Fuzzy Adaptive Regularization Method for Inverse Steady-State Heat Transfer Problem

Abstract

For the steady-state heat transfer process, a fuzzy adaptive regularization method (FARM) is proposed to estimate the distributed thermal boundary condition in heat transfer system. First, the relationship model between temperatures at measurement points and parameters to be estimated is established based on sensitivity matrix. The regularization term is introduced into the least-squares objective function, and then the distributed thermal boundary condition is estimated by optimizing the new objective function. A fuzzy inference mechanism is developed to ensure the adaptive ability of FARM in which the regularization parameter is updated based on the residual norm between calculated and measured temperatures at measurement points and the norm of inversion parameters. Taking the plate heat conduction system and fluid–solid conjugate heat transfer system as research objects, the effects of the parameter distribution, the number of measurement points, and measurement errors on the inversion results are discussed by numerical experiments, and comparison with the classical regularization method is also conducted. Results indicate that FARM exhibits a good adaptive ability.