Damage identification and scanning imaging of glass fiber reinforced polymer composite plates based on empirical mode decomposition and correlation coefficient
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摘要: 针对外界环境噪声等因素造成损伤因子不敏感，导致复合材料损伤识别困难和成像误差大等问题，提出了一种基于经验模态分解（Empirical mode decomposition, EMD）和相关系数的损伤因子。用空气耦合探头采集损伤前后的Lamb波信号进行EMD分解获取多个本征模态分量（Intrinsic mode function, IMF）。根据相关系数获取与信号相关性最大的IMF分量，并定义其能量值的相对变化为损伤因子。在模拟噪声环境前后，分别对玻璃纤维增强聚合物复合材料（GFRP）板中的分层缺陷进行识别和扫查成像，验证了该损伤因子的有效性。结果表明：信号经过EMD分解后，与其相关性最大的IMF分量对损伤最敏感，能够定义为识别损伤的损伤因子。将该损伤因子结合概率成像方法进行空耦Lamb波扫查，不仅能够有效对复合材料中的缺陷进行成像，而且在模拟强噪声环境中具有良好的抗噪性。Abstract: Aiming at the problem that the influence of environmental noise and insensitive damage factor make damage identification difficult and imaging error large for composite plate, a damage factor based on empirical mode decomposition(EMD) and correlation coefficient was proposed. The air-couple probe was used to obtain Lamb wave signal before and after the damage, and a group of intrinsic mode function (IMF) components of signal was obtained by EMD. According to the correlation coefficient, the IMF component which has the greatest correlation with the signal was obtained, and the relative change of its energy value was defined as the damage factor. The validity of the proposed algorithm was assessed by identifying damage and scaning imaging at composite plate. The results show that after EMD, the IMF component with the greatest correlation with the original signal is most sensitive to damage, and can be used as a damage factor to identify damage. Combining this damage factor with probability imaging algorithm for the air-coupled Lamb wave scanning can not only effectively image the defect in composite plate, but also has good noise resistance in simulated strong noise environment.
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图 1 空气耦合超声检测实验系统示意图
Figure 1. Schematic diagram of air-coupled ultrasonic experimental system
图 2 空气耦合超声探头入射角度频散曲线
Figure 2. Air-coupled ultrasonic probe incidence angle dispersion curves
图 3 无损伤信号的前四阶本征模态（IMF）分量
Figure 3. Intrinsic mode function(IMF) components of the first four orders of no damage signal
图 4 无损伤信号的前四阶IMF分量频谱
Figure 4. Spectra of IMF components of the first four orders of no damage signal
图 5 IMF分量与原始信号的相关系数
Figure 5. Correlation coefficient between IMF components and original signal
图 6 损伤前后信号的各阶IMF能量差
Figure 6. All IMF components energy differences of signals before and after damage
图 8 GFRP本征模态能量损伤因子(IEDI)与扫查距离的关系
Figure 8. Relationship between intrinsic mode function energy damage index(IEDI) and scanning distance of GFRP
图 10 添加噪声信号后GFRP有无损伤信号
Figure 10. No damage and damage signal with adding noise signal of GFRP
图 11 GFRP噪声信号与其IMF分量的相关系数
Figure 11. Correlation coefficients between noise signals with their IMF components of GFRP
图 12 GFRP损伤前后噪声信号与参考信号IMF分量的能量差异
Figure 12. Energy differences of IMF components of noise signal and reference signal before and after damage of GFRP
图 13 基于IEDI在不同等级噪声下GFRP的损伤成像
Figure 13. Damage imaging based on IEDI under different levels of noise of GFRP
图 14 基于计盒维数损伤因子（BDI）在不同等级噪声下的损伤成像
Figure 14. Damage imaging based on box-counting dimension damage index(BDI) under different levels of noise
表 1 GFRP不同损伤因子的对比结果
Table 1. Comparison results of different damage factors of GFRP
Noise level Box counting-dimension BDI IMF energy IEDI No damage Damage No damage Damage No noise 1.14 1.53 0.057 25.85 2.62 0.90 9 dB 1.55 1.60 0.03 19.55 1.15 0.94 5 dB 1.58 1.63 0.03 21.39 1.09 0.94 1 dB 1.62 1.66 0.02 19.61 1.52 0.92 0.1 dB 1.63 1.66 0.01 15.77 1.92 0.87 
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表 2 GFRP成像定位结果
Table 2. Imaging location results of GFRP
Noise level Actual position IEDI position Error/mm BDI position Error/mm (x,y) (x,y) (x,y) No noise (92,98) (92,99) 1.00 (92,100) 2.00 9 dB (92,98) (93,98) 1.00 (92,100) 2.00 5 dB (92,98) (93,98) 1.00 (91,100) 2.23 1 dB (92,98) (93,99) 1.41 (90,100) 2.82 0.1 dB (92,98) (93,99) 1.41 (90,101) 3.60
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表 3 GFRP不同损伤因子成像后在x和y方向上的定量结果
Table 3. Imaging results of different damage factors in the x and y directions of GFRP
Noise level Autal size IEDI size Error/mm BDI size Error /mm x/mm y/mm x/mm y/mm x/mm y/mm x/mm y/mm x/mm y/mm No noise 35.00 35.00 38.40 37.20 3.40 2.20 30.20 31.50 4.80 3.50 9 dB 35.00 35.00 38.70 39.70 3.70 4.70 27.90 29.60 7.10 5.40 5 dB 35.00 35.00 39.10 39.90 4.10 4.90 27.70 30.40 7.30 4.60 1 dB 35.00 35.00 38.90 40.30 3.90 5.30 30.00 98.20 5.00 63.20 0.1 dB 35.00 35.00 38.20 38.40 3.20 3.40 52.60 98.80 17.60 63.80
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