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Details of Grant 

EPSRC Reference: EP/W000873/1
Title: Transient tomography for defect detection
Principal Investigator: Lesnic, Professor D
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Applied Mathematics
Organisation: University of Leeds
Scheme: Standard Research - NR1
Starts: 01 October 2021 Ends: 30 September 2022 Value (£): 75,994
EPSRC Research Topic Classifications:
Continuum Mechanics Non-linear Systems Mathematics
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
22 Mar 2021 EPSRC Mathematical Sciences Small Grants Panel March 2021 Announced
Summary on Grant Application Form
The ability to locate, estimate the size and shape, along with the properties of a hidden defect concealed in an exterior enclosure is of importance to the sectors of Security (landmine detection or detecting explosive material or illicit substances in vehicles stationary or in motion), Energy (detecting underground pipe blockages or, monitoring the structural integrity of a reactor while reducing human exposure in harmful and hostile environments), Health (detecting anomalies/ tumours/viruses), etc. Unlike similar tomographic techniques, e.g., electrical impedance/ resistive/capacitance tomography, which are stationary methods, time-dependent tomography uses transient data information to detect hidden defects which may be static or moving in time. In comparison with its stationary boundary potential + current flux formulation, the transient boundary temperature + heat flux formulation provides more temporal information to retrieve the unknown physical properties of the defect that is imaged. As such, the proposed research enhances non-destructively monitoring the integrity of structures, and practically it can be used to detect foreign obstacles concealed inside other objects.

Any tomography technique has at its heart a difficult inverse problem that needs to be solved, hence the mathematical analysis on the well- or ill-posedness of the model is necessary to be undertaken for scientific justification, as well as to be able to improve it. Difficulties arise due to the non-existence, non-uniqueness or the instability of solution, and establishing the degree of ill-posedness of the operator that needs inverting, is non-trivial. Moreover, concerning the actual inversion, to detect buried/hidden objects based on the transient approach one has to solve a difficult nonlinear and ill-posed moving boundary problem, which leads to a non-convex multi-dimensional optimization that needs to be further regularized to achieve stable results.

The thermographic principle of taking surface temperature measurements as we dynamically heat or cool an object offers an interesting transformative idea, but the approach is yet to be tested in an uncontrolled environment, and current understanding of the applicability of the technique to industrial scenarios is yet to be apprehended. Therefore, this mathematical modelling project using thermal-waves will provide a solid platform on which improved instrumentation for imaging can be built. The adventure of the research is to verify and validate the appropriateness of the new model by inverting both numerically simulated and experimental data in order to ultimately become available for real life application.
Key Findings
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Organisation Website: http://www.leeds.ac.uk