Abstract
In this contribution we focus on recovery of spatial distribution of material parameters utilizing only non-invasive boundary measurements. Such methods has gained its importance as imaging techniques in medicine, geophysics or archaeology. We apply similar principles for non-stationary heat transfer in civil engineering. In oppose to standard technique which rely on external loading devices, we assume the natural fluctuation of temperature throughout day and night can provide sufficient information to recover the underlying material parameters. The inverse problem was solved by a modified regularised Gauss-Newton iterative scheme and the underlying forward problem is solved with a finite element space-time discretisation. We show a successful reconstruction of material parameters on a synthetic example with real measurements. The virtual experiment also reveals the insensitivity to practical precision of sensor measurements.
Highlights
Non-invasive methods are gaining increasing interest in various disciplines spanning from medicine to geophysics
Such process often requires a set of samples which do not have to be available and features a rather limited description of the studied material. In this contribution we propose a non-invasive parameter identification technique based merely on boundary observations of some structure. This idea was inspired by a medical imaging technique named Electric Impedance Tomography (EIT)
A single set of surface measurements for a given loading conditions might result in a number of possible conductivity fields, Calderón surpassed this problem by sequentially implying multiple loading conditions each followed by a measurement, which in essence has the potential to contain the complete information about the underlying conductivity distribution
Summary
Non-invasive methods are gaining increasing interest in various disciplines spanning from medicine to geophysics. Today trend is in favour of complex models described by multiple parameters which have to be properly identified from real measurements, often requiring a specially designed set destructive tests with a high precision laboratory equipment Such process often requires a set of samples which do not have to be available and features a rather limited description of the studied material. A single set of surface measurements for a given loading conditions might result in a number of possible conductivity fields, Calderón surpassed this problem by sequentially implying multiple loading conditions each followed by a measurement, which in essence has the potential to contain the complete information about the underlying conductivity distribution In this contribution we will employ similar techniques of Calderón inverse problem paradigm to a parabolic partial differential equation with two independent parameters to describe thermal properties of some structure. Our method is designed to be external loading-free, i.e. it completely relies on the environmental factors as a source of changes which are necessary in order to identify the material inside a domain
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