基于MVDR加权稀疏重建的CFRP损伤成像

冯继启; 叶波; 邹杨坤; 朱之贞; 杨常春

doi:10.13801/j.cnki.fhclxb.20240507.002

基于MVDR加权稀疏重建的CFRP损伤成像

doi: 10.13801/j.cnki.fhclxb.20240507.002

冯继启^{1, 2},
叶波^{1, 2, ,},
邹杨坤^{2, 3},
朱之贞⁴,
杨常春^{1, 2}

1.
昆明理工大学　信息工程与自动化学院，昆明 650000
2.
昆明理工大学　云南省智能控制与应用重点实验室，昆明 650000
3.
昆明理工大学　民航与航空学院，昆明 650000
4.
陆装驻重庆军代局驻昆明地区第一军代室，昆明 650000

基金项目: 国家自然科学基金(62063012)；云南省中青年学术和技术带头人后备人才项目(202305AC160062)

详细信息

通讯作者:
叶波，博士，教授，博士生导师，研究方向为结构健康监测、电磁无损检测　E-mail: yeripple@hotmail.com

中图分类号: TB332；TP206+.1
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- 被引次数: 0
出版历程
- 收稿日期: 2023-12-04
- 修回日期: 2024-04-14
- 录用日期: 2024-04-26
- 网络出版日期: 2024-05-08
- 刊出日期: 2024-10-15

CFRP damage imaging based on MVDR weighted sparse reconstruction

FENG Jiqi^{1, 2},
YE Bo^{1, 2
, ,},
ZOU Yangkun^{2, 3},
ZHU Zhizhen⁴,
YANG Changchun^{1, 2}

1.
School of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650000, China
2.
Yunnan Key Laboratory of Intelligent Control and Application, Kunming University of Science and Technology, Kunming 650000, China
3.
School of Civil Aviation and Aeronautics, Kunming University of Science and Technology, Kunming 650000, China
4.
The First Military Representative Office of the Chongqing Military Representative Bureau of the Army Equipment Department in Kunming, Kunming 650000, China

Funds: National Natural Science Foundation of China (62063012); The Young and Middle-Aged Academic and Technical Leaders Reserve Talents Project of Yunnan Province (202305AC160062)

摘要

摘要: 碳纤维增强复合材料(CFRP)因性能优异而广泛用于航天等领域，其在服役中会出现损伤。利用稀疏重建(SR)算法可对CFRP损伤进行成像，定位损伤位置，但因原子失配问题会造成伪影，甚至误判损伤。针对上述问题，提出一种最小方差无失真响应(MVDR)加权的稀疏重建成像法。将CFRP监测区域划分为若干网格点，基于Lamb波散射模型构造字典，与散射信号和稀疏解变量组成SR模型；其次用MVDR成像法进行成像，基于成像结果构建MVDR权重因子，以此对稀疏解变量进行加权；最后采用基追踪去噪算法求解加权SR模型，得到最优稀疏解并转换为像素值，实现CFRP的损伤成像。CFRP损伤成像实验结果表明：所提方法在相同正则化参数下成像效果均优于SR成像法，而在3种不同正则化参数下的定位误差相比SR成像法分别降低了72.9 mm、77.4 mm与14.7 mm；在4种不同损伤位置下，MVDR-SR成像法成像结果具有更少的伪影，损伤定位误差最大为7.9 mm，相比MVDR和SR成像法具有更好的成像性能，验证了所提方法的正确性和有效性。
- CFRP /
- 稀疏重建 /
- MVDR权重因子 /
- Lamb波 /
- 损伤成像
Abstract: Carbon fiber reinforced polymer (CFRP) is widely used in aerospace and other fields due to its excellent performance, and it will be damaged in service. Sparse reconstruction (SR) algorithm can be used to image the CFRP damage and locate the damage, but the atomic mismatch problem will cause artifacts and even misjudge the damage. Aiming at the above problems, it was proposed that a sparse reconstruction imaging method weighted by minimum variance distortionless response (MVDR). The CFRP monitoring area was divided into several grids, the dictionary was constructed based on the scattering model of Lamb wave to form the SR model with the scattering signal and the sparse solution variables. Secondly, the MVDR imaging method was used for imaging. Based on the imaging results, the MVDR weighting factor was constructed to weight the sparse solution variables. Finally, the basis pursuit denoising algorithm was adopted to solve the weighted SR model, the optimal sparse solution was obtained and converted into pixel value to realize the damage imaging of CFRP. The experimental results of CFRP damage imaging show that the imaging effect of the proposed method is better than that of the SR imaging method under the same regularization parameters, the localization errors are reduced by 72.9 mm, 77.4 mm and 14.7 mm respectively compared with the SR imaging method under three different regularization parameters. Under four different damage locations, the imaging results of MVDR-SR imaging method have fewer artifacts and the maximum damage localization error is 7.9 mm. Compared with MVDR and SR imaging methods, MVDR-SR imaging method has better imaging performance, which verifies the correctness and effectiveness of the proposed method.
- CFRP /
- sparse reconstruction /
- MVDR weighting factor /
- Lamb wave /
- damage imaging

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图 1 Lamb波散射示意图

Figure 1. Scattering plot of Lamb wave

r₁—Distance from the excitation source to the scattering source; r₂—Distance from the scattering source to the receiving source; r₃—Distance from the excitation source to the receiving source

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图 2 最小方差无失真响应(MVDR)-稀疏重建(SR)成像法流程

Figure 2. Flowchart of the minimum variance distortionless response (MVDR)-sparse reconstruction (SR) imaging method

BPDN—Basic pursuit denoise

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图 3 碳纤维增强复合材料(CFRP)层合板

Figure 3. Carbon fiber reinforced polymer (CFRP) laminates

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图 4 传感器/损伤坐标示意图

Figure 4. Coordinate plot of sensor and damage

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图 5 激励信号

Figure 5. Excitation signal

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图 6 D4处不同正则化参数下的SR与MVDR-SR成像法成像结果

Figure 6. SR and MVDR-SR imaging results under different regularization parameters at D4

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图 7 损伤D1成像结果

Figure 7. Damage D1 imaging results

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图 8 损伤D2成像结果

Figure 8. Damage D2 imaging results

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图 9 损伤D3成像结果

Figure 9. Damage D3 imaging results

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图 10 损伤D4成像结果

Figure 10. Damage D4 imaging results

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表 1 T700 M21型CFRP参数

Table 1. Material parameters of T700 M21 CFRP

Parameter	Value	Parameter	Value
${E_{{11}}}$/GPa	125.5±2.4	$ {v_{{12}}} $	0.37±0.08
${E_{{22}}}$/GPa	8.7±0.1	${v_{{23}}}$	0.45±0.02
${G_{{12}}}$/GPa	4.135	$\rho $/(kg·m⁻³)	1571±2
Notes: E₁₁, E₂₂—Elasticity modulus; G₁₂—Shear modulus; v₁₂, v₂₃—Poisson's ratio; ρ—Density.

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表 2 传感器坐标

Table 2. Sensor coordinate

Sensor	Coordinate/mm	Sensor	Coordinate/mm
T1	(450, 470)	T7	(450, 30)
T2	(370, 470)	T8	(370, 30)
T3	(290, 470)	T9	(290, 30)
T4	(210, 470)	T10	(210, 30)
T5	(130, 470)	T11	(130, 30)
T6	(50, 470)	T12	(50, 30)
Notes: T represents sensor; The subscript represents the sequence number.

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表 3 损伤坐标

Table 3. Damage coordinate

Damage	Coordinate/mm	Damage	Coordinate/mm
D1	(65, 415)	D2	(265, 412)
D3	(320, 260)	D4	(250, 75)
Notes: D represents damage; The following number represents the serial number.

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表 4 D4处不同正则化参数σ²下的SR与MVDR-SR成像法定位结果

Table 4. Location results of SR and MVDR-SR imaging methods under different regularization parameters σ² at D4

${\sigma ^2}$	SR		MVDR-SR
${\sigma ^2}$	Imaging center/mm	Location error/mm	Imaging center/mm	Location error/mm
$ 0.55\left\\| {\boldsymbol{y}} \right\\|_2^2 $	(187.5, 7.5)	91.9	(257.5, 92.5)	19.0
$ 0.75\left\\| {\boldsymbol{y}} \right\\|_2^2 $	(187.5, 7.5)	91.9	(257.5, 87.5)	14.5
$ 0.95\left\\| {\boldsymbol{y}} \right\\|_2^2 $	(247.5, 97.5)	22.6	(247.5, 82.5)	7.9

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表 5 3种成像法在不同损伤位置成像定位结果

Table 5. Imaging positioning results of the three imaging methods at different damage localizations

Damage	MVDR		SR		MVDR-SR
Damage	Imaging center/mm	Location error/mm	Imaging center/mm	Location error/mm	Imaging center/mm	Location error/mm
D1	(82.5, 412.5)	17.6	(2.5, 387.5)	68.2	(62.5, 412.5)	3.5
D2	(267.5, 432.5)	20.7	(262.5, 402.5)	9.8	(257.5, 412.5)	7.5
D3	(307.5, 257.5)	12.7	(492.5, 257.5)	172.5	(312.5, 257.5)	7.9
D4	(247.5, 67.5)	7.9	(247.5, 97.5)	22.6	(247.5, 82.5)	7.9

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