基于参数优化变分模态分解的瞬时模态参数识别

陈祥祥; 史治宇; 赵宗爽

doi:10.13224/j.cnki.jasp.20220301

基于参数优化变分模态分解的瞬时模态参数识别

doi: 10.13224/j.cnki.jasp.20220301

1.
南京航空航天大学航空学院机械结构力学及控制国家重点实验室，南京 210016
2.
中国商用飞机有限责任公司上海飞机制造有限公司，上海 201324

基金项目: 国家自然科学基金（12272172）

详细信息

作者简介:
陈祥祥（1996-），男，硕士生，主要从事时变动力学参数识别研究

通讯作者:
史治宇（1967-），男，教授、博士生导师，博士，主要从事动力学参数识别与有限元模型修正研究。E-mail：zyshi@nuaa.edu.cn

中图分类号: V214；O324；TB123
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- 被引次数: 0
出版历程
- 收稿日期: 2022-05-03
- 网络出版日期: 2023-11-20

Instantaneous modal parameter identification based on parameter optimized variational mode decomposition

1.
State Key Laboratory of Mechanics and Control of Mechanical Structures，College of Aerospace Engineering，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China
2.
Shanghai Aircraft Manufacturing Company，Limited，Commercial Aircraft Corporation of China，Limited，Shanghai 201324，China

摘要

摘要:
针对变分模态分解的模态数和二次惩罚因子难以确定的问题，提出了基于正交性指标、能量比值和变分能量熵的参数优化算法；对于分解得到的单分量信号，发展了基于多项式调频小波变换的瞬时频率识别方法和基于能量法的瞬时阻尼比识别方法。开展了三自由度时变结构仿真研究和时变钢梁实验研究。研究结果表明：优化后的变分模态分解法能够精确分离多自由系统的各阶时变分量，具有较强的抗噪性能；基于多项式调频小波变换的瞬时频率识别方法具有很强的时变频率追踪性能、抗噪声能力强，时变频率识别精度高，平均误差不超过1%；能量法能够较准确地识别结构的瞬时阻尼比，识别误差保持在10%左右，抗噪优势明显。
- 模态参数识别 /
- 参数优化 /
- 变分能量熵 /
- 变分模态分解 /
- 多项式调频小波变换 /
- 能量法
Abstract:
In view of the problem of determining the modal number and quadratic penalty factor of variational mode decomposition (VMD), a parameter optimization algorithm based on orthogonality index, energy ratio and variational energy entropy (VEE) was proposed. For the decomposed single component signal, the instantaneous frequency identification method based on polynomial chirplet transform (PCT) and the instantaneous damping ratio identification method based on energy method were developed. The simulation research of 3-DOF (degree of freedom) time-varying structure and the experimental research of time-varying steel beam were carried out. The results showed that the optimized VMD method can accurately separate the time-varying components of the multi-DOF system with strong anti-noise performance. The instantaneous frequency identification method based on PCT had strong time-varying frequency tracking performance, strong anti-noise ability, and high accuracy of time-varying frequency identification, and the average error was less than 1%. The energy method can accurately identify the instantaneous damping ratio of the structure with obvious anti-noise advantage, and the identification error was maintained at about 10%.
- modal parameter identification /
- parameter optimization /
- variational energy entropy /
- variational mode decomposition /
- polynomial chirplet transform /
- energy method

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图 1 参数优化算法

Figure 1. Parameter optimization algorithm

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图 2 三自由度时变结构

Figure 2. 3-DOF time-varying structure

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图 3 第二自由度加速度响应谱

Figure 3. Acceleration response of the second DOF

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图 4 各分量正交性指标

Figure 4. Orthogonality indexes of each component

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图 5 各分量能量比值

Figure 5. Energy ratios of each component

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图 6 不同α对应的变分能量熵

Figure 6. VEE values of different α

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图 7 三阶分量的幅值谱和包络

Figure 7. Amplitude spectrums and envelopes of three order components

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图 8 瞬时频率识别结果

Figure 8. Identification results of instantaneous frequency

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图 9 瞬时阻尼比识别结果

Figure 9. Identification results of instantaneous damping ratio

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图 10 各信噪比下瞬时频率识别误差

Figure 10. Identification errors of instantaneous frequency under each SNR

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图 11 各信噪比下瞬时阻尼比识别误差

Figure 11. Identification errors of instantaneous damping ratio under each SNR

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图 12 时变结构实验设备

Figure 12. Time varying structure experimental equipment

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图 13 测点2的加速度响应谱

Figure 13. Acceleration response of measuring point 2

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图 14 实验中的瞬时频率识别结果

Figure 14. Identification results of instantaneous frequency in experiment

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