基于变分模态分解的结构裂纹识别

杨启航; 李林安; 李利青; 米少瑄

doi:10.21656/1000-0887.420338

基于变分模态分解的结构裂纹识别

doi: 10.21656/1000-0887.420338

天津大学机械工程学院，天津 300354

基金项目: 国家自然科学基金（11572218）

详细信息

作者简介:
杨启航（1996—），男，硕士生（E-mail：18838010785@163.com）

李林安（1966—），男，教授，硕士，博士生导师（通讯作者. E-mail：lali@tju.edu.cn）

中图分类号: U447
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- 被引次数: 0
出版历程
- 收稿日期: 2021-11-08
- 录用日期: 2022-04-01
- 修回日期: 2022-03-04
- 网络出版日期: 2022-11-15
- 刊出日期: 2022-12-01

Structural Crack Identification Based on the Variational Mode Decomposition

School of Mechanical Engineering, Tianjin University, Tianjin 300354, P.R.China

摘要

摘要:
为完善桥梁损伤检测方法，进一步提高桥梁损伤识别的精度，以动载作用下带裂纹简支梁模型为研究对象，提出了一种不基于完整有限元模型的裂纹检测方法。该方法在不阻塞交通的前提下，仅需对简支梁跨中加速度响应进行分析处理，减少了实际工程中传感器的装卸及维护工作。同时，基于该模型推导出了简支裂纹梁跨中加速度解析式。在理论推导的支撑下，利用变分模态分解和Hilbert变换构造出了瞬时能量和均值能量差，这两个裂纹识别指标能够有效地识别出裂纹深度占比为5%的小裂纹。基于此，开展了不同轮载大小、环境噪声以及损伤程度对检测结果影响的研究。结果表明：① 瞬时频率对裂纹位置具有较好的识别效果；② 均值能量差对不同裂纹深度占比以及轮载大小具有一定的敏感度；③ 该方法具有较强的噪声鲁棒性。
- 变分模态分解 /
- 加速度响应 /
- 裂纹识别 /
- 车轮荷载
Abstract:
In order to enrich the bridge damage detection method and further improve the accuracy of bridge damage identification, a detection method for simply supported beams with cracks under dynamic loads was proposed not based on the complete finite element model. Under the premise of not blocking traffic, the method only needs to analyze and deal with the acceleration responses of the simply supported beam span, which reduces the mounting, dismounting and maintenance of sensors in practical engineering. At the same time, based on the model, an analytical formula of the acceleration at the midspan of the simply supported cracked beam was derived. Based on the theoretical derivation, the instantaneous energy and the mean energy difference were constructed through the variational mode decomposition and the Hilbert transform, and these 2 crack identification indexes were used to effectively identify small cracks with a crack depth ratio of only 5%. Then the influences of different wheel loads, environmental noises and damage degrees on detection results were studied. The results show that: ① the instantaneous frequency has a better recognition effect for crack positions; ② the mean energy difference is sensitive to crack depth ratio δ and the wheel load magnitude; ③ this method has strong noise robustness.
- variational mode decomposition /
- acceleration response /
- damage identification /
- wheel load

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图 1 移动荷载下的裂纹梁模型

Figure 1. A cracked beam model under a moving load

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图 2 积分常数

Figure 2. Integration constants

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图 3 跨中位移

Figure 3. The midspan displacement

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图 4 跨中加速度

Figure 4. The midspan acceleration

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图 5 车轮荷载：（a）集中荷载；（b）非均布荷载

Figure 5. The wheel load: (a) a concentrated load; (b) an ununiform load

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图 6 VMD

Figure 6. The VMD

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图 7 IMF 4瞬时频率

Figure 7. The IMF 4 instantaneous frequency

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图 8 IMF 5瞬时能量

Figure 8. The IMF 5 instantaneous energy

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图 9 $ \delta $为2$ 0\text{%} $，15$ \text{%} $，$ 10\text{%} $，5$ \text{%} $的瞬时频率对比

Figure 9. Comparison of instantaneous frequencies for $\delta $ = 20%, 15%, 10%, 5%

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图 10 $ \delta $为$ 20\text{%} $，15$ \text{%} $，$ 10\text{%} $，5$ \text{%} $的瞬时能量对比

Figure 10. Comparison of instantaneous energy for $\delta $ = 20%, 15%, 10%, 5%

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图 11 均值能量差

注　为了解释图中的颜色，读者可以参考本文的电子网页版本，后同。

Figure 11. The mean energy difference

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图 12 三种轮载大小作用下瞬时能量对比

Figure 12. Comparison of instantaneous energies under 3 wheel loads

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图 13 均值能量差（轮载大小）

Figure 13. The mean energy difference (wheel load size)

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图 14 $ \delta $为2$ 0\text{%} $，15$ \text{%} $，$ 10\text{%} $，5$ \text{%} $的瞬时频率对比（双位置）

Figure 14. Comparison of instantaneous frequencies for $\delta $ = 20%, 15%, 10%, 5% (2 positions)

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图 15 $ \delta $为$ 20\text{%} $，15$ \text{%} $，$ 10\text{%} $，5$ \text{%} $的瞬时能量对比（双位置）

Figure 15. Comparison of instantaneous energy for $\delta $ = 20%, 15%, 10%, 5% (2 positions)

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图 16 均值能量差（双位置）

Figure 16. Mean energy differences (2 positions)

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图 17 信噪比为$ 5\;{\rm{dB}} $

Figure 17. The SNR is $ 5\;{\rm{dB}} $

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图 18 信噪比为$ 10\;{\rm{dB}} $

Figure 18. The SNR is $ 10\;{\rm{dB}} $

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图 19 信噪比为$ 15\;{\rm{dB}} $

Figure 19. The SNR is $ 15\;{\rm{dB}} $

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表 1 模拟工况

Table 1. The simulation condition

condition	elastic modulus E_t /($ {\rm{N}}/{{\rm{m}}}^{3} $)	density $ \rho $/($ {\rm{kg}}/{{\rm{m}}}^{3} $)	Poisson’s ratio $ \mu $	moving load velocity $ V/({\rm{km/h}} )$	wheel load P $/{\rm{kN} }$	crack location $ {L}_{1} $/m	crack depth ratio $ \delta $ = d/H
1	$ 4.54\times {10}^{10} $	$ 2\;549 $	$ 0.2 $	$ 6 $	$ 10 $	$ 9 $	0.15

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