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

Hua Liu,Jiang Wang,Yanjun Duan,Jian Li,Zhongcan Chen,Zuo Chen,Xingzhou Zhang,Caobing Wei,Xue Chen,Nan Ren

doi:10.3390/en14206593

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.

Highlights

Participating medium is widely presented in many engineering fields, such as aerospace engineering, energy and power systems, and information communications.The conductive and radiative properties of participating medium can be determined from transient temperature measurements by solving an inverse problem [1,2,3]
We ‘simulated’ the measurements by using the output of the forward model with the values measurements by usingparameters the output to of the forward model with the the actual of the unknown be retrieved, and the measurements were actual values corrupted of the unknown parameters to be retrieved, and the measurements were by Gaussian noise with a mean and standard deviation of zero
We proposed a stochastic Cramér–Rao bound-based consuming Monte Carlo simulations, and it was shown that the method was able to d numerical methodology to estimate the error of the conductive and radiative properties termine, a priori, the error of the retrieved parameters

Summary

Introduction

The conductive and radiative properties of participating medium can be determined from transient temperature measurements by solving an inverse problem [1,2,3]. This procedure consists of comparing the measured temperatures to the responses predicted from combined conductive and radiative heat transfer simulation [4,5,6,7]. The experimental measurements are noise-free and the predictions perfectly reflect the reality; the conductive and radiative properties may be precisely recovered. There is a crucial need to investigate the uncertainties of the recovered properties in the inverse scheme, and to make efforts to improve the accuracy of the retrieved parameters

Objectives

Methods

Results

Conclusion