基于Hermite插值的简化风场模拟

针对传统Deodatis谐波合成法的模拟效率受Cholesky分解次数制约的问题，通过对互谱密度矩阵分解引入Hermite插值，推导了基于Hermite插值的简化风场模拟方法，将传统谐波合成法中的Cholesky分解次数由n×N次缩减为n×2k次（2k < N），从而大幅度提升了传统谐波合成法的计算效率。以某大跨度三塔悬索桥主梁风场模拟为例，分别基于传统Deodatis法、三次Lagrange插值法、Hermite插值法模拟了时长为4096 s的脉动风速时程，三者在模拟耗时与模拟精度方面的对比表明:Hermite插值法与Lagrange插值法均能显著提高传统谐波合成法的模拟效率；Hermite插值法的模拟效率略低于三次Lagrange插值法，但其对H矩阵的模拟精度明显高出一个层次，因而Hermite插值法在风场模拟中表现更优。采用基于Hermite插值的简化方法，模拟脉动风速的功率谱与相关函数均能与目标值吻合较好，表明所模拟的脉动风速仍具有较高的保真度。在此基础上，通过插值间距的优化分析给出了插值间距的建议取值区间。

REDUCED SIMULATION OF THE WIND FIELD BASED ON HERMITE INTERPOLATION

Owing to the problem that the computational efficiency of traditional spectral representation (SR) method by Deodatis is restricted to the times of Cholesky decompositions, Hermite interpolation is included in the decomposition of cross-spectral density matrix. A reduced method for wind field simulation is derived accordingly. With the reduced method, the time of Cholesky decomposition in the traditional SR method can be decreased from n×N to n×2k (2k<N), hence the efficiency will be sharply increased. Taking the wind field simulation of the girder of a long-span triple-tower suspension bridge as an example, a 4096s-long fluctuating wind field is simulated by traditional SR method, third-order Lagrange interpolation method and the derived Hermite interpolation method. The comparison of the computational efficiency and its corresponding accuracy indicate that both the third-order Lagrange interpolation method and the Hermite interpolation method can prominently improve the computational efficiency of SR method. The efficiency of the Hermite interpolation method is slightly lower than that of the third-order Lagrange one, but its computing accuracy of Matrix H is on a much higher level which shows great superiority in wind field simulation. When the reduced method with Hermite interpolation is adopted, both the power spectral density and correlation functions of the simulated wind field can well conform to the targets. Based on the work above, the suggested boundaries for the interpolation intervals are given according to an optimization analysis.