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IDENTIFICATION ALGORITHM
State Transfer and Observation Equations
For simplicity we formulate the system transfer and observation equations for a single degree of
freedom system. The equation of motion for a structural system is
in which, m is the mass, h the damping ratio,
y 4- 2hcoy + co 2 y = -X g (16)
co the natural circular frequency , and y is the
relative displacement to the ground. X^ is the ground acceleration. And the state vector is chosen as
follows:
x= [y y h co} T (17)
The state transfer equation is expressed by a nonlinear equation as follows:
in which, g is a vector composed of four components
gCx^Xf+W, (18)
g={-2h(ay-(D 2 y-X 9 y 0 0) r (19)
When the relative velocity and displacement are observed, the observation equation is defined as
follows:
n f f n (2Q)
in which, H is given by
H
o
O i o o
(21)
Identification Algorithm Using Hybrid Filter
In Hybrid Filter, the state vector in the MCF is divided into two parts , in which one represents the
responses of the structural system, \ a and the other represents the structural dynamic parameters,
\p as follows:
**={^v} r (22)
Xp = [h,a)\ T (23)
The distribution of x a is assumed to be Gaussian and identified by the KF algorithm. The
distrubution of \ fl is expressed by many particles and identified by the MCF algorithm.
The Hybrid filter algorithm is defined by the following steps:
1 . Define an initial value of the state vector x ff 0 and its covariance matrix P 0 .