有限散射信号下二维缺陷形状识别的罚函数法

A PENALTY FUNCTION METHOD FOR SHAPE IDENTIFICATION OF 2-D FLAW BASED ON LIMITED SCATTERING SIGNALS

研究在有限照射角度和频带宽度下二维缺陷的形状识别问题．首先，通过引进介质参数 扰动函数，建立介质参数扰动函数和弹性波散射场之间的非线性关系，并将所关心的缺陷的形 状识别问题转化为关于扰动函数的反演；然后，利用变分技术和优化方法求解，为了弥补散射 数据的不足，在总的目标函数中，采用附加度量函数作为罚函数；最后，对后场散射远场测量 时有限照射角度和频带宽度下几种典型缺陷进行了模拟识别，表明了罚函数法的有效性．

This paper focuses specifically on means of solving the underdetermined problem of limited scattering data inversion. Firstly, by introducing perturbation function of medium parameter, a set of integral equation formulation of elastic wave scattering of 2-D flaw is derived, in which two integral equations are solved for the unknown perturbation function and wave field, given the incident field and scattering data as input. In view of the nonlinear relation between the perturbation function and wave field, variational techniques are applied to find a solution to these equations, and a scheme for regularizing the underdetermined inversion of elastic wave scattering data is further presented which fills in unavailable data such that the boundary of the reconstructed flaw is minimized. This inversion technique is called as a penalty function method. Finally, a lot of identification results are presented for the case of far field measurements taken over limited angular apertures and limited frequency bandwidths. The numerical simulations show that the method presented here is effective in estimating the geometry of discontinuous boundary scattering objects. The demonstrated effectiveness of the regularization suggests possible utility in applications such as nondestructive evaluation for cracks and voids, and the identification of submerged structures.