Research On Temperature Field Reconstruction Algorithm Based On Ill-condition Improvement

The temperature field reconstruction technology of Computer Tomography(CT)requires the placement of multiple acoustic transceivers around the measured layer to form multiple acoustic lines.The distribution of sound slowness(the reciprocal of sound speed)in the target area is calculated by measuring the flight time of sound waves in each sound line and the appropriate reconstruction algorithm.The temperature distribution is obtained by using the relationship between sound speed and temperature.The technology has the advantages of no interference with the measured temperature field,strong adaptability to the environment,low cost,convenient maintenance,real-time monitoring and so on,which is favored by academia and industry.The reconstruction algorithm is an important factor to determine the accuracy of temperature field reconstruction in acoustic CT.The more grids divided in the measured layer,the stronger the ability to describe the complex temperature field.However,a large number of grids usually correspond to a large number of invalid grids that are not traversed by acoustic lines,which will significantly increase the morbidity of the reconstruction matrix and further affect the reconstruction accuracy.This thesis studies the reconstruction algorithm based on the improved ill-condition of inverse matrix,so as to obtain higher accuracy of temperature field reconstruction.The main work completed in this thesis can be summarized as follows.The principle of acoustic CT temperature field reconstruction is described,and two typical temperature field reconstruction algorithms,least square method(LSM)and direct regularization method based on singular value decomposition(svd DR),are introduced,and the common temperature field error evaluation indexes are given.A temperature field reconstruction algorithm based on principal component analysis(PCA)dimensionality reduction is proposed.Firstly,the radial basis function is used to approximate the complex acoustic slowness distribution,and the forward problem model of acoustic CT is established.Then PCA was used to reduce dimension to improve the pathology of the inverse problem.Then the inverse problem is solved by iterative regularization method,and the temperature distribution is obtained.The simulation results show that compared with LSM method and svd DR method,the reconstructed image of Pca IR method is closer to the real temperature distribution.Taking the three-peak complex temperature field as an example,the root mean square errors are reduced by 49.36% and27.04%,respectively.A temperature field reconstruction algorithm based on improved regularization matrix is proposed,which is referred to as Irm IR algorithm.First,the radial basis function is used to approximate the acoustic slowness distribution,and the forward problem model is established.Then,the mean square error matrix corresponding to ridge estimation is inverted and its diagonal elements are taken to form an improved regularization matrix.Then the inverse problem is solved by iterative regularization method,and the temperature distribution is obtained.The simulation results show that compared with LSM and svd DR,the reconstructed image of Irm IR method is closer to the real temperature distribution.Taking the three-peak complex temperature field as an example,the root mean square errors are reduced by 49.06% and 34.31%,respectively.An experimental system was built,three temperature fields were formed by electric heater,and the temperature fields were reconstructed by the above four algorithms.Compared with the Kelvin temperature obtained by thermocouple,the average hot spot temperature errors corresponding to LSM,svd DR,Pca IR and Irm IR methods are respectively 0.34%,0.35%,0.11% and 0.02%,which again verifies that Pca IR and Irm IR methods have better reconstruction performance.