Static condensation optimal port/interface reduction and error estimation for structural health monitoring
This work addresses the need for efficient model reduction in structural health monitoring when geometries change due to defects, offering a method to reuse port spaces across different geometries.
The paper proposes optimal reduced port spaces for static condensation that achieve exponential convergence on structures with changing geometries, enabling efficient reuse across significantly different geometries for structural health monitoring.
Having the application in structural health monitoring in mind, we propose reduced port spaces that exhibit an exponential convergence for static condensation procedures on structures with changing geometries for instance induced by newly detected defects. Those reduced port spaces generalize the port spaces introduced in [K. Smetana and A.T. Patera, SIAM J. Sci. Comput., 2016] to geometry changes and are optimal in the sense that they minimize the approximation error among all port spaces of the same dimension. Moreover, we show numerically that we can reuse port spaces that are constructed on a certain geometry also for the static condensation approximation on a significantly different geometry, making the optimal port spaces well suited for use in structural health monitoring.