Displacement and Strain Fields from Sparse Sensor Data Using Peridynamics
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Recovering spatially continuous deformation fields from a limited number of sensors remains a fundamental challenge in shape sensing and structural monitoring. In realistic applications, measurements are sparse, irregularly distributed, and affected by noise, which limits the effectiveness of classical reconstruction techniques relying on local differentiation or predefined interpolation functions. These limitations are particularly critical for strain evaluation, where numerical differentiation of sparse displacement data often leads to instability and loss of physical consistency. This work presents a Peridynamic Differential Operator (PDDO) [1] based nonlocal kinematic framework for reconstructing displacement and strain fields directly from sparse sensor measurements. The proposed approach employs nonlocal neighborhood interactions to populate discrete sensor information into spatially continuous fields without relying on mesh connectivity, element-based interpolation, or pointwise differential operators. Strain–displacement compatibility is enforced through nonlocal integral relations defined over finite spatial horizons, allowing kinematic consistency to be maintained even for irregular sensor layouts. A central feature of the framework is the concurrent recovery of displacement and strain within a unified formulation. By avoiding sequential differentiation or post-processing steps, the approach mitigates error amplification commonly observed in sparse sensing environments. The formulation is purely kinematic and independent of external loading conditions or constitutive assumptions, which enables its application across a wide range of structural systems and operating scenarios. Numerical examples illustrate the robustness of the proposed method under sparse and noisy measurements, demonstrating stable reconstruction of physically admissible displacement and strain fields. The results indicate that nonlocal kinematic reconstruction provides a reliable alternative to classical local approaches for full-field shape sensing and offers strong potential for advanced monitoring applications in aerospace, civil, and mechanical engineering structures. REFERENCES [1] Madenci, E., Barut A., and Dorduncu M., 2019, “Peridynamic Differential Operator for Numerical Analysis,” Springer, Boston, MA (ISBN 978-3-030-02646-2)
