【摘要】 基于平稳多变量随机过程理论,推导了基于正交随机变量的本征正交分解(POD)公式,在此基础上,通过定义POD公式中正交随机变量集的随机函数形式,建议了平稳多变量随机过程模拟的POD-随机函数方法。该方法与传统基于随机相位角的POD都是基于正交随机变量POD的特例,然而该方法仅需两个基本随机变量即可实现对平稳多变量随机过程的精细表达。根据线性化的Morison方程,推导了波浪力多变量随机过程的功率谱密度函数矩阵,利用POD-随机函数方法,实现了波浪力多变量随机过程模拟的高效降维。最后,结合P-M波浪谱,给出了水平向波浪力多变量随机过程的功率谱密度矩阵,并对水平向波浪力随机场进行数值模拟分析。算例表明,该方法所需的基本随机变量最少,生成的代表性样本数量少且构成一个完备的概率集,在模拟精度方面亦具有显著优势。更多还原

【Abstract】 Due to the theory of multivariate stationary stochastic process, the proper orthogonal decomposition(POD) formula based on the orthogonal random variables was derived. On the basis of this, by defining the random function form of the orthogonal random variable set in the POD formula, a POD-random function approach was suggested for simulating the multivariate stationary stochastic process. Note that the proposed approach and the conventional approach based on the random phase angles are both the special cases of the POD approach based on the orthogonal random variables. However, the proposed approach can accurately represent the multivariate stationary stochastic process with just two elementary random variables. The power spectrum density matrix involved in the multivariate stationary stochastic process of wave force was derived according to the linearized Morison formula. Then by means of the proposed approach, effective dimension reduction simulation for the multivariate stationary stochastic process of wave force could thus be realized. Finally, combined with the P-M wave spectrum, the power spectrum density matrix involved in the multivariate stochastic process of the horizontal wave force was derived. And the numerical simulation analysis of the horizontal stochastic wave force field was carried out. The example shows that the proposed approach requires the least number of the elementary random variables and a small number of representative samples which constitute a complete set of probabilities. It has significant advantages in terms of simulation accuracy.更多还原