@article{banks_joyner_2019, title={ADAPTION OF AKAIKE INFORMATION CRITERION UNDER LEAST SQUARES FRAMEWORKS FOR COMPARISON OF STOCHASTIC MODELS}, volume={77}, ISSN={["1552-4485"]}, DOI={10.1090/qam/1542}, abstractNote={In this paper, we examine the feasibility of extending the Akaike Information Criterion (AIC) for deterministic systems as a potential model selection criteria for stochastic models. We discuss the implementation method for three different classes of stochastic models: continuous time Markov chains (CTMC), stochastic differential equations (SDE), and random differential equations (RDE). The effectiveness and limitations of implementing the AIC for comparison of stochastic models is demonstrated using simulated data from the three types of models and then applied to experimental longitudinal growth data for algae.}, number={4}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, H. T. and Joyner, Michele L.}, year={2019}, month={Dec}, pages={831–859} }
 @article{banks_joyner_wincheski_winfree_2002, title={Real time computational algorithms for eddy-current-based damage detection}, volume={18}, ISSN={["0266-5611"]}, DOI={10.1088/0266-5611/18/3/318}, abstractNote={In the field of nondestructive evaluation, new and improved techniques are constantly being sought to facilitate the detection of hidden corrosion and flaws in structures such as aeroplanes and pipelines. In this paper, we explore the feasibility of detecting such damage by application of an eddy-current-based technique coupled with reduced order modelling. We begin by developing a model for a specific eddy current method in which we make some simplifying assumptions reducing the three-dimensional problem to a two-dimensional problem (we do this for proof of concept). Theoretical results are then presented which establish the existence and uniqueness of solutions as well as continuous dependence of the solutions on the parameters which represent the damage. We further discuss theoretical issues concerning the least squares parameter estimation problem used in identifying the geometry of the damage. To solve the identification problem, 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. In constructing these computational methods, we employ reduced order proper orthogonal decomposition (POD) techniques. This approach permits one to create a set of basis elements spanning a data set consisting of either numerical simulations or experimental data. We discuss two different algorithms for forming the POD approximations, a POD/Galerkin technique and a POD/interpolation technique. Finally, results of the inverse problem associated with damage detection are given using both simulated data with relative noise added as well as experimental data obtained using a giant magnetoresistive sensor. The experimental results are based on successfully using experimental data to form the POD basis elements (instead of numerical simulations), thus illustrating the effectiveness of this method on a wide range of applications. In both instances the methods are found to be efficient and robust. Moreover, the methods were fast; our findings demonstrate a significant reduction in computational time.}, number={3}, journal={INVERSE PROBLEMS}, author={Banks, HT and Joyner, ML and Wincheski, B and Winfree, WP}, year={2002}, month={Jun}, pages={795–823} }
 @article{banks_joyner_wincheski_winfree_2000, title={Nondestructive evaluation using a reduced-order computational methodology}, volume={16}, ISSN={["0266-5611"]}, DOI={10.1088/0266-5611/16/4/304}, abstractNote={This paper uses eddy current based techniques and reduced-order modelling to explore the feasibility of detecting subsurface damage in structures such as air foils and pipelines. To identify the geometry of the 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 techniques. For proof of concept, we implement the methodology on a 2D problem and find the methods to be efficient and robust even with data containing 10% relative noise. Furthermore, the methods are fast: our findings suggest we can reduce the computational time on average by a factor of 3000.}, number={4}, journal={INVERSE PROBLEMS}, author={Banks, HT and Joyner, ML and Wincheski, B and Winfree, WP}, year={2000}, month={Aug}, pages={929–945} }
 @article{banks_durso_goodhart_joyner_1998, title={On the radio-frequency inputs in dipolar heating of adhesives}, volume={33}, DOI={10.1080/08327823.1998.11688380}, abstractNote={The form of the radio-frequency (RF) or dielectric input expression in the heat equation which arises in the modeling of the curing of epoxy adhesives in bonding of composites was considered. Two standard derivations of a commonly used expression for the RF heating source term were reviewed. In this context difficulties involving the associated inherent polarization assumption and asymptotic behavior of dielectric parameters as a function of the frequency of the RF signal were discussed. These difficulties cast doubt on the validity of the standard RF expression. Two standard polarization models (Debye and Lorentz) then were used to demonstrate how one can systematically derive general RF heating expressions which do not suffer the inconsistencies that arise in the standard RF expression.}, number={4}, journal={Journal of Microwave Power and Electromagnetic Energy}, author={Banks, H. T. and Durso, S. R. and Goodhart, M. A. and Joyner, M. L.}, year={1998}, pages={231–242} }