多变量随机过程的模拟方法研究

A simulation method for multivariate stochastic processes

在对自然风或地震等随机过程的模拟中,具有随机振幅、频率含量和相位角的随机过程模拟模型能更加真实地反映其随机性。该文推导一种可以描述上述随机特性的单变量和多变量随机过程的模型,并从理论上证实所模拟的样本具有平稳性,各态历经性以及高斯性等统计特性。经过数值算例分析证明模型的准确性以及有效性。

According to the spectral representation theorem, a weakly stationary stochastic process, such as the stochastic wind velocity fluctuations, can be simulated as a summation of a series of harmonic functions with random properties. In the present paper, a new model based on the spectral representation technique is proposed to simulate the random processes. The harmonic functions have random amplitudes, random phase angles and random frequencies that can represent the natural stochastic process properly. For the univariate case, probabilistic characteristics of the simulated sample, including the stationarity, ergodicity and Gaussianness, are firstly verified. Then a multivariate stationary model is proposed and formulated. At last, an example involving simulation of turbulent wind velocity is given to show the capability and accuracy of the proposed model.