Based on the finite difference method and the artificial bee colony algorithm, the thermal conductivity in the two-dimensional unsteady-state heat transfer system is deduced. An improved artificial bee colony algorithm (IABCA), that artificial bee colony algorithm (ABCA) coupled with calculated deviation feedback, is proposed to overcome the shortcomings of insufficient local exploitation capacity and slow convergence rate in the late stage of the artificial bee colony algorithm (ABCA). For the forward problems, the finite difference method (FDM) is used to calculate the required temperature value of a discrete point; for the inverse problems, the IABCA is applied to minimize the objective function. In the inversion problem, the effects of colony size, number of measuring points, and the existence of measurement errors on the results are studied, and the inversion convergence rate of IABCA and ABCA is compared. The results demonstrate that the methods adopted in this paper had good effectiveness and accuracy even if colony sizes differ and measurement errors exist; and that IABCA has a more efficient convergence rate than ABCA.

A shape identification scheme was developed to determine the geometric shape of the inaccessible parts of two-dimensional objects using the measured temperatures on their accessible surfaces. The finite volume method was used to calculate the measured point’s temperature in the forward problem. In the inversion problem, the decentralized fuzzy adaptive Proportion Integral Differential (PID) control (DFAC) algorithm was used to compensate for the inversion boundary by using the difference between the measurement temperature and the calculation temperature. More accurate inversion results were obtained by introducing the weighted and synthesized normal distribution. In the inversion problem, the effects of the initial guess, the number of measuring points, and the measurement error were studied. The experiment calculation and analysis showed that the methods adopted in this paper still maintain good validity and accuracy with different initial guesses and decrease the number of measuring points and the existence of measurement errors.