3D reconstruction of temperature field using Gaussian Radial Basis Functions (GRBF)

3D temperature field reconstruction is of practical interest to the power, transportation and aviation industries and it also opens up opportunities for real time control or optimization of high temperature fluid or combustion process. In this paper, a new algorithm for the reconstruction of 3D temperature field is proposed based on Gaussian Radial Basis Functions (GRBF). A 3D temperature field is a space distribution profile evolving over time which is infinite dimensional in nature, the proposed GRBF-based approach can approximate the temperature field as a finite summation of space-dependent basis functions and time-dependent coefficients. According to the acoustic pyrometry principle, these Gaussian functions are integrated along a number of paths which are determined by the number and distribution of sensors. This inversion problem to estimate the unknown parameters of the Gaussian functions can be solved with the measured times-of-flight (TOF) of acoustic waves and the length of propagation paths using the recursive least square method (RLS). Compared with polynomial interpolation and functions parameterization, GRBF provides better approximation capability for most nonlinear functions over irregular regions. It is also superior in scalability and more efficient when extended to higher dimensional space. The simulation result shows an error less than 2% between the reconstructed temperature field and the ideal one. It demonstrates the availability and efficiency of GRBF framework for temperature field reconstruction.