基于本征正交分解的谱表示法模拟风场的误差

Errors produced with proper orthogonal decomposition-based spectral representation method in wind velocity field simulation

推导了本征正交分解(Proper Orthogonal Decomposition,POD)型谱表示法模拟所得平稳正态脉动风场的偏度误差和随机误差。从POD型谱表示法的模拟公式出发,推导了N变量风场模拟结果序列的样本均值、相关函数、功率谱函数和根方差等前二阶矩统计特征的时域估计表达式;并证明了时域估计相关函数是正态过程,功率谱函数为非正态随机过程。进一步,计算上述样本时域估计二阶矩特征的均值和根方差,即得到了POD型谱表示法模拟所得风场的各统计量时域估计的偏度误差和随机误差,并以此给出了误差计算的通式。算例中统计误差和理论误差值的对比验证了所推导的解析解。

The bias errors and the stochastic errors produced in wind field simulation using a proper orthogonal decomposition（POD）-based spectral representation method were derived.An N-point Gaussian wind field was considered by taking its simulation formulas into account.The temporal first-and second-order statistics of the simulated wind process,i.e.,its mean values,correlation functions,power spectral densities and standard deviations,were derived.Mean values and standard deviations of these derived random variables or processes thus led to the bias errors and the stochastic errors of the temporal sample statistics,respectively.Finally,these closed-form solutions to the errors were validated with a numerical example.