A decentralized fuzzy inference method for the inverse geometry heat conduction problem

This paper studies an inverse internal geometry problem with two-dimensional heat conduction system by using the boundary element method (BEM) and fuzzy inference method (FIM). BEM is utilized to solve the direct heat conduction problem for the assumed inner shape in advance, and a set of fuzzy inference units is established to obtain a set of fuzzy inference components by the deviations between the computed temperature and measured temperature. Finally, the fuzzy inference components are weighted and synthesized to gain the compensations of inner shape. Numerical experiments are carried out to analyze the performance of two weighted ways, and the effects of initial guesses of inner geometry shape, the number of measured point and measurement errors on the inversion results are discussed respectively by comparing the inversion results of the conjugate gradient method (CGM). For the inverse geometry boundary heat conduction problem researched by this paper, the results show that compared with the CGM, FIM can significantly reduce the dependence of the inversion results on the number of measured point and improve the anti-interference ability on measurement errors, which has better anti ill-posed characteristic.