碳纤维层合板Lamb波损伤检测的加权块稀疏成像法
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摘要
针对Lamb波稀疏阵列损伤成像方法中存在的成像分辨率低、伪点干扰大的问题,基于损伤在被测结构中的稀疏先验,提出了一种加权块稀疏重构的Lamb波损伤成像方法。首先通过Lamb波在薄板类结构中的线性传播模型,结合稀疏传感器阵列信息,构造过完备Lamb波散射的块稀疏字典;其次将测量得到的Lamb波散射信号在所构建的过完备字典下进行稀疏表示,将Lamb波损伤成像问题转化为加权l_1范数最小化的凸优化问题;最后通过谱梯度投影法,求解所建立的加权块稀疏凸优化模型,得到损伤散射信号在该字典下的稀疏表示系数并以此作为损伤指标,实现对被测结构的损伤成像。碳纤维层合板上的模拟损伤成像结果表明:所提方法在单损伤成像中的定位误差为3.16 mm,在双损伤成像中的最大定位误差为4.24 mm。实验验证了所提方法的有效性,与传统延迟叠加成像法的对比表明,所得损伤成像结果具有更高的分辨率,更小的伪点干扰,但同时也需要更大的计算量。
A weighted group-sparse imaging method is proposed via sparse priori-knowledge of damage in the measured structure. This approach attempts to deal with the cases of low imaging resolution and large interference of pseudo-points in the traditional Lamb wave imaging methods. An over-complete group-sparse dictionary of Lamb wave scattering is constructed with Lamb wave propagation model in thin plates, and the measured scattering Lamb waves are sparsely decomposed in the pre-built over-complete dictionary, so the Lamb wave imaging is transformed into convex optimization with weighted l_1 norm minimization. The weighted group-sparse convex optimization is solved by the spectral gradient projection method, and the sparse reconstruction coefficients of scattering Lamb waves are obtained. The coefficients are then taken as damage indicators to generate an image, which can locate damages in the measured structure. The results of imaging conducted on a plate of 16-layer CFRP laminate verify the effectiveness of the proposed method. The localization errors of the proposed method are 3.16 mm in single damage imaging case and 4.24 mm in double damage imaging case, respectively. The corresponding imaging results using the delay-and-sum imaging method are also comparatively presented.The imaging results obtained with the proposed method demonstrate higher resolution and smaller pseudo-point interference, but the computational task becomes heavier.
A weighted group-sparse imaging method is proposed via sparse priori-knowledge of damage in the measured structure. This approach attempts to deal with the cases of low imaging resolution and large interference of pseudo-points in the traditional Lamb wave imaging methods. An over-complete group-sparse dictionary of Lamb wave scattering is constructed with Lamb wave propagation model in thin plates, and the measured scattering Lamb waves are sparsely decomposed in the pre-built over-complete dictionary, so the Lamb wave imaging is transformed into convex optimization with weighted l_1 norm minimization. The weighted group-sparse convex optimization is solved by the spectral gradient projection method, and the sparse reconstruction coefficients of scattering Lamb waves are obtained. The coefficients are then taken as damage indicators to generate an image, which can locate damages in the measured structure. The results of imaging conducted on a plate of 16-layer CFRP laminate verify the effectiveness of the proposed method. The localization errors of the proposed method are 3.16 mm in single damage imaging case and 4.24 mm in double damage imaging case, respectively. The corresponding imaging results using the delay-and-sum imaging method are also comparatively presented.The imaging results obtained with the proposed method demonstrate higher resolution and smaller pseudo-point interference, but the computational task becomes heavier.
引文
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[3] 于海宁,高长星,王艳华.浅析CFRP在轨道交通领域的应用 [J].新材料产业,2018(10):23-26.YU Haining,GAO Changxing,WANG Yanhua.Application of CFRP in rail transit [J].New Material Industry,2018(10):23-26.
[4] SU Z,YE L,LU Y.Guided Lamb waves for identification of damage in composite structures:a review [J].Journal of Sound and Vibration,2006,295(3/4/5):753-780.
[5] 袁慎芳.结构健康监控 [M]:北京:国防工业出版社,2007:1-4.
[6] MITRA M,GOPALAKRISHNAN S.Guided wave based structural health monitoring:a review [J].Smart Materials and Structures,2016,25(5):53001.
[7] ZUO Hao,YANG Zhibo,XU Caibin,et al.Damage identification for plate-like structures using ultrasonic guided wave based on improved MUSIC method [J].Composite Structures,2018,203:164-171.
[8] WANG C H,ROSE J T,CHANG F.A synthetic time-reversal imaging method for structural health monitoring [J].Smart Materials and Structures,2004,13(2):415-423.
[9] HALL J S,MICHAELS J E.Minimum variance ultrasonic imaging applied to an in situ sparse guided wave array [J].IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control,2010,57(10SI):2311-2323.
[10] HALL J S,MCKEON P,SATYANARAYAN L,et al.Minimum variance guided wave imaging in a quasi-isotropic composite plate [J].Smart Materials and Structures,2011,20(2):25013.
[11] ZHAO Xiaoliang,GAO Hhuidong,ZHANG Guangfan,et al.Active health monitoring of an aircraft wing with embedded piezoelectric sensor/actuator network:I Defect detection,localization and growth monitoring [J].Smart Materials & Structures,2007,16(4):1208-1217.
[12] XU Caibin,YANG Zhibo,CHEN Xuefeng,et al.A guided wave dispersion compensation method based on compressed sensing [J].Mechanical Systems and Signal Processing,2018,103:89-104.
[13] ZHAO W,LI M,HARLEY J B,et al.Reconstruction of Lamb wave dispersion curves by sparse representation with continuity constraints [J].J Acoust Soc Am,2017,141(2):749-763.
[14] HARLEY J B,MOURA J M.Sparse recovery of the multimodal and dispersive characteristics of Lamb waves [J].The Journal of the Acoustical Society of America,2013,133(5):2732-2745.
[15] MESNIL O,RUZZENE M.Sparse wavefield reconstruction and source detection using compressed sensing [J].Ultrasonics,2016,67:94-104.
[16] LEVINE R M,MICHAELS J E.Model-based imaging of damage with Lamb waves via sparse reconstruction [J].The Journal of the Acoustical Society of America,2013,133(3):1525.
[17] LEVINE R M,MICHAELS J E.Block-sparse Lamb wave structural health monitoring using generic scattering models [EB/OL].[2018-11-12].http://www.researchgate.net/publication/278108415.
[18] GAO Fei,ZENG Liang,LIN Jin,et al.Damage assessment in composite laminates via broadband Lamb wave [J].Ultrasonics,2018,86:49-58.
[19] XU B,GIURGIUTIU V.Single mode tuning effects on Lamb wave time reversal with piezoelectric wafer active sensors for structural health monitoring [J].Journal of Nondestructive Evaluation,2007,26(2/3/4):123-134.
[20] VAN DEN BERG E,FRIEDLANDER M P.Sparse optimization with least-squares constraints [J].SIAM Journal on Optimization,2011,21(4):1201-1229.
[21] HUANG Liping,ZENG Liang,LIN Jin.Baseline-free damage detection in composite plates based on the reciprocity principle [J].Smart Materials and Structures,2018,27(1):15026.
[22] ROSE J L,PILARSKI A,DITRI J J.An approach to guided-wave mode selection for inspection of laminated plate [J].Journal of Reinforced Plastics and Composites,1993,12(5):536-544.