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Dimension-reduction simulation for continuous random wave force field
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摘要: 根据水质点的水平速度和加速度过程的功率谱密度，利用线性化的Morison方程，从平稳随机过程自相关函数的角度推导了随机波浪力的功率谱密度函数。在平稳随机过程的源谱表达基础上，通过将标准正交随机变量集定义为仅含1个基本随机变量的正交函数形式，实现了随机波浪力连续场的降维模拟。同时，结合快速傅里叶变换（FFT）技术，给出了随机波浪力连续场降维模拟的快速算法。应用该方法对某一单个小尺度直立圆柱桩所受的随机波浪力进行模拟，给出了随机波浪力过程的均值、标准差、自相关函数及互相关函数等数值特征，并与Monte Carlo方法的结果进行对比分析。研究表明，降维模拟方法具有较高的模拟精度与效率。
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关键词:
- 随机波浪力 /
- 线性化Morison方程 /
- 源谱表达 /
- 降维模拟 /
- 快速傅里叶变换(FFT)
Abstract: According to the power spectral density (PSD) of the horizontal velocity and acceleration process for water mass point, the PSD function of random wave force is derived from the point of view of auto-correlation function for the stationary stochastic process using the linearized Morison equation. Then, based on the original spectral representation for the stationary random process, the standard orthogonal random variable set is defined as the form of orthogonal functions only containing one elementary random variable, which realizes the dimension-reduction simulation of the continuous stochastic wave force field. Meanwhile, combined with the fast Fourier transform (FFT) technology, the fast algorithm of dimension reduction simulation for the continuous stochastic wave force field is given. In the end, the random wave force acting on a small-scale straight cylindrical pile is simulated as an example. This paper provides the numerical characteristics of the method, such as mean, standard deviation, autocorrelation functions and cross-correlation functions, and the calculation results of the proposed method are compared with the Monte Carlo method. The research shows that the proposed method has a higher simulation accuracy and efficiency, which verifies the validity of the proposed method. -
图 3 不同高度处波浪力代表性时程三维图
Figure 3. 3-D figure of representative time-histories for wave force at different heights
图 4
$\textit{z} = 17\; {\rm{m}}$ 处均值及标准差比较Figure 4. Comparison of mean and standard deviation at
$\textit{z} = 17\;{\rm{m}}$ 
图 5
$\textit{z} = 17\; {\rm{m}}$ 处自相关函数比较Figure 5. Comparison of auto-correlation functions at
$\textit{z} = 17\;{\rm{m}}$ 
图 6
${\textit{z}_1} = 17\;{\rm{m}}$ 和${\textit{z}_2} = 21\;{\rm{m}}$ 处互相关函数比较Figure 6. Comparison of cross-correlation functions between
${\textit{z}_1} = 17\;{\rm{m}}$ and${\textit{z}_2} = 21\;{\rm{m}}$ -
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