Optimal Experimental Design for Inverse Identification of Conductive and Radiative Properties of Participating Medium

Abstract

The conductive and radiative properties of participating medium can be estimated by solving an inverse problem that combines transient temperature measurements and a forward model to predict the coupled conductive and radiative heat transfer. The procedure, as well as the estimates of parameters, are not only affected by the measurement noise that intrinsically exists in the experiment, but are also influenced by the known model parameters that are used as necessary inputs to solve the forward problem. In the present study, a stochastic Cramér–Rao bound (sCRB)-based error analysis method was employed for estimation of the errors of the retrieved conductive and radiative properties in an inverse identification process. The method took into account both the uncertainties of the experimental noise and the uncertain model parameter errors. Moreover, we applied the method to design the optimal location of the temperature probe, and to predict the relative error contribution of different error sources for combined conductive and radiative inverse problems. The results show that the proposed methodology is able to determine, a priori, the errors of the retrieved parameters, and that the accuracy of the retrieved parameters can be improved by setting the temperature probe at an optimal sensor position.

Keywords

• conductive and radiative properties
• inverse problem
• error analysis
• stochastic Cramér–Rao bound (sCRB)
• experimental design