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Figure 4. Iteration history in terms of the objective function. Deterministic and uncertain models(Example 1)
that the optimal choice of this parameter from the
algorithm performance point of view depends on
the particular type of problem. The reader is re-
ferred to (Svanberg, 2002) for a general discussion
of the values of this parameter in the context of
conservative, convex and separable approxima-
tions.
tions. It is observed that the value of the objective
function at the final design of the uncertain model
is greater than the corresponding value of the
deterministic model. This in turn implies that the
structural components (columns) of the uncertain
model are bigger than the corresponding compo-
nents of the deterministic model. This result can
be seen from Figure 6, where the final designs of
the deterministic and uncertain models are shown
in the design space corresponding to the uncertain
model. Note that the final design obtained from
the deterministic model is not feasible. Finally,
it is seen from Figures 4 and 5 that the method
generates a series of steadily improved feasible
designs that move toward the optimum.
Results
The iteration history of the optimization process in
terms of the objective function and the reliability
constraints is shown in Figure 4 and figure 5, re-
spectively. For comparison, the results obtained
with the deterministic model are also shown in
the figures. In this context, the deterministic
model considers the damping ratio equal to its
most probable value. The objective function is
normalized by the cost of the initial design. It is
seen that, starting from a feasible initial design,
the process converges in less than four iterations.
Therefore, the entire optimization process takes
few excursion probability and sensitivity estima-
Example No.2
Structural Model
A four-story reinforced concrete building under
earthquake motion is considered for analysis. A
3D view of the system is shown in Figure 7. Each
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