Comparing field data using Alpert multi-wavelets
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ORIGINAL PAPER
Comparing field data using Alpert multi-wavelets Maher Salloum1
· Kyle N. Karlson2 · Helena Jin2 · Judith A. Brown3 · Dan S. Bolintineanu4 · Kevin N. Long5
Received: 11 February 2020 / Accepted: 2 July 2020 © This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2020
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. We verify the methods on two-dimensional and three-dimensional discretizations of analytical functions. We then deploy the methods to compare full-field strain data from a simulation of elastomeric syntactic foam. Keywords Comparison · Wavelets · Field data · Mesh · Error metric · Compression · Threshold · Error field
1 Introduction Simulation is a critical part of the development of new designs because simulations can predict the performance of the designs in expected environments. These predictions can
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Maher Salloum [email protected] Kyle N. Karlson [email protected] Helena Jin [email protected] Judith A. Brown [email protected] Dan S. Bolintineanu [email protected] Kevin N. Long [email protected]
1
Sandia National Laboratories, 7011 East Ave., MS 9158, Livermore, CA 94550, USA
2
Sandia National Laboratories, 7011 East Ave., MS 9042, Livermore, CA 94550, USA
3
Sandia National Laboratories, 1515 Eubank SE., MS 0828, Albuquerque, NM 87123, USA
4
Sandia National Laboratories, 1515 Eubank SE., MS 1064, Albuquerque, NM 87123, USA
5
Sandia National Laboratories, 1515 Eubank SE., MS 0840, Albuquerque, NM 87123, USA
then be used to improve different aspects of the design and guarantee all requirements for the design are met. The models behind these simulations frequently require calibration and validation to ensure the accuracy and predictivity of their results. During the calibration and validation processes, quantitative comparisons are made between simulations results and experimental results of a system representative of the problem of interest. Typically, these quantitative comparisons have been done using point-wise local data from local sensors or global data from point sensors that measure a global characteristic of a system (e.g. mass, external load, etc.). A small number of local and global quantities-of-interest are identified and measured for model calibration or validation activities. Comparing a small number of these measurements to simulation results is done by comparing the measured quantitie
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