Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

generated and SQP is run from each one. The minimum-cost design is then identified
from the results. The cost and design variables listed for this algorithm in the tables
are the best of the ten runs, and the number of iterations and function evaluations are
the sum of the values from each individual run. The exhaustive search is conducted
by discretizing the tuning masses into fifty distinct values within the allowable range
and performing a full-factorial search of the space, neglecting any mass combinations
that violate the constraints.
First, consider the tuning results for the worst-case PT design (Figure 4-1). The
SA-SQP combination finds the optimal tuning solution in the shortest amount of time.
The combined time required to tune the PT design using first SA and then SQP is
54.21 seconds, while MC SQP with ten initial guesses takes over almost four times as
long (210.51 seconds). The MC-SQP and SA-SQP results are equivalent indicating
that a global optimum is found. The SA design providesa a good starting point for the
SQP optimization in that the tuned performance is very close to the optimial design
and the majority of the mass is placed at m2. The SA-SQP combination is a good
way to handle convexity issues when the space is not well known. The exhaustive
search results further support this conclusion, as does the surface plot of the solution
space, Figure 4-1(b). The light and dark regions in the plot indicate high and low
performance variance, respectively. The darkest area is along the constraint boundary
of zero m1, nearm2 = 200 kg.
The RPT AO results, Figure 4-2, show similar trends to the PT results. Both the
SA-SQP and MC-SQP algorithms find an optimal tuning solution, but SA-SQP does
so much more quickly (37 seconds, instead of 264 seconds). SA finds a sub-optimal
design due to the randomness of the search, but provides a good starting point for
SQP. The exhaustive search design is nearly equivalent to the SA-SQP and MC-SQP
designs indicate that a global optimum is found. The ES design is slightly sub-optimal
due to coarse discretization of the tuning parameter values. The accompanying plot of
the tuning space, Figure 4-2(b), shows that the tuning solution is a global minimum.
A comparison of the performance scale of the RPT space to that of the PT space
indicates that the RPT design is less tunable. In Figure 4-1(b) the performance
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