The mathematical-physical models and the neural network exploitation for time prediction of cooling down low range specimen

Abstract

The method exploits sufficient similarity between cooling down curves of individual specimens from the same material but when specimens vary in geometric shape. Time scale altering for individual specimens leads from practical point of view to coincidence of all curves with so called “general curve” for given material which is calculated from measured values by means of statistic methods. This operation can be denoted as a definition of time transformation coefficient ( TTC ) (for known specimens). If an artificial neural network learns itself to assign time transformation coefficient to known dimensions of specimens, it is then with sufficient accuracy able to determine time transformation coefficient even for specimens with different shapes, for which it has not been learnt. By backward time transformation is then possible to predict probable time course of the cooling down curve and accordingly also the moment of accomplishment of given temperature. To obtain more general results, when above mentioned exploration of TCC, coupling with the numerical solutions of partial differential equations of the heat fields together with their initial and boundary conditions solutions can be used. The initial conditions in the most cases are unique or they can be with the sufficient precision determined, whereas the boundary conditions of heat transfer equations are usually wary hard to set. So some potential methods of boundary conditions determining and some difficulties by their time behavior settings can be illustrated, too. The advantages of both methods can be mixed and sufficient speedy and accuracy solution may be got.