A multi-scale online method to predict the unsteady pressure of the ventilated cavities around an axisymmetric body

During the underwater motion of an axisymmetric body, unsteady shedding of the ventilated cavity causes severe pressure fluctuations on its downstream surface, affecting the motion stability. A traditional control system relies on monitoring data for posture adjustment, but may fail due to the hysteresis effect. To address this, a multi-scale online method is proposed to predict the unsteady pressure caused by cavitation shedding. This method decomposes the unsteady pressure into two scales: large-scale pressure, predicted using a medium support vector regression (SVR) model, and small-scale fluctuating pressure, predicted via a multi-round online deployment (MROD) method. The MROD method employs an offline-trained double-layer long short-term memory network, iteratively invoked to intermittently incorporate real-time data for advanced predictions. The prediction accuracy and speed of this method are influenced by key hyperparameters, including the input sequence length, output sequence length, real-time interval between time steps, and time step interval between consecutive real-time data inputs. Results show that both MROD and SVR models exhibit high prediction accuracy and robust generalization ability for predicting the small-scale fluctuating pressure and large-scale pressure, respectively. The proposed method achieves weighted mean relative errors below 1% for both interpolation and extrapolation of unsteady pressure, demonstrating its effectiveness in predicting unsteady pressure for axisymmetric bodies under unknown operating conditions. This high-accuracy prediction ensures stable motion of the axisymmetric body in complex marine environments.