Research On The Inverse Scattering Problem With A Crack Based On Machine Learning

The crack inversion problem has a wide range of applications in real life,such as medical imaging and nondestructive detection.Due to the strong ill-posedness and non-linearity of the crack inversion problem,it brings a great challenge to the numerical solution of this problem.Currently,the commonly used numerical solution methods are iterative and non-iterative methods.The iterative method has accurate inversion results but low computational efficiency;the non-iterative method has high computational efficiency but poor inversion effect.Therefore,to explore a numerical calculation method with low computational complexity and high reconstruction accuracy for the crack inversion problem has become one of the important contents of scholars’ research.In the crack scattering direct problem we use PML technique and Finite element method to solve direct scattering problem of the crack and obtain the scattered-field data.Consider reconstructing the shape and location of cracks in the crack inversion problem,For the far-field data generated at the full-aperture and the limit-aperture,we constructed a sequence-to-sequence neural network model,which uses each component of the far-field data to extract the far-field information corresponding to the cracks,obtains the feature vector containing the crack shape information,and then further inverse the extracted features into the crack shape parameters.Meanwhile,in order to continuously optimize the network,the loss function in this paper is chosen as the mean square error function,namely the crack shape parameters predicted by the network are made mean square error with their true values,and the Adam algorithm is used to iteratively update the network weights during the training process.Finally,the trained model is used to inverse the shape parameters of the crack,namely the parameters of the crack boundary curve equation,and then reconstruct the shape of the crack,which overcomes the difficulty of inversion due to the singularity of the two tip points of the crack.The numerical experiments in this paper consider fixing a single incident wave in the full aperture,and then observing the far-field data under the conditions of full aperture and limit-aperture.The results show that the application of neural network method can reconstruct the shape of cracks more accurately under different observed apertures;when multiple cracks exist or when only phaseless far-field data can be obtained,the shape can also be reconstructed,and when noise is added to the data set,the reconstruction effect is acceptable as long as the noise level is within a certain interval,namely the error between the predicted cracks and the real cracks is not large.