Comparing field data using Alpert multi-wavelets

Salloum, Maher; Karlson, Kyle N.; Jin, Helena; Brown, Judith A.; Bolintineanu, Dan S.; Long, Kevin N.

doi:10.1007/s00466-020-01878-2

Title: Comparing field data using Alpert multi-wavelets

Abstract

In this paper we introduce a method to compare sets of full-field data using Alpert tree-wavelet transforms. The Alpert tree-wavelet methods transform the data into a spectral space allowing the comparison of all points in the fields by comparing spectral amplitudes. The methods are insensitive to translation, scale and discretization and can be applied to arbitrary geometries. This makes them especially well suited for comparison of field data sets coming from two different sources such as when comparing simulation field data to experimental field data. We have developed both global and local error metrics to quantify the error between two fields. Additionally, we verify the methods on two-dimensional and three-dimensional discretizations of analytical functions. Furthermore, we then deploy the methods to compare full-field strain data from a simulation of elastomeric syntactic foam.

Authors:

^[1]; Karlson, Kyle N. ^[1]; Jin, Helena ^[1]; Brown, Judith A. ^[2]; Bolintineanu, Dan S. ^[2]; Long, Kevin N. ^[2]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:: Sat Jul 25 00:00:00 EDT 2020

Research Org.:: Sandia National Lab. (SNL-CA), Livermore, CA (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1650144

Report Number(s):: SAND-2020-7731J
Journal ID: ISSN 0178-7675; 687674

Grant/Contract Number:: AC04-94AL85000; NA0003525

Resource Type:: Accepted Manuscript

Journal Name:: Computational Mechanics

Additional Journal Information:: Journal Volume: 66; Journal ID: ISSN 0178-7675

Publisher:: Springer

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; Comparison; wavelets; field data; mesh; error metric; compression; threshold; error field

Citation Formats


                    Salloum, Maher, Karlson, Kyle N., Jin, Helena, Brown, Judith A., Bolintineanu, Dan S., and Long, Kevin N. Comparing field data using Alpert multi-wavelets.  United States: N. p., 2020. 
Web.  doi:10.1007/s00466-020-01878-2.

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                    Salloum, Maher, Karlson, Kyle N., Jin, Helena, Brown, Judith A., Bolintineanu, Dan S., & Long, Kevin N. Comparing field data using Alpert multi-wavelets.  United States.  https://doi.org/10.1007/s00466-020-01878-2

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                    Salloum, Maher, Karlson, Kyle N., Jin, Helena, Brown, Judith A., Bolintineanu, Dan S., and Long, Kevin N. Sat .  
"Comparing field data using Alpert multi-wavelets".  United States.  https://doi.org/10.1007/s00466-020-01878-2.  https://www.osti.gov/servlets/purl/1650144.

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@article{osti_1650144,

  title        = {Comparing field data using Alpert multi-wavelets},

  author       = {Salloum, Maher and Karlson, Kyle N. and Jin, Helena and Brown, Judith A. and Bolintineanu, Dan S. and Long, Kevin N.},

  abstractNote = {In this paper we introduce a method to compare sets of full-field data using Alpert tree-wavelet transforms. The Alpert tree-wavelet methods transform the data into a spectral space allowing the comparison of all points in the fields by comparing spectral amplitudes. The methods are insensitive to translation, scale and discretization and can be applied to arbitrary geometries. This makes them especially well suited for comparison of field data sets coming from two different sources such as when comparing simulation field data to experimental field data. We have developed both global and local error metrics to quantify the error between two fields. Additionally, we verify the methods on two-dimensional and three-dimensional discretizations of analytical functions. Furthermore, we then deploy the methods to compare full-field strain data from a simulation of elastomeric syntactic foam.},

  doi          = {10.1007/s00466-020-01878-2},

  journal      = {Computational Mechanics},

  number       = ,

  volume       = 66,

  place        = {United States},

  year         = {Sat Jul 25 00:00:00 EDT 2020},

  month        = {Sat Jul 25 00:00:00 EDT 2020}

}

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Title: Comparing field data using Alpert multi-wavelets

Abstract

Citation Formats

Digital Volume Correlation: Review of Progress and Challenges journal, June 2018

A Class of Bases in $L^2$ for the Sparse Representation of Integral Operators journal, January 1993

Image analysis by Tchebichef moments journal, January 2001

Image analysis by discrete orthogonal dual Hahn moments journal, October 2007

Visual pattern recognition by moment invariants journal, February 1962

Shape features and finite element model updating from full-field strain data journal, June 2011

Image Analysis Using Hahn Moments journal, November 2007

On the validation of solid mechanics models using optical measurements and data decomposition journal, March 2015

Big Data in Experimental Mechanics and Model Order Reduction: Today’s Challenges and Tomorrow’s Opportunities journal, July 2017

Singularity detection and processing with wavelets journal, March 1992

A region-based shape descriptor using Zernike moments journal, September 2000

SO(3)-invariance of informed-graph-based deep neural network for anisotropic elastoplastic materials journal, May 2020

Frequency response functions of shape features from full-field vibration measurements using digital image correlation journal, April 2012

Adaptive wavelet compression of large additive manufacturing experimental and simulation datasets journal, July 2018

Optimal Compressed Sensing and Reconstruction of Unstructured Mesh Datasets journal, August 2017

A survey of moment-based techniques for unoccluded object representation and recognition journal, September 1992

A multiscale study of damage in elastomeric syntactic foams journal, April 2018

Fast and numerically stable methods for the computation of Zernike moments journal, July 2010

Decomposing Strain Maps Using Fourier-Zernike Shape Descriptors journal, November 2011

The Lifting Scheme: A Construction of Second Generation Wavelets journal, March 1998

High Temperature Vibratory Response of Hastelloy-X: Stereo-DIC Measurements and Image Decomposition Analysis journal, September 2015

Wavelets and filter banks: theory and design journal, January 1992

An approach to the validation of computational solid mechanics models for strain analysis journal, July 2012

Radial Tchebichef Invariants for Pattern Recognition conference, November 2005

Numerical error analysis in Zernike moments computation journal, September 2006

Three-dimensional shape analysis using moments and Fourier descriptors journal, January 1988

Biorthogonal diffusion wavelets for multiscale representations on manifolds and graphs conference, August 2005

Computing invariants of Tchebichef moments for shape based image retrieval journal, November 2016

Image analysis by discrete orthogonal Racah moments journal, April 2007

High temperature modal analysis of a non-uniformly heated rectangular plate: Experiments and simulations journal, March 2019

Resolving the sign ambiguity in the singular value decomposition journal, January 2008

Simplified CSP analysis of a stiff stochastic ODE system journal, April 2012

Lie-group interpolation and variational recovery for internal variables journal, June 2013

Vibration mode shape recognition using image processing journal, October 2009

Wavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations journal, January 1993

Basis-updating for data compression of displacement maps from dynamic DIC measurements journal, January 2019

Full-field finite element model updating using Zernike moment descriptors for structures exhibiting localized mode shapes journal, April 2019

An Introduction to Statistical Learning book, January 2013

Invariant image recognition by Zernike moments journal, May 1990

Digital Volume Correlation: Review of Progress and Challenges
journal, June 2018

A Class of Bases in $L^2$ for the Sparse Representation of Integral Operators
journal, January 1993

Image analysis by Tchebichef moments
journal, January 2001

Image analysis by discrete orthogonal dual Hahn moments
journal, October 2007

Visual pattern recognition by moment invariants
journal, February 1962

Shape features and finite element model updating from full-field strain data
journal, June 2011

Image Analysis Using Hahn Moments
journal, November 2007

On the validation of solid mechanics models using optical measurements and data decomposition
journal, March 2015

Big Data in Experimental Mechanics and Model Order Reduction: Today’s Challenges and Tomorrow’s Opportunities
journal, July 2017

Singularity detection and processing with wavelets
journal, March 1992

A region-based shape descriptor using Zernike moments
journal, September 2000

SO(3)-invariance of informed-graph-based deep neural network for anisotropic elastoplastic materials
journal, May 2020

Frequency response functions of shape features from full-field vibration measurements using digital image correlation
journal, April 2012

Adaptive wavelet compression of large additive manufacturing experimental and simulation datasets
journal, July 2018

Optimal Compressed Sensing and Reconstruction of Unstructured Mesh Datasets
journal, August 2017

A survey of moment-based techniques for unoccluded object representation and recognition
journal, September 1992

A multiscale study of damage in elastomeric syntactic foams
journal, April 2018

Fast and numerically stable methods for the computation of Zernike moments
journal, July 2010

Decomposing Strain Maps Using Fourier-Zernike Shape Descriptors
journal, November 2011

The Lifting Scheme: A Construction of Second Generation Wavelets
journal, March 1998

High Temperature Vibratory Response of Hastelloy-X: Stereo-DIC Measurements and Image Decomposition Analysis
journal, September 2015

Wavelets and filter banks: theory and design
journal, January 1992

An approach to the validation of computational solid mechanics models for strain analysis
journal, July 2012

Radial Tchebichef Invariants for Pattern Recognition
conference, November 2005

Numerical error analysis in Zernike moments computation
journal, September 2006

Three-dimensional shape analysis using moments and Fourier descriptors
journal, January 1988

Biorthogonal diffusion wavelets for multiscale representations on manifolds and graphs
conference, August 2005

Computing invariants of Tchebichef moments for shape based image retrieval
journal, November 2016

Image analysis by discrete orthogonal Racah moments
journal, April 2007

High temperature modal analysis of a non-uniformly heated rectangular plate: Experiments and simulations
journal, March 2019

Resolving the sign ambiguity in the singular value decomposition
journal, January 2008

Simplified CSP analysis of a stiff stochastic ODE system
journal, April 2012

Lie-group interpolation and variational recovery for internal variables
journal, June 2013

Vibration mode shape recognition using image processing
journal, October 2009

Wavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations
journal, January 1993

Basis-updating for data compression of displacement maps from dynamic DIC measurements
journal, January 2019

Full-field finite element model updating using Zernike moment descriptors for structures exhibiting localized mode shapes
journal, April 2019

An Introduction to Statistical Learning
book, January 2013

Invariant image recognition by Zernike moments
journal, May 1990