Simulation of Multivariate and Multidimensional Random Processes
Simulation of Multivariate and Multidimensional Random Processes
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DOI：
10.1121/1.1912338
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发表时间：
1971
影响因子：
2.4
通讯作者：
M. Shinozuka
中科院分区：
文献类型：
--
作者：
M. Shinozuka
提出了具有指定互谱密度的模拟多变量和多维过程的有效和实用的方法。当n变量过程的互谱密度矩阵被指定时，其分量过程可以被模拟为具有随机频率和随机相位角的余弦函数之和。这种类型的典型例子是，为了振动台测试的目的，模拟代表在航天器底部测量的加速度（例如，由于助推发动机关闭）的六个分量的多变量过程，以及模拟水平和垂直地震加速度的分量。一个均匀的多维过程也可以用随机频率和随机相位角的余弦函数的和来模拟。这里考虑的多维过程的例子包括垂直于细长结构的轴（x轴）的风速的水平分量f0（t，x）、冻结在空间中的垂直阵风速度场f0（x，y）和边界层压力场f0（x，y，t）。最后通过一个算例说明了本文方法在一类非线性结构振动分析中的方便应用。
Efficient and practical methods of simulating multivariate and multidimensional processes with specified cross‐spectral density are presented. When the cross‐spectral density matrix of an n‐variate process is specified, its component processes can be simulated as the sum of cosine functions with random frequencies and random phase angles. Typical examples of this type are the simulation, for the purpose of shaker test, of a multivariate process representing six components of the acceleration (due to, for example, a booster engine cutoff) measured at the base of a spacecraft and the simulation of horizontal and vertical components of earthquake acceleration. A homogeneous multidimensional process can also be simulated in terms of the sum of cosine functions with random frequencies and random phase angles. Examples of multidimensional processes considered here include the horizontal component f0(t,x) of the wind velocity perpendicular to the axis (x axis) of a slender structure, the vertical gust velocity field f0(x,y) frozen in space, and the boundary‐layer pressure field f0(x,y,t). Also, a convenient use of the present method of simulation in a class of nonlinear structural vibration analysis is described with a numerical example.