基于高阶剪切水平模式的深度分辨弹性属性层析成像

中文摘要 AI 辅助

早期材料退化会在裂纹或空洞形成之前产生弹性刚度的微弱局部变化，但传统超声测量通过路径和厚度平均稀释了这些变化。本文引入DEPTH（使用高阶模式的深度分辨弹性属性层析成像），该方法利用高阶导波之间的模式间散射来重建弹性属性随板中轴向位置和深度的变化。公式使用剪切水平（SH）模式开发，重建的属性为剪切模量。Born公式表明，每个入射-接收模式对至多包含两个余弦深度阶数，从而允许通过跨模式对和频率的多样化模式混合恢复厚度方向场。无矩阵正则化反演使用直接二维模态数据、实际单表面激发和接收以及全三维有限元数据进行评估。在10 mm板中，理想二维情况给出厚度方向点扩散半高全宽为0.84-1.03 mm，而单表面配置在正确深度恢复四个紧凑目标。这首次证明了在激发和接收限制在单一物理板表面的多模导波传输中进行深度分辨弹性属性层析成像。在全三维传播和有限宽度换能条件下，重建保持紧凑目标位置，与匹配的采集受限重建的整体图像相关性为0.899。这些模拟结果表明，高阶导波模式转换可以从表面访问测量提供局部深度分辨弹性属性层析成像，具有表征疲劳等早期损伤的潜力。

英文摘要

Early material degradation can produce weak, local changes in elastic stiffness before a crack or void forms, but conventional ultrasonic measurements dilute these changes through path and thickness averaging. This paper introduces DEPTH (Depth-resolved Elastic Property Tomography using Higher-order modes), which uses mode-to-mode scattering among higher-order guided waves to reconstruct elastic-property variations as a function of axial position and depth through a plate. The formulation is developed using shear-horizontal (SH) modes, for which the reconstructed property is shear modulus. A Born formulation shows that each incident-received mode pair contains at most two cosine depth orders, allowing the through-thickness field to be recovered from diverse modal mixtures across mode pairs and frequency. The matrix-free regularised inverse is evaluated using direct two-dimensional modal data, practical single-surface excitation and reception, and full three-dimensional finite-element data. In a 10 mm plate, the ideal two-dimensional case gives a through-thickness point-spread FWHM of 0.84-1.03 mm, while the single-surface configuration recovers four compact targets at the correct depths. This provides the first demonstration of depth-resolved elastic-property tomography from multimode guided-wave transmission with excitation and reception confined to a single physical plate surface. With full three-dimensional propagation and finite-width transduction, the reconstruction retains the compact-target positions with a whole-image correlation of 0.899 against a matched acquisition-limited reconstruction. These simulation results demonstrate that higher-order guided-wave mode conversion can provide local depth-resolved elastic-property tomography from surface-access measurements, with potential for characterising early-stage damage such as fatigue.

发表机构

• Department of Mechanical Engineering, Imperial College London（帝国理工学院机械工程系）

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