Research On Conjugate Gradient Algorithm In Electromagnetic Tomography

Electromagnetic tomography technology(EMT)is a process detection technology developed in recent 30 years,which has the advantages of non-invasive,low cost,high real-time performance,strong adaptability and simple structure.The technology is based on the principle of electromagnetic induction can be conductive or magnetic conductive material online detection,so as to achieve image reconstruction.At present,it has been widely used in industry,medicine,transportation,food and other fields.In addition,with the rapid development of industry,production efficiency and real-time requirements in industrial production are increasing,so EMT technology also needs to be improved.EMT problems are mainly divided into positive and inverse problems.The positive problem is to obtain the inductive electrical signals generated by the excitation signals of the object field through the sensor array.The inverse problem is to reconstruct the spatial distribution of object field according to the obtained data.The conjugate gradient algorithm is used to realize image reconstruction in inverse problem,the advantages of this algorithm and other algorithms are analyzed and compared,and the spectral parameter conjugate gradient algorithm and hybrid conjugate gradient algorithm are designed and implemented.A typical disturbance model is established in the simulation system,and the convergence,image quality and correlation of the algorithm are compared.It is concluded that the spectral parameter conjugate gradient algorithm and the hybrid conjugate gradient algorithm have higher quality of reconstructed image.In this paper,Comsol simulation software is used to establish the object field space of 16 coils,in which the coils are evenly arranged around the object field according to the "O" shape,forming a fan-shaped object field.The interior of EMT system is a soft field,so there are many unsteadiness and instability in EMT problem.In order to improve this situation,the finite element method is used to divide the object field,and the modified sensitivity matrix is obtained by normalization.The inverse problem is studied,the advantages and disadvantages of different reconstruction algorithms are introduced,and the algorithm formula suitable for EMT system is given.These algorithms are used for image reconstruction of three disturbance models,and the results show that conjugate gradient algorithm has good reconstruction effect and fast convergence speed.The comparison shows that the reconstruction effect of the conjugate gradient algorithm is good and the convergence speed is fast.It is proved from the convergence rate and time that nonlinear conjugate gradient algorithm is more suitable for the study of EMT inverse problem.The iterative process of nonlinear conjugate gradient algorithm is more stable and the reconstructed image quality is higher,but the image accuracy is slightly lower than Tikhonov and Landweber algorithms.In order to improve the image accuracy and correlation of nonlinear conjugate gradient algorithm,two modified conjugate gradient algorithms are proposed.A new spectral parameter is proposed in the first modified algorithm,which improves the search direction by controlling the Angle between the old and new search directions,and searches for the optimal solution according to the judgment of each iteration.The results are as follows: in different models,the image reconstructed by modified spectral conjugate gradient algorithm has higher quality and better numerical performance,but the convergence time is similar to that of traditional conjugate gradient algorithm.In the second modification method,the conjugate parameters of FR algorithm and PRP algorithm are mixed in a certain proportion to obtain a new conjugate parameter.This algorithm combines the advantages of fast convergence of FR algorithm and good numerical performance of PRP algorithm.As can be seen from the results,the convergence speed of hybrid conjugate gradient algorithm is faster than PRP algorithm,and the image quality is higher than PRP algorithm and FR algorithm,which combines the advantages of the two algorithms and has higher applicability.The comparison experiments of the two modified conjugate gradient algorithms show that the convergence effect and numerical performance are better.