Geology Reference
In-Depth Information
Some Results of the
Optimization Studies
the same numerical size. Figure 7b presents the
normalized optimisation history. When comparing
these results with those of Figure 5c we should
remember that now the fitness function is the sum
of energy intake and compensator mass. Figure
7c draws the distribution of the stiffness and mass
along the buildings height, where we plotted the
masses to the left of the vertical axes using the
negative value of the mass. Both mass and stiff-
ness are normalized to a predefined value. We
realize that there is a large potential of reduction
of the impact on the building using a total mass
of the compensators of about 2% of the buildings
mass. On the other hand it should be mentioned,
that this result depends essentially on the defini-
tion of the relative weighting factors
w
2
and
w
1
.
Switching e.g. to
w
2
= 0.5*
w
1
yields significantly
different results. It is obvious that the design of
this absorbing system would be not trivial using
conventional methods.
As a general remark it should be mentioned
that the evolutionary process including a not-too-
small mutation radius is not well-suited for the
close approximation of nearby lying local maxi-
ma or minima. Therefore it might be a good idea
to switch to a local gradient search if one feels
that the process is close to an interesting summit
(Brieger 2008, Plevris, V. and Papadrakakis, M.
2011).
The method of evolutionary optimization of
compensators may be applied to other structures as
well. If the mass-, stiffness- and damping-matrices
are available, the entries for the additional dof for
the compensators may be added and the system
solved like outlined. As the time and storage
requirements depend on the square of the total
number of dof of the dynamic system, the amount
of time will grow essentially. Consequently an eco-
nomical handling of the resources will be needed
to come up with reliable results in reasonable time.
Grid computing by assembling all the available
computing power at night or during lunch breaks
proves to be very efficient.
The studies performed until now correspond well
to the results of other approaches and long-lasting
experience in the field. To summarise the most
important results, it should be mentioned that
•
Essential reduction of the impact of an
earthquake up to a factor of 5 and more is
possible (Figure 5c).
•
Larger numbers of compensators are more
efficient (Figure 6a).
•
Single compensators at higher floors are
more efficient than those at lower floors
(Figure 6b).
•
At a given number of compensators, an op-
timal or at least efficient distribution along
the building's height may be found (Table 1
and Figure 6a) by the modal contributions.
•
Damping should not be too high as it re-
duces the energy transferred to the com-
pensator mass (Figure 3e).
•
Designs for the compensators on different
floors are proposed.
•
Interaction of the efficiency of compensa-
tors may be analysed.
The method proves to be an efficient tool for
the design of compensators especially when larger
numbers of compensators are to be used.
The large number of jobs to be run keeps seems
prohibitive. But if we think of a problem with 40
compensators and 120 dof, the effort of a gradient
search is not very much smaller. The numerical
derivation (Equation (4)) requires 241 data. If we
need 20 steps to find the maximum a total of about
5000 runs have to be performed. As we are not
sure, whether our optimisation sticks to the next
local maximum, we should repeat the study using
different initial values. So numbers of 20 000 or
more runs are not uncommon. But then we are
in the range of the evolutionary process, so the
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