A METHOD FOR SOLVING THE OBSERVATION PROBLEM FOR A NONSTATIONARY TEMPERATURE-FIELD (A LINEAR CASE)

The functioning of many modern technical objects is followed by intens ive heat flows. In a number of cases, it becomes necessary to observe the object's current heat state in order to control it further. Since the heat conduction equation is applied as a model of the process of h eat conduction, the observation is reduced to the solution of the inve rse problem for this equation in a real (or close to real) time mode. In this paper, the observation algorithm for a nonstationary temperatu re field of a one-dimensional object is proposed. This algorithm is ba sed on a procedure of solving the inverse heat conduction problem that is formulated on a small time interval that precedes the current inst ant. The source problem is reduced to an algebraic form and regularize d by the Tikhonov method. When a solution is constructed on the basis of a small sample of observations, it is shown that the application of methods for choosing a regularization parameter, widely used in the p ractice of solving ill-posed problems, does not lead to satisfactory r esults. Therefore, the source problem and the algorithm of its solutio n are interpreted as a digital filter, and optimal values of all param eters that affect the accuracy of estimation are chosen on the basis o f analysis of the corresponding transfer functions and a priori inform ation related to the measurement error and the boundary heat action.