Omitted coordinate systems and artificial constraints in spatially incomplete identification

Optimal selection of artificial boundary conditions for model update and damage detection

“…The method of artificial boundary conditions [13], or ''pseudo-tests'' [14] offers those benefits while avoiding some of their drawbacks. The theory of ABC originates in the concept of the omitted coordinate system (OCS) [15] which plays a central role in the underlying properties of advanced model reduction techniques and frequency domain updating; see for example, [16][17][18][19][20][21][22]. With respect to an experimentally derived model, an OCS is the dynamic system which results when some of the measured coordinates are restrained (i.e.…”

Artificial Boundary Conditions for Model Updating and Damage Detection

“…In short, a measured FRF matrix represents an in"nite-dimensional system dynamically reduced to the measured coordinates. This is a central fact in this work, and a complete development of this fact is found in [2,3].…”

“…The ABCs are implicitly de"ned in any set of spatially incomplete frequency response function data, and are those boundary conditions which de"ne an omitted coordinate set system or OCS [2,3]. This system is de"ned by the set of all unmeasured coordinates.…”

Extraction of artificial boundary frequencies for damage identification

“…It was demonstrated by Gordis (1996) that, by manipulating the incomplete frequency response function matrix measured at specific points on the existing structure, it is possible to identify resonance frequencies from the resulting frequency spectrum that exactly correspond to the natural frequencies of the structure as if additional pin supports were imposed at the specific locations. Since no physical pin supports are actually involved, such altered boundary conditions are referred to as "artificial boundary conditions", and the corresponding natural frequencies are referred to as artificial boundary condition frequencies, or in short ABC frequencies as used by the authors.…”

“…The development of the "artificial boundary method (ABM)" (Gordis 1996(Gordis , 1999 paves the way for such an idea to be considered in civil engineering applications. It was demonstrated by Gordis (1996) that, by manipulating the incomplete frequency response function matrix measured at specific points on the existing structure, it is possible to identify resonance frequencies from the resulting frequency spectrum that exactly correspond to the natural frequencies of the structure as if additional pin supports were imposed at the specific locations.…”