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Identification of nonlinear SDOF system
The performances of the UPF and the EKF are evaluated on nonlinear identification problem
with Bouc-Wen's hysteretic spring mode mentioned in previous section (see Eqn. (3.2)). Fig.
3.4 compares the estimates generated from a single run of EKF and UPF. The extend Kalman
filter shows divergence phenomena whereas unscented particle filter (UPF) shows good
estimation capability.
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io
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1 ft
-8
-10
fl
D.erge ^ ji
y/JV , i ! I ! !
•«' y» i / i i
i
— observed response
— UPFestmaton
— EKF estimation
I l\
i f i
f "hi
'• ¥\ / \ / ^
\ i y v -
r I i I i
V II li ' * :
V j
Time (sec)
i i \ 'i j.
i I la A /\
15 "j 1 5 — EKF estmaton
f ',
^5
1 5
nllnearpar
a
z
tn o
^\ — 'Exact values
S
,|
f^
i
;
-10
^
Diverge
1
-IS
05 1 IS 2 IS 3 3.5 4 45 5
Time (sec)
-
Diverge
— Exact values
— UPF esUmaHon
— EKF estmaton
Time (sec)
a) states and parameter estimation b) probability density functions estimated
by unscented particle filter
Fig. 3.4 Estimations by the extended Kalman filter and unscented particle filter