Optimal Estimation of Thermal Diffusivity in an Energy Transfer Problem

TL;DR

This paper develops an optimal estimation method for thermal diffusivity in a one-dimensional heat transfer problem, utilizing optimal design techniques to improve accuracy with noisy data.

Contribution

It introduces an optimal design approach to enhance the estimation accuracy of thermal diffusivity in a heat transfer model with noisy observations.

Findings

Optimal design improves estimation accuracy.

Robustness of estimates against noise levels.

Enhanced parameter estimation performance.

Abstract

This work focuses on determining the coefficient of thermal diffusivity in a one-dimensional heat transfer process along a homogeneous and isotropic bar, embedded in a moving fluid with heat generation. A first type (Dirichlet) condition is imposed on one boundary and a third type (Robin) condition is considered at the other one. The parameter is estimated by minimizing the squared errors where noisy observations are numerically simulated at different positions and instants. The results are evaluated by means of the relative errors for different levels of noise. In order to enhance the estimation performance, an optimal design technique is chosen to select the most informative data. Finally, the improvement of the estimate is discussed when an optimal design is used.