Physics-constrained normalizing flow for identification and modeling of vortex-induced vibration in stay cables

Stay cables of long-span bridges are highly susceptible to wind-induced oscillations due to their high flexibility, low frequency, and low damping. Accurate identification and modeling of vortex-induced vibrations (VIV) of stay cables is a critical challenge. First-principle modeling and analysis of cable VIV is intractable due to insufficient physical knowledge about the complex fluid–structure interaction and the damping mechanism. This study develops a novel physics-constrained normalizing flow (PCNF) framework for data-driven identification and predictive modeling of the intricate dynamics of cable VIV from their state response only. Specifically, the PCNF incorporates the general formulations of the nonlinear normal modes (NNMs) with invariant manifolds for representation of the nonlinear dynamics of cable VIV via mathematically invertible normalizing flow deep neural networks. Moreover, a dynamics layer is embedded in the latent space of PCNF to model the intricate dynamic evolution of cable VIV NNMs. Such a modeling architecture ensures strict adherence to fundamental dynamic principles while providing an interpretable and invertible representation of the system dynamics for accurate and efficient identification and predictive modeling of time-varying cable VIV dynamics. The developed PCNF model is validated through extensive simulations of cable VIV responses using a phenomenological wake oscillator. It is observed that the PCNF is capable of accurately identifying the NNMs of cable VIV under constant wind speed excitation, where the self-excited and self-limiting characteristics of the VIV dynamics are represented by NNMs’ invariant manifolds. Furthermore, the PCNF framework is validated in accurate predictive modeling of the dynamic evolution of cable VIV under varying wind speed by efficiently capturing higher-order modal lock-in phenomena and time-varying dynamics. The applicability and limitation of this method for cable VIV are also discussed.