基于Hermite插值的简化风场模拟

发布时间：2019-02-10 19:18

【摘要】：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(2kN),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。
[Abstract]:Aiming at the problem that the simulation efficiency of traditional Deodatis harmonic synthesis method is restricted by the number of Cholesky decomposition, a simplified wind field simulation method based on Hermite interpolation is derived by introducing Hermite interpolation into the cross-spectral density matrix decomposition. The Cholesky decomposition times of traditional harmonic synthesis method are reduced from n 脳 N order to n 脳 2k order (2kN), thus the computational efficiency of traditional harmonic synthesis method is greatly improved. Taking the wind field simulation of the main girder of a long-span three-tower suspension bridge as an example, based on the traditional Deodatis method, the cubic Lagrange interpolation method and the Hermite interpolation method, the pulsating wind velocity time history of 4096 s is simulated, respectively. The comparison of the simulation time and accuracy shows that the Hermite interpolation method and the Lagrange interpolation method can improve the simulation efficiency of the traditional harmonic synthesis method. The simulation efficiency of Hermite interpolation method is slightly lower than that of cubic Lagrange interpolation method, but the simulation accuracy of H matrix is obviously higher than that of Hermite interpolation method, so Hermite interpolation method is better in wind field simulation. By using the simplified method based on Hermite interpolation, the power spectrum and the correlation function of the simulated pulsating wind speed are in good agreement with the target value, which indicates that the simulated pulsating wind speed still has a high fidelity. On this basis, the suggested interval of interpolation spacing is given through the optimization analysis of interpolation spacing.
【作者单位】：东南大学混凝土及预应力混凝土教育部重点实验室;
【基金】：国家973计划青年科学家专题项目(2015CB060000) 国家自然科学基金项目(51378111,51438002) 霍英东青年教师应用研究项目(142007) 教育部新世纪优秀人才支持计划项目(NCET-13-0128) 江苏高校优势学科建设工程项目(CE02-2-15)
【分类号】：TU312.1

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