Uncertainty in Damage Detection, Dynamic Propagation and Just-in-Time Networks

Abstract

We report significant findings in three distinct areas of investigation: I. Uncertainty Quantification: Propagation and Stochastic Systems; II. Numerical Interface Methods; III. Non-smooth Variational Problems and Inverse Methods. Topics investigated include effects of different types of delays on the dynamics of stochastic systems; the performance of different methods for quantifying parameter uncertainty due to measurement error: asymptotic theory, bootstrapping, and Bayesian estimation; very general optimal design problem for the selection of best states to observe and optimal sampling times and locations (i.e., selections of what, when, and where to observe) for parameter estimation or inverse problems involving complex nonlinear partial differential equation, ordinary differential equation and/or delay differential equation systems; the identification of thermal degradation using probabilistic models in reflectance spectroscopy; optimal control based ideas (bang-bang system stimulation) for enhancing the information content and minimizing related estimated parameter uncertainty in dynamic data sets; high order compact finite difference schemes for Helmholtz equations with discontinuous wave numbers across interfaces; numerical sensitivity analysis with respect to the Reynolds number for the flow past obstacle problems; efficient, 3D fast Poisson solver for bio-molecular simulations; adaptive Cartesian method for Immersed Boundary (IB) and Immersed Interface Method (IIM) for elliptic interface problems and for two phase flows with moving interfaces; efficient numerical methods for non-smooth variational problems; staggered-grid based ed central finite difference scheme is developed for Stokes and Navier-Stokes equations and Maxwell equations; probing methods for inverse medium problems, including electric impedance tomography and the diffusive optical tomography.

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Document Details

Document Type
Technical Report
Publication Date
Aug 03, 2015
Accession Number
ADA621658

Entities

People

  • Harvey T. Banks
  • Kazufumi Ito
  • S. Hu
  • Zheng Li

Organizations

  • North Carolina State University

Tags

Communities of Interest

  • Biomedical
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force Research Laboratories
  • Algorithms
  • Applied Mathematics
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Damage Detection
  • Differential Equations
  • Equations
  • Inverse Problems
  • Navier Stokes Equations
  • Partial Differential Equations
  • Probabilistic Models
  • Probability
  • Statistical Algorithms
  • Statistical Analysis
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Nanoscale Plasmonic Nanotechnology

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms