A PENALTY FUNCTION METHOD FOR SHAPE IDENTIFICATION OF 2-D FLAW BASED ON LIMITED SCATTERING SIGNALS
有限散射信号下二维缺陷形状识别的罚函数方法

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.