Geology Reference
In-Depth Information
ing a single objective GA optimizer, each of the
objective functions separately is minimized. Then,
using a fast and elitist non-dominated sorting
genetic algorithm (NSGA-II) approach is used
to find Pareto-optimal solutions in Pareto space
(Pourzeynali & Zarif, 2008).
As the GA is a stochastic search methodology,
it is difficult to formally specify convergence crite-
ria. In practice, the common rule is to terminate the
GA after a predefined number of generations and
then test the quality of solutions. If the solutions
are not acceptable, then the GA may be restarted
by more generation numbers or by taking fresh
initial values. For single objective GA optimizer
the following parameters are chosen (Gen &
Cheng, 1997):
The results of the isolated building responses
for four selected earthquakes, as well the ensemble
average values of its stories responses for the
18 reference earthquakes, all optimized by GA,
are shown in Table 4. In last row of the table the
ensemble average reduction ratios on building
stories displacements are also shown. It is seen
from the table that NSGA-II is significantly ef-
fective in minimizing the objective functions and
calculating the design parameters. It can be seen
that in average a reduction of 64.47% is obtained
on building top story horizontal displacement
response (Pourzeynali & Zarif, 2008).
Multi-Objective Optimization by
Considering Non-Linear Behavior of
the Bearings
•
Number of chromosomes = 25
•
Number of generations = 300
Herein, the material non-linearity of the isolator
bearings has been taken into account by assuming
that the lead rubber bearings have been used. For
simplification, the non-linear hysteretic curve of
the bearings, as shown in Figure 1, is divided into
two linear parts (bilinear models).
Main parameters of the bilinear isolators are:
the base mass shown by
m
b
(similar linear case);
isolator stiffness in elastic phase shown by
k
b1
,
and its stiffness in plastic phase
k
b2
; its time pe-
riod in elastic phase and after yielding shown by
•
Probability of crossover,
P
c
=
0.25
•
Probability of mutation,
P
m
=0.01
The GA iterations terminated after 300 gen-
erations and the best results for the parameters
of base isolators are obtained as (Pourzeynali &
Zarif, 2008):
m
=
1.20 ,
k
=
0 05
.
,
ξ
=
0 25
.
0
0
b
Table 4. Controlled responses (Optimized by GA) of the isolated building supported on linear isolators
(Pourzeynali & Zarif, 2008)
Stories of the building
Earthquake
Base
1
st
2
nd
3
rd
4
th
5
th
6
th
7
th
8
th
9
th
10
th
Kobe
0.303
0.051
0.075
0.088
0.094
0.099
0.104
0.110
0.113
0.116
0.118
El Centro
0.168
0.025
0.044
0.056
0.063
0.068
0.073
0.082
0.090
0.095
0.097
Loma Prieta
0.207
0.032
0.053
0.065
0.070
0.074
0.084
0.094
0.100
0.104
0.107
Northridge
0.475
0.064
0.098
0.117
0.131
0.144
0.154
0.167
0.174
0.178
0.183
Ensemble average re-
sponses (m) (Optimized
by GA)
0.115
0.025
0.022
0032
0.081
0.050
0.058
0.066
0.072
0.077
0.080
Ensemble average
Reduction Ratios (%)
-------
53.10
61.80
62.36
59.20
62.80
63.00
63.34
63.95
61.50
64.47
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