Geology Reference
In-Depth Information
inputs are considered as: big negative (BN), small
negative (SN), zero (Z), small positive (SP), and
big positive (BP), and if the space between
SP
and
Z
is
a
, and that of the
SP
and
BP
is
b
, then
the parameter
P
i
is defined as (Figure 6):
Figure 7, if the first input is
SP
and the second
input is
BN
, then the output is zero. Table 6 shows
the obtained fuzzy rule base from Figure 7a. As
mentioned, the output of the fuzzy system is
ξ
stmd
( )
. It has five triangular membership func-
tions which lie between 0 and 0.5. Therefore, the
damping value can guarantee the stability of the
structure, and STMD system always acts as an
under damped system. The design variables are
P
s
, P
i
, θ,
m
0
,
β
and
ξ
stmd
( )
that should be designed
by multi-objective optimization method.
P
i
=
b
a
(25)
According to the symmetry between the inputs
variables, the space between
SN
and
Z
, and the
space between
SN
and
BN
are also
a
and
b
, re-
spectively. Referring to Equation (25), if
P
i
is
more than one, then the
SP
value is close to zero,
and if
P
i
is less than one, then the
SP
value is far
from the zero, and if
P
i
is equal to one, then the
inputs values are placed with the same intervals
respect to each other and to zero. These concepts
are shown in Figure 7.
The angle
θ
is measured with respect to the
horizon for the grid lines which divide the rule
base space into different regions with the number
of output linguistic variables. For example, in
Figure 7, the angle
θ
is 45 degrees for all cases.
In this method, it will be assumed that if the inputs
are zero, then the output is, also, zero and if the
inputs have their maximum value, then the output
is, also, maximum. By considering above assump-
tions, output linguistic variables place in various
regions according to Figure 7. As a result, for each
combination of input linguistic variables, proper
output is equal to the amount which is located in
the desired area. As an example, according to
Numerical Study
In order to evaluate the performance of the pro-
posed control devices (STMD/TMD), a reality
12-story steel building is considered and modeled
as a 3-D frame, and analyzed under application of
7 earthquake accelerogrames presented in Table 1.
Three non-commensurable objective functions
namely, maximum displacement, maximum ve-
locity, and maximum acceleration of each floor
are considered as the objective functions to be
minimized simultaneously by multi-objective
optimization process. These objective functions
are expressed in the following:
( )
c
D t
J
1
=
max max
(26)
i
( )
D t
uc
i
t
i
Figure 6. Definition of the parameter P
i
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