基于三次样条插值谐波叠加技术的随机路面重构方法研究

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摘要汽车虚拟试验仿真研究的关键点在于：如何在获取准确的试验道路信息的基础上重现三维虚拟路面模型，其中道路谱的重构和分析是建立模型的核心内容。本文首先以砂石路面为研究对象，对其进行了高程数据采集和预处理，获得了路面不平度的频谱分布。其次，在谐波叠加法基础上创新性地引入三次样条插值技术，对中心频率点间的互功率谱密度矩阵采取正定平方(Cholesky)分解，并且采用不同条件下的插值方法获取了重构功率谱密度模型。最后通过对谐波叠加法及三类插值重构谱与原始谱的相关系数r的横向对比发现：第一类边界条件下三次样条插值方法在重构精度与效率方面有着明显的优势。此外本文基于该方法的拓展性利用MATLAB/GUI建立了试验道路谱数据库以及软化操作平台，为车辆虚拟试验仿真提供了可靠支撑。

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	金红杰1
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	吕添5

关键词 ：道路谱重构, 三次样条插值, 谐波叠加法, 正定平方分解

Abstract：The key point of vehicle virtual test simulation research is how to reproduce the three-dimensional virtual road model on the basis of obtaining accurate test road information, and the core contents of the model are the reconstruction and analysis of road spectrum. In this paper, the elevation data acquisition and preprocessing of the sand road are carried out, and the spectrum distribution of road roughness is obtained. Secondly, the cubic spline interpolation technique is innovatively introduced on the basis of harmonic superposition method, the mutual power spectral density matrix between the center frequency points is decomposed by Cholesky method, and the reconstructed power spectral density model is obtained by interpolation method under different conditions. Finally, by comparing the correlation coefficient (r) of harmonic superposition method and three kinds of interpolation reconstruction spectrum with the original spectrum, it is found that the cubic spline interpolation method under the first boundary condition has obvious advantages in accuracy and efficiency of reconstruction. In addition, based on the expansion of this method, this paper uses MATLAB/GUI to establish the relevant test road spectrum database and software-based operation platform which provide reliable support for vehicle virtual test simulation.

Key words： road spectrum reconstruction cubic spline interpolation harmonic superposition method Cholesky decomposition

收稿日期: 2022-03-30 出版日期: 2023-05-28

引用本文:

金红杰1,2，钟岳3，臧利国4,5，吕添5. 基于三次样条插值谐波叠加技术的随机路面重构方法研究[J]. 振动与冲击, 2023, 42(10): 23-30.
JIN Hongjie1,2，ZHONG Yue3，ZANG Liguo4,5，L Tian5. A study on harmonic superposition method based on cubic spline interpolation of random road reconstruction. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(10): 23-30.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2023/V42/I10/23

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