Strategic games in thermophysical studies under uncertainties

Yu.F.Gortyshov, V.I.Ivanov

Kazan State Technical University named after A.N.Tupolev

K.Marx str, 10, 420111, Kazan, Russia

 

The aim of this work is to establish a possibility of applying the theory of matrix game theory, more specifically, the theory of strategic games (games with nature) to thermo-physical studies in the presence of uncertainties.

We show the necessity for "mathematization" of researcher's behavior to reduce or even eliminate any probability of influence of the distinguishing features of a subject of study upon the final results of research or development.

The presence of uncertainties makes it possible to look on the investigation as being a conflict. In this connection, it should be noted that there does not exist any optimal settlement of the conflict aroused.

Nonetheless, it is possible to work out and apply for these purposes the optimal strategy of researcher's behavior that guarantees for him, regardless of his/her partner's actions, a minimal loss or a maximal win. By the term "partner" we shall mean from here the "nature".

In this paper, we shall consider some examples of using the strategic game theory in solving the coefficient inverse problem of heat conduction (IPHC).

In these examples, we solve some problems connected with proper arrangement of temperature sensors (when solving IPTSs) and selection of calculating and measuring data for their subsequent processing.

The use of the strategic game theory only in three herein-considered examples allows:

-         to arrange the temperature sensors optimally (when solving IPHCs);

-         to correct TS locations ( inљ case of temperature sensors misplacement)

-         to point out to an increase of the probability of successful IPTS solution, if a set of sensors are installed;

-         toљ retain a possibility of successful IPTS solution when using only one sensor or, at proper preparation of experiments, without their multiple replications.

-         to make use of the calculated and experimental data more properly and completely for their subsequent processing without a significant increase of labor intensity, and, hence, without cost of studies.

By and large, this paper proves a possibility of successful application of the theory of strategic games in developing the optimal strategies of thermo-physical studies in the presence of uncertainties.