Data-knowledge-driven semi-empirical model augmentation method for nonlinear vortex-induced vibration

Vortex-induced vibration is a typical nonlinear fluid–structure interaction phenomenon. Significant challenges to high-precision prediction by the prevalent methods rely on three complex nonlinear dynamic behaviors: nonlinear evolution (NE), vibration peak deviating from the resonance (PD), and nonlinear hysteresis. Although the semi-empirical model is a theoretical and efficient manner, it is difficult to accurately predict the above nonlinear phenomena due to the incomplete mathematical expressions and uncertain parameters. In this paper, a data-knowledge-driven (DKD) augmentation method is proposed to modify the typical wake oscillator model. A comprehensive analysis is first conducted for the effect of the potential aerodynamic damping terms. Motivated by the above analysis, a delay damping term is proposed which contributes to the NE and PD phenomenon by affecting the growth rate of the flow frequency and triggers the mode transition of the coupled system. With these physical understandings, a new model architecture is constructed by combining the delay damping and the Rayleigh damping. Besides, experimental data are utilized to identify the empirical parameters of the model by the ensemble Kalman filter data assimilation technique. The results indicate that the DKD model (marked as Van-Delay-Rayleigh) can accurately compute these nonlinear behaviors for 25 different cylinders. Compared with the original model, the prediction accuracy of the DKD model is improved by 2–5 times. It also shows the generalization capability with various mass-damping parameters, which can reduce the number of wind tunnel tests by 70%.