Equation-Free Digital Twins for Nonlinear Structural Dynamics

2026-05-01

AI Summary

This study addresses the challenge of real-time state reconstruction for high-dimensional engineering structures operating under extreme conditions, where nonstationary excitations, nonlinear kinematics, and stochastic disturbances are coupled, and sensor failures or incomplete observations hinder conventional model-driven or purely data-driven approaches. To overcome this, the authors propose a physics-free digital twin framework grounded in Koopman operator theory, Hankel matrix embedding, and dynamic mode decomposition. By mapping operational data into a linear invariant subspace, the method enables autonomous state reconstruction without requiring prior knowledge of system inputs or governing equations. The introduced rank-optimized Koopman–Hankel manifold approach separates structural resonances from deterministic harmonics even without known mass or stiffness matrices and defines a Lyapunov-predictability timescale under information constraints. Validation on the NREL 5 MW floating wind turbine demonstrates reconstruction coefficients of determination exceeding 0.95 at 1 Hz data assimilation and surpassing 0.99 at higher sampling rates, significantly outperforming traditional subspace identification techniques.

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.

Problem

• nonlinear structural dynamics
• extreme environments
• partial observability
• sensor failure
• real-time monitoring

Innovation

• Koopman operator
• Digital Twin
• Hankel embedding
• Dynamic Mode Decomposition
• Virtual Sensing