A Data-Driven Approach to Study Nonlinear Dynamics of Wind-Driven Water Runback Flows Pertinent to Aircraft Icing Phenomena

Abstract

Icing has been widely acknowledged as a significant threat to flight safety for decades. The wind-driven runback water film (WDRWF) flow significantly impacts ice shape evolution. In this study, we used the sparse identification of nonlinear dynamics (SINDy) technique to determine the nonlinear dynamics of a real-world multiphase WDRWF flow. We attempted the POD method and variational autoencoder to reduce the dimension of the original high-dimensional WDRWF flow. The SINDy method can generate an accurate and interpretable ODE system for WDRWF flow based on three POD modes. To improve the accuracy of the WDRWF flow reconstruction, the POD method is replaced with the variational autoencoder (VAE). With just three latent variables, VAE can accurately reconstruct a WDRWF flow. However, the phase points in the latent space of VAE are not continuous in time, creating challenges for the SINDy method to discover an accurate ODE. To the authors' knowledge, this is the first attempt to use the data-driven method SINDy and the VAE to determine the nonlinear dynamics of actual WDRWF flow. Our preliminary findings provide future researchers with valuable insight into the challenges associated with applying the SINDy method to the complex multiphase WDRWF flow analysis.