ABSTRACT
The difficulty every researcher approaching a physical phenomenon faces is choosing the model that best suits the requirement. For this purpose, knowledge of the parameters and=or the functions of modeling is imperative. These data can, indeed, be obtained not
only in the literature but also by way of inverse techniques. In an inverse problem, we have information (measurements of temperatures, heat flux, deformations, etc.) which are the effects of the causes we try to estimate. It is, thus, a question of identifying the laws of physics that we study. Although the inverse techniques apply to all the domains of physics, we discuss only the problems of heat diffusion here. In this chapter, we particularly emphasize the quality of the measurements, which is
constantly necessary to try to obtain. Figure 16.1 summarizes the usually followed inverse and direct approaches. We find five types of estimation errors. If we do not take the effects of coupling between these various terms into account, the global error can be defined as the sum of these types of errors:
eg ¼ e1 þ e2 þ e3 þ e4 þ e5: (16:1)
The direct problem is only a mathematical image of our experiment. If the hypotheses made for the definition of this problem are not relevant to the experiment, an error e1 can lead us to a nonrealistic estimation. Furthermore, the resolution of the direct problem appeals to various methods. The calculated answer is more or less different from the exact answer required by the model. The errors of resolution (error of numerical scheme connected to the steps of time, to the steps of space, and to the precision of the computer) will lead to an error e2 of estimation. The first two errors generally occur during the modeling of a phenomenon for which we
do not completely know the physics, in particular in the case of coupling between several domains (heat conduction, electricity, phase change, etc.). Other errors for the inverse
3 is an resulting from objectives of the experiment=reverser. The composed questions are as follows:
1. Do we have some knowledge of the shape of the law that we want to estimate?
