Equation-Free Digital Twins for Nonlinear Structural Dynamics

TL;DR

This paper presents a novel digital twin framework using Koopman operator theory and Hankel embeddings for real-time, input-blind structural dynamics monitoring of complex engineering systems.

Contribution

It introduces a rank-optimized Koopman-Hankel method enabling autonomous, high-fidelity reconstruction without prior structural parameters, validated on offshore wind turbine data.

Findings

Separates structural resonances from rotor harmonics under noise

Achieves >0.95 R^2 at 1 Hz data assimilation

Estimates a Lyapunov time of ~1 second for predictability

Abstract

Monitoring high-dimensional engineering structures in extreme environments is limited by non-stationary excitation, nonlinear structural kinematics, and stochastic forcing. Traditional model-based and black-box data-driven methods often struggle to resolve these dynamics in real time, particularly under sensor failure or partial observability. This paper introduces a rank-optimized digital twin framework based on Koopman operator theory, Hankel-matrix embeddings, and dynamic mode decomposition. By lifting operational data into a linear invariant subspace, the method enables autonomous, input-blind reconstruction of structural states without requiring a priori mass or stiffness matrices. The framework is validated on an NREL 5MW spar-buoy floating offshore wind turbine, representing a challenging coupled aero-hydro-servo-elastic system. Results show that the rank-optimized Koopman-Hankel manifold separates structural resonances from deterministic 3P rotor harmonics under colored noise, where standard subspace identification can be unreliable. A rolling-horizon virtual sensing strategy achieves high-fidelity reconstruction at critical structural hotspots, with coefficient of determination greater than 0.95 at 1 Hz data assimilation and accuracy exceeding 0.99 at higher sampling rates. By estimating a physical Lyapunov time of approximately 1.0 s, the study defines the predictability horizon associated with the system information barrier. The proposed framework provides a computationally efficient and resilient digital twin approach for real-time identification and virtual sensing of complex structural dynamics.