With the evolution of machine learning and deep learning, more and more researchers have utilized these methods in the field of underwater acoustic target recognition. In these studies, convolutional neural networks (CNNs) are the main components of recognition models. In recent years, a neural network model Transformer that uses a self-attention mechanism was proposed and achieved good performance in deep learning. In this paper, we propose a Transformer-based underwater acoustic target recognition model STM. To the best of our knowledge, this is the first work to introduce Transformer into the underwater acoustic field. We compared the performance of STM with CNN, ResNet18, and other multi-class algorithm models. Experimental results illustrate that under two commonly used dataset partitioning methods, STM achieves 97.7% and 89.9% recognition accuracy, respectively, which are 13.7% and 50% higher than the CNN Model. STM also outperforms the state-of-the-art model CRNN-9 by 3.1% and ResNet18 by 1.8%.

The normal mode model is important in computational atmospheric acoustics. It is often used to compute the atmospheric acoustic field under a time-independent single-frequency sound source. Its solution consists of a set of discrete modes radiating into the upper atmosphere, usually related to the continuous spectrum. In this article, we present two spectral methods, the Chebyshev-Tau and Chebyshev-Collocation methods, to solve for the atmospheric acoustic normal modes, and corresponding programs are developed. The two spectral methods successfully transform the problem of searching for the modal wavenumbers in the complex plane into a simple dense matrix eigenvalue problem by projecting the governing equation onto a set of orthogonal bases, which can be easily solved through linear algebra methods. After the eigenvalues and eigenvectors are obtained, the horizontal wavenumbers and their corresponding modes can be obtained with simple processing. Numerical experiments were examined for both downwind and upwind conditions to verify the effectiveness of the methods. The running time data indicated that both spectral methods proposed in this article are faster than the Legendre-Galerkin spectral method proposed previously.

The longitudinal motion amplitude and phase for two ships with forward speed at close proximity in waves are investigated by the frequency-domain potential flow theory, which is based on the mathematical kernel of three-dimension translating-pulsating source. On the foundation of numerical validation for a modified Wigley ship, the frequency-domain method is then extended to the kinematic characteristics for two ships. The two-ship model test is focused on the surge, heave and pitch mode motions. The numerical and experimental results shows that it is applicable to solve the hydrodynamic interaction problem for two advancing ships in waves by the introduction of translating-pulsating source Green function.