Inverse methods and parameter estimation. Part 1

Inverse techniques are defined as methods for tracing unknown causes or influencing variables by observing their consequences. By their very name, they are opposed to "direct" methods.

We can illustrate the difference between direct and inverse methods by taking an example from mechanics: we know how to calculate the velocity at any instant of a material point of mass m subjected to a known force, if its initial position and velocity are given (this is the direct problem). One of the corresponding inverse problems is as follows: from the measurement of the positions (or velocities) of this material point, how can we "trace back" to the force that set it in motion?

These inverse problem-solving methods and their applications are currently being developed in various areas of physics. Generic tools exist for all fields, as do appropriate methodologies that go beyond mathematical formalism alone. These make it possible to revisit the experiment-model relationship.

We're going to look at reverse engineering from the point of view of the inverter's objective. Indeed, it is the latter that will dictate its approach. This approach has been developed within the thermal engineering community, see in particular the work [8][9] of the METTI Group of the Société Française de Thermique.

These inverse techniques are the subject of two dossiers [AF 4 515] and [AF 4 516] which are not independent of each other. Please refer to [Doc. AF 4 516] for bibliographical references.