Physical Insight into System Identification Parameters Applied to Inverse Heat Conduction Problems

Abstract

This paper compares the noninteger system identification method to an analytic formulation of transient inverse heat conduction containing a spatially lumped temperature sensor model for extracting physical meaning to noninteger system identification parameters. The two-sided noninteger system identification expansion coefficients are compared term-by-term to the resulting analytic model in the semi-infinite geometry. This physically motivated equivalence suggests which noninteger system identification expansion coefficients are dominant and should be retained for producing the best identification from a physical point of view. The analytical results are compared to an idealized one-dimensional semi-infinite noninteger system identification case with the goal of correlating parameters and obtaining their physical meaning. It is shown that one parameter is connected to the effusivity of the system in use, which substantiates that there is a physical meaning for the noninteger system identification parameters. The parameters on the temperature side are connected to the thermocouple time constant and thermocouple lead losses. In this study, the effusivity value has been examined. With a numerical simulation, the sensitivity is analyzed, showing that the comparison gives reasonable effusivity values. In a laboratory experiment using copper, the measured effusivity is , which is in favorable agreement with the nominal value .