Subspace projections to localise damage: A comparative model error robustness study

A model-based branch of damage localisation methods relates damage-induced changes in vibration signals to a theoretical model resembling the reference structure. One such method is the recently proposed Subspace Exclusion Zone (SEZ) scheme, whose methodological premise rests on the fact that a damage-induced shift in any field quantity, outside a closed boundary encompassing the damage, can be generated by stress fields acting on said boundary. Specifically, the interrogation procedure is to postulate one such boundary at a time, using a theoretical model, and then declare damage within the particular boundary that enables reconstruction of the damage-induced shifts. Needless to say, the SEZ scheme hinges on a sufficiently accurate model of the reference structure, as generally is the case for model-based approaches. To ascertain the SEZ scheme's robustness to model error, the present paper seeks a comparison to two other damage localisation schemes, namely, the Dynamic Damage Locating Vector (DDLV) and the Shaped Damage Locating Input Distribution (SDLID), which incorporate a theoretical model to, respectively, pinpoint damage by mapping forces to stresses and tailor controllable inputs to cancel the effect of damage. The robustness study is conducted in the context of numerical examples in which model errors are introduced.