Enhancing operational performance assessment of structures with seismic response modification devices: The role of observability and symmetry analysis under limited sensor deployment

To manage structural responses under various external forces, the increasing incorporation of seismic isolation and supplementary damping systems in modern civil engineering necessitates post-installation performance assessments. The challenge of accurately inferring system information from these complex dynamical structures, especially with limited sensor deployment, could be significant. From the perspective of solving inverse problems, this challenge hinges on constructing an input-output mapping that assures unique solutions, achievable through theoretical observability or symmetry analysis. We introduce a unified algorithm framework designed to accommodate various definitions of Lie derivatives, specifically for observability and symmetry analysis in dynamic systems with affine, non-affine, and unknown inputs—capabilities not fully achieved in previous studies. We demonstrate its application across typical dynamic scenarios, including both linear and nonlinear examples. We also present a numerical example featuring complex isolation systems with limited sensor layouts, illustrating how uniform convergence can be achieved in estimating all system states when an observable input-output mapping is utilized. Furthermore, an experimental example employing shaking table tests showcases the potential complications that arise when an unobservable input-output mapping is used.