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

[+] Author and Article Information
Kun Wang

School of Energy and Power Engineering, Chongqing University, Chongqing400044, PR China; College of Mechanical and Power Engineering, Chongqing, University of Science and Technology, Chongqing, 401331, PR China

Guangjun Wang

School of Energy and Power Engineering, Chongqing University, Chongqing400044, PR China; Key Laboratory of Low-grade Energy Utilization Technologies and Systems (Chongqing University), Ministry of Education, Chongqing 400044, P. R. China

1Corresponding author.

ASME doi:10.1115/1.4042462 History: Received June 16, 2018; Revised December 18, 2018


For steady-state heat transfer process, a fuzzy adaptive regularization method (FARM) is proposed to estimate distributed thermal boundary condition in the heat transfer system. First, the relationship model between temperatures at measurement points and parameters to be estimated is established through sensitivity matrix. Introducing regularization term into least-squares objective function, then, the distributed thermal boundary condition is estimated by optimizing the new objective function. Based on fuzzy inference theory, a fuzzy inference mechanism is established, which performs fuzzy inference according to the residual norm between calculated and measured temperatures at measurement points and the norm of unknown parameters, and updates the regularization parameter of the inverse method to ensure the adaptive ability of FARM. Taking the plate heat conduction system and fluid-solid conjugate heat transfer system as research objects, the effects of the distribution of parameters, 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 has a good adaptive ability.

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