Validation of Methods for Computing Correction Kernels
Jonathan W. Woolley, Howard B. Wilson and Keith A. Woodbury
International Conference on Inverse Problems in Engineering
Dourdan (Paris), France, June 15 - 19, 2008
This article is available from the publisher here.
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 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.
