Geology Reference
In-Depth Information
Figure 2. Flow diagram of FLC optimization us-
ing micro genetic algorithm
to define the distance between the premise
points along the premise line.
Thus only two variables are required to be
encoded for optimization of the rule base. Making
consequent line angle to be 45
◦
and consequent
region spacing to be 1, we get a rule base as
shown in Table 2 analogous to the rule base that
can be derived from the first mode vibration of
the structure.
A micro genetic algorithm (μ-GA) (Krishna-
kumar, 1989; Ali and Ramaswamy, 2009a) is used
to optimize the fuzzy logic control parameters.
Figure 2 demonstrates the computational flow of
micro genetic algorithm. For the GA used in this
study, each chromosome represents a complete
FLC inference system i.e., membership function
optimization parameters, fuzzy input-output scal-
ing gains and the rule base optimization param-
eters. The rule base is modified using a geometric
approach keeping the symmetry in the rule base
structure as noted earlier. This reduces the com-
putational overhead of the optimization scheme.
For the present study an off-line trained FLC
is adopted. The off-line training is carried out by
providing an initial base displacement of 0.025m
and then allowing the hybrid system to come to
rest. The FLC that minimizes the following cost
function is adopted for the study.
Apart from the inherent advantages of the FLC
i.e., robust to uncertainty, noise etc., one important
advantage of using FLC in present situation is that
the voltage output,
v(t)
from the FLC, unlike the
clipped optimal, can take any value in the range
[0, 1]. Therefore FLC covers the full voltage
range available for the damper. In the process,
the voltage switch is gradual and does not jump
between zero and maximum. Secondly, μ-GA used
for the optimization process is computationally
less intensive.
x
x
x
x
J
=
b
+
b
(5)
ga
b
b
unc
unc
The above cost function considers minimiza-
tion (
L
2
norm) of the ratio of base displacement
(
x
b
) with controller and base displacement
x
b
un
( )
)without the controller, at the same time minimiz-
ing the corresponding ratio of acceleration norms.
The rule base obtained from this optimization is
then used to control the hybrid base isolated build-
ing.
EXPERIMENTAL VERIFICATION
OF OPTIMAL FUZZY CONTROL
A three storey base isolated building is considered
for the experimental evaluation. The schematic
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