Abstract A renewed methodology for simulating two-spatial dimensional stochastic wind field is addressed in the present study. First, the concept of cross wavenumber spectral density (WSD) function is defined on the basis of power spectral density (PSD) function and spatial coherence function to characterize the spatial variability of the stochastic wind field in the two-spatial dimensions. Then, the hybrid approach of spectral representation and wavenumber spectral representation and that of proper orthogonal decomposition and wavenumber spectral representation are respectively derived from the Cholesky decomposition and eigen decomposition of the constructed WSD matrices. Immediately following that, the uniform hybrid expression of spectral decomposition and wavenumber spectral representation is obtained, which integrates the advantages of both the discrete and continuous methods of one-spatial dimensional stochastic field, allowing for reflecting the spatial characteristics of large-scale structures. Moreover, the dimension reduction model for two-spatial dimensional stochastic wind field is established via adopting random functions correlating the high-dimensional orthogonal random variables with merely 3 elementary random variables, such that this explicitly describes the probability information of stochastic wind field in probability density level. Finally, the numerical investigations of the two-spatial dimensional stochastic wind fields respectively acting on a long-span suspension bridge and a super high-rise building are implemented embedded in the FFT algorithm. The validity and engineering applicability of the proposed method are thus fully verified, providing a potentially effective approach for refined wind-resistance dynamic reliability analysis of large-scale complex engineering structures.

中文翻译：

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二维随机风场的降维模型：谱分解和波数谱表示的混合方法

摘要 本研究提出了一种新的二维随机风场模拟方法。首先，在功率谱密度（PSD）函数和空间相干函数的基础上定义了交叉波数谱密度（WSD）函数的概念，以表征随机风场在两个空间维度上的空间变异性。然后，分别从构造的WSD矩阵的Cholesky分解和特征分解中推导出谱表示和波数谱表示的混合方法以及适当正交分解和波数谱表示的混合方法。紧接着，得到谱分解和波数谱表示的统一混合表达式，集一维随机场离散法和连续法的优点于一身，可以反映大尺度结构的空间特征。此外，通过采用将高维正交随机变量与仅3个基本随机变量相关联的随机函数，建立二维随机风场的降维模型，从而在概率密度上明确地描述了随机风场的概率信息等级。最后，嵌入FFT算法对分别作用于大跨度悬索桥和超高层建筑的二维随机风场进行数值研究。