基于VMD-Hilbert变换的铁路路基填料振动压实动力响应研究

doi:10.13722/j.cnki.jrme.2021.0415

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摘要以京雄城际铁路路基填筑所采用的粗粒土填料为例，开展表面振动压实试验，研究不同振动频率和激振力组合下填料的干密度阈值。随后，采用变分模态分解(VMD)–希尔伯特(Hilbert)变换研究压实过程中振动设备与填料间的非线性动力响应，并基于能量守恒定律分析压实过程的能量变换，利用加速度信号的Hilbert边际谱能量评价填料的压实程度。研究结果表明：填料的干密度在表面振动压实试验中呈现出为“迅速增长，缓慢增长，保持稳定”的变化趋势，且在不同压实工艺参数下，填料所能达到的干密度阈值不同。利用变分模态分解(VMD)算法对加速度信号进行分解，可以精确地识别和分离出基波与各次谐波分量，且不存在模态混叠。分析Hilbert变换得到的加速度信号Hilbert谱和Hilbert边际谱得到压实过程中加速度信号能量在时频域上传播规律，表现为低频基波分量向高频谐波分量的转移。此外，激振头加速度信号的Hilbert边际谱能量与填料的干密度之间存在高度相关的对数关系，采用VMD分解后的振动信号Hilbert边际谱能量评价填料的压实程度是可行的。

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	杨长卫1
	张良1
	苏珂1
	董陇军2
	蔡德钩3
	叶阳升3
	童心豪1
	马洪生4

关键词 ：路基工程, 振动压实, 动力响应, 变分模态分解, Hilbert变换, 压实度评价

Abstract：The coarse-grained soils used in the subgrade filling of Beijing—Xiongan intercity railway was selected to carry out surface vibration compaction test，and the dry density threshold of the coarse-grained soils under different vibration frequency and excitation force combination was studied. Then，the nonlinear dynamic response between vibration equipment and filling material is studied by using VMD Hilbert transform. The energy transformation of compaction process is analyzed based on the law of energy conservation. And the compaction degree of the filling material is evaluated by the Hilbert marginal spectral energy of acceleration signal. The results show that：the dry density of the filling material in the surface vibration compaction test presents a trend of “rapid growth，slow growth，keep stable”，and the dry density threshold of filling material is different under different compaction parameters. By using the VMD to decompose the acceleration signal，the fundamental and harmonic components can be accurately identified and separated，and there is no mode aliasing. By analyzing the Hilbert spectrum and Hilbert marginal spectrum of acceleration signal，the propagation law of acceleration signal energy in time-frequency domain during compaction process is obtained，which shows the transfer from low-frequency fundamental component to high-frequency harmonic component. In addition，there is a logarithmic relationship between the Hilbert marginal spectral energy of the exciter acceleration signal and the dry density of the filling material， so it is feasible to use the Hilbert marginal spectral energy of the vibration signal decomposed by VMD to evaluate the compaction degree of the filling material.

Key words： subgrade engineering vibration compaction dynamic response variational mode decomposition Hilbert transform compaction degree evaluation

引用本文:

杨长卫1，张良1，苏珂1，董陇军2，蔡德钩3，叶阳升3，童心豪1，马洪生4 . 基于VMD-Hilbert变换的铁路路基填料振动压实动力响应研究[J]. 岩石力学与工程学报, 2022, 41(S1): 2991-3001.
YANG Changwei1，ZHANG Liang1，SU Ke1，DONG Longjun2，CAI Degou3，YE Yangsheng3，TONG Xinhao1，MA Hongsheng4. Research on dynamic response of railway subgrade filling material under vibration compaction based on VMD-Hilbert transform. , 2022, 41(S1): 2991-3001.

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http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2021.0415 或 http://rockmech.whrsm.ac.cn/CN/Y2022/V41/IS1/2991

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