3D Temperature Distribution Reconstruction in Furnace Based on Acoustic Tomography

3D temperature distribution measurement in a furnace based on acoustic tomography (AT) calculates temperature field through multipath acoustic time-of-flight (TOF) data. In this paper, a new 3D temperature field reconstruction model based on radial basis function approximation with polynomial reproduction (RBF-PR) is proposed for solving the AT inverse problem. In addition, the modified reconstruction method that integrates the advantages of the TSVD and Tikhonov regularization methods is presented to reduce the sensitivity of noise on perturbations with the ill-posed problems and improve the reconstruction quality (RQ). Numerical simulations are implemented to evaluate the effectiveness of the proposed reconstruction method using different 3D temperature distribution models, which include the one-peak symmetry distribution, one-peak asymmetry distribution, and two-peak symmetry distribution. To study the antinoise ability of our method, noises are added to the value of TOF. 3D display of reconstructed temperature fields and reconstruction errors is given. The results indicate that our model can reconstruct the temperature distribution with higher accuracy and better antinoise ability compared with the truncated generalized singular value decomposition (TGSVD). Besides that, the proposed method can determine the hot spot position with higher precision, and the temperature error of the hot spot is lower than the other compared methods.