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Inverse characterization from partial-field data using direct inversion with Gappy POD initialization and the adjoint method

An approach for inverse characterization from partial-field response measurements will be presented. Characterization of the spatial distribution of material properties has applications spanning medicine (e.g., tumor characterization) to civil engineering (e.g., damage characterization or material optimization). However, measurement availability is often limited, with only a portion of the spatial domain and/or incomplete response components provided. These limitations on measurements substantially increase the difficulty of the associated inverse problem to characterize the material properties. Lack of measurement data oftentimes leads to highly non-convex inverse solution search spaces and issues of nonuniqueness, and ultimately limits the ability to apply computationally efficient algorithms, such as gradient-based search methods. To overcome these challenges, the approach that will be presented utilizes a novel and highly efficient technique to provide an initial estimate to the unknown material property distribution that is sufficiently accurate to allow a gradient-based approach to refine the solution and ultimately produce an accurate inverse characterization estimate at limited computational cost. The initial estimate is generated by reconstructing a full-field response for the system through the Gappy proper orthogonal decomposition (POD) machine learning technique, and then using the full-field response with a direct inversion algorithm to estimate the material property distribution. This estimate is then applied as the initial guess in a gradient-based optimization algorithm that utilizes the adjoint method for computationally efficient gradient calculations to complete the inverse solution estimation process. Through simulated test problems based on the characterization of localized, but arbitrarily shaped, inclusions within simple structures, the three-step ((1) Gappy POD, (2) direct inversion, (3) gradient-based optimization) inverse characterization approach will be shown to efficiently provide accurate and relatively unique inverse characterization estimates for material property distributions from incomplete response field measurements.

Author(s):

Mengyu Wang    
Duke University
United States

John Brigham    
University of Pittsburgh
United States