Switch Search Direction Algorithm versus GN and LM Parameter Estimation Algorithms in Modeling Inverse Heat Transfer Problem

Abstract

The SSDPE method is a robust parameter estimation technique which minimizes the error. Modeling inverse heat transfer is estimating values of parameters of a mathematical model from measured data. A governing differential equation, its boundary and initial conditions are used to derive the solution, and then the solution is coupled with an efficient parameter estimation algorithm to search for the unknown thermal parameters. The SSDPE technique was developed to couple with a Green’s function solution of a biological system to estimate three unknown parameters [1]. A Green’s function solution is combined from superimposing all finite effects caused by the applied forcing function; such as, step-, ramp-, or pulsed- function. The common nonlinear least squares techniques are hard or impossible to couple with this kind of nonlinear discontinued solution. The preciseness of a parameter estimation technique can be measured from its ability to minimize the random noise effect on the estimated results. Therefore, the SSDPE is compared with two known methods. The three techniques are investigated with different levels of random noise added on top of the simulated measured data. This paper validates the ability of the SSDPE to estimate parameters by testing the method versus the Gauss-Newton, and the Levenberg Marquardt estimation techniques.