An Inverse Analysis for Parameter Estimation Applied to a Non-Fourier Conduction–Radiation Problem

Abstract

Retrieval of parameters in a non-Fourier conduction and radiation heat transfer problem is reported. The direct problem is formulated using the lattice Boltzmann method (LBM) and the finite-volume method (FVM). The divergence of radiative heat flux is computed using the FVM, and the LBM formulation is employed to obtain the temperature field. In the inverse method, this temperature field is taken as exact. Simultaneous estimation of parameters, namely, the extinction coefficient and the conduction-radiation parameter, is done by minimizing the objective function. The genetic algorithm (GA) is used for this purpose. The accuracies of the estimated parameters are studied for the effects of measurement errors and genetic parameters such as the crossover and mutation probabilities, the population size, and the number of generations. The LBM-FVM in combination with GA has been found to provide a correct estimate of parameters.

Application of the hybrid particle swarm optimization algorithms for simultaneous estimation of multi-parameters in a transient conduction–radiation problem

“…To circumvent this issue, the intelligent optimization algorithms based on the population exhaustive search has been proposed to solve the ill-posed inverse heat transfer problems in recent years, such as the Genetic Algorithm (GA), the Particle Swarm Optimization (PSO), the Ant Colony Optimization (ACO), and the Neural Network Algorithm (NNA) [12][13][14][15][16][17][18][19]. A characteristic feature of these evolutionary search optimization methods is that they can solve the global optimal problem reliably and obtain high quality global solutions with enough computational time.…”

Nongray inverse boundary design problems in enclosures at radiative equilibrium

“…The inverse problems can be solved by the regularization (explicit) and optimization (implicit) methods . Optimization techniques can be classified as gradient‐based methods and heuristic or gradient‐free methods . In the gradient‐based methods, the local topography of the objective function is used to find a path toward the minimum point of the objective function, that is, by using the first and sometimes the second derivative of the objective function.…”

“…These kinds of problems are known as inverse problems. The inverse problems may be classified into two categories of "design" [1][2][3][4][5][6][7][8][9][10][11][12][13] and "identification" [14][15][16][17][18][19][20][21][22] problems. The inverse problems can be solved by the regularization (explicit) and optimization (implicit) methods.…”

“…11 Optimization techniques can be classified as gradient-based methods 4,8,10,23 and heuristic or gradient-free methods. 19,20,[24][25][26][27] In the gradientbased methods, the local topography of the objective function is used to find a path toward the minimum point of the objective function, that is, by using the first and sometimes the second derivative of the objective function. The heuristic or gradient-free methods use a constructed random sampling of the objective function over the entire feasible region to find the minimum point of the objective function.…”

Three-Parameter Estimation Study in a Radial Fin Geometry Using FDM-Based Simplex Method

“…The required temperature or heat flux distributions can be obtained either from experiments or by solving a forward problem using any computational fluid dynamics (CFD) techniques such as the FDM, the finite-element method, the finite-volume method, and so on. For the purpose of optimization, the suitable tools are the CGM [3,5], the LSM [4,6], the SSM [10,11], the GA [9,12,13], and so on. Additional details about the suitable optimization methods available for solving inverse problems can be found in reference [14].…”