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A ROBUST AND EFFICIENT INVERSE MESHLESS METHOD FOR NON-DESTRUCTIVE THERMOGRAPHIC EVALUATION

DOI: 10.1615/ICHMT.2015.IntSympAdvComputHeatTransf.1660
pages 1719-1722

Eduardo Divo
Department of Mechanical Engineering, Embry-Riddle Aeronautical University, 600 S Clyde Morris Blvd, Daytona Beach, Florida, USA

Sandra Boetcher
Embry-Riddle Aeronautical University, Daytona Beach, FL, 32114

Jeff Brown
Department of Civil Engineering Embry-Riddle Aeronautical University, Daytona Beach, FL, USA

Alain J. Kassab
Department of Mechanical and Aerospace Engineering, University of Central Florida, 4000 Central Florida Blvd, Orlando, Florida, USA

Résumé

A novel computational tool based on the Localized Radial-basis Function (RBF) Collocation (LRC) Meshless method, capable of accurately and efficiently solving transient multi-dimensional heat conduction problems in composite and heterogeneous media is formulated and implemented. The LRC Meshless method is coupled with a Volume-of-Fluid (VoF) scheme for the purpose of modeling heterogeneities in the conducting media. While the LRC Meshless method lends its inherent advantages of spectral convergence and ease of automation, the VoF scheme allows to effectively and efficiently simulate the location, size, and shape of cavities, voids, inclusions, defects, or de-attachments in the conducting media without the need to regenerate point distributions, boundaries, or interpolation matrices. To this end, the Inverse Geometric problem of Cavity Detection is formulated as an optimization problem that minimizes an objective function that computes the deviation of measured temperatures at accessible locations to those generated by the LRC-VoF Meshless method. The LRC-VoF Meshless algorithms is driven by an optimization code based on the Genetic Algorithms (GA) technique which can effectively search for the optimal set of design parameters (location, size, shape, etc.) within a predefined design space. Initial guesses to the search algorithm are provided by the classical 1D semi-infinite composite analytical solution which can predict the approximate location of the cavity. The LRC-VoF formulation is tested and validated through a series of controlled numerical experiments. This approach allows solving the onerous computational inverse geometric problem in a very efficient and robust manner while affording its implementation in modest computational platforms, thereby realizing the disruptive potential of this multi-dimensional high-fidelity non-destructive evaluation (NDE) method.

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