A Normal Mode Separation Method Based on Particle Swarm Optimization

Using data acquired by a vertical line array (VLA) to perform normal-mode separation and extract modal depth functions as well as modal horizontal wavenumbers is crucial for applications such as acoustic source localization and environmental parameter inversion in underwater acoustic propagation. For the normal-mode separation method based on horizontal-wavenumber consistency constraints, the embedded grid-search algorithm suffers from high computational cost and low search efficiency when addressing modal degeneracy. This paper proposes an improved mode-separation method integrated with the particle swarm optimization (PSO) algorithm. By adopting the standard deviation of the vertical distribution of horizontal wavenumbers as the fitness function, the proposed method employs PSO to search for the optimal linear transformation matrix mapping degenerate modes to true modes, thereby achieving effective mode separation. Numerical simulation results demonstrate that the improved method effectively resolves modal degeneracy, accurately reconstructs true modal functions, and precisely estimates horizontal wavenumbers. Compared with the grid-search algorithm, the PSO-based method achieves superior estimation accuracy, significantly lower computational cost, and faster convergence. In particular, under scenarios involving simultaneous degeneracy of multiple modes, the PSO-augmented algorithm exhibits an order-of-magnitude improvement in computational efficiency, striking an optimal balance between accuracy and efficiency in normal-mode separation.