基于标准正交基的随机过程展开法  

Expansion Method of Stochastic Processes Based on Normalized Orthogonal Bases

作　　者：李杰[1] 刘章军[1] 

机构地区：[1]同济大学建筑工程系,上海200092

出　　处：《同济大学学报（自然科学版）》2006年第10期1279-1283,共5页Journal of Tongji University:Natural Science

基　　金：国家杰出青年科学基金资助项目(59825105);国家创新研究群体科学基金资助项目(50321803)

摘　　要：建议了一类基于标准正交基的随机过程展开方法.提出此方法的主要目的,在于希望能用少量的独立随机变量来反映随机过程的主要概率特性,以便为工程结构的随机动力响应及可靠度分析奠定基础.该方法是在随机过程相关特性或频谱特性的基础上,预先指定标准正交基的形式,通过随机向量的相关分解对展开系数实施正交化,它在形式上等价于Karhunen-Loeve分解法.研究表明,随机过程正交展开所需独立随机变量的数量,主要取决于随机过程的频谱特性与持续时间,同时与标准正交基的选取也有一定的关系.A method based on normalized orthogonal bases is proposed to decompose stochastic processes, so as to capture main probabilistic characters of a stochastic process with only a few random variables, and establish a solid foundation for structure stochastic dynamic response and reliability assessment. By prescribing normalized orthogonal bases, and based on the auto-correlation function or power spectral density function of stochastic processes with finite energy, the expansion coefficients of decomposed stochastic process become orthogonal. The decomposition of stochastic process based on this method is equivalent to Karhunen-Loeve decomposition in the form. The study shows that the number of expansion terms mainly depends upon the spectrum bandwidth and the duration, and upon the form of normalized orthogonal bases.

关 键 词：工程结构 随机过程 随机变量 标准正交基 自相关函数 正交展开 

分 类 号：O324[理学—一般力学与力学基础] O211.6[理学—力学]