Simultaneous estimation of temperature-dependent thermal conductivity and heat capacity based on modified genetic algorithm

Abstract

An inverse heat conduction analysis is presented to simultaneously estimate the temperaturedependent thermal conductivity and heat capacity based on a modified elitist genetic algorithm (MEGA). In this study, MEGA is used to minimize a least squares objective function containing estimated and simulated (filtered) temperatures. The estimated temperatures are obtained from the direct numerical solution (finite differences method, or FDM) of the finite one-dimensional conductive model by using an estimate for the unknown temperaturedependent thermophysical properties (TDTPs). The accuracy of the MEGA is assessed by comparing the estimated and the preselected TDTPs. The results of the MEGA are used as the starting point for a locally convergent optimization algorithm, i.e., the Levenberg-Marquardt (L-M) method. It is shown in this work that hybridization of the MEGA with the L-M method can lead to accurate estimates. From the results, it is found that the RMS error between estimated and simulated temperatures is very small irrespective of whether measurement errors are included or excluded. In addition to estimation of the TDTPs, sensitivity analysis is performed to investigate the effects of heating duration. Also, it is found that the results of the MEGA are highly satisfactory with only single-sensor measurements on the heated surface.

Optimization of experimental design for an inverse estimation of the metal-mold heat transfer coefficient in the solidification of Sn–10% Pb

“…(12) could conceivably be performed by any optimization technique. However, parameter estimation has generally been performed with only a few methods as reported Imani et al (2006). The use of one method over another is often specific to a certain field of study.…”

“…Inverse parameter estimation methods are based on the minimization of an objective function containing both estimated and measured temperatures reported by Beck and Arnold (1977) and Imani et al (2006). Ordinary least squares (OLS) estimator is by far the most frequently used method for the estimation of TDTPs as no prior knowledge is needed as Beck and Arnold (1977) and Imani et al (2006) reported. OLS estimator was considered in this research.…”

An inverse problem in estimation of interfacial heat transfer coefficient during two‐dimensional solidification of Al 5%Wt‐Si based on PSO

“…Al 5%Wt-Si four unknown parameters has called the fitness function 10 4 times (50 £ 200 ¼ 10 4 ) while almost the same case (four unknown parameters) needed fitness function 10 5 times (100 £ 1000 ¼ 10 5 ) by MEGA as demonstrated by Imani et al (2006) or 6 £ 10 4 times (80 £ 750 þ 80 £ 30 < 6 £ 10 4 ) by MEGA as demonstrated by Ranjbar et al, 2010. Since each fitness function's average CPU cost is 3 seconds, MEGA (Ranjbar et al, 2010) needs 40 more hours to reach the goal. This point has clearly shown the efficiency of the PSO even in its basic form.…”

Simultaneous Identification of Temperature-Dependent Thermal Properties via Enhanced Genetic Algorithm

“…The only problem of GAs is that the iterative solution can be time consuming, and in case of a new temperature measurement, a new genetic run is needed to solve the IHCP. GAs are successfully applied in all kinds of IHCPs; the estimated parameters or functions can be connected to the initial temperature [19], boundary condition [20][21][22][23][24][25], or material property [26][27][28][29][30][31][32][33]. In such cases, when an unknown function was estimated, the function was usually defined by data points instead of a formula.…”