Flexibility-based damage localization from stochastic realization results

Localization of damage from changes in flexibility in structures identified from operational or ambient vibration has long been hindered by the fact that the flexibility cannot be extracted exclusively from output signals. This obstacle is substantially removed here by noting that the null space of the flexibility change contains the damage localization information and that vectors in this null space can be estimated from output signals without having explicit flexibility matrices. The central pillar of the contribution is a derivation showing that although the spatial distribution of the input that generates the observed output is unknown, the state-space triplet {A(c)B(c)D(c)(-1)C(c)} connected with a collocated input distribution (for a model order up to twice the number of sensors) can be extracted from output measurements. The fact that vectors in the null space of the change in flexibility can be extracted from this triplet falls from the expression for the flexibility in terms of the state-space matrices and from the fact that the damage is assumed to have no effect on the inertial properties.