基于变分模态分解和奇异值分解的结构模态参数识别方法

沈健; 赵文涛; 丁建明

doi:10.19818/j.cnki.1671-1637.2019.06.008

基于变分模态分解和奇异值分解的结构模态参数识别方法

doi: 10.19818/j.cnki.1671-1637.2019.06.008

1.
中铁二院工程集团有限责任公司科学技术研究院, 四川成都 610031
2.
西南交通大学牵引动力国家重点实验室, 四川成都 610031

基金项目:

国家自然科学基金项目 51875481

四川省重点研发项目 2017GZ0088

详细信息

作者简介:
沈健(1981-), 男, 四川西昌人, 中铁二院工程集团有限责任公司副研究员, 从事车线测试技术研究

中图分类号: U270.1
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出版历程
- 收稿日期: 2019-05-30
- 刊出日期: 2019-12-25

Structural modal parameter identification method based on variational mode decomposition and singular value decomposition

1.
Research Institute of Science and Technology, China Railway Eryuan Engineering Group Co., Ltd., Chengdu 610031, Sichuan, China
2.
State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, Sichuan, China

More Information

Author Bio:
SHEN Jian (1981-), male, associate professor, 5435918@qq.com

Article Text (Baidu Translation)

摘要

摘要: 为了准确获得结构的固有频率、阻尼比与振型, 将变分模态分解与奇异值分解相结合, 提出一种新的结构模态参数识别方法; 基于已有时频参数识别方法, 根据测量的脉冲激励与加速度响应估计系统的频响函数, 对系统的频响函数进行反傅里叶变换得到脉冲响应函数; 对各测点的脉冲响应函数进行变分模态分解, 得到与结构固有频率对应的本征模态分量; 提取本征模态分量的固有频率, 利用与固有频率相近的本征模态分量作为行向量构造奇异值分解矩阵, 对所构矩阵做奇异值分解, 利用最大奇异值重构左、右奇异值向量, 识别结构的振型、固有频率和阻尼比; 通过四自由度质量-弹簧-阻尼模态仿真试验和车体横梁锤击模态试验, 验证了所提出的模态参数识别方法的有效性。研究结果表明: 在四自由度理论模型参数识别中, 系统固有频率和阻尼比的识别结果与理论计算结果的最大相对误差分别不超过0.025%和1.490%, 理论计算与识别的1~4阶振型的模态置信度分别为0.999、1.000、0.999和0.999;在车体横梁锤击模态试验中, 提出方法识别的固有频率和阻尼比与理论计算结果的最大相对误差分别不超过1.57%和1.47%, 且车体横梁的理论振型与识别振型趋势相同。可见, 提出的方法能有效识别结构的模态参数。
- 车辆工程 /
- 结构 /
- 模态参数 /
- 脉冲响应函数 /
- 变分模态分解 /
- 奇异值分解 /
- 参数识别
Abstract: To obtain the structural natural frequency, damping ratio and vibration mode, a new modal parameter identification method was proposed by combining the variational mode decomposition with the singular value decomposition. Based on the existing time-frequency parameter identification method, the system frequency response function was estimated according to the measured impulse excitations and accelerations. The inverse Fourier transform was applied to the system frequency response function to obtain the impulse response function. The intrinsic mode components corresponding to the structural natural frequencies were obtained by executing the variational mode decomposition on the impulse response function for each measuring point. The natural frequencies of intrinsic mode components were extracted, and the intrinsic mode components close to the natural frequency were used as the row vectors to construct the singular value decomposition matrix, and the singular value decomposition was performed on the constructed matrix. The left and right singular value vectors reconstructed by the maximum singular values were used to identify the vibration mode, natural frequency and damping ratio of the structure. The effectiveness of the proposed modal parameter identification method was verified through a four-degree-of-freedom mass-spring-damping theoretical model and a hammering modal test on the vehicle body crossbeam. Research result indicates that in the parameter identification of four-degree-of-freedom theoretical model, the maximum relative errors of system natural frequencies and damping ratios between the identified and theoretical values are no more than 0.025% and 1.490%, respectively. The modal assurance criterions of 1 to 4-order vibration modes between the theoretical and identified values are 0.999, 1.000, 0.999 and 0.999, respectively. In the hammering modal test on the vehicle body crossbeam, the maximum relative errors of natural frequency and damping ratio between the results identified by the proposed method and the theoretical results are not more than 1.57% and 1.47%, respectively, and the theoretical and identified vibration modes have the same trend. Therefore, the proposed method can effectively identify the structural modal parameters.
- vehicle engineering /
- structure /
- modal parameter /
- impulse response function /
- variational mode decomposition /
- singular value decomposition /
- parameter identification

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图 1 基于变分模态分解和奇异值分解的结构模态参数识别模型

Figure 1. Structure modal parameter identification model based on variational mode decomposition and singular value decomposition

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图 2 四自由度质量-弹簧-阻尼系统

Figure 2. Four-degree-of-freedom mass-spring-damping system

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图 3 m₁的加速度响应曲线

Figure 3. Acceleration response curves of m₁

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图 4 m₁的加速度响应频谱

Figure 4. Acceleration response frequency spectrums of m₁

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图 5 x₁₄经变分模态分解得到的分解信号

Figure 5. Decomposed signals of x₁₄ obtained by VMD

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图 6 经变分模态分解得到的分解信号频谱

Figure 6. Frequency spectrums of decomposed signals obtained by VMD

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图 7 x₁₄由经验模态分解得到的分解信号

Figure 7. Decomposed signals of x₁₄ obtained by EMD

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图 8 由经验模态分解得到的分解信号频谱

Figure 8. Frequency spectrums of decomposed signals obtained by EMD

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图 9 参数识别过程

Figure 9. Process of parameter identification

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图 10 理论振型与识别振型比较

Figure 10. Comparison of identified and theoretical vibration modes

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图 11 MAC矩阵

Figure 11. MAC matrix

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图 12 动车组车体横梁结构及测点布置

Figure 12. Structure and measuring points arrangement of vehicle body crossbeam of EMU

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图 13 车体横梁锤击模态试验

Figure 13. Hammering modal test on vehicle body crossbeam

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图 14 锤击模态试验数据和H₁估计

Figure 14. Hammering modal test data and H₁ estimation

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图 15 本文方法识别1阶模态参数

Figure 15. First-order modal parameters obtained by method in this paper

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图 16 本文方法识别2阶模态参数

Figure 16. Second-order modal parameter obtained by method in this paper

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图 17 本文方法识别3阶模态参数

Figure 17. Third-order modal parameter obtained by method in this paper

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图 18 本文方法识别部分测点的模态振型

Figure 18. Modal vibration modes of some measuring points identified by method in this paper

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图 19 车体横梁前4阶模态振型

Figure 19. First four orders vibration modes of vehicle body crossbeam

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表 1 仿真信号模态参数识别结果

Table 1. Modal parameter identification results of simulation signals

模态阶数		1	2	3	4
固有频率/Hz	本文方法	61.163	227.955	460.121	848.794
	传统方法	60.987~61.203	227.873~227.964	460.032~460.155	≤848.724
	HHT方法	60.559~67.399	214.119~234.096	423.554~460.169
	理论值	61.148	227.951	460.183	848.771
固有频率的相对误差/%	本文方法	0.025	0.002	0.013	0.003
	传统方法	0.089~0.263	0.006~0.034	0.006~0.033	≤0.006
	HHT方法	0.963~10.223	2.696~6.068	0.003~7.959
阻尼比/%	本文方法	0.126	0.529	0.244	0.045
	传统方法	0.136~0.280	0.530	0.240~0.250	≤0.049
	HHT方法	≤0.189	0.499~0.522	0.212~0.268
	理论值	0.126	0.537	0.245	0.045
阻尼比的相对误差/%	本文方法	0	1.490	0.408	0
	传统方法	7.937~122.222	1.304	2.041	8.889
	HHT方法	≤50	2.793~7.076	9.388~13.469

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表 2 模态参数识别结果对比

Table 2. Comparison of modal parameter identification results

模态阶数		1	2	3	4
固有频率/Hz	本文方法	66.113	212.886	444.962	754.787
	传统方法	63.783~69.194	210.443~220.124	438.926~458.232	754.789~764.964
	仿真结果	65.072	214.086	447.108	762.899
固有频率的相对误差/%	本文方法	1.57	0.56	0.48	1.08
固有频率的相对误差/%	传统方法	1.981~6.335	1.702~2.820	1.830~2.488	0.271~1.063
阻尼比/%	本文方法	1.47	0.55	0.25	0.14
阻尼比/%	传统方法	1.41~2.51	0.53~0.72	0.23~0.31	0.14~0.17

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