Within vibration-based structural health monitoring — a field concerned with monitoring structural integrity through measured vibrations — a series of model-based methods have been developed which, granted that damage has been detected, employ a theoretical model of the structure to pinpoint the damaged locations.
Despite decades of research, the topic of model-based damage localisation has yet to see methods emerge which are fitting for general industrial application. A reason could be that these methods often involve solving an inverse problem, implying that they rely on system identification to establish accurate models from vibration signals; a feat not easily achieved due to, for example, extraneous noise. Within this category of methods lies the Dynamic Damage Locating Vector (DDLV) scheme, which relies on system identification to compute an experimental transfer matrix shift, from which null vectors are extracted and used as load vectors on a theoretical model to produce a stress field of zero magnitude over damaged regions.
We have recently seen emergence of schemes that may circumvent system identification, such as the Shaped Damage Locating Input Distribution (SDLID) scheme, which utilises a theoretical model to shape inputs that — when applied to the damaged and undamaged states of the system — render certain vibration quantities dormant. One can then declare damage when the subdomain containing the damage is suppressed, consequently producing identical vibration signatures in the two states. Another recent scheme residing in this category is the Subspace Exclusion Zone (SEZ) scheme, whose methodological premise rests on the fact that a damage-induced field quantity shift, outside a structural subdomain enveloping the damage, can be reconstructed by applying linearly independent stress fields on the boundary of said subdomain. We recognise that the SEZ scheme is not yet fully matured and, for that reason, place this scheme as the primary subject matter of this thesis. Initially, we present a performance demonstration of the SEZ scheme in the contexts of analytical, numerical and experimental application examples; of which the latter is concerned with locating mass perturbations spatially distributed on a cantilever beam. The outcome of the experimental study indicates that the SEZ scheme has no issues with clearly locating the mass perturbations. The results indicate that the scheme, even in its current state, is fully capable of locating damage in more complicated settings.
Secondly, we address an issue in which the scheme does not guarantee that the damage-induced shift is uniquely reproduced from the subdomain containing damage; in turn leading to false damage postulations, dubbed inseparable elements (IEs). This issue is addressed by proposing a method that aids in optimally distributing sensors — based on maximisation of linear independence between transfer matrix rows — such that the number of IEs is minimised. Despite not being able to guarantee the optimum, the suboptimal configurations proposed by the method turn out to be good candidates. The method is demonstrated to have merit due to a correlation existing between linear independence between the transfer matrix rows and the number of IEs.
Lastly, we present a comparative robustness study, in which the SEZ scheme is compared to the two previously mentioned model-based schemes, namely, the DDLV scheme, which relies on system identification, and the SDLID scheme, which operates unconditionally without system identification. The studies confirm the initial conjecture which placed system identification as a major reason for the lack of robustness of model-based schemes. The DDLV scheme initially performed well, but as noise was increased, the performance expeditiously decreased, establishing the SDLID and SEZ schemes as being more robust.