Koopman Operator Methods in Structural Health Monitoring: A Systematic Review Towards Hybrid Physics–Data Frameworks

Structural health monitoring (SHM) is essential for the safety and long-term performance of civil and mechanical infrastructure, yet traditional vibration-based approaches often struggle with nonlinear behavior and environmental variability. Koopman operator theory provides a promising alternative by enabling linear analysis of nonlinear structural dynamics through observable functions. This review examines 67 peer-reviewed studies published between 2010 and 2025 and selected using Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines. We outline the development of Koopman-based methods from Dynamic Mode Decomposition (DMD) and Extended-DMD (EDMD) to recent applications in civil, mechanical, and aerospace systems. This review clarifies the mathematical foundations of Koopman analysis and its relationship to structural dynamics. It also identifies major research gaps, including limited damage-sensitive observable design, insufficient use of structural mechanics constraints, the absence of quantitative links between Koopman spectra and physical damage, inadequate benchmarking, and the need for real-time deployment strategies. We conclude by outlining a hybrid Koopman framework that integrates physics-based information with data-driven learning to support interpretable and scalable SHM.