拓展导热逆问题原理测算物体导热系数方法的最优化问题再探讨

Optimization Analysis for Determining the Heat Conductivity of a Solid by Developing IHCP Principle

对拓展导热逆问题原理测算物体导热系数方法的最优化问题进行了更广泛、深入的研究，揭示了敏感度系数Ｘｋ＋、Ｘｈ＋的变化规律，得到了最优化判别式和判据。实验测算中，探讨并确定了实测环境与条件、参数优选及最优化测算程序。对于导热系数ｋ值数量级为１０－２～１０Ｗ／（ｍ·℃）的三种不同试材测量与计算结果表明，本方法所测算的ｋ值与传统方法所测值相比，相对误差在１．５９％～４．００％之内：而本方法简单、可靠且适应性广；借助于计算机，求解过程亦较准确迅速。

Based on the present researches the optimization is investigated for the method of determining the heat conductivity published in 1982. The results of theory analysis and calculation reveal the variation pattern and influence factors of the sensitivity coefficients and and some optimization criterion equations are obtained.The experimental circumstances and conditions, procedure of the real measurement and calculation are executed and studied in the experiments of this paper. The results also indicate that the relative deviation between the deterimined value of k got by this method and by others is within 1 .50%￣4% for three meterials which k varying from 10-2 to 10W/(m℃) in order of magnitude when optimization steps done. Comparing with other methods, this measurement process is more simply and more reliably, the calculation of this method is more accurately and more quickly. All above results not only promote the development of the abbreviatin of inverse heat conduction problem (IHCP) theory but also make a firm base for the application of this method.