Incorporation of measurement models in the IHCP: validation of methods for computing correction kernels

Abstract

Thermocouples or other measuring devices are often imbedded into a solid to provide data for an inverse calculation. It is well-documented that such installations will result in erroneous (biased) sensor readings, unless the thermal properties of the measurement wires and surrounding insulation can be carefully matched to those of the parent domain. Since this rarely can be done, or doing so is prohibitively expensive, an alternative is to include a sensor model in the solution of the inverse problem. In this paper we consider a technique in which a thermocouple model is used to generate a correction kernel for use in the inverse solver. The technique yields a kernel function with terms in the Laplace domain. The challenge of determining the values of the correction kernel function is the focus of this paper. An adaptation of the sequential function specification method[1] as well as numerical Laplace transform inversion techniques are considered for determination of the kernel function values. Each inversion method is evaluated with analytical test functions which provide simulated "measurements". Reconstruction of the undisturbed temperature from the "measured" temperature and the correction kernel is demonstrated.