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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.
Based on the orthogonal expansion of stochastic process, a kind of orthogonal expansion-stochastic function model of stochastic process is proposed, and the stochastic process is expanded to a linear combination of standard orthogonal basis function and standard orthogonal stochastic variable. , The standard orthonormal stochastic variables in the expansions are expressed as the function forms of the basic stochastic variables, and the purpose of expressing the stochastic process with a basic stochastic variable is achieved through the construction of three commonly used orthogonal function forms. Compared with the existing Compared with the orthogonal expansion method, the method requires the least number of basic random variables and can obtain accurate second-order statistics information.According to the power spectral density function of the steady ground motion acceleration process, the orthogonal of the steady ground motion process Expand - stochastic function model example analysis, verify the effectiveness and superiority of this method.