无需物理模型,实时重建复杂结构动态行为。
Equation-Free Digital Twins for Nonlinear Structural Dynamics

- 基于柯普曼算子与荷尔蒙矩阵,将非线性系统升维至线性空间。
- 在1Hz采样下重建精度达R²>0.95,更高采样率下准确率超0.99。
- 适用于传感器故障或部分可观测场景,适合海上风电等复杂系统。
在极端环境下监测高维工程结构受限于非平稳激励、非线性运动学及随机扰动。传统基于模型和黑箱数据驱动方法难以实现实时解析,尤其在传感器失效或部分可观测情况下。本文提出一种基于柯普曼算子理论、赫尔曼矩阵嵌入与动态模态分解的秩优化数字孪生框架。通过将运行数据提升至线性不变子空间,实现无需先验质量或刚度矩阵的自主、输入无关的状态重构。在代表典型气-水-伺服弹性耦合系统的NREL 5MW浮式海上风力机上验证,该框架在有色噪声下成功分离结构共振与确定性3P转子谐波,而标准子空间识别方法不可靠。滚动窗口虚拟传感策略在关键结构热点实现高保真重建,在1Hz数据融合下决定系数超过0.95,更高采样率下准确率超过0.99。通过估计物理李雅普诺夫时间约为1.0秒,定义了系统信息屏障相关的可预测时间窗。所提框架为复杂结构动力学的实时识别与虚拟传感提供了计算高效且鲁棒的数字孪生方案。
原文摘要 · Abstract (English)
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.
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