Application of grey prediction to inverse nonlinear heat conduction problem

The purpose of this research is to estimate the thermal conductivity with the inverse method which is modified by grey prediction; herein the thermal conductivity is a nonlinear function. When the thermal conductivity is the function of position and temperature, if one would try to obtain the thermal conductivity with the inverse method, then the measuring points of the temperature shall be distributed in whole object, consequently there would be a large number of measuring points for the relevant temperatures. The method of grey prediction will be able to dramatically decrease the number of measuring points for the temperature accordingly. However, the method of grey prediction should be accompanied with the prediction errors, thus the estimation of inverse method will produce a major deviation. This paper adopts the methods of the “rolling grey prediction” and the “comparison of temperature measurement” to correct the errors of grey prediction, and then proceed the inverse method to estimate the thermal conductivity. The estimated value obtained by the proposed method and the actual value compares very well.