基于数据截断和变间隔插值的空间脉动风场模拟

Simulation of spatial fluctuating wind field based on truncation and variable intervals interpolation

对大跨度桥梁空间脉动风场模拟提出一种改进的谐波合成法。研究分解谱函数随频率的变化规律,确定分解谱函数矩阵不同位置元素对应的有效截止频率。对互谱矩阵的Cholesky分解仅需在插值节点频率进行,而对于其他频率点的分解谱函数则采用三次拉格朗日插值拟合,并探讨不同插值节点间隔对拟合精度的影响。根据谐波合成法中相关矩阵的特点,仅对下三角部分采用一维存储,以节省存储空间。综合考虑计算效率和拟合精度,提出变间隔插值算法。对某一大跨度斜拉桥进行空间脉动风场的模拟。研究结果表明:随着频率增大,分解谱函数矩阵非对角线元素超过峰值后迅速单调趋近于0,即当频率超过其对应的有效截止频率后,分解谱函数对风速的贡献可忽略,据此即可对计算过程进行合理截断;分解谱函数在低频部分线形变化显著,宜采用较小的插值节点间隔,而在高频部分线形比较平缓,可采用较大的插值节点间隔。通过检验风速样本的功率谱密度函数和相关函数,验证了改进谐波合成法的正确性、高效性和可靠性。

The improved wave superposition method for simulating spatial fluctuating wind field of long-span bridges was presented. The variation tendency of factorized spectral function with frequency was investigated, the maximum effective frequency of every element of factorized spectral function matrix was determined. Cross spectral matrix was factorized with Cholesky algorithm only on one part of interpolation nodes＇ frequencies, and factorized spectral function on other frequencies fitted with Cubic Lagrange interpolation according to the computed values on interpolation nodes＇ frequencies, and the effects of different intervals of interpolation points on the fitting precision were studied. According to the characteristics of the matrix of wave superposition method, only the lower triangular part was stored with one-dimensional storage to save a large number of memory space. In comprehensive consideration of the calculation efficiency and fitting precision, variable intervals interpolation algorithm was proposed. Finally, the spatial fluctuating wind field of a long-span cable-stayed bridge was simulated. The results show that non-diagonal element of factorized spectral function matrix monotonously decrease to 0 with the increase of frequency after exceeding its peak, and its contribution to wind velocity can be neglected when the frequency exceeds the maximum effective frequency, therefore, the calculation is truncated properly. The denser interpolation points in low frequency section should be adopted for thecurve of the factorized spectral function changed sharply and sparser interpolation points in high frequency section should be used for smoother curve. The improved wave superposition method proves to be, efficient and reliable by verifying the power spectral density function and correlation function of wind velocity sample.