Boundary estimation problems arising in thermal tomography

Abstract

Problems on the identification of two-dimensional spatial domains arising in the detection and characterization of structural flaws in materials are considered. For a thermal diffusion system with external boundary input, observations of the temperature on the surface are used in a output least-squares approach. Parameter estimation techniques based on the 'method of mappings' are discussed and approximation schemes are developed based on a finiteelement Galerkin approach. Theoretical convergence results for computational techniques are given and the results are applied to experimental data for the identification of flaws in thermal testing of materials.

Thermal-based damage detection in porous materials

“…We use a variational or weak formulation to avoid these concerns [7]. Let k p denote the thermal conductivity of the pores and k m denote that of the material.…”

“…There are numerous viable NDE methods including ultrasound, magnetic particle imaging, eddy current, acoustic emission, and radiology to mention a few [17]. These methods have been successfully developed for a large range of problems, particularly for homogeneous metallic structures [3]- [7]. Composite materials are lighter and stronger than metallic materials, however, are inherently nonhomogenous and often are fabricated with acceptable levels of porosity.…”

Structure Characterization with Thermal Wave Imaging

“…by using its surface temperature response to an external heating. Some recent work on this subject is detailed in [2], [3], [4] and [6].…”

Sensitivity equations for a size-structured population model

“…However, to the best of our knowledge, thus far there is no literature on sensitivity equations and the related analysis for size-structured population models. Sensitivity analysis of dynamical systems has drawn the attention of numerous researchers [1,6,9,10,11,13,14,15,16,17,20,24,25,27,28,35,38,40] for many years because the resulting sensitivity functions can be used in many areas such as optimization and design [16,26,27,34,38], computation of standard errors [9,10,19,21,36], and information theory [12] related quantities (e.g., the Fisher information matrix) as well as control theory, parameter estimation and inverse problems [5,8,9,10,11,40,41]. One of our motivations for investigating sensitivity for size-structured population models derives from our efforts reported in [7], where a shrimp biomass production system and a…”

“…Hence, the sensitivity analysis of u with respect to our model parameters is not readily carried out using either a semigroup or a variational approach because the domains of A and A * are dependent on the model parameters. It might be possible to apply the idea of the method of mappings employed in sensitivity analysis for optimal shape design problems (e.g., [5,22,23,26,34]), which deals with computation of derivatives with respect to shape variation. However, it is not a straightforward application to our problem since the domain here is an operator domain (functional domain) instead of a geometric domain as used in optimal shape design problems.…”