Advanced uncertainty evaluation: example and software for industrial uptake

Short Name: TBCUnc, Project Number: 15SIP05
Image showing mathematical equations on blackboard
Mathematical equations on blackboard

Applying novel uncertainty evaluation software to refine measurements of thermal conductivity of layered coatings

The confidence provided by known uncertainties for measured values offers competitive advantages in industry. For example, measurement uncertainty values for heat transfer modelling improves design decision-making in materials processing, food manufacturing, power generation, and aerospace sectors. However, reliable results require reliable material property data, that can be hard to obtain, particularly for operations at high or low temperatures.

The EMRP project Uncertainty developed methods to calculate measurement results and associated uncertainties for situations requiring considerable computational resources, such as finite element analysis in design processes.

New methods were put to the test for measurements of thermal conductivity of thermal barrier coatings (TBCs). Here, measurement uncertainty is important for determining whether a coating design provides adequate protection, but the layered nature of TBCs complicates these measurements, typically leaving uncertainties to be estimated using approximate methods.


This project promoted and demonstrated the new probabilistic method.

Measurements of thermal diffusivity were shown to be suitable, and estimates made for the thermal conductivities of individual layers of a TBC system. Recommendations in Guide to the Expression of Uncertainty in Measurement (GUM) Supplement 1 were followed.

The uncertainty evaluation method was applied to historical data to obtain uncertainty estimates using input uncertainty estimates. The resulting best estimate of thermal conductivity of the topcoat was higher than expected.

To automate the mathematically challenging aspects of these calculations, this project developed a freely available  software package for the uncertainty evaluation methodology. This software enables users to estimate thermal conductivities and associated uncertainties of parts of layered systems by matching the predictions of a model to values measured using a laser flash thermal diffusivity experiment. Outputs include mean, standard deviation and cumulative distribution function for thermal conductivity, and correlations between input and conductivity


The EMPIR project Hi-TRACE, builds on this work by enabling simulation of layered material systems with de-bonds and poor thermal bonds and establishing the thermophysical properties of any solid material up to 3000 C.

By supporting reliable measurement practices, this project advanced understanding of high-temperature materials and supported development of innovative materials in industries such as power generation and aeronautics.


Participating EURAMET NMIs and DIs
LNE (France)
NPL (United Kingdom)