# Developing Optimal Strategies for Structural Health Monitoring: Stochastic Inverse Methodologies for Interrogating Dielectric Materials Using Microwaves

17 Oct 2011-
TL;DR: In this paper, a stochastic inversion technique based on the Metropolis-Hasting algorithm was applied to the problem of quantitative nondestructive evaluation (QNDE) of material aging parameters.
Abstract: : The quantitative nondestructive evaluation (QNDE) of material aging parameters continues to be a very challenging problem. In our approach, we formulated a forward problem arising in specific micro guided wave test. A stochastic inversion technique based on the Metropolis-Hasting algorithm was applied to the problem. The feasibility and validity of the approach was demonstrated through computational experiments.
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TL;DR: Numerical experiments and numerical comparisons show that the PML technique works better than the others in all cases; using it allows to obtain a higher accuracy in some problems and a release of computational requirements in some others.

9,875 citations

### "Developing Optimal Strategies for S..." refers methods in this paper

• ...In order to prevent spurious reflections from the edge of the problem space, the perfectly matched layer (PML) is adopted to two dimensional domain ( See [13] for more details )....

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• ...(1), (3), and (4) into the finite differencing scheme results in the following difference equations: D n+1/2 3 [i, j] − D n−1/2 3 [i, j] ∆t = 1 √ 0µ0 { Hn2 [i + 1/2, j] − Hn2 [i − 1/2, j] ∆x1 −H n 1 [i, j + 1/2] − Hn1 [i, j − 1/2] ∆x2 } Hn+11 [i, j + 1/2] − Hn1 [i, j + 1/2] ∆t = − 1√ 0µ0 E n+1/2 3 [i, j + 1] − E n+1/2 3 [i, j] ∆x2 Hn+12 [i, j + 1/2] − Hn2 [i, j + 1/2] ∆t = − 1√ 0µ0 E n+1/2 3 [i + 1, j] − E n+1/2 3 [i, j] ∆x1 In order to prevent spurious reflections from the edge of the problem space, the perfectly matched layer (PML) is adopted to two dimensional domain ( See [13] for more details )....

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Book
01 Oct 1997
TL;DR: Model Adequacy Model Choice: MCMC Over Model and Parameter Spaces Convergence Acceleration Exercises Further topics in MCMC are explained.
Abstract: Introduction Stochastic simulation Introduction Generation of Discrete Random Quantities Generation of Continuous Random Quantities Generation of Random Vectors and Matrices Resampling Methods Exercises Bayesian Inference Introduction Bayes' Theorem Conjugate Distributions Hierarchical Models Dynamic Models Spatial Models Model Comparison Exercises Approximate methods of inference Introduction Asymptotic Approximations Approximations by Gaussian Quadrature Monte Carlo Integration Methods Based on Stochastic Simulation Exercises Markov chains Introduction Definition and Transition Probabilities Decomposition of the State Space Stationary Distributions Limiting Theorems Reversible Chains Continuous State Spaces Simulation of a Markov Chain Data Augmentation or Substitution Sampling Exercises Gibbs Sampling Introduction Definition and Properties Implementation and Optimization Convergence Diagnostics Applications MCMC-Based Software for Bayesian Modeling Appendix 5.A: BUGS Code for Example 5.7 Appendix 5.B: BUGS Code for Example 5.8 Exercises Metropolis-Hastings algorithms Introduction Definition and Properties Special Cases Hybrid Algorithms Applications Exercises Further topics in MCMC Introduction Model Adequacy Model Choice: MCMC Over Model and Parameter Spaces Convergence Acceleration Exercises References Author Index Subject Index

1,834 citations

Book
20 Jul 2000

1,169 citations

### "Developing Optimal Strategies for S..." refers methods in this paper

• ...The finite-difference time-domain method (FDTD) in two spatial dimensions can be implemented to construct the forward model [12]....

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01 Nov 1989
TL;DR: In this paper, the identification of two-dimensional spatial domains arising in the detection and characterization of structural flaws in materials is considered for a thermal diffusion system with external boundary input, observations of the temperature on the surface are used in a output least squares approach.
Abstract: Problems on the identification of two-dimensional spatial domains arising in the detection and characterization of structural flaws in materials are considered. For a thermal diffusion system with external boundary input, observations of the temperature on the surface are used in a output least squares approach. Parameter estimation techniques based on the method of mappings are discussed and approximation schemes are developed based on a finite element Galerkin approach. Theoretical convergence results for computational techniques are given and the results are applied to experimental data for the identification of flaws in the thermal testing of materials.

80 citations

Book
01 Jan 1987
TL;DR: Theoretical methods for dielectrics with supraconductive boundary and physical modeling for general polarization models are described, as well as methods for acoustically backed dielectric models.
Abstract: Preface 1. Introduction 2. Introduction and physical modeling 3. Wellposedness 4. Computational methods for dielectrics with supraconductive boundary 5. Computational methods for general polarization models 6. Computational methods for acoustically backed dielectrics 7. Concluding summary and remarks of potential applications Bibliography Index.

71 citations

### "Developing Optimal Strategies for S..." refers background in this paper

• ...For OLSI related to electromagnetic inversion, we refer [3][4][5][6][7]....

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