Structural Crack Identification Based on the Variational Mode Decomposition
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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。
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.
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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
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%
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%
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
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)
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)表 1 模拟工况
Table 1. The simulation condition
condition elastic modulus
Et /($ {\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} $/mcrack depth
ratio $ \delta $ = d/H1 $ 4.54\times {10}^{10} $ $ 2\;549 $ $ 0.2 $ $ 6 $ $ 10 $ $ 9 $ 0.15 
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