stochastic inverse analysis for nondestructive evaluation
TRANSCRIPT
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
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,...