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MODULE CODE FEEG6009W2
UNIVERSITY OF SOUTHAMPTONFEEG6009W2
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.
Part A (Short Questions)
Answer all four questions.
- The function 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]
- 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
- 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]
- 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
Part B (Long Questions)
Answer only one of these three questions.
Only the first answer on your script will be marked.
- 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]
- 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]
- 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