Boundary Shape Inversion of Two-Dimensional Steady-State Heat Transfer System Based on Finite Volume Method and Decentralized Fuzzy Adaptive PID Control

Abstract

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.

Sequential Inverse Heat Conduction Problem in OpenFOAM

“…The inverse heat conduction problem (IHCP) comprises measurements of the internal or surface temperature of a heat conduction system and a subsequent numerical determination of the unknown thermal boundary conditions [1], initial temperature distribution [2], thermo-physical properties [3], boundary shape [4], internal heat sources [5] or the thermal contact conductance (TCC). Nowadays, the IHCP is useful in many engineering applications such as metallurgy [6], material processing [7], non-destructive testing [8], geometry optimization [9], nuclear physics [10], power engineering [11], manufacturing engineering [12], chemical engineering [13], nanotechnology [14], bioengineering [15], aerospace engineering [16], etc. The IHCP methodology frequently remains interchangeable between different application fields regardless of the unknown parameters.…”

Finite Volume Method for the Launch Safety of Energetic Materials

“…e finite volume method (FVM) is widely used in computational fluid dynamics [23][24][25][26][27][28]. In recent years, the finite volume method has been increasingly applied in the field of solid mechanics [29,30].…”

Joint estimation of Robin coefficient and domain boundary for the Poisson problem

“…There is a considerable amount of literature available, dealing with both theoretical and computational aspects of both the individual problems, i.e. estimation of the Robin coefficient or estimation of the domain shape, see e.g [1][2][3][5][6][7][8][9][10][11][12][13][14][15], as well as of the problem of joint estimation [16][17][18][19][20][21][22][23][24][25][26]. We also mention the works [27,28], in which a similar problem is considered using a generalized impedance boundary condition.…”

“…Current approaches to handling the shape estimation problem can be loosely separated into those which use boundary integral methods (such as the boundary element method), see e.g. [24][25][26], and those which use volume integral methods (such as the finite element method) [21,34,[42][43][44]. Both of these approaches, however, suffer from several limitations.…”