Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

π
2 Lρ
2�
i=1
0.03 − di ≤ 0 ∀i =1, 2 (2.35)
−mi ≤ 0 ∀i =1, 2 (2.36)
� � 2
di + mi − 0.90M¯ ≤ 0 (2.37)
where ¯ M is the total system mass allocated to the design. Only 90% of the mass
budget is allocated at design in order to reserve 10% as margin. Note that the mass
constraint is nonlinear in the cross-sectional diameters.
The equations presented throughout this section describe the PT formulation for
the SCI development model and are summarized in Equation 2.38. The objective is
to minimize the RMS of the performance metric over all frequencies given a white
noise disturbance input. Four design variables, a symmetric distribution of the cross-
sectional areas of the four truss segments and two lumped masses, are considered.
The variables are constrained by a mixed set of linear and nonlinear inequalities that
ensure the optimized design meets practical criteria. In the following section the
optimization algorithm used to produce performance tailored designs are discussed
and results from the SCI development model are presented.
�x T =
�
d1 d2 m1 m2
�
�x ∗ = argmin
x∈X σz (�x) (2.38)
s.t. 0.03 − di ≤ 0 ∀i =1, 2
−mi ≤ 0 ∀i =1, 2
π
2 Lρ
2� � � 2
di + mi − 0.90M¯ ≤ 0
i=1
2.4 Optimization Algorithms
The field of optimization is quite large and there are many algorithms available to
solve problems such as the PT formulation given in Equation 2.38. In general, the
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