Reconstruction Of Temperature Field Based On Improved Tikhonov Regularization

Acoustic CT(Acoustic Computer Tomography)temperature field reconstruction technology is a temperature field measurement technology based on computer tomography.Compared with the traditional temperature measurement method,acoustic temperature measurement technology has the characteristics of wide measurement range,non-contact and real-time monitoring,and has obvious advantages in harsh,high temperature and complex environments.This technology has been successfully applied to atmospheric temperature field monitoring,industrial boiler temperature field monitoring and other fields.The application of this technology to monitor the temperature field of deep-sea hydrothermal vents and stored grain temperature field is also a representative application research.The successful application of acoustic CT temperature field reconstruction technology depends on the temperature field reconstruction algorithm to a great extent.This thesis mainly studies the reconstruction algorithm.Typical acoustic CT temperature field reconstruction algorithms can be divided into two categories.One is the reconstruction algorithm based on the length of sound rays in the grid,such as the least square method;The other is the reconstruction algorithm based on basis function approximation of sound velocity,such as Markov radial basis function & Tikhonov regularization method,which is called standard Tikhonov regularization method in this thesis.The advantage of standard Tikhonov regularization method is that the mesh section number of the measured area is not limited by the number of sound rays,and it is more suitable for the reconstruction of complex temperature field.However,the standard Tikhonov regularization method has the problems of over-correction and under-correction because it corrects all singular values with the same amplitude.Therefore,this thesis proposes an improved Tikhonov regularization reconstruction algorithm.By improving the filter function,a correction method is realized,in which the large singular value is not corrected,and the correction amplitude of the small singular value increases with the decrease of the singular value.The reconstruction results based on simulation data and measured data show that the improved Tikhonov regularization algorithm has better reconstruction ability of complex temperature field than the standard Tikhonov regularization algorithm.At present,most of the regularization parameters are selected by numerical experiments to determine an empirical value.Due to the large search range,it is difficult to balance speed and accuracy.To solve this problem,this thesis uses the root mean square error value of typical reconstructed temperature field to construct the optimization objective function of regularization parameters,and uses genetic algorithm to find the optimal solution.Simulation results show that the genetic algorithm can calculate the optimal regularization parameters under different noise environments,and the effect of temperature field reconstruction with the optimal solution as the regularization parameter is better than that of the regularization parameter selected by experience.Moreover,the reconstruction effect of the improved Tikhonov regularization algorithm is still better than that of the standard Tikhonov regularization algorithm when both the standard Tikhonov regularization algorithm and the improved Tikhonov regularization algorithm take their respective optimal solutions as regularization parameters.