Stochastic-Integral Models for Propagation-of-Uncertainty Problems in Nondestructive Evaluation (Preprint)

Abstract

Generalized polynomical chaos (gPC) and the probabilistic collocation method (PCM) are finding considerable application to problems of interest to engineers in which random parameters are an essential feature of the mathematical model. So far the applications have been mainly to stochastic partial differential equations, but we extend the method to volume-integral equations, which have met great success in electromagnetic nondestructive evaluation (NDE), especially with eddy-currents. The problems of main interest to the NDE community in this connection are concerned with the issue of 'propagation of uncertainty' when the relevant parameters are not well characterized, or are known simply as random variables. We demonstrate the ideas by considering a metallic surface that has undergone a shot-peening treatment to reduce residual stresses, and has, therefore, become a random conductivity field.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2012
Accession Number
ADA564985

Entities

People

  • Elias H. Sabbagh
  • Harold A. Sabbagh
  • Jeremy Knopp
  • John C. Aldrin
  • Mark P. Blodgett
  • R. K. Murphy

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Air Force
  • Air Force Research Laboratories
  • Computational Science
  • Conductivity
  • Differential Equations
  • Eddy Currents
  • Equations
  • Integral Equations
  • Integrals
  • Mathematical Models
  • Military Research
  • Models
  • Partial Differential Equations
  • Probability
  • Random Variables
  • Shot Peening
  • Surface Finishing

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Structural Health Monitoring of Composite Structures.