Evolving parametric aircraft models for design exploration and optimisation
Introduction
Parametric systems are changing the conceptual design process in the same way as spreadsheets changed finance. Both operate on the same principle. The user defines the relationships in a system and then changes variables in that system to rapidly explore alternative possibilities. Instead of manually creating a CAD model by dragging and dropping components, the parametric design is specified using variables and functions. Just as changing the value in a cell causes the spreadsheet to recalculate all related values, changing a variable that defines part of a model will adapt all the connected components so as to maintain a coherent design. Although there is a longer lead time to implement the initial model, once it is encoded the user can easily create endless variations on the original.
Evolutionary algorithms (EAs) have shown their ability to optimise the shape and form of designs [1], [2]. One of the primary considerations when applying an evolutionary algorithm to a design problem is the representation used. The representation limits the search space by defining all the designs the algorithm could possibly generate. Poor representations generate designs that are invalid (internal faces, unconnected parts), infeasible (wrong scale) or missing the desired functionality. Creating a suitable representation is a difficult task that requires knowledge of both programming and of the specific domain.
Parametric systems provide a novel solution to the representation problem. A well-implemented parametric system will only generate valid designs and incorporates domain knowledge. It also allows a designer with no formal programming experience to define the representation for the evolutionary algorithm. The designer provides the initial model and specifies the range limits so as to generate appropriate variations of their design. Parametric models make evolutionary optimisation directly accessible to the designer and allows them to use their domain knowledge to create a representation that generates feasible designs.
This work combines NASA׳s parametric aircraft system (OpenVSP) and a computational fluid dynamics solver (OpenFOAM) with an evolutionary algorithm to generate a variety of optimised and novel designs. Section 2 gives an overview of parametric design systems and their application in industry. Section 3 describes the fluid dynamics solver used to generate the fitness values for the model. Section 4 discusses previous aircraft optimisation examples that used evolutionary approaches. Three parametric aircraft models are optimised in this work. The settings consistent for all the experiments are shown in Section 5. Section 6 describes the experiments carried out on the blended wing body model where the airfoil and the wing were varied. Section 7 describes the experiments carried out on the Cessna 182 model where the wing was exclusively varied. Section 8 describes the experiments carried out on the MIG 21 model where the wing and the tail section were optimised simultaneously. Finally 9 Discussion, 10 Conclusions discuss the results of the experiments and the conclusions that can be drawn from them respectively.
Section snippets
Parametric design
Parametric design defines the relationships between components in a design. Generating a model consisting of hierarchical and geometric relations allows for exploration of possible variations on the initial design while still limiting the search space. Instead of manually placing and connecting components as is done in traditional CAD, component generating algorithms are linked with user definable variables. Defining the relationship between the components prevents invalid design generation. A
Computational fluid dynamics
Computational Fluid Dynamics (CFD) uses numerical methods to solve how liquids and gases interact with surfaces. Although the calculations are computationally intensive, the dramatic increase in the power of standard hardware enables basic CFD analysis to be carried out on standard desktop machines. OpenFOAM (open-source field operations and manipulation) [10] is used as the CFD solver in the experiments. Although primarily used for fluid dynamics simulations, it provides a toolbox of different
Evolutionary aircraft optimisation
Design problems inevitably involve some trade off between desirable attributes [16]. In aircraft design there is a trade off between lift and drag which is known as aerodynamic efficiency. A design must have not only a minimal“Since design problems defy comprehensive description and offer an inexhaustible number of solutions the design process cannot have a finite and identifiable end. The designer׳s job is never really done and it is probably always possible to do better.” [15].
Experimental settings
A standard genetic algorithm (GA) was used in all the experiments. The settings used by the GA are shown in Table 1. The source code is freely available to download at [25] under the GNU public license. A context free grammar mapping [26] was used to convert the integer values of the GA representation into values for the parametric model. As the grammar was changed for different optimisation tasks, each grammar is shown in its respective section. Both lift and drag are being used as fitness
Optimisation of blended wing body design
In traditional aircraft the fuselage provides little or no lift to the craft. Originally developed by NASA, the blended wing body (BWB) flattened the fuselage into the shape of an airfoil so that the entire craft generates lift. The BWB model has been used extensively as a test case for multidisciplinary design optimisation (MDO) [27]. MDO uses optimisation techniques to solve design problems that span multiple disciplines. A parametric model of the BWB design was used as a test case due to the
Optimisation of the Cessna 182 wing
This section demonstrates the selective optimisation possible with the parametric representation. Only the wing structure of a Cessna 182 aircraft is optimised. The section and the airfoil of the wing are varied while the fuselage, propeller, tail section and undercarriage remain fixed. The Cessna 182 is the second most popular Cessna variant in production. The model is more complex than the BWB design as it is composed of 13,476 facets. Although the increased complexity affects the amount of
Optimisation of the MIG 21 wing and tail sections
As an extension of the previous experiment multiple surfaces of the MIG 21 model are optimised simultaneously. The MIG 21 model was chosen as it is composed of 26,600 facets, highlighting the complexity of aircraft models it is possible to optimise. Different components of a design cannot be optimised individually and be expected to perform similarly when combined. The wing and the tail section of the MIG 21, as shown in red in Fig. 17, are varied in this experiment. One additional limitation
Discussion
The results from the experiments, with the exception of the BWB airfoil optimisation results, indicate that an evolutionary approach generates more aerodynamically efficient aircraft than a brute force approach. Although more runs will have to be conducted before this can be conclusively shown, it is a promising result. One unexpected result was that a brute force approach still produced designs that surpassed the original design. Normally a random approach generates poor optimisation results
Conclusions
A parametric system allows the designer, not the programmer, to specify the design to be evolved. Three different aircraft modelled using the OpenVSP design tool were optimised. The experiments showed that the level of design optimisation could be varied. Specific components of the model can be optimised or the model can be used as the basis for generating entirely different aircraft configurations. Although the sample size of the experiment is too small to draw any significant conclusions,
Acknowledgements
We would like to thank Science Foundation Ireland, the Financial Mathematics Computation Cluster and Andrea McMahon for her help during this project. We also wish to acknowledge the DJEI/DES/SFI/HEA Irish Centre for High-End Computing (ICHEC) for the provision of computational facilities and support. This work was funded by the SFI Grants 08/RFP/CMS1115, 08/IN.1/I1868 and 08/SRC/FM1389.
Jonathan Byrne is a research scientist working with the Urban Modelling Group in UCD. His research focuses on design optimisation, structural wind modelling and 3D printing.
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Jonathan Byrne is a research scientist working with the Urban Modelling Group in UCD. His research focuses on design optimisation, structural wind modelling and 3D printing.
Dr Philip Cardiff is a post-doctoral research fellow with the mechanical engineering department in UCD. His research focuses on finite volume methodologies for numerical analysis.
Professor Anthony Brabazon is currently the Associate Dean of the Smurfit School of Business and head of the Financial Mathematics Computation Cluster.
Professor Michael O'Neill is currently the director of the Complex and Adaptive Systems Laboratory and head of the Natural Computing Research and Applications Group.