Application of Grey Prediction to Inverse Heat Transfer Problems

• Main Authors: Jaw-Yeong Chiang, 江照勇
• Other Authors: Cha`o-Kuang Chen
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/66221404697119960269

博士 === 國立成功大學 === 機械工程學系碩博士班 === 96 === This article applies Grey Prediction Method of Grey System Theory to improve the problem of errors in inverse operation due to the error of temperature measurement when analyze Inverse Heat Transfer Problems (IHTP) with Reversed Matrix Method. For IHTP, this research adopted Revered Matrix Method with Linear Least-squares Error Method to construct a linear inverse model. With finite difference method, we discretized governing equation that is designed to solve IHTP to construct a linear matrix equation. Through the re-arrangement of matrix equation, the unknown conditions (such as initial conditions, boundary conditions, thermal property or geometrical shape) could be demonstrated clearly and independently. Then substitute a small amount of successive measuring points temperature into the linear inverse model and solve the problems by Linear Least-squares Error Method. The process of inverse operation only need to measure a small amount points temperature to estimate the solution of IHTP, but in practical measurement of temperature, the errors of measurement of temperature are inevitable. Such errors will affect the accuracy of estimation value of inverse operation or even lead to an erroneous results. One of improvement method is to increase the number of temperature measurement points. Certainly, more accurate results of inverse operation we want to obtain, the number of measurement points we should increase. Therefore, this research uses the Grey Prediction Method to improve the defect with a hope that significant reduction of the number of practical temperature measurement points could also obtain the same accurate results of inverse operation. The small amount of direct temperature measurement points can increase to more amount of temperature points by Grey Prediction Method, and the temperatures of those increased points could still keep the correlations with previous temperatures from direct measurement. The increased number of temperature points could replace the number of temperature points that is necessary to increase for inverse operation. In other words, Grey Prediction Method could significantly reduce the number of practical temperature measurement points while keep the same accuracy as the results of inverse operation using a great number of direct temperature measurement points.