Application of Swarm Approach and Artificial Neural Networks for Airfoil Shape Optimization
Manas S. Khurana, Hadi Winarto, Arvind Kumar Sinha · 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference · 2008
The Direct Numerical Optimization (DNO) approach for airfoil shape design requires the integration of modules: a) A geometrical shape function; b) Computational flow solver and; c) Search model for shape optimization. These modules operate iteratively until convergence based on defined objectives and constraints. The DNO architecture is to be validated to ensure efficient optimization simulations and is the focus of this paper. The PARSEC airfoil shape function is first validated by observing the effect of design coefficients on airfoil geometry and aerodynamics. The design variables provide independent one-to-one control over airfoil geometry, for imposing shape constraints. The aerodynamic performance of PARSEC airfoils through variable perturbations, conform to established aerodynamic principles. It confirms the design flexibility of the shape function in providing direct control over airfoil geometry. The Particle Swarm Optimization (PSO) algorithm is introduced as the search agent. A PSO simulation requires userinputs to define the search pattern. A methodology is presented to validate these parameters on pre-defined benchmark mathematical functions. Self Organizing Maps (SOM) are applied to illustrate trade-offs between PSO search variables. An Adaptive Inertia Weight (APSO) scheme that dynamically alters the search path of the swarm by monitoring the position of the particles, provides an acceptable convergence. Validation tests indicated the maximum velocity of the particles is less than 1% of computational domain size for convergence. The DNO approach is computationally inefficient, thus a surrogate model to address this issue is presented. An Artificial Neural Network (ANN) model with a training dataset of 3000 airfoils is applied to develop a model that applies the PARSEC airfoil geometry variables as inputs and the equating aerodynamic coefficient as output. System validation with 1000 randomly generated airfoils indicated 70% of the simulated solutions were within 10% of actual solver run. Future research will involve reducing the percentage error of the surrogate model against the theoretical solution.