建立了无需反复迭代的非高斯随机过程模拟算法，避免了反复迭代可能出现不收敛的问题。首先，基于非线性平移过程，详细分析了潜在高斯随机过程与非高斯随机过程的转换关系。其次，通过反证法证明了非高斯随机过程的目标功率谱与边缘概率分布函数需要协调一致，并建立了判断非高斯目标功率谱与边缘概率分布函数是否协调的标准，即潜在高斯目标功率谱是否出现负值。然后，对于目标函数不协调的情况提出了相应的修正方案，建立了模拟单变量非高斯随机过程的非迭代算法。最后，采用该算法对不同斜度的非高斯脉动风压进行了数值模拟分析，并通过相关函数、功率谱、概率密度函数与目标函数的对比验证了该算法的有效性。
Abstract
A non-iterative algorithm for simulating non-Gaussian random process was proposed to avoid the divergence problem in iteration. Firstly, based on the nonlinear translation process, the conversion relationship between latent Gaussian stochastic process and non-Gaussian one was analyzed in detail. Then, it was proved with the reduction to absurdity that the target power spectral density (PSD) and the marginal probability distribution (MPD) function for an arbitrary non-Gaussian random process being compatible is necessary. Thereby, the criterion to judge the compatibleness between the target PSD and the MPD was established (i.e., the target PSD function of the latent Gaussian stochastic process must be a nonnegative function). Furthermore, the modification programs were developed for the case of the target PSD and the MPD being incompatible, a non-iterative algorithm was proposed for simulating a non-Gaussian random process with a single variable. Finally, a non-Gaussian fluctuating wind pressure with different skewness was simulated with the proposed non-iterative algorithm. Its feasibility and validity were verified through comparing correlation functions, PSD, and MPD with their corresponding targets.
关键词
高斯 /
非高斯 /
随机过程 /
脉动风压 /
非线性平移 /
模拟算法
{{custom_keyword}} /
Key words
Gaussian /
non-Gaussian /
stochastic process /
fluctuating wind pressure /
nonlinear translation /
simulation algorithm
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] 李春祥, 刘晨哲, 申建红, 李锦华. 土木工程下击暴流风速数值模拟的研究[J]. 振动与冲击, 2010, 29(12):49-54.
Li Chunxiang, Liu Chenzhe, Shen Jianhong, et al. Numerical simulations of downburst wind speeds in civil Engineering[J]. Journal of Vibration and Shock, 2010, 29(12):49-54.
[2] 张文福, 谢 丹, 刘迎春, 计静.下击暴流空间相关性风场模拟 [J]. 振动与冲击, 2013, 32(10):12-16.
Zhang Wenfu, Xie Dan, Liu Yingchun, et al. Simulation of downburst wind field with spatial correlation[J]. Journal of Vibration and Shock, 2013, 32(10):12 -6.
[3] 叶继红, 侯信真. 大跨屋盖脉动风压的非高斯特性研究[J]. 振动与冲击, 2010, 29(7):9-15.
Ye Jihong, Hou Xinzhen. Non-Gaussian features of fluctuating wind pressures on long span roofs [J]. Journal of Vibration and Shock, 2010, 29(7):9-15.
[4] 罗尧治, 蔡朋程, 孙 斌, 童若飞, 沈雁彬, 王洽亲. 国家体育场大跨度屋盖结构风场实测研究[J]. 振动与冲击, 2012, 31(3):64-68.
Luo Yaozhi, Cai Pengcheng, Sun Bin, Dong Ruofei, Shen Yanbin, Wang Qiaqin. Field measurement of wind characteristics on roof of the national stadium [J]. Journal of Vibration and Shock, 2012, 31(3):64-68.
[5] Yang Qingshan, Tian Yuji. A model of probability density function of non-Gaussian wind pressure with multiple samples. Journal of Wind Engineering and Industrial Aerodynamics, 2015, 140: 67-78.
[6] Seong SH, Peterka JA. Digital generation of surface-pressure fluctuations with spiky features. Journal of Wind Engineering and Industrial Aerodynamics, 1998, 73(2): 181-192.
[7] Suresh Kumar K, Stathopoulos T. Computer simulation of fluctuating wind pressures on low building roofs. Journal of Wind Engineering and Industrial Aerodynamics, 1997, 69-71: 485-495.
[8] Gurley K, Kareem A. Simulation of Correlated Non-Gaussian Pressure Fields. Meccanica, 1998, 33: 309-317.
[9] Yamazaki F, Shinozuka M. Digital generation of non-Gaussian stochastic fields. Journal of Engineering Mechanics, 1988, 114(7):1183-1197.
[10] Deodatis G, Micaletti RC. Simulation of highly skewed non-Gaussian stochastic processes. Journal of Engineering Mechanics, 2001, 127(12): 1284-1295.
[11] Gurley K. Simulation of a class of non-normal random processes. International Journal of Non-Linear Mechanics, 1996, 31(5): 601-617.
[12] Puig B, Akian JL. Non-Gaussian simulation using Hermite polynomials expansion and maximum entropy principle. Probabilistic Engineering Mechanics, 2004, 19(4): 293-305.
[13] Grigoriu, M. Simulation of stationary non-Gaussian translation processes. Journal of Engineering Mechanics, 1998, 124 (2): 121-126.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(768 KB)
