Evaluation of Computational Parameters of the Levenberg-Marquardt Method for Solving Inverse Heat Conduction Problems in Heat Flux Prediction

Abstract

Most of the inverse problems are ill conditions in which the numerical solution has the potential to become unstable. This paper discusses the Inverse Heat Conduction Problem for 2D thin plate structures. By using the temperature measurement data, the Levenberg-Marquardt Method is applied to predict the heat flux. The efficacy of this method was tested using synthetic data where the temperature measurement error was assumed to be small. The evaluation gives the result that whatever the initial values of the computational parameters (flux guess, damping coefficient and finite difference step) have no significant effect on the final results. The solution tends to be stable. The deviation of the calculation results is satisfying, less than 1% compared to the ideal heat flux. Experimentally, the Levenberg-Marquardt Method has also been applied to predict flux at 3 different heater flux levels. For fluxes with a nominal power of 6, 17 and 37 Watts, the errors are 5.2%, 0.8% and 6.1%, respectively, compared to experimental reference values. These errors are still acceptable.