Sparse-sensor flow reconstruction and motion prediction during water exit of an underwater-launched vehicle

Abstract

Real-time monitoring of the complex hydrodynamic states of underwater-launched vehicles during water-exit processes remains challenging due to highly nonlinear multiphase evolution, wake instability, and strong fluid–structure coupling. In this study, a physics-guided sparse sensing framework is developed to establish the relationship between limited wall-pressure measurements, global flow structures, and vehicle motion responses. The framework employs a proper orthogonal decomposition (POD) and Transformer-based multi-task learning strategy, where POD provides a physically interpretable latent representation of flow dynamics, while Transformer-based feature learning captures global correlations among modal features and sensor locations. By incorporating operating-condition information through feature modulation and attention-based fusion, the proposed framework simultaneously reconstructs pressure, velocity, and vorticity fields and predicts vehicle motion states. The results demonstrate that sparse wall-pressure measurements contain sufficient information to recover the dominant coherent structures and dynamic responses during the water-exit process. Under varying Froude number conditions, reconstruction errors are mainly concentrated in wake shear layers and vortex-dominated regions associated with highly unsteady flow structures, whereas the large-scale flow characteristics governing overall evolution remain accurately captured. Furthermore, sensor configuration analysis reveals that for the investigated vehicle geometry and flow conditions, a 12-sensor layout provides an effective balance between measurement sparsity and reconstruction accuracy, indicating the existence of an effective sensing threshold for capturing essential flow information. These findings provide new insights into the observability of complex water-exit flows, the encoding mechanism between sparse wall measurements and global flow dynamics, and the coupling between hydrodynamic evolution and vehicle motion responses.