Page 311 - AWSAR 2.0

problem (that is, seeking the right sequence to minimize the distance) can drive the entire delivery process to be time and cost-effective. Similarly, we approach the present problem of maximizing L/D ratio of a MAV wing through shape optimization route, wherein we seek an optimal geometrical shape of the wing surface to achieve better aerodynamic performance. To accomplish this, we employ a well-known optimisation technique -- the Genetic Algorithm (GA), which is based on Darwin’s theory of natural selection.
Firstly, we employ a surface parameterization technique to represent the baseline wing through a set of 30 control points. Secondly, we assign bounds on each control point such that they can take any possible location within this allowable range, known as the design space. Moving these control points within their allowable range can resultinaninfinitenumberofnewgeometries. The aim of the optimization
procedure (GA here) is to identify the right combination of these control points (that is their individual location within the design space) such that the resulting wing geometry has the best value of L/D ratio.
Now to intuitively
understand the fundamental
concepts of GA, let us consider
the process of natural selection
in the evolution of giraffes.
Imagine a wildlife habitat that
hosts a population of giraffes
with varying neck lengths. Now
let us assume that these giraffes
are affected by severe shortage of food. In such a setting, giraffes with shorter necks will have access to food only from ground and small plants, whereas giraffes with longer necks would have access to food even from tall trees. Hence in such a scenario, nature
Mr. Pranesh Chandrasekaran || 287
favours long-necked giraffes with a greater probability to survive and allow them to pass on their beneficial traits to the next generation of offspring. Likewise, the GA code applied in the present work ensures that only wings with better values of L/D ratio are selected to survive and create offspring (that is, new wing shapes by combination) for the next generation, while the poor designs are eliminated at every generation. In other words, only the fitter individuals survive for the next generation. Over time, the geometric characteristics beneficialforbetterL/Dratioemergeinan increasing fraction of the population and hence the average L/D ratio of the entire population increases. This process is repeated until no further significant improvement is observed in the best individual of subsequent generations.
As an example let us assume that the search for the optima begins with an initial population of 300 wings, which eventually evolves
through 200 generations before finally arriving at an optimal wing shape. This essentially translates to estimating the L/D ratio of 60,000 (=300×200) wing shapes. Our CFD simulation for computing the flow around a wing using the N-S equations roughly takes 2’1/2 days of computer time on a modern computer. Hence, the overall process would consume more than 400 years of computer time which is practically not possible if attempted by a brute-force approach.
To address this issue, we devise a surrogate-based framework that employs a statistical-based mathematical model, which significantly reduces the time taken per L/D evaluation. To achieve this, we first choose a particular set of wing geometries from the design space and estimate their
Our CFD simulation for computing the flow around a wing using the N-S equations roughly takes 2’1/2 days of computer time on a modern computer. Hence, the overall process would consume more than 400 years of computer time which is practically not possible if attempted by a brute-force approach.