两相介质随机场的随机谐和函数表达

Simulation of TwoPhase Random Field by Stochastic Harmonic Functions

摘要:

给出了两相介质随机场的定义，引入均匀性假定以作为两相介质随机场表达的基础.采用随机谐和函数生成标准高斯随机场，并将其作为生成两相介质随机场的中间量.通过引入Nataf变换和Hermite多项式展开，给出了两相介质随机场和标准高斯随机场之间的变换关系.由此,可以给出标准正态随机场与两相介质随机场之间相关函数的关系，将标准高斯随机场转化为目标两相介质随机场.通过数值算例验证了采用随机谐和函数表述两相介质随机场的正确性.

Abstract:

In the present paper, a method was proposed to represent the twophase, homogeneous random field. In the first place, the framework of twophase random field was put forward and the homogeneous and isotropic assumption was given as the premise of the work. Then, the stochastic harmonic function (SHF) representation for the Gaussian random field was provided as the intermedia for the twophase random field. With the SHF based random field, the Nataf’s transformation was applied to convert Gaussian random field into the target random field. The Hermite polynomials were used as the numerical solution for the bivariate Gaussian pdf involved in the Nataf’s transformation. Finally, several numerical examples were given to clarify the validity of stochastic harmonic function based twophase random field.