Improved structural health monitoring using a nonlocal PDDO-iFEM framework for sparse-sensor displacement reconstruction

Real-time reconstruction of full-field displacements from discrete strain measurements is a fundamental challenge in structural health monitoring of aerospace and lightweight structures. The inverse finite element method (iFEM) provides a well-established load-independent framework for shape sensing; however, its accuracy degrades significantly when sensor coverage is sparse or spatially restricted. This paper presents a novel computational framework that integrates the peridynamic differential operator (PDDO) as a nonlocal strain-preprocessing stage within the iFEM formulation. The PDDO reconstructs a spatially continuous full-field strain estimate from discrete sensor measurements by weighted integral interpolation over a finite-horizon neighborhood, enabling the iFEM functional to operate effectively even in structural regions devoid of direct sensor coverage. The proposed framework is formulated within the first-order shear deformation theory and applies to isotropic plate and shell structures instrumented with surface-mounted or embedded strain sensors. Three benchmark problems are considered to assess the accuracy and sensor efficiency of the method: a cantilevered beam under tip shear load, supported square plate under uniform transverse pressure, and a tapered-wing geometry subjected to a prescribed tip displacement. Numerical results demonstrate that the PDDO–iFEM coupling consistently improves displacement reconstruction accuracy relative to standard iFEM under identical sparse-sensor configurations.