| Abstract: | Modal updating is a crucial problem in Structure Health
Monitoring (SHM) and has strongly attracted researchers' attentions.
Recently the structures have been becoming much huger and more complex, so
it's getting harder to update the global structural model precisely using
the classical model updating methods. In general, only some local
substructure model is important and it is not necessary to update the whole
structure. Therefore the substructure technologies are important for that
they require only few sensors and the local dynamic information to
accurately update the interested substructure model.
Usually the updating of the element stiffness is enough to reflect the
damage and the structural dynamic performance. This paper proposes a concept
of the Isolated Substructure. It aims at updating local substructure element
stiffness only by the relative mode at the substructure location. The
present Isolated Substructure refers to a new structure formed by isolating
the substructure from the global structure. Then the substructure can be
updated indirectly through updating the Isolated Substructure, such that the
optimizing variables become much less and the convergent speed is fastened.
The key process of this method is to construct the flexibility matrix of the
Isolated Substructure by measured data. First the lower order frequencies
and shape modes of the substructure are identified from the measured impulse
response by utilizing Eigensystem Realization Algorithm (ERA), and the
relative modal masses are estimated by Least Square Method (LSM); Second,
according to its independence and convergence properties, the flexibility
matrix corresponding to the substructure can be approximately constructed by
the identified lower order modes and be improved by the calculated higher
order modes from the theoretical model; and then utilizing the concept of
the flexibility matrix, the substructure is isolated from the global
structure through applying numerical supporting on the substructure
boundary; synchronously the flexibility matrix of the Isolated Substructure
is constructed from the advanced obtained flexibility matrix of the global
structure, and is used to update the Isolated Substructure, that is, to
equally update the substructure.
The optimization method based on sensitivity idea is adopted, and the
relative formulas are deduced. It makes the iteration and convergence
faster.
A numerical example of a plane truss separately with 5% or 10% rms
Gaussian measurement error validates that the substructure can be updated
effectively by the Isolated Substructure model updating method. |
