Email Alerts
RSS
Dimension-reduction simulation for continuous random wave force field
-
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。
-
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${\textit{z}_2} = 21\;{\rm{m}}$ -
[1] MORISON J R, JOHNSON J W, SCHAAF S A. The force exerted by surface waves on piles[J]. Journal of Petroleum Technology, 1950, 2(5): 149-154. doi: 10.2118/950149-G [2] BORGMAN L E. Computation of the ocean-wave forces on inclined cylinders[J]. Eos, Transactions American Geophysical Union, 1958, 39(5): 885-888. doi: 10.1029/TR039i005p00885 [3] BORGMAN L E. Spectral analysis of ocean wave forces on piling (coastal engineering conference in Santa Barbara, California, October 1965)[J]. Journal of the Waterways and Harbors Division, 1967, 93(2): 129-156. [4] 俞聿修. 随机波浪及其工程应用[M]. 大连: 大连理工大学出版社, 1992. YU Yuxiu. Random wave and its applications to engineering[M]. Dalian: Dalian University of Technology Press, 1992. (in Chinese) [5] HAN S M, BENAROYA H. Comparison of linear and nonlinear responses of a compliant tower to random wave forces[J]. Chaos, Solitons & Fractals, 2002, 14(2): 269-291. [6] MARDFEKRI M, GARDONI P. Probabilistic demand models and fragility estimates for offshore wind turbine support structures[J]. Engineering Structures, 2013, 52: 478-487. doi: 10.1016/j.engstruct.2013.03.016 [7] 武昕竹, 柳淑学, 李金宣. 聚焦波浪与直立圆柱作用的数值模拟[J]. 水利水运工程学报,2015(6):31-39. (WU Xinzhu, LIU Shuxue, LI Jinxuan. Numerical simulation of interactions of focusing wave with a vertical cylinder[J]. Hydro-Science and Engineering, 2015(6): 31-39. (in Chinese) [8] 刘章军, 刘玲. 随机海浪过程模拟的随机函数方法[J]. 振动与冲击,2014,33(20):1-6. (LIU Zhangjun, LIU Ling. Simulation of stochastic ocean states by random function methods[J]. Journal of Vibration and Shock, 2014, 33(20): 1-6. (in Chinese) [9] 刘章军, 刘磊, 汪峰. 基于本征正交分解的波浪力随机场降维模拟[J]. 振动与冲击,2019,38(12):98-104. (LIU Zhangjun, LIU Lei, WANG Feng. POD-based dimension reduction simulation of stochastic wave force field[J]. Journal of Vibration and Shock, 2019, 38(12): 98-104. (in Chinese) [10] CHEN J B, LI J. A note on the principle of preservation of probability and probability density evolution equation[J]. Probabilistic Engineering Mechanics, 2009, 24(1): 51-59. doi: 10.1016/j.probengmech.2008.01.004 [11] LIU Z J, LIU Z H. Random function representation of stationary stochastic vector processes for probability density evolution analysis of wind-induced structures[J]. Mechanical Systems and Signal Processing, 2018, 106: 511-525. doi: 10.1016/j.ymssp.2018.01.011 [12] 竺艳蓉. 海洋工程波浪力学[M]. 天津: 天津大学出版社, 1991. ZHU Yanrong. Wave mechanics for ocean engineering[M]. Tianjin: Tianjin University Press, 1991. (in Chinese) [13] LIU Z J, LIU Z H, PENG Y B. Simulation of multivariate stationary stochastic processes using dimension-reduction representation methods[J]. Journal of Sound and Vibration, 2018, 418: 144-162. doi: 10.1016/j.jsv.2017.12.029 [14] YANG J N. Simulation of random envelope processes[J]. Journal of Sound and Vibration, 1972, 21(1): 73-85. doi: 10.1016/0022-460X(72)90207-6 [15] BRIGHAM E O. The fast Fourier transform and its applications[M]. Englewood Cliffs, NJ: Prentice Hall, 1988. [16] PIERSON JR W J, MOSKOWITZ L. A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii[J]. Journal of Geophysical Research, 1964, 69(24): 5181-5190. doi: 10.1029/JZ069i024p05181 -
下载:
点击查看大图
图(7)
计量
- 文章访问数: 553
- HTML全文浏览量: 174
- PDF下载量: 15
- 被引次数: 0
