Efficient Robust Optimization of Structures Subjected to Earthquake Load and Characterized by Uncertain Bounded System Parameters - Structural Seismic Design Optimization and Earthquake Engineering - page 121

creases the time requirement by the LSM based
approach. Thus the computational involvement
with regard to generation of training data point
will be substantially high whereas, there is a
higher computational demand with regard to re-
peated evaluation of response surface. Of course,
it needs further study to comprehend which one
will be more efficient.
Now, the optimization task is performed by
the sequential quadratic programming (SQP) us-
ing built-in MATLAB routine. The weight of the
frame is optimized by the proposed importance
factor based RDO approach as described by Eq.
(29) and the conventional RDO approach as de-
scribed by Eq. (6) considering uncertainty in both
the DVs and DPs. The results are studied through
Figures 4, 5, 6, 7 and 8. The optimal weight of
the frame versus the dispersion of the DVs and
DPs are plotted in Figure 4. For comparison, the
results obtained by the conventional RDO ap-
proach are also shown in the same figure. The
variations of the optimal weight of the frame
(indicates the measure of robustness) versus the
dispersion of the input DVs and DPs, as obtained
by the proposed and conventional RDO ap-
proaches are depicted in Figure 5. The value of

the penalty factor, kj and the bi-objective weight
factor, α are considered to be 1.0 and 0.5, respec-
tively. It can be noted that the optimization results
obtained by the proposed approach indicate an
improved robustness compared to the conven-
tional RDO method.
The optimal weight and its dispersion are plot-
ted in the Figures 6 and 7, respectively, with respect
to the upcrossing level, β for different values of
kj. The dispersion of the inputs and α are set as
10% and 0.5, respectively. It can be noted from
these figures that the same nature of variations
and improvement are observed for all the values
of kj considered in the study. In general, it has
been observed that the effect on the robustness is
more prominent for smaller values of β. This is
obvious as the smaller value of β represents more
stringent failure criterion and makes the constraints
more critical. Thus, the effect of the importance
of the sensitivity derivatives introduced by the
proposed RDO approach becomes more.
One of the important tasks in an RDO proce-
dure like any other multi-objective optimization
problem is to obtain the Pareto front (Deb, 2001).
It is generally observed that there is a trade-off
between the objective value of a design and its

Figure 4. The optimal weight of the frame with increasing range of uncertainty