Physics-Guided Symbolic Regression for Changing Dynamical Systems

Changing dynamic behaviours in engineering structures arise from many factors, including variations in operational loads, boundary conditions and environmental influences. In Structural Health Monitoring (SHM), changes in a structure’s dynamic behaviour are often used as potential indicators of damage. To do this reliably, however, it is essential to understand and isolate the many other factors that can influence these dynamics. Symbolic Regression (SR) offers a data-driven yet interpretable way to uncover the underlying relationships governing such changes, enabling models that not only fit observed behaviour but also explicitly capture how system dynamics evolve under varying conditions. In this work, physical constraints are incorporated to ensure that the recovered equations remain physically meaningful, preventing the search from producing overly flexible expressions that may fit the data well but do not correspond to plausible physical behaviour. An experimental case study is used to evaluate the approach on a cantilever beam and strut assembly subjected to multi-axial loading with a variable preload. As the preload applied to the strut increases, the system exhibits a clear stiffening effect in its dynamic response. The resulting models successfully extract, characterise and interpret this stiffening behaviour while maintaining strong predictive performance across the multiple dynamic regimes induced by the varying preload.