We explore the use of fractional continuum models to perform 2D tomographic imaging of interest for applications to structural damage detection. Fractional models allow a more flexible approach to field transport simulations in inhomogeneous media and, under certain conditions, enable capturing physical phenomena that cannot be accounted for by integer order models. This study addresses the specific example of heat conduction in a two- dimensional inhomogeneous domain and the reconstruction of the internal parameters based on temperature boundary measurements. The field evolution is assumed to be governed by a fractional diffusion equation while the parameter identification problem is formulated in inverse form. The reconstruction is performed with respect to the characteristic parameters of the fractional model, with particular attention to the order of the derivative. Numerical results show that the inverse procedure correctly identifies the spatial location of the inhomogeneity and, to some extent, the order of the fractional model.
Salvatore Buonocore, Mihir Sen, and Fabio Semperlotti, "An application of fractional calculus to the tomographic identification of structural damage," Proc. SPIE 9803, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2016, 98030Y (Presented at SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring: March 22, 2016; Published: 20 April 2016); https://doi.org/10.1117/12.2219195.
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