MmPiFNN: A multi-mode physics-informed fuzzy neural network for passive recognition of surface ships by underwater equipment using ship radiated noise signals

Ship radiated noise (SRN) is a key acoustic cue for underwater platforms such as submarines to detect, identify, and track surface vessels in long-range sonar confrontation scenarios. Accurate classification of SRN signals is thus critical for underwater target recognition and maritime situational awareness. However, under complex and dynamic marine environments, SRN recognition remains highly challenging due to strong background noise, sample imbalance, and limited availability of labeled data. To enhance recognition performance under these constraints, this paper proposes a novel multi-mode physics-informed fuzzy neural network (MmPiFNN) that integrates multi-mode features, fuzzy inference, and physics-based constraints. The model applies Wasserstein generative adversarial network-based data augmentation to address class imbalance and data scarcity. It then extracts time domain, time-frequency domain, and spatial domain features in parallel, followed by a fuzzy inference mechanism that adaptively fuses multi-mode information, improving interpretability. The fused features are input into a physics-informed neural network enhanced with three physics-based constraints: classification loss, multi-mode consistency loss, and physics-informed residual loss, enabling end-to-end physically consistent learning. The experimental results demonstrate that the proposed MmPiFNN achieves a classification precision of 91.22% on the DeepShip Dataset, outperforming existing models. Moreover, it maintains stable and high recognition performance even under small sample conditions, indicating strong practical value and promising application potential.