Optimization and Computational Fluid Dynamics - Department of ...

156 René A. Van den Braembussche
f
Objective function value
50
40
30
20
Standard settings - Best individual
Optimal settings - Best individual
0 1000 2000 3000 4000 5000
Function evaluations
Fig. 6.5 GA convergence for a 27 parameter test case (standard versus optimal parameter
setting)
6.2.2 Objective Function
The OF measures how far a geometry satisfies the aero-requirements and if
the performance goals that have been set forward are reached.
High aero-performance is not the only objective of an optimization. A
good design must also provide good off-design performance (multipoint optimization)
and respect the mechanical and manufacturing constraints (multidisciplinary
optimization). Some constraints must be satisfied without any
compromise (i.e., maximum stress level). They result in an inequality and a
more detailed discussion is given in Sect. 6.6.2. Others tolerate some margin
(i.e., cost or weight) that can be corrected for after the design is finished (i.e.,
by adjusting the blade length to achieve the required mass flow). A possible
alternative for these inequalities is to add penalty terms to the OF that
increase when the constraints are violated [13].
The following lists some contributions to the global OF that are common
for the different applications. Each term is multiplied by a weight factor to
adjust its relative importance in the optimization procedure.
OF2D = wη · Pperf + wa · PaeroBC + wm · Pmech + wM · PMach
+wd · Pdischarge + wG · PGeom + wS · PSide