A computationally efficient approach for inverse material characterization combining Gappy POD with direct inversion

Wang, Mengyu; Dutta, Debaditya; Kim, Kang; Brigham, John C.

doi:10.1016/j.cma.2015.01.001

Cited by 23 publications

(14 citation statements)

References 37 publications

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“…To be clarified, the contributions and novelty to combine gradient adjoint approach with direct inversion with gappy POD are not just minimal or incremental in comparison to our previous work focusing on direct inversion with gappy POD for inverse characterization [16]. The results of the numerical examples in this work have consistently shown that the solutions by gradient adjoint approach with direct inversion with gappy POD were noticeably more accurate than the solutions by direct inversion with gappy POD only.…”

Section: Discusionssupporting

confidence: 72%

“…This work is a direct extension of the prior work of the authors that displayed the capability of a highly computationally efficient direct inversion characterization strategy using Gappy proper orthogonal decomposition (POD) [16]. The prior work showed the promise of using Gappy POD to significantly improve the quality of direct inversion characterization solution estimates without significant additional computing cost (particularly in terms of the online portion of the process).…”

Section: Introductionmentioning

confidence: 81%

“…Then this full-field measurement estimate is used to directly invert the governing equations describing the physics of the tested system to estimate the unknown material property distribution. Details of this Gappy POD-direct inversion approach utilized for obtaining an initial estimate of the unknown material property distribution can be found in the prior work of the authors [16], and only key points are discussed briefly herein.…”

Section: Direct Inversion With Gappy Podmentioning

confidence: 99%

“…The direct inversion procedure utilized herein (discussed in the context of elastography) first assumes that the elastic modulus distribution can be approximated in a finite element format similar to the format of the standard displacement approximation [16]. Thus, utilizing the full-field solution estimate provided by Gappy POD and applying a standard weak form Galerkin procedure, the finite element equations for the direct inversion elastography problem to determine nodal values describing the elastic modulus (E) from the nodal values describing the full-field displacement response (u) can be written as:…”

Section: Direct Inversion With Gappy Podmentioning

confidence: 99%

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A generalized computationally efficient inverse characterization approach combining direct inversion solution initialization with gradient-based optimization

Wang

Brigham

2016

Comput Mech

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The nal publication is available at Springer via https://doi.org/10.1007/s00466-016-1362-3Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractA computationally efficient gradient-based optimization approach for inverse material characterization from incomplete system response measurements that can utilize a generally applicable parameterization (e.g., finite elementtype parameterization) is presented and evaluated. The key to this inverse characterization algorithm is the use of a direct inversion strategy with Gappy proper orthogonal decomposition (POD) response field estimation to initialize the inverse solution estimate prior to gradient-based optimization. Gappy POD is used to estimate the complete (i.e., all components over the entire spatial domain) system response field from incomplete (e.g., partial spatial distribution) measurements obtained from some type of system testing along with some amount of a priori information regarding the potential distribution of the unknown material property. The estimated complete system response is used within a physics-based direct inversion procedure with a finite element-type parameterization to estimate the spatial distribution of the desired unknown material property with minimal computational expense. Then, this estimated spatial distribution of the unknown material property is used to initialize a gradient-based optimization approach, which * Corresponding author Email addresses: mengyu_wang@meei.harvard.edu (Mengyu Wang), john.brigham@durham.ac.uk (John C. Brigham) Preprint submitted to Computational MechanicsNovember 23, 2016 uses the adjoint method for computationally efficient gradient calculations, to produce the final estimate of the material property distribution. The three-step ((1) Gappy POD, (2) direct inversion, and (3) gradient-based optimization) inverse characterization approach is evaluated through simulated test problems based on the characterization of elastic modulus distributions with localized variations (e.g., inclusions) within simple structures. Overall, this inverse characterization approach is shown to efficiently and consistently provide accurate inverse characterization estimates for material property distributions from incomplete response field measurements. Moreover, the solution procedure is shown to be capable of extrapolating significantly beyond the initial assumptions regarding the potential nature of the unknown material property distribution.

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Section: Discusionssupporting

confidence: 72%

Section: Introductionmentioning

confidence: 81%

Section: Direct Inversion With Gappy Podmentioning

confidence: 99%

Section: Direct Inversion With Gappy Podmentioning

confidence: 99%

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A generalized computationally efficient inverse characterization approach combining direct inversion solution initialization with gradient-based optimization

Wang

Brigham

2016

Comput Mech

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“…Measurement coefficients reconstruction The first online step reconstructs POD coefficients of the measured quantities of interest using information provided by incomplete snapshotsq m , m = 1, ..., M . The measurement POD basis computed offline (1) are used to estimate the coefficients via gappy POD; [45][46][47][48] M linear systems is the form…”

Section: A Multistep-rom Proceduresmentioning

confidence: 99%

Sensor placement strategy to inform decisions

Mainini

Willcox

2017

18th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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This paper introduces a computational strategy to determine optimal sets of sensor locations to support real-time operational decisions. We exploit unsupervised learning strategies (specifically self-organizing maps) to identify the most informative locations to place sensors. The sensor placement procedure is then combined with a Multi-Step-Reduced Order Modeling approach that exploits the low-dimensional map between the sparse sensed data and the decisions at hand. The approach is demonstrated for the real-time assessment of an unmanned aircraft wing panel undergoing structural degradation. For this application, we compare the optimal sets of sensor locations with random placements for a variety of sensor availabilities. By adopting our placement strategy, we achieve improvements in accuracy and robustness of capability predictions, even when measured data are sparse and cover less than 10% of the reference data.

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Non‐intrusive reduced‐order modeling for multiphase porous media flows using Smolyak sparse grids

Xiao

Lin

Fang

et al. 2016

Numerical Methods in Fluids

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SUMMARYIn this article, we describe a non-intrusive reduction method for porous media multiphase flows using Smolyak sparse grids. This is the first attempt at applying such an non-intrusive reduced order modelling (NIROM) based on Smolyak sparse grids to porous media multiphase flows. The advantage of this NIROM for porous media multiphase flows resides in that its non-intrusiveness, which means it does not require modifications to the source code of full model. Another novelty is that it uses Smolyak sparse grids to construct a set of hyper-surfaces representing the reduced porous media multiphase problem. This NIROM is implemented under the framework of an unstructured mesh control volume finite element (CVFEM) multiphase model. Numerical examples show that the NIROM accuracy relative to the high fidelity model is maintained whilst the computational cost is reduced by several orders of magnitude.

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A computationally efficient approach for inverse material characterization combining Gappy POD with direct inversion

Cited by 23 publications

References 37 publications

A generalized computationally efficient inverse characterization approach combining direct inversion solution initialization with gradient-based optimization

A generalized computationally efficient inverse characterization approach combining direct inversion solution initialization with gradient-based optimization

Sensor placement strategy to inform decisions

Non‐intrusive reduced‐order modeling for multiphase porous media flows using Smolyak sparse grids

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