Identification of the Heat Flux in a Quasi-Static Thermoelastic System

This paper treats the problem of estimating the heat flux through the free end of a thermoelastic rod, which is allowed to come into contact with a rigid obstacle. This problem is motivated by the need to develop techniques for indirect measurement of heating in applications, such as, brake systems and machine tools. Under a quasi-static approximation, the problem becomes that of characterizing thermal processes in the rod. Assuming that direct and exact measurements at the contacting end of the rod cannot be taken, the problem is to determine if there is contact with the obstacle; and if there is contact, to characterize the conductivity processes at the contacting end. We study the case of weighted-average temperature measurements throughout the rod. Identifiability results and on-line recursive estimation procedures are developed.