Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

ence in cost is due to the fact that the standard deviation metric is less conservative
in this implementation. Note that both optimization algorithms take a very long
time to converge when Monte Carlo standard deviations are calculated. This jump in
computational effort is due to the fact that to get a good estimate of standard devia-
tion it is necessary to run a large number of uncertainty combinations. In the case of
the SQP algorithm, it is important that the Monte Carlo uncertainty distribution is
chosen before running the optimization so that the uncertainty space are consistent
from one iteration to the next. Otherwise, the gradients given in Equation 3.14 do
not track the design changes.
The differences between the SQP and SA designs are similar to the other cases
considered thus far in that SA finds a sub-optimal design, but provides a starting point
for SQP that is very close to the optimal design. Although the Monte Carlo method
provides a more accurate measure of the standard deviation, the results indicate that
the increase in accuracy is not worth the additional computational effort required.
The combination of SA and SQP optimization with the vertex method converges in
17 minutes compared to 151 minutes required for the Monte Carlo metric. Although
the vertex method may not be an accurate measure of standard deviation for the
uniform distribution, it does provide a conservative measure of robustness for bounded
uncertainty models.
In order to assess the effect of the weighting parameter, α, the statistical robust-
ness algorithm is run over a range of relative weightings from 0.0 to1.0. The nominal
and worst-case performance for the resulting designs are plotted in Figure 3-5 along
with the standard deviation measure obtained from the vertex method. The nominal
performance is depicted with circles and the standard deviation with stars. As α
increases, the weight on the standard deviation decreases and that on nominal per-
formance increases as evidenced by the figure. The nominal performance decreases as
α increases while the standard deviation shows the opposite trend. At α =0.0, the
nominal performance is not included in the cost at all and only the standard deviation
is minimized. At the other extreme, when α =1.0, the standard deviation is elimi-
nated from the cost function and the problem is equivalent to the PT optimization.
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