H. Xiao et al., An input/output-based procedure for fully evaluating and monitoring dynamic properties of structural systems via a subspace identification method, J SOUND VIB, 246(4), 2001, pp. 601-623
Dynamic behaviour of complex structural systems may be modelled by a system
of second order linear ordinary differential equations, i.e., Mw(t) + Dw(t
) + Sw(t) = f (t), by means of either structural analysis for finite degree
-of-freedom systems or discretization procedures (e.g., FE methods) for con
tinuous systems. Here, w(t) and f(t) are the displacement vector and the fo
rce vector. Owing to erosion, friction, and internal damage and cracks, etc
., a working process of a system always accompanies gradual degradation of
the performance of this system: the stiffness of the system weakens, wherea
s the damping of the system strengthens. To evaluate such degradation, the
usual way is to model the evolution of property of a system, obtain system
property parameters, trace the history of motion and loading, carry out com
plicated analysis and computation under prescribed initial and boundary val
ue conditions, and finally derive the degraded property and responses of th
e system. This traditional way, however, might be cumbersome and unsatisfac
tory in some cases due to the lack of adequate experimental data and well-f
ounded theoretical basis, etc. Another way is to apply "inverse" methods, s
uch as modal analysis methods with FFT and a subspace identification method
, etc., developed in the theory of system identification, which extracts in
formation about system properties directly from experimental input/output m
easurement data and hence do not involve the foregoing traditional analysis
. The latter method, however, could not supply full information about syste
m properties due to the assumption of the "black box" viewpoint. In this wo
rk, with suitable experimental input/output measurement data, a simple, eff
ective procedure is described by which the stiffness matrix S and the dampi
ng matrix D may be determined in a complete, unique manner using a subspace
identification method. The possibility of such a procedure arises from the
observation of the self-evident fact: the conservation of mass of any part
of a structural system implies that the mass matrix M of this system is co
nstant and hence is given by its initial value. The stiffness and damping m
atrices S and D determined by the proposed procedure may be used to evaluat
e and monitor, in a full sense, the degradation of dynamic properties of st
ructural systems. Further, with the information about the stiffness distrib
ution of constituent elements of a structural system it is shown that it ma
y be possible to estimate the locations of the damaged or faulty elements i
n this system. An example is given to illustrate the application of the pro
posed procedure. (C) 2001 Academic Press.