Fit for purpose models for metrology: a model selection methodology

We describe a model selection methodology for partial differential equation (PDE) based models and show the results of applying it to a test problem derived from a model of the laser flash thermal diffusivity measurement technique. A methodology for comparing and choosing simplified models is of benefit to the model development process in metrology. It is assumed that the computational aim is not only to solve the model to obtain the results that the metrologist requires, but to ensure that the model is no more complex than necessary to achieve this and that results can be obtained in a reasonable time using the available computing resources. The advantage of the proposed method is that it avoids the need to solve directly the underlying complex model. We present the results of comparisons of four models of the laser flash problem and identify the further work needed to extend the approach to a wider range of problems and to identify suitable measures for comparing residuals.