The development of a hybridized particle swarm for kriging hyperparameter tuning

Optimizations involving high-fidelity simulations can become prohibitively expensive when an exhaustive search is employed. To remove this expense a surrogate model is often constructed. One of the most popular techniques for the construction of such a surrogate model is that of kriging. However, the construction of a kriging model requires the optimization of a multi-model likelihood function, the cost of which can approach that of the high-fidelity simulations upon which the model is based. The article describes the development of a hybridized particle swarm algorithm which aims to reduce the cost of this likelihood optimization by drawing on an efficient adjoint of the likelihood. This hybridized tuning strategy is compared to a number of other strategies with respect to the inverse design of an airfoil as well as the optimization of an airfoil for minimum drag at a fixed lif

Use of response surface methods to aid understanding and visulatization in aircraft design

A two dimensional visualization of a representative military aircraft problem is described and then extended to five dimensions. The paper includes the optimization problem specification and introduces a modus operandi for a design process. The visualization developed is compared to alternative techniques, such as scatter plots and Kohonen map visualisations. Possible applications of the different visualization methods are also described

Learning inexpensive parametric design models using an augmented genetic programming technique

Previous applications of Genetic Programming (GP) have been restricted to searching for algebraic approximations mapping the design parameters (e.g. geometrical parameters) to a single design objective (e.g. weight). In addition, these algebraic expressions tend to be highly complex. By adding a simple extension to the GP technique, a powerful design data analysis tool is developed. This paper significantly extends the analysis capabilities of GP by searching for multiple simple models within a single population by splitting the population into multiple islands according to the design variables used by individual members. Where members from different islands `cooperate', simple design models can be extracted from this cooperation. This relatively simple extension to GP is shown to have powerful implications to extracting design models that can be readily interpreted and exploited by human designers. The full analysis method, GP-HEM (Genetic Programming Heuristics Extraction Method), is described and illustrated by means of a design case study

Shape optimisation using CAD linked free-form deformation

Free-form deformation (FFD) is a method first introduced within the graphics industry to enable flexible deformation of geometric models. FFD uses an R3 to R3 mapping of a deformable space to the global Cartesian space to produce the geometry deformation. This method has been extensively used within the design optimisation field as a shape parameterisation technique. Typically it has been used to parameterise analysis meshes, where new design geometries are produced by deforming the original mesh. This method allows a concise set of design variables to be used while maintaining a flexible shape representation. However, if a computer aided design (CAD) model of the resulting geometry is required, reverse engineering techniques would need to be utilised to recreate the model from the deformed mesh. This paper extends the use of FFD within an optimisation routine by using FFD to directly parameterise a CAD geometry. Two methods of linking the FFD methods with the CATIA V5 CAD package are presented. Each CAD integration technique is then critiqued with respect to shape optimisation. Finally the set-up and initialisation of a case study is illustrated. The case study chosen is the aerodynamic optimisation of the wing-fuselage junction of a typical passenger aircraft

Geometric filtration using proper orthogonal decomposition for aerodynamic design optimization

When carrying out design searches, traditional variable screening techniques can find it extremely difficult to distinguish between important and unimportant variables. This is particularly true when only a small number of simulations is combined with a parameterization which results in a large number of variables of seemingly equal importance. Here the authors present a variable reduction technique which employs proper orthogonal decomposition to filter out undesirable or badly performing geometries from an optimization process. Unlike traditional screening techniques, the presented method operates at the geometric level instead of the variable level. The filtering process uses the designs which result from a geometry parameterization instead of the variables which control the parameterization. The method is shown to perform well in the optimization of a two dimensional airfoil for the minimization of drag to lift ratio, producing designs better than those resulting from traditional kriging based surrogate model optimization and with a significant reduction in surrogate tuning cos