随机场的随机谐和函数表达

Simulation of multi-dimensional random fields by stochastic harmonic functions

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。

Abstract:

The subject of this paper is to propose the stochastic harmonic functions into the multi-dimension, homogeneous, Gaussian random fields. In the first place, it proved that in the two-dimensional random field 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. Meanwhile, the power spectral density function is equal to the target one. Then, it proved that stochastic harmonic random field is asymptotic to the normal distribution. In addition, the stochastic harmonic functions can be expanded into multi-dimensional random fields by the uniformed expression in the paper. Finally, several numerical examples are given to clarify the validity of stochastic harmonic function.