Estimation of distributed thermal boundary based on fuzzy clustering of temperature observable points

Abstract

In the inverse heat transfer problem, the reasonable allocation and placement of temperature measurement points is the key to the successful retrieve of thermal condition. For the inverse problems of heat transfer process with irregular heat transfer domain, the reasonable selection scheme of representative measurement points in temperature observable space is studied in this paper, and a selection mechanism of representative temperature measurement points based on fuzzy clustering technology is established. Firstly, based on dynamic response coefficients of heat transfer system, the characteristic vectors of temperature observable points to thermal boundary conditions of heat transfer system is constructed, and then the fuzzy partition of temperature observable domain is conducted by the fuzzy c-means (FCM) clustering of temperature characteristic vector. Furthermore, the categories of observable points are clearly defined by the defuzzification according to the principle of maximum membership degree. The spatial location of representative measurement points can be determined according to the shortest distance principle between the clustering center and the temperature observable points. Based on the obtained representative measurement points and the model predictive estimation algorithm, the estimation of the distributed thermal boundary conditions in heat transfer process with irregular heat transfer domain is realized. The validity of the above optimal placement scheme is verified by numerical simulation experiments, and comparison with the uniform measurement point allocation scheme is also conducted. The results show that the estimation results based on clustering of observable points are significantly better than those based on the uniform measurement point allocation scheme. In addition, under the same estimation accuracy, the established allocation scheme of the measurement points in this paper significantly reduces the dependence of the estimation results on the number of measurement points.