随机场的随机谐和函数表达  

Simulation of Multi-dimensional Random Fields by Stochastic Harmonic Functions

作　　者：梁诗雪[1] 孙伟玲[1] 李杰[1,2] 

机构地区：[1]同济大学土木工程学院,上海200092 [2]同济大学土木工程防灾国家重点实验室,上海200092

出　　处：《同济大学学报（自然科学版）》2012年第7期965-970,995,共7页Journal of Tongji University:Natural Science

基　　金：国家"八六三"高技术研究发展计划(2008AA05Z413);国家自然科学基金(90715033)

摘　　要：首先证明,采取随机谐和函数表述二维随机场,则当随机波数与相位服从独立均匀分布、幅值由随机波数和目标功率谱密度共同决定时,随机谐和函数的功率谱密度精确地等于目标功率谱密度.对这类随机谐和函数的平稳性和渐进正态性进行了讨论.进而,将二维随机场的随机谐和函数表达推广至多维,给出了统一表达式.最后,通过数值算例验证了采用随机谐和函数表述随机场的正确性.When the random phase angles and random circular frequencies are independent and uniformly distributed,the amplitude can be obtained by the target power spectral density function and the random circular frequencies specifically in the two-dimensional random field.Meanwhile,the power spectral density function is equal to the target one.Then,stochastic harmonic random field proves to be asymptotic to the normal distribution.In addition,the stochastic harmonic functions can be expanded into multi-dimensional random fields by the uniformed expression.Finally,several numerical examples are given to validate the stochastic harmonic function.

关 键 词：随机场 随机谐和函数 功率谱密度 平稳性 渐进正态性 

分 类 号：O211.6[理学—概率论与数理统计]