Download FEEG6009_2014 - University of Southampton

UNIVERSITY OF SOUTHAMPTON
FEEG6009W2
SEMESTER 2 EXAMINATION 2014/15
Design Search and Optimisation
Duration: 120 mins
Answer all four short questions in Part A and one of the three long
essay questions in Part B (only the first long essay question on your
script will be marked).
A total of 75 marks are available for this paper.
Marks available for answering parts of the questions are shown in
brackets thus [ ]
Only University approved calculators may be used.
An Engineering Data Book by Calvert and Farrar is provided.
A foreign language translation dictionary (paper version) is permitted
provided it contains no notes, additions or annotations.
Copyright 2014/2015 ©University of Southampton
Number of Pages
4
2
MODULE CODE FEEG6009W2
Part A (Short Questions)
Answer all four questions.
1. The function f ( x1, x2 )  x1  x2  2x12  2x1 x2  x2 2 is to be minimized
using the method of conjugate gradients, starting from the point
(0,0). The first iteration of the scheme results in a step length of 1
in the direction (-1, 1). Carry out one further iteration of the
scheme, clearly showing how you have decided the correct step
length and search direction and thus how you have derived the
next iterate.
[10 marks]
2. The lift coefficient of an aircraft wing, CL , is given by 0.09(α+2)
where α is the angle of attack in degrees. The drag coefficient,
CD , is given by 0.02+0.055CL2. If the lift to drag ratio is to be
maximized what is the optimal angle of attack the aircraft should
fly at and what then is the lift to drag ratio.
If the cruise speed is 40 m/s and the landing speed is 15 m/s,
while the maximum angle of attack is constrained by stall limits to
be no more than 14°, what is the best cruise lift to drag ratio that
can actually be achieved without changing the wing geometry for
landing.
The coefficients are found from the lift and drag by dividing by
½ρV2A where the symbols have their usual meanings.
[10 marks]
PLEASE TURN OVER
3
MODULE CODE FEEG6009W2
3. A multi objective design problem of a single positive variable is
defined by the functions f1=1/x and f2=x2. These are to be
combined into a single objective function using fuzzy logic with
linear membership functions such that both functions are
considered unacceptable when above 2.0 and acceptable when
below 0.5.
By considering the five possible combinations of membership,
calculate the optimal setting for x and the equivalent function
values. What is the worst setting for x and the equivalent function
values?
[10 marks]
4. Produce two new members of a population from two parents
using single point cross-over and one bit random mutation of
both children, for a binary encoded Genetic Algorithm with 6 bits.
The two parents are -0.42857 and 0.04762 and the upper and
lower bounds on the variables are -1 and 1.
The next three random numbers available from your random
number generator, which generates numbers in the interval 0-1,
are assumed to be 0.3772, 0.1397 and 0.8425.
[10 marks]
PLEASE TURN OVER
4
MODULE CODE FEEG6009W2
Part B (Long Questions)
Answer only one of these three questions.
Only the first answer on your script will be marked.
5. Describe how the requirement for robust designs may be codified
as design search and optimization problems. Pay attention to the
differences between a robust final design and the robustness of
the process used to achieve that design.
[35 marks]
6. Describe the way that optimization tools may be used to tackle
design problems with multiple goals, paying particular attention
to how goals may be combined or dealt with simultaneously and
how goals and constraints may be interchanged. Distinguish
between the construction of Pareto sets and the selection of
designs from within such sets.
[35 marks]
7. Describe the role of curve and function fitting in optimization
methods, paying particular attention to the differences between
implicit and explicit curve fits, local versus global approaches,
interpolation versus regression and the roles of experiment and
surrogate design, validation and updating. Give examples of
different search methods to illustrate your discussion.
[35 marks]
END OF PAPER