数形式,通过3种常用正交函数形式的构造,实现了用一个基本随机变量表达原随机过程的目的.与已有的正交展开方法相比,本文方法所需基本随机变量的数量最少,且能获取精确的二阶统计量信息.结合平稳地震动加速度过程的功率谱密度函数,进行了平稳地震动过程的正交展开-随机函数模型实例分析,验证了本文方法的有效性和优越性.

Referring to the of hogonal expansion of stochastic processes, a hybrid orthogonal expansion-random function approach was proposed. Firstly, the stochastic process was expanded as a linear combination of normalized orthogonal basis functions and standard orthogonal random variables. Using the definition of random function, these standard orthogonal random variables in the expanded formula were then denoted by the orthogonal function form of a basic random variable. Through investigating three different forms of orthogonal random functions, the original stochastic process can be readily functioned by a single basic random variable. Compared to the existing representative schemes of stochastic process such as the classic Karhunen-Loeve decomposition and the pure orthogonal expansion, the proposed approach can accurately capture the second-order statistics using only a basic random variable, which bypasses the essential challenge in solving the Fredholm integral equation. A numerical example with power spectral density function of stationary ground motion was investigated to demonstrate the effectiveness and advantages of the hybrid approach.