Application of Grey Theory to estimate time-varyingheat sources on a long solid cylinder

• Main Authors: Chun-Kai Hsu, 許淳凱
• Other Authors: Ming-I Char
• Format: Others
• Language: zh-TW
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/cgi-bin/gs32/gsweb.cgi/login?o=dnclcdr&s=id=%22107NCHU5507023%22.&searchmode=basic

碩士 === 國立中興大學 === 應用數學系所 === 107 === In this research, Grey theory is applied to estimate the time-varying heat sources on a long solid cylinder. Controllable factors will be investigated and discussed on the results of experimental data produced by measuring points, measuring errors and different changes with/without smoothing points. This study applied the grey predictive model (Grey model, GM(1,1)) introduced by professor Ju-long Deng in 1982 as a research method to estimate the distribution of the heat source. The characteristic of a grey prediction model can be established as long as there is a small amount of data (experimental data). For the researchers in designing the experiment, the process is quite convenient. The analytic form of the measured temperature is loaded into the simulated software, added the measuring errors, and obtained the inverse solutions. In this article, three different types of the time-varying heat sources will be discussed. The results show that the grey prediction model can improve the accuracy of the unknown heat source. In the third type of the heat source function with a trigonometric distribution, the influence of the grey prediction model is insensitive with a smaller measuring error; however, it is significant with a larger measuring error. Overall, the grey theory can effectively reduced measuring error and obtained the better prediction results. It is a very important reference value for researchers in the field of inverse engineering.