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 lm and 20 lm 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.

Response to “Comment on ‘Photothermal radiometry parametric identifiability theory for reliable and unique nondestructive coating thickness and thermophysical measurements’” [J. Appl. Phys. 122, 066101 (2017)]

“…Phys. 122, 066101 (2017)] X. Guo, A. Mandelis, J. Tolev, and K. Tang In our recent article, 5 we investigated the application of identifiability theory to reliable and unique thermophysical measurements using thermal waves. The comparison of photothermal and independent measurements of coating thicknesses underscores the great importance of identifiability analysis (sensitivity coefficient plots) in the design of experiments for reliable parameter extractions.…”

Comment on “Photothermal radiometry parametric identifiability theory for reliable and unique nondestructive coating thickness and thermophysical measurements” [J. Appl. Phys. 121, 095101 (2017)]

“…Guo et al 1 recently presented what they consider "a detailed reliability analysis of estimated parameters to a three-layer theoretical model of photothermal radiometry frequency domain signals by applying parameter identifiability conditions". The model they used for representing the photothermal radiometry experiment and the dynamic temperature of the material front surface is a one-dimensional four-layer model: the air layer and the substrate layer are semi-infinite and a coating of thickness 2 L , diffusivity 2  and conductivity 2  is associated with a thin "roughness layer"; all three solid layers are considered opaque.…”