Non-destructive measurement of natural frequencies provides a simple means of detecting the location and severity of damage in a structure through changes in its eigenvalues.  Further information is provided by changes in vibration modes (i.e. the eigenvectors), but this requires a scan of the whole structure which may be impractical for in situ assessment.
Eigenvalue changes for a single occurrence of damage give a "damage signature" which can be found numerically and normalised so that its components are functions of the damage location but are independent of its severity.  Thus, by using measured natural frequencies from the structure before and after the occurrence of damage, the location is found by solving an inverse problem, and then the severity is determined by comparison with the unnormalised damage signature.
The procedure has been evaluated for simulated and actual cracks in a frame structure, using interval arithmetic to allow for noise in the frequency measurements.  It is currently being extended to cracks and delaminations in stiffened plates such as aircraft wing panels.  Theoretical enhancements include analytical and determinant-based expressions for the damage signature and the formulation of multi-dimensional inverse problems to detect multiple occurrences of damage in combination with environmental effects.