Fuzzy Identification of Seismically Excited Smart Systems - Structural Seismic Design Optimization and Earthquake Engineering - page 336

7. CONCLUSION squared errors (MSE); is the fitting rate (FR), e.g.,

if the proposed fuzzy models produce the same
responses as the simulation model, FR is 100; is
the output of the proposed MIMO ARX-TS fuzzy
models; and and are the output data from the
simulation model and the associated mean value,
respectively. The performance of the proposed
HRC approach is compared with benchmark
clustering algorithms, the fuzzy C-means and the
subtractive clustering techniques. It is found from
Table 2 that the proposed HRC MIMO ARX-TS
fuzzy model outperforms over the other methods
in terms of acceleration responses (i.e., ). The
performance of identifying displacement (i.e., )
and acceleration responses using the proposed
HRC MIMO ARX-TS fuzzy model is much bet-
ter than the one of the subtractive clustering-based
approach. It is, however, shown from the table
that the identified displacement response of the
fuzzy C-means clustering-based approach is bet-
ter than that of the proposed HRC MIMO ARX-
TS fuzzy model. In other words, the proposed
HRC-approach effectively identifies the accel-
eration responses while the fuzzy C-means clus-
tering approach better captures the behavior of
displacement responses. Note that accelerometers
are selected in the field of large-scale civil infra-
structures in general in order to implement struc-
tural control systems and/or structural health
monitoring systems because the acceleration re-
sponses are readily available, compared to other
quantities such as displacements and velocities.

In this chapter, a nonlinear fuzzy logic modeling
framework has been proposed to model nonlinear
behavior of structural systems employing smart
control devices: the hierarchical clustering-based
(HRC) multi-input, multi-output (MIMO) Au-
toregressive eXogenous (ARX) Takagi-Sugeno
(TS) fuzzy model (HRC MIMO ARX-TS fuzzy
model). The HRC MIMO ARX-TS fuzzy model
is developed through the integration of the HRC
technique, a family of local linear ARX input
models, TS fuzzy model and weighted least squares
estimator. The proposed modeling framework can
be directly applied to the structure-MR damper
system without the decoupling process because
it is inherently a nonlinear system identification
(SI) method; 2) it is more appropriate to iden-
tify incomplete and incoherent measurements
of large civil structures than typical parametric
SI approaches; and 3) it provides a systematic
design framework for the parallel distributed
compensation (PDC)-based nonlinear TS fuzzy
controller. To demonstrate the effectiveness of the
proposed HRC MIMO ARX-TS fuzzy model, a
seismically excited building-MR damper system
is investigated. It is demonstrated from the time
history response analysis that the proposed fuzzy
model is effective in identifying nonlinear behav-
ior of the building-MR damper system subjected
to earthquakes.

REFERENCES

6. FUTURE RESEARCH DIRECTIONS

Abonyi, J., Babuska, R., Verbruggen, H. B., &
Szeifert, F. (2000). Incorporating prior knowl-
edge in fuzzy model identification. Interna-
tional Journal of Systems Science , 31 , 657-667.
doi:10.1080/002077200290966

In near future, the authors intend to optimize the
architecture of the proposed HRC MIMO ARX-
TS fuzzy model. Also, it is recommended that the
proposed models be validated using a variety of
other disturbance signals.