1. Charles L. Karr Rodney Bowersox Vishnu Singh
Minimization of Sonic Boom on Supersonic Aircraft Using an Evolutionary Algorithm
Charles L. Karr
Rodney Bowersox
Vishnu Singh

2. Introduction Things that we are going to cover. What is GA?
The Problem at hand?
How GA is used to solve it.
How good is the solution.
Conclusion.

3. Evolutionary algorithms
search algorithms based on the mechanics of natural selection
growing in popularity (genetic algorithms, evolutionary strategies, evolutionary programming, etc.)
effective in complex, nonlinear problems
developed to the point of “cookbook” application?
still require some expert tuning: “flavors” of crossover and mutation operators – dynamic genetic algorithm

4. The GA Start Initialize a Population of Strings
Evaluate Each String’s Fitness
Value
Select the Superior Strings for Reproduction
Apply Crossover Methods 1….N
Apply a Mutation Operator
Termination
Stop
Criterion

5. The Problem Minimization of Sonic Boom
The development of supersonic transport vehicles will require much work in sonic boom mitigation
Numerous approaches have been considered (pulse detonation, keel design, etc)
Here, we are interested in designing a spike or keel that will mitigate the sonic boom

6. Changing the Area Distribution
The Keel
Basically, adding a keel will change the area distribution
This change in area distribution will change the ground signature of the aircraft

7. Ground Signatures

8. In Real Life

9. Like With Any EA Application…
There are two fundamental issues:
Coding
How do I represent the problem as a string of characters so that the EA can operate on them
Fitness Function
How do I determine how good a proposed solution really is

10. Coding We have to represent an area distribution
Fit third or higher order polynomials through five different sections
Constraints
Continuous through the second derivatives
Twenty four (24) coefficients to be determined

11. Equations
The five different sections are represented by the equations shown below
We want to determine the coefficients

12. Coefficients
Now to find the Values of the first four coefficients we use the following method. Lets consider
The above equations can be written in a matrix form as

13. Coefficients (continued)
Now using matrix inversion method we can find the values of the coefficients
By using the other equations and applying the same method the
remaining coefficients can be found.

14. The Strings These strings are basically floating point arrays.X1 X2 … Y1 Y2
Y 3 … Xo …
1.1349
1.1555
0.2367
0.3356
4.3459 C1 …
C18
These strings are basically floating point arrays.
They represent the different values of X,Y and Y` which are needed to fully describe an area distribution.
They will be operated on by the evolutionary algorithm (dynamic GA)

15. Fitness Function How good is a potential solution
Given an area distribution, can we come up with a representation of the effectiveness of the solution
It turns out that this is a two-step process:
Use a modified version of Whitham’s theory to generate the near field pressure signature
Compute the ground signature using NFBOOM, an atmospheric propagation code
Compute the magnitude of the sonic boom

16. Whitham’s Theory IT WORKS!!!
Comparison of Quasi-Linear Theory with the Frontal Spike (r = 50.8 cm) Data of Swigart [11].
IT WORKS!!!

17. GA Particulars GA Parameters Population size = 50
Number of generations = 250
Selection scheme = tournament selection
Crossover schemes= ArithXover, Heuristic Xover, SimpleXover
Mutation schemes = Uniform, Gaussian, Random

18. Feasibility Study Compare to a known solution
“Best” solution for this aircraft was dB
The genetic algorithm found a solution of for the given conditions

19. Conclusions This is a preliminary study
The initial results are promising
Next step is to develop a design tool