Research On The Obstacle Inverse Problem Based On Broad Learning System

Obstacle reconstruction problems are widely found in various fields such as medical imaging,military radar detection,remote sensing technology in aerospace and non-destructive testing in industry.Due to the strong ill-posedness of obstacle reconstruction,theoretical analysis and numerical solution are difficult.There are two numerical methods to solve obstacle reconstruction problems:direct method and indirect method.Generally speaking,direct methods are with less computational complexity and poorer inversion accuracy;Indirect methods are with high inversion accuracy and relatively higher computational complexity.Therefore,scholars are devoted to a numerical method with less computational complexity for accurate inversion of obstacles.In this paper,a method based on Random Forest-Broad Learning System inversion method（RF-BLS）is proposed for the inversion of impenetrable obstacles in a two-dimensional time-harmonic uniform medium.Firstly,the sampling method is used to obtain partial information of the obstacle,and the shape and position of the obstacle are represented by Fourier coefficients.Then,the random forest is used to classify the shape and position,and the classified data set is substituted into the width learning system for training.Finally,the trained model is used to inverse the shape parameters.In the numerical experiments,RF-BLS model can accurately reconstruct the shape of obstacles;When the far-field data contain noise,the model can still ensure that the mean square error of the retrieved shape parameters is small;Secondly,we also compare the RF-BLS model with the single-layer LSTM network（SPIMNNG）.The results show that the model proposed in this paper not only ensures the calculation accuracy,but also needs one thousandth of the training time of SPIMNNG method;At the same time,considering the observation in limited aperture in the more challenging case,the effect of RF-BLS model on obstacle reconstruction is still good.As to the inversion of the shape and location of impenetrable obstacles at the same time,the broad learning and Naive Bayes are combined to construct a parameter reversion model for re-constructing the shape and location of obstacles,or namely the Naive Bayes Broad Learning System（NB-BLS）for inversion of geometric parameters of obstacles.Firstly,using the sampling method,the Fourier expansion form of obstacles is obtained,in which the Fourier coefficient is the shape and position parameters of obstacles,and the training set is classified according to the shape parameters by Naive Bayes;Secondly,the Broad Learning System is used to construct the geometric parameter inversion model of impenetrable obstacles,and then the trained parameter inversion model is used to reconstruct the shape and position of obstacles.The numerical experiments show that NB-BLS model can accurately reconstruct the shape and position of obstacles,and this method is effective in solving the problem of obstacle inversion with noise in far-field data.In the case of limited aperture,the mean square error of geometric parameters retrieved by this method is less than10^-2,and the training time is short.