Time Series Prediction of Aerodynamic Noise Based on Variational Mode Decomposition and Echo State Network

Time series prediction of aerodynamic noise is critical for oscillatory instabilities analyses in fluid systems. Due to the significant dynamical and non-stationary characteristics of aerodynamic noise, it is challenging to precisely predict its temporal behavior. Here, we propose a method combining variational mode decomposition (VMD) and echo state network (ESN) to accurately predict the time series of aerodynamic noise induced by flow around a cylinder. VMD adaptively decomposes the noise signal into multiple modes through a constrained variational optimization framework, effectively separating distinct frequency-scale features between vortex shedding and turbulent fluctuations. ESN then employs a randomly initialized reservoir to map each mode into a high-dimensional dynamical system, and learns their temporal evolution by leveraging the reservoir’s memory of past states to predict their future values. Aerodynamic noise data from cylinder flow at a Reynolds number of 90,000 is generated by numerical simulation and used for model validation. With a rolling prediction strategy, this VMD-ESN method achieves accurate prediction within 150 time steps with a root-mean-square-error of only 3.32 Pa, substantially reducing computational costs compared to conventional approaches. This work enables effective aerodynamic noise prediction and is valuable in fluid dynamics, aeroacoustics, and related areas.