Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

metric to the cost function. Note, however, that the uncertainty parameters do not
appear in the constraint equations. The RPT optimizations considered in this thesis
do not include constraints that are a function of the uncertainty parameters. For
example, the uncertainty parameters chosen for the sample problem affect only the
stiffness matrix and not the constraint on total system mass. In the most general
form of Equation 3.3, uncertainty does affect the constraints and can be incorporated
by requiring that the tailoring parameters satisfy the constraint equations for the
uncertainty values that are worst-case in relation to the constraints. Examples of
such problems are found in [42] and [103].
There are many possible formulations for JRP T since there are numerous ways to
account for uncertainty and penalize design sensitivity. In the following sections three
known techniques are presented and discussed in detail.
3.2.1 Anti-optimization
Optimization with anti-optimization (AO) is a design approach for structural opti-
mization with bounded uncertainty formulated by Elishakoff, Haftka and Fang in [42].
The authors discuss both of the formulations described below and demonstrate the
design method on a standard ten-bar truss optimization problem using sequential lin-
ear programming. The truss is subjected to uncertain loads, and the cross-sectional
areas of the truss members are optimized for minimum mass subject to stress and
minimum gage constraints.
Anti-optimization can be defined as a min-max optimization problem that includes
the process of identifying the critical uncertainty parameter values.
min
�x
JAO
� �� �
max
�p∈P
s.t �g(�x) ≤ 0
f (�x, �p) (3.4)
At each iteration of tailoring parameters, �x, an uncertainty analysis is run to de-
termine the values of uncertainty parameters, �p, that result in the worst-case per-
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