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assumed as a white noise random process and most of existing buildings have no sensors to measure
the ground motion directly underneath the building. Therefore, the direct identification of structural
parameters at the element level in the time domain attracts more and more attention from researchers
and engineers.
As far as identification of a structure under seismic excitation is concerned, several techniques have
already been proposed to estimate the structural parameters and input excitation from the measured
response alone. Toki (1989) and Hoshiya (1995) solved this problem by assuming that the coda of the
measured response time history represented the free vibration response of the structural system and
estimated the structural parameters using the extended Kalman filter technique from this part of the
measurements. The input ground motion was then estimated using the obtained parameters. However,
it is difficult to decide the exact starting time of the free response part without knowing time history of
the ground motion. Moreover, the performance of Kalman filter is sensitive to the initial condition
selected. Wang and Haldar (1994) proposed another approach to simultaneously identify the input
excitation and structural parameters in the element level. In their method, the input was initially
assumed to be zero at the first four sampling time points, structural parameters were estimated at this
four points using the least-squares technique. Then, the input information on all the sampling time
instants was computed using the estimated parameters and measured responses. Afterward, structural
parameters could be identified again using the estimated input excitation and measured responses of
the full length. The iteration procedure was stopped when the identified input excitation at the first
four points converged to a predetermined tolerance level. Later on, by combining with the extended
Kalman Filter, this approach was expanded (Wang and Haldar, 1997) for the case that the response
measurements of a structure were available at only limited locations. More recently, Cho (2000)
improved this approach into a more generalized style and ameliorated the convergence of least-squares
method by using multiple model QR decomposition algorithm.
In this paper, the element-level time-domain approach suggested by Wang and Haldar (1994) is
improved for simultaneous identification of earthquake excitation and structural parameters from
measured structural responses using a combination of the least-squares-technique and the statistical
average method. Numerical examples using shear type buildings are carried out to demonstrate the
feasibility of the improved method, named the dynamic compound inverse method.
DYNAMIC COMPOUND INVERSE METHOD
Basic Equations
The response of a N-story shear building subjected to a base acceleration X g (t) is governed by the
following equation
MX(t) + CX(t) -f KX(t) = -MX g (2.1)
where M is the diagonal mass matrix of the building with all the elements provided. C and K, each
of order N by N, are the damping and stiffness matrices that consist of structural parameters k,, c,
(i=l,N) to be identified X(t), X(t) and X are the relative displacement, velocity and acceleration
response vectors of the building with respect to the ground. Eq.(l) can be rearranged into the following
form for identification.