【摘要】 介绍了随机过程Karhunen-Loeve分解的基本原理,指出了其在随机过程展开中所具有的优势与局限性.针对Karhunen-Loeve分解在求解特征问题中存在的困难,采用Hartley正交基作为展开函数,发展了一类基于Hartley正交基的随机过程展开方法.考虑到直接对地震动加速度随机过程实施正交展开,很难达到以较少展开项数反映原随机过程的目的.为此,提出了从地震动位移过程的正交展开出发,引入一类能量等效原理,获得了地震动加速度随机过程的正交展开式,进而将地震动随机过程展开为由10个独立随机变量所调制的确定性函数的线性组合形式.更多还原

【Abstract】 The paper first introduces the basic principle of Karhunen-Loeve decomposition for stochastic processes,and outlines the essential properties of the decomposition.A method based on the Hartley orthogonal bases is proposed to decompose stochastic processes.It is proposed to directly carry out the orthogonal expansion of the seismic displacement to capture main probbilistic characteristics of the seismic ground motion with only a few terms of the series.Based on the principle of energy equivalence,the expanding expression of seismic acceleration process is achieved.The seismic process is expanded into a linear combination of deterministic functions modulated by 10 uncorrelated random variables.更多还原