Inversion of Thermal Conductivity in Two-Dimensional Unsteady-State Heat Transfer System Based on Boundary Element Method and Decentralized Fuzzy Inference

Based on the boundary element method and the decentralized fuzzy inference algorithm, the thermal conductivity in the two-dimensional unsteady-state heat transfer system changing with the temperature is deduced. The more accurate inversion results are obtained by introducing the variable universe method. The concrete method is as follows: using experimental means to obtain the instantaneous temperature in the material or on the boundary, to determine the thermal conductivity of the material by solving the inversion problem. The boundary element method is used to calculate the regional boundary and internal temperature in the direct problem. With the inversion problem, the decentralized fuzzy inference algorithm is used to compensate for the initial guess of the thermal conductivity by using the difference between the temperature measurement and the temperature calculation. In the inversion problem, the influence of the initial guess of different thermal conductivities, different numbers of measuring points, and the existence of measurement errors on the results is discussed. The example calculation and analysis prove that, with different initial guesses, existence of measurement errors, and the number of boundary measurements decrease, the methods adopted in this paper still maintain good validity and accuracy.