Deep learning based on PINN for solving 2 DOF vortex induced vibration of cylinder

Vortex-induced vibration (VIV) exists widely in natural and industrial fields. The main approaches for solving VIV problems are numerical simulations and experimental methods. However, experiment methods are difficult to obtain the whole flow field information and also high-cost while numerical simulation is extraordinary time-consuming and limited in low Reynolds number and simple geometric configuration. In addition, numerical simulations are difficult to handle the moving mesh technique. In this paper, physics informed neural network (PINN) is utilized to solve the VIV and wake-induced vibration (WIV) of cylinder with different reduced velocities. Compared to tradition data-driven neural network, the Reynolds Average Navier-Stokes (RANS) equation, by implanting an additional turbulent eddy viscosity, coupled with structure's dynamic motion equation are also embedded into the loss function. Training and validation data is obtained by computational fluid dynamic (CFD) technique. Three scenarios are proposed to validate the performance of PINN in solving VIV and WIV of cylinders. In the first place, the stiffness parameter and damping parameter are calculated via limited force data and displacement data; secondly, the turbulence flow field and lifting force/drag force are inferred by scattered velocity information; eventually, the displacement can be directly predicted only through lifting forces and drag forces based on LSTM. Results demonstrate that, compared with traditional neural network, PINN method is more effective in inferring and re-constructing the unknown parameters and flow field with different Reynolds numbers under VIV and WIV circumstances.