Photothermal radiometry parametric identifiability theory for reliable and unique nondestructive coating thickness and thermophysical measurements

Abstract

In this paper, we present a detailed reliability analysis of estimated parameters to a three-layer theoretical model of photothermal radiometry frequency domain signals by applying parameter identifiability conditions from two steel samples coated with ∼10 μm and 20 μm thick ceramic coating, to measure the thermophysical parameters of the coating, such as thermal diffusivity, thermal conductivity, and coating thickness. The three parameters are unique only when their sensitivity coefficients are linearly independent over the range of measurements. The study demonstrates the complexity of the identifiable experimental conditions through identifiability maps (calculated nonidentifiable locations) and sensitivity coefficient plots, even when the three separated parameters are grouped into two parameters. The validation of the reliability analysis theory by comparing the independently measured, with the fitted thicknesses of two coatings under random and optimized conditions, underscore the great importance of identifiability analysis (sensitivity coefficient plots) in the design of experiments for reliable parameter extractions, especially when the number of parameters is greater than the measurement data channels.