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

Abstract

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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“…There are several different approaches that have been used to define the spatial distribution of material properties in similar applications, such as elastography. 32 These approaches generally vary depending on how much information can be assumed a priori about the distribution. For example, some studies have assumed that properties will only have localized variations and used a radial basis function description of the spatial distribution.…”

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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…”