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Title: Characterization of a random anisotropic conductivity field with Karhunen-Loeve methods

Abstract

While parametric uncertainty quantification for NDE models has been addressed in recent years, the problem of stochastic field parameters such as spatially distributed electrical conductivity has only been investigated minimally in the last year. In that work, the authors treated the field as a one-dimensional random process and Karhunen-Loeve methods were used to discretize this process to make it amenable to UQ methods such as ANOVA expansions. In the present work, we will treat the field as a two dimensional random process, and the eigenvalues and eigenfunctions of the integral operator will be determined via Galerkin methods. The Karhunen-Loeve methods is extended to two dimensions and implemented to represent this process. Several different choices for basis functions will be discussed, as well as convergence criteria for each. The methods are applied to correlation functions collected over electron backscatter data from highly micro textured Ti-7Al.

Authors:
 [1];  [2]; ;  [3]
  1. University of Dayton Research Institute, Structural Integrity Division, 300 College Park, Dayton, OH 45469-0020 (United States)
  2. Victor Technologies, LLC, PO Box 7706, Bloomington, IN 47407-7706 (United States)
  3. Air Force Research Labs, Materials and Manufacturing Directorate, 2230 10th St., WPAFB, OH 45433 (United States)
Publication Date:
OSTI Identifier:
22263752
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1581; Journal Issue: 1; Conference: 40. annual review of progress in quantitative nondestructive evaluation, Baltimore, MD (United States), 21-26 Jul 2013, 10. international conference on Barkhausen noise and micromagnetic testing, Baltimore, MD (United States), 21-26 Jul 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANISOTROPY; CORRELATION FUNCTIONS; EIGENFUNCTIONS; EIGENVALUES; ELECTRIC CONDUCTIVITY; ELECTRONS

Citation Formats

Cherry, Matthew R., Sabbagh, Harold S., Pilchak, Adam L., and Knopp, Jeremy S. Characterization of a random anisotropic conductivity field with Karhunen-Loeve methods. United States: N. p., 2014. Web. doi:10.1063/1.4864996.
Cherry, Matthew R., Sabbagh, Harold S., Pilchak, Adam L., & Knopp, Jeremy S. Characterization of a random anisotropic conductivity field with Karhunen-Loeve methods. United States. doi:10.1063/1.4864996.
Cherry, Matthew R., Sabbagh, Harold S., Pilchak, Adam L., and Knopp, Jeremy S. Tue . "Characterization of a random anisotropic conductivity field with Karhunen-Loeve methods". United States. doi:10.1063/1.4864996.
@article{osti_22263752,
title = {Characterization of a random anisotropic conductivity field with Karhunen-Loeve methods},
author = {Cherry, Matthew R. and Sabbagh, Harold S. and Pilchak, Adam L. and Knopp, Jeremy S.},
abstractNote = {While parametric uncertainty quantification for NDE models has been addressed in recent years, the problem of stochastic field parameters such as spatially distributed electrical conductivity has only been investigated minimally in the last year. In that work, the authors treated the field as a one-dimensional random process and Karhunen-Loeve methods were used to discretize this process to make it amenable to UQ methods such as ANOVA expansions. In the present work, we will treat the field as a two dimensional random process, and the eigenvalues and eigenfunctions of the integral operator will be determined via Galerkin methods. The Karhunen-Loeve methods is extended to two dimensions and implemented to represent this process. Several different choices for basis functions will be discussed, as well as convergence criteria for each. The methods are applied to correlation functions collected over electron backscatter data from highly micro textured Ti-7Al.},
doi = {10.1063/1.4864996},
journal = {AIP Conference Proceedings},
number = 1,
volume = 1581,
place = {United States},
year = {Tue Feb 18 00:00:00 EST 2014},
month = {Tue Feb 18 00:00:00 EST 2014}
}
  • By computing the Karhunen-Loeve decomposition (KLD) correlation length {xi}{sub KLD} of a reaction-diffusion system in the extensive chaos regime, we show that it is a sensitive measure of spatial dynamical inhomogeneities. It reveals substantial spatial nonuniformity of the dynamics at the boundaries and can also detect slow spatial variations in system parameters. The intensive length {xi}{sub KLD} can be easily computed from small local subsystems and is found to have a similar parametric dependence as the two-point correlation length computed over the full system size. (c) 2000 The American Physical Society.
  • We show that the number of KLD (Karhunen-Loeve decomposition) modes D{sub KLD} needed to capture a fraction f of the total variance of an extensively chaotic state scales extensively with subsystem volume V. This allows a correlation length {xi}{sub KLD} to be defined that is easily calculated from spatially localized data. We show that {xi}{sub KLD} has a parametric dependence similar to that of the dimension correlation length and demonstrate that this length can be used to characterize high-dimensional inhomogeneous spatiotemporal chaos. {copyright} {ital 1997} {ital The American Physical Society}
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