O(n) Local Eigenvalue Modification Procedure for real-time updating of structural digital twins with sub-millisecond-latency performance

Real-time structural digital twins require rapid and reliable model updating to maintain accuracy as the physical system evolves, particularly in high-rate dynamic environments where microsecond- to millisecond-scale decisions are critical. Traditional finite element (FE)-based updating methods rely on repeatedly solving the Generalized Eigenvalue (GE) Problem, whose O ( n 3 ) computational cost prevents deployment in real-time digital-twin frameworks for even moderately sized structural models. This work numerically validates a two-dimensional extension of the Local Eigenvalue Modification Procedure (LEMP) as a reduced-order, physics-based updating strategy that enables fast model updating of structural digital twins without resolving the full eigenvalue problem. Using a steel plate modeled with bilinear quadrilateral finite elements, a systematic mesh-convergence and modal-error study identifies a 25-node reduced-order model (ROM) that maintains about < 10% modal-frequency error relative to a high-fidelity reference mesh. Localized stiffness changes are introduced across the plate to emulate evolving structural states, and comparisons between the Generalized Eigenvalue Procedure (GEP) and LEMP show that mode seven (7) offers a more reliable accuracy for real-time updating. Across all introduced local changes, LEMP maintains frequency-prediction errors below 10% while avoiding recomputing global eigenvalues. Timing analyses demonstrate that LEMP achieves update latencies as low as 0.46 ms for the 25-node model and remains below 2 ms at 169 nodes, offering speedups exceeding 2500 × relative to GEP. Empirical scaling analysis confirms near-linear ( O ( n ) ) algorithmic complexity for LEMP compared to the cubic ( O ( n 3 ) ) scaling of GEP. These results establish LEMP as a computationally efficient and numerically benchmarked mechanism for real-time digital-twin updating of 2D structural systems, and provide a computational basis toward integrating physics-based methods into high-rate structural model updating, active control, and edge-deployed digital-twin applications.