Structure damage identification method of inverse finite element method-pseudo-excitation method based on 2D continuous wavelet transform and data fusion technology
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摘要: 在逆有限元法(iFEM)与伪激励法(PE)相结合的损伤识别方法框架下，通过引入二维连续小波变换与数据融合技术，增强了iFEM-PE方法的抗噪能力及工程适用性。通过算例分析可知，iFEM能够借助有限应变测量数据实时准确地重构结构位移，进而使PE方法摆脱了对在线位移测量的依赖。另一方面，PE法对结构损伤具有高敏感性，适用于损伤的精确定位与定量。针对iFEM-PE方法对噪声的敏感性，二维连续小波变换可以在时频域实现信号联合分析，加强损伤特征并抑制噪音。另一方面，数据融合技术通过对不同工况下损伤识别结果的综合处理，有效提升了损伤识别的适用性与稳定性。结果显示，以上方法在噪音影响下可对复合材料结构的分层损伤进行精确定位。Abstract: The two-dimensional continuous wavelet transform (2D-CWT) and data fusion technique to enhance the noise immunity and engineering applicability of the framework of damage called iFEM-PE method which combines the inverse finite element method (iFEM) and pseudo-excitation method (PE) to identify damage were introduced. The example analyses show that iFEM can reconstruct the structural displacement accurately in real time with the finite strain measurement data, which makes the PE method get rid of the dependence of online displacement measurement. On the other hand, PE method has high sensitivity to structural damage, which is suitable for accurate location and quantification of damage. Because the iFEM-PE method is sensitive to the noise, 2D-CWT can realize joint signal analysis in time and frequency domain, strengthen damage characteristics and suppress noise. Moreover, data fusion technology effectively improves the applicability and stability of damage identification through the comprehensive processing of damage identification results under different working conditions. The results show that the above methods can accurately locate the delamination damage of composite structures under the influence of noise.
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图 1 iQS4逆壳单元 (a) 和其局部自由度 (b)
Figure 1. iQS4 inverse element (a) and its local nodal degrees of freedom (b)
u, v—Displacement of x and y directions in the plane, respectively; w—Transverse deflection displacement in the z direction; θx, θy and θz—Rotation angles with the positive x, y and z axes as normals, respectively
图 2 iQS4单元上离散应变测量
Figure 2. Discrete surface strains measured on the iQS4 element
${\varepsilon _{xx}^ + } $ , ${\varepsilon _{yy}^ + } $ , ${\gamma _{xy}^ + } $ , ${\varepsilon _{xx}^{\rm{ - }}} $ , ${\varepsilon _{yy}^{\rm{ - }}} $ , ${\gamma _{xy}^{\rm{ - }}} $ —Strain components measured on structural surface; h—Element thickness
图 3 改进后的逆有限元-伪激励法框架流程图
Figure 3. Flowchart of the improved inverse finite element method-pseudo-excitation method framework
2D-CWT—Two dimensional continuous wavelet transform; PE—Pseudo-excitation approach; iFEM—Inverse finite element method
图 4 碳纤维增强树脂复合材料(CFRP)层合板分层的位置与尺寸
Figure 4. Location and size of delamination of carbon fiber reinforced polymer (CFRP)
图 5 CFRP层合板逆有限元方法(iFEM)单元尺寸对计算精度的影响
Figure 5. Influence of element size of CFRP laminate on calculation accuracy using inverse finite element method (iFEM)
图 6 有限元方法(FEM)计算得到的 (a) 及iFEM反演得到的(b)CFRP层合板振动位移
Figure 6. Vibration displacements of CFRP laminate computed by direct finite element method (FEM) (a) and reconstructed by iFEM (b)
图 7 基于引入1% (a) 和2% (b) 噪声后的应变数据iFEM反演得到的CFRP层合板振动位移
Figure 7. Vibration displacements of CFRP laminate reconstructed by iFEM based on strains with noise level of 1% (a) and 2% (b)
图 8 基于引入误差为0 (a)、1% (b) 和2% (c) 的FEM位移数据计算得到的CFRP层合板损伤指数ID
Figure 8. Damage index ID of CFRP laminate based on the displacement computed by FEM with 0 (a), 1% (b) and 2% (c) error
图 9 基于引入误差为0% (a)、1% (b)、2% (c)的iFEM位移数据计算得到的CFRP层合板损伤指数ID
Figure 9. Damage index ID of CFRP laminate based on the displacement computed by iFEM with 0% (a), 1% (b) and 2% (c) error
图 10 基于引入误差为0% (a)、1% (b)、2% (c) 的iFEM位移数据计算并经过二维小波处理得到的CFRP层合板损伤指数ID
Figure 10. Damage index ID of CFRP laminate based on the displacement computed by iFEM and treated by 2D-CWT with 0% (a), 1% (b) and 2% (c) error
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