Using artificial intelligence (AI) for structural health monitoring (SHM) offers powerful capabilities for detecting, localizing and quantifying damage in complex composite structures. However, many data-driven models are 'black boxes', providing limited interpretability and a weak connection to the underlying wave physics. This study explores a physics-guided AI framework that combines dispersion-aware sparse decomposition and tensor analysis for guided-wave-based SHM. This approach combines features that are compact and physically meaningful, linked to propagation distance, attenuation and dispersion, with machine learning to enable efficient, interpretable decision-making. A comparative study was conducted against conventional data-driven approaches using a representative complex composite structure under various damage scenarios. The results show that, although pure AI models can achieve high detection accuracy, the proposed hybrid framework achieves similar or superior performance with enhanced robustness and explainability. The physically grounded representation provides direct insight into damage mechanisms, enabling reliable monitoring and facilitating the integration of AI into maintenance and certification processes. Thus, this interpretable hybrid approach provides a promising route towards trustworthy, physics-informed SHM of next-generation aerostructures.