基于超声导波逆散射理论的板结构微小缺陷定量重构方法研究

The ultrasonic guided wave is one of the promising tools for non-destructive testing & evaluation. But getting information of flaws from scattered signals faces difficulty due to the multi-mode and dispersive properties of guided waves. The widely-used pitch-catch or pulse-echo methods can locate the positions of flaws but fail to describe their sizes, shapes and severities. The diffraction tomography technique can only tell approximate ranges of thinning flaws on a single-layer plate, and is difficult to be extended into multi-layered cases due to theoretical limitations. On the other hand, the inverse scattering approach has been well developed in the inverse reconstruction using electro-magnetic waves, seismic waves and ultrasonic bulk waves. However, its usage in guided wave cases has rarely been seen due to theoretical and practical complexities. The research proposes a methodology of quantitative inverse reconstruction for flaws in plate structures, such as surface thinnings, inner cavities, and delaminations of multi-layer plates. The method starts from accurate elastodynamic wave equations; and expresses the scattered guided wave field as a boundary/volume integral equation of the flaw; then obtain the linearized or iterative inversion forms by introducing proper mathematical approximations. The method stands on a firm theoretical background, makes full use of scattered field information within a broad-band frequency range, and produces accurate images of minor flaws. As a new quantitative non-destructive testing technique, the proposed method is innovative and has prospective applications in the future.

超声导波是一种极具潜力的无损检测工具。然而现有pitch-catch和pulse-echo等方法仅能定位缺陷，难以定量重构；而衍射层析成像法也存在理论限制。另一方面，逆散射理论已被应用于求解电磁波、地震波和超声体波的反问题，惟尚未推广至较复杂的超声导波场。本项目拟开发一种基于逆散射理论，利用超声导波，对板类结构中表面减薄、内部孔洞、层合板脱层等微小缺陷进行定量化重构成像的方法。基于弹性波动方程，通过数学推导，将波数域的散射波场信息表示为关于板结构中微小缺陷的边界或体积分方程式；然后通过引入合理的近似，得到缺陷重构的线性化逆散射重构格式，以及精度更高的逐次迭代格式；并开展数值和实验验证。本项目系首次针对超声导波研究基于三维弹性波动方程的逆散射方法；该法充分利用宽频带散射波场信息；对于微小缺陷成像具有较高的精度；直观描绘缺陷位置和形态。作为一种定量无损检测新方法，具有原创性和应用前景。

超声导波是一种极具潜力的无损检测工具。然而现有pitch-catch和pulse-echo等方法仅能定位缺陷，难以定量重构；而衍射层析成像法也存在理论限制。本项目拟开发一种基于弹性波逆散射理论，利用超声导波，对板类结构中表面减薄、内部孔洞、层合板脱层等微小缺陷进行定量化重构成像的方法。研究主要从四个方面进行了探索。(1) 导波的传播机理分析和弥散曲线计算方面：提出了一种基于模值收敛的模态弥散曲线跟踪搜索算法，具有良好的普适性，可推广至多层、各向异性波导结构。此外，我们还在此基础上研究了如何将弥散曲线散点图按模态分离的算法。(2) 导波的散射正问题计算方面：提出了用修正边界元计算导波遇缺陷后的散射场的正问题计算方法。将远端散射场的导波形式代入边界单元法的基本表达式，可有效消除因边界截断而导致的虚假回波，求得近场波动场和远场散射系数，并显著提高计算效率，为反问题的研究提供了理论基础和数据准备。(3) 导波对波导结构内部和表面微小缺陷进行重构的反问题方面：通过理论推导，证明了缺陷的几何特征函数和波数域反射系数之间的数学关系，从而可以定量化重构缺陷的位置、形状和严重程度。目前，已将此方法应用于平板表面和内部缺陷，多层板层间孔洞类缺陷，薄壁管表面轴对称形式减薄缺陷的定量化检测。(4) 对反问题算法进行实验，研究了随机环境噪声对缺陷重构影响，研发相关电磁超声导波激发换能器，以及建立超声导波实验系统。