超声兰姆波逆散射拓扑成像方法研究

Ultrasonic inverse scattering imaging technology will play its core role in Lamb wave industrial application for urgently solving the problems of accurate positioning, quantitative evaluation and visualized characterization of defects. In view of current Lamb wave diffraction tomography based on the first order Born approximation being applicable to only the weak scatterer case, this project will use the topological asymptotic method originally proposed in the theory of shape optimization, which breaks through the limitation of the weak scattering approximation, and fully considers the scattering characteristics of the defects, and realizes the inversion and topological imaging for different types of defects. For inhomogeneous scatterer defects such as holes or inclusions in isotropic plates, combining the theory, simulation and experiment, this project will study the scattering and mode conversion characteristics of the interaction of Lamb wave with the defect so as to establish the relationship between Lamb wave scattering acoustic fields and the defect features. The theoretical model of Lamb wave topological imaging under the mode conversion condition is constructed, which can reflect the actual characteristics of Lamb wave acoustic fields. The characterization method of general topology sensitivity function is explored to solve the inverse scattering problem of scatterers with different boundary conditions. The influence of key detecting factors such as transmitting frequency, measurement noise on topological imaging results is revealed to improve the resolution and precision of quantitative defect image. The achievements of this project will provide a new academic way for Lamb wave inverse scattering problem and lay the theoretical groundwork for Lamb wave nondestructive evaluation technique in the application.

缺陷的准确定位、定量评估和形象化表征是兰姆波工业应用中迫切需要解决的问题，超声逆散射成像技术将发挥其核心作用。目前发展的基于一阶Born近似的兰姆波衍射层析成像仅适用于散射体极弱的情况。本项目拟采用源于形状优化理论的拓扑渐近方法，突破弱散射近似的限制，完整考虑缺陷的散射特性，实现对不同类型缺陷的反演及拓扑成像。针对各向同性板中的异质散射体缺陷（孔洞或夹渣类），综合理论、数值模拟和实验，研究兰姆波与缺陷相互作用发生的散射和模式转换问题，建立兰姆波散射声场与缺陷特征之间的关系；构建模式转换条件下兰姆波拓扑成像的理论模型，使其能反映实际兰姆波声场的特性；探索通用型拓扑灵敏度函数的表征方法，解决不同边界条件散射体的逆散射问题；揭示激发频率、测量噪声等关键因素对拓扑成像结果的影响，提高定量化缺陷图像的分辨率和精度。在学术上提供解决兰姆波逆散射问题的新途径，在应用上为兰姆波无损评价奠定理论基础。

本项目采用源于形状优化理论的超声兰姆波逆散射拓扑成像方法，实现了缺陷的准确定位、定量评估和形象化表征，取得了一系列具有理论和实际价值的基础性研究成果。主要包括：①构建了模式转换条件下兰姆波拓扑成像的理论模型。创新性地将时间反转理论与拓扑优化思想结合在一起，在拓扑成像中引入了直接声场和伴随声场的概念。让直接声场与伴随声场相乘，消除了无缺陷处多模式混叠的干扰，最大限度的消除了多余伪像；②研究了近场缺陷的兰姆波拓扑成像方法。借鉴海洋、地球物理等领域中格林函数恢复思想，将两传感器接收到的扩散场信号进行互相关处理，恢复出两传感器之间的格林函数响应，重建新的全矩阵。该重建全矩阵削弱了直接耦合采集响应信号中存在的早期饱和非线性效应信号，恢复被遮盖的近场缺陷散射信号；③将拓扑成像与全矩阵数据理论模型相结合，获得高分辨率的超声相控阵后处理成像算法。全矩阵采集获得的数据蕴含着丰富的信息，将拓扑成像方法用于全局阵数据后处理，通过兰姆波时间反转聚焦、图像融合，消除了多模式、有噪声环境下伪像的干扰，提高了缺陷的成像分辨率；④研究了超声阵列稀疏优化方法，提高拓扑成像的检测效率。基于遗传算法优化各有效阵元的位置，保证稀疏后阵列的成像质量与满阵情况下基本一致。以峰值旁瓣电平最小值为优化目标，构建二进制编码稀疏方法，达到提高成像效率的目的；⑤探讨了拓扑成像方法对层状非均质结构中缺陷的适用性。拓扑成像方法，无需事先假设任何关于缺陷的信息（如位置、形状等），直接利用测量信号对试样做拓扑渐近，可应用于复杂非均质结构中缺陷（如复合材料中的孔洞缺陷、混凝土粘接结构中的脱空缺陷）的准确定位和定量评估。本项目的研究成果为兰姆波定量无损评价奠定理论基础。