This paper uses eddy current based techniques and reduced order modeling to explore the feasibility of detecting a subsurface damage in structures such as air foils and pipelines. To identify the geometry of a damage, an optimization algorithm is employed which requires solving the forward problem numerous times. To implement these methods in a practical setting, the forward algorithm must be solved with extremely fast and accurate solution methods. Therefore, our computational methods are based on the reduced order Karhunen-Loeve or Proper Orthogonal Decomposition POD techniques. For proof-ofconcept, we implement the methodology on a 2-D problem and nd the methods to be e cient and robust even with data containing 10 relative noise. Furthermore, the methods are fast; our ndings suggest we can reduce the computational time on average by a factor of 3000.

This paper explores the feasibility of detecting damage within structures such as air foils by application of eddy current based techniques and reduced order modeling. To identify the geometry of a damage, an optimization algorithm is employed which requires solving the forward problem numerous times. Therefore, the forward algorithm must be solved with extremely fast and accurate solution methods. In constructing these forward methods, we employ reduced order Proper Orthogonal Decomposition (POD) techniques.The POD technique is a method which creates an "optimal" ordered basis in the sense that information captured in the first few basis elements is maximized. One then uses a fixed number (based on a quantitative formula for percentage energy captured) of the first few basis elements, called the reduced POD basis, in the forward algorithm. Since one uses only a small number of basis elements, one is able to create a fast forward algorithm that accurately represents the relevant information.In this paper, for illustrative purposes and proof-of-concept, we consider rectangular "cracks" parameterized by a vector parameter q representing the length, thickness, depth, center, etc. of the damage. We attempt to recapture the parameters of a damage assuming we have access to the magnetic flux density B . Our analysis uses simulated data perturbed with normally distributed noise to represent corrupted experimental data. When recapturing the length and thickness of a damage using the component of the magnetic flux density orthogonal to the eddy current flow in the sample, the methods are shown to be efficient and robust even with data containing 10% relative noise.

In this review we discuss methodology to ascertain the amount of information in given data sets with respect to determination of model parameters with desired levels of uncertainty. We do this in the context of least squares (ordinary, weighted, iterative reweighted weighted or “generalized”, etc.) based inverse problem formulations. The ideas are illustrated with several examples of interest in the biological and environmental sciences.

In this paper, we develop a stochastic differential equation model to simulate the movement of a social/subsocial spider species, Anelosimus studiosus, during prey capture using experimental data collected in a structured environment. In a subsocial species, females and their maturing offspring share a web and cooperate in web maintenance and prey capture. Furthermore, observations indicate these colonies change their positioning throughout the day, clustered during certain times of the day while spaced out at other times. One key question was whether or not the spiders spaced out ``optimally'' to cooperate in prey capture. In this paper, we first show the derivation of the model where experimental data is used to determine key parameters within the model. We then use this model to test the success of prey capture under a variety of different spatial configurations for varying colony sizes to determine the best spatial configuration for prey capture.

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