Stochastic Inverse Analysis for Nondestructive Evaluation ...

Stochastic Inverse Analysis for

Nondestructive Evaluation using

Generalized Polynomial Chaos

Fumio KOJIMA

Graduate School of System Informatics

Kobe University

1-1, Rokkodai-cho, Nada-ku, Kobe 657-8501 JAPAN

[email protected]

2014 A3 Foresight Program Conference on

Modeling and Computation of Applied Inverse Problems

November 20-23, 2014,

International Convention Center, Jeju Island, Korea

SHM is Converged Infrastructure

What is Structural Health Monitoring ?

Health Assessment

Signal Processing Data Interpretation Visualization

Data Acquisition Robotics Measurements

2

It involves the broad concept of assessing ongoing and in-service

performance of structures, data acquisition, data management, data

interpretation, diagnosis, etc.

Data Interpretation

Health Assessment

Signal Processing Data Interpretation Visualization

Data Acquisition Underwater robots Measurements

Flexible multi-coil ECT sensor device

3

Insulation degradation of electrical cables of instruments and

control facilities is one of the critical phenomena for ageing

management. (Technical Review Manuals from JNES, 2005)

In this issue, use of microwaves includes potential applications

in nondestructive test for cable degradation.

Background of research:

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Framework is simple but huge

computational cost is required.

Crucial Issues on Bayesian Inverse Analysis

+Field AnalysisMeasurement

Apparatus

Measurement

Noise ek

dk

Test Signal G (z)k

Degradation

Parameterz

Signal Response Model

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Generalized Polynomial Chaos Galerkin method are taken

to overcome this difficulty.

Inverse Methodologies using Bayesian Inference

Uncertain Qualification

parameter uncertainties

Step 1:

Step 2: Inverse Problems in Measurements

Forward Problem

likelihood functional

gPC Galerkin method

FDTD method

Inverse Problem

Sampling Mechanism

Step 3:

A lossy dielectric medium

a priori probability density function

Bayes formula

a posteriori probability density function

MCMC sampling

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Likelihood ratio functional can be

constructed by NDT model

Forward Problem

likelihood functional

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Step 2.1: Likelihood Functional associated with NDT

Signal response model with mutually independent measurement noise is made by

where the signal response is governed by the random field of electromagnetic

propagation;

.

gPC has advantages on solving the forward problem

Step 2.2: Reconstruction by gPC Galerkin method

Forward Problem

gPC Galerkin method

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Let be generalized polynomial chaos (gPC) basis functions with

the orthogonal properties;

Experimental Results

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(c) 50% (a) 30% (b) 40%

Proportion of degradation (%) 30 40 50

Min 32.30 33.96 35.07

Mean 36.69 37.51 41.36

Max 41.07 41.07 47.66

Summary of estimated results

Marginal probability densities (nominal value : )

Mathematical Issues

Kullback-Leibler divergence (KLD):

: gPC approximation w.r.t. UQ of NDE parameters

: Numerical model w.r.t time and spatial variables

Concluding Remarks:

Inverse problem was considered for aging degradation of cable

insulation as used to perform signal controlling or power

supplying in complex artifacts.

The mathematical model of NDE system was described by

stochastic Maxwell's equations with the uncertain quantities for

material degradations.

The forward problem was formulated by reconstructing the

stochastic Galerkin solution based on the generalized

Polynomial Chaos basis functions.

The Bayesian inverse approach for estimating the material

degradation parameter was proposed with the aid of the

stochastic algorithm based on Markov Chain Monte Carlo.

The validity and feasibility of our proposed method were

demonstrated through computational experiments for appropriate

specific examples.

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ISEM 2015 Awaji Yumebutai International Conference Center

Awaji-Island, Kobe, Japan

Sep. 15-18, 2015

ISEM2015 Topics • Nanotechnology Applications • Laser and Particle Beams,

Plasmas • Inverse Problems • Maintenance and Reliability

Engineering • Micromagnetism, Hysteresis • Electromagnetic Functional

Materials and Adaptive Systems • Electromagnetic Smart Fluids,

Electromagnetics Processing of Materials

• Advanced Magnetic Engineering, Dynamics, Control

• Nuclear Fusion Technology • Applied Superconductivity • Nondestructive Evaluation

(Electromagnetic and Mechanical methods) and Advanced Signal processing

• Biomedical Engineering • Micro Electro-Mechanical

Systems (MEMS) • Analysis and Simulation of

Electromagnetic Devices • Electromagnetic Sensors and

Actuators • Robotics in Applied

Electromagnetics and Mechanics

and Others: OS proposal is welcome!, ex. Magnetic levitation,...