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

Abstract An approach for computationally efficient inverse material characterization from partial-field response measurements that combines the Gappy proper orthogonal decomposition (POD) machine learning technique with a physics-based direct inversion strategy is presented and evaluated. Gappy POD is used to derive a data reconstruction tool from a set of potential system response fields that are generated from available a priori information regarding the potential distribution of the unknown material properties. Then, the Gappy POD technique is applied to reconstruct the full spatial distribution of the system response from whatever portion of the response field has been measured with the chosen system testing method. Lastly, a direct inversion strategy is presented that is derived from the equations governing the system response (i.e., physics of the system), which utilizes the full-field response reconstructed by Gappy POD to produce an estimate of the spatial distribution of the unknown material properties. The direct inversion technique is a particularly computationally efficient inversion technique, requiring a cost equivalent to a single numerical analysis. Therefore, the majority of the computational expense of the presented approach is the one-time potential response generation for the Gappy POD technique, which leads to an approach that is substantially computationally efficient overall. Two numerically simulated examples are shown in which the elastic modulus distribution was characterized based on partial-field displacement response measurements, both static and dynamic. The inversion procedure was shown to have the capability to efficiently provide accurate estimates to material property distributions from partial-field response measurements. The direct inversion with Gappy POD response estimation was also shown to be substantially tolerant to noise in comparison to the direct inversion given measured full-field response. Lastly, a physical example regarding elastography of an arterial construct from ultrasound imaging response measurements is shown to validate the practical applicability of the direct inversion approach with Gappy POD response reconstruction.

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