Emerging Methods for Multidisciplinary Optimization

Multidisciplinary design optimization

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At these levels there is an exploration phase where there is no need for great precision, the most time consuming solvers at the top levels should be used only for the most promising solutions as they become more refined. A comparison study of the results obtained using a single population or a hierarchical topology of solvers or resolutions can be found in Whitney et al.

In this paper the optimisation was parallelised on a network of computers at The University of Sydney. The system has ten machines with performances varying between 2. The master computer carries on the optimisation process while the remote machines compute the solver code.

The parallel implementation requires modifications to the canonical ES [26], which ordinarily evaluates entire populations simultaneously.

Emerging Methods for Multidisciplinary Optimization

Figure 7. Parallel Computing and Asynchronous Evaluation Figure 8. Design variables for multidisciplinary wing design. The distinctive method of an asynchronous approach is that it generates only one candidate solution at a time and only re- incorporates one individual at a time, rather than an entire population at every generation as is usual with traditional EAs Consequently solutions can be generated and returned out of order. This allows the implementation of an asynchronous fitness evaluation giving the method its name.

Figure 6b shows a schematic representation of this approach. The optimisation method-HAPEA has been applied to different design problems including deceptive and multi modal Pareto solutions, viscous two-dimensional nozzle optimisation and multi-criteria constrained aerofoil design problems. In all these cases the algorithm successfully converged to an optimal solution or set of solutions. The benefit of using an asynchronous approach can be found in Whitney et al. One of the benefits of using an Evolutionary optimiser is that EAs require no derivatives of the objective function.

The coupling of the algorithm with different analysis codes is by simple function calls and input and output data files. There are many strategies proposed for multi-criteria and MDO and the development of these optimisation methods, architectures and decomposition methodologies has been an active field of research. The framework developed in this research is applicable to an integrated analysis or distributed MDO analysis Examples on the application of the method for these formulations are presented in section 5.

The framework has also capabilities for parallel computing; different candidate members of the population can be sent to remote parallel heterogeneous computers. Once a solution is computed it is returned to the optimiser and framework. Applications The framework has been used to evaluate several real world problems including inverse and direct problems for aerofoil, high- lift aircraft system, multidisciplinary and multi-criteria wing and aircraft design and optimisation problems [24,25,28]. In the following we illustrate the application of the method for a multi-criteria multidisciplinary UAV wing design and optimisation problem.

This test case considers the UAV to be flying at cruise Mach number 0. The wing area is set to 2. For the solution we initially compute the pressure distribution over the wing using a potential flow solver to obtain the wing aerodynamics characteristics that include the spanwise pressure distribution, CL and total drag coefficients CDw. Concentrated loads replace the lift distribution and the spar cap area is calculated to resist the bending moment. The weight is then approximated as the sum of the span-wise cap weight.

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The strong interaction between the aerodynamic pressure distribution and the structural deflections is ignored. Design Variables and Constraints. The wing geometry is represented by three aerofoil sections and five variables for the wing planform. In total fifty-three design variables are used for the optimisation.

The aerofoil geometry is represented by the combination of a mean line and thickness distribution, which is a very common concept in classical aerodynamics [32]. In this case we take six free control points on the mean line and ten free control points on the thickness distribution. If any of these constraints is violated both fitness are linearly penalised to ensure an unbiased Pareto set. Table 1. Upper and lower bounds for multidisciplinary wing design variables. Aerodynamics and Weight Analysis The aerodynamic characteristics of the wing configurations are evaluated using FLO22, a 3-D full potential wing analysis software.

This program uses sheared parabolic coordinates and accounts for wave drag [30]. FLO22 was developed by A. Jameson and D. Caughey for analysing inviscid, isentropic, transonic shocked flow past 3-D swept wing configurations. The algorithm is based on free stream Mach numbers limited by the isentropic assumption and weak shock waves are automatically captured wherever they occur in the flow.

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Also the finite difference form of the full equation for the velocity potential is solved by a relaxation method, after the flow exterior to the aerofoil is mapped to the upper half plane. The mapping procedure allows exact satisfaction of the boundary conditions and use of transonic free stream velocities. Details on the formulation and implementation can be found in Reference [30]. The fixed lift requirement can be satisfied by performing an extra two function evaluations by varying the angle of attack at the wing root and assuming a linear variation of the lift coefficient.

Multidisciplinary design optimization - Wikipedia

The lift distribution is summed into concentrated loads. The wing weight is estimated from the wing spar cap area designed to resist the bending moment. Fitness Functions The two fitness functions to be optimised are defined as minimisation of wave drag CDwave and minimisation of the sum of the spanwise cap weight WSC to resist the bending moment. Implementation We use the wing design and optimisation module to solve this problem section 4.

The second approach uses a hierarchical topology of resolutions with the following settings: Top Layer: A population size of 30, and a computational mesh of 96 x 12 x Middle Layer: A population size of 30 and a computational mesh of 72 x 9 x Numerical Results The algorithm was run five times for function evaluations and took in average six hours to compute. Figure 8 shows the Pareto fronts obtained by using the two approaches. It can be seen how the optimisation technique gives a uniformly distributed front in both cases.

By inspection we can see that the use of a hierarchical approach gives an overall lower front as compared to a single model approach. The combination of low fidelity models for a rapid exploration of the design space and higher fidelity models for the most promising solutions has used in the optimisation. Figure 9 illustrates the Pareto front for the hierarchical approach and a representative top view of the wing geometries.

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Figure 10 shows the corresponding aerofoils at root, break and tip for some of the Pareto configurations and table 2 indicates the final values design variables. Pareto Fronts after function evaluations. Figure 9. Pareto fronts and wing planforms. Table 2: Optimum design variables for some members of the Pareto front.

Results indicate a computational gain on using a hierarchical topology of fidelity models as compared to a single model during the optimisation. Results also show how the algorithm was capable of identifying the trade-off between the multi-physics involved and provide classical aerodynamic shapes as well as alternative configurations from which the design team can choose and proceed into more detailed phases of the design process.

Conclusions This paper presents the requirements, formulation and implementation of a robust design framework with which different aeronautical problems can be analysed. The paper gives a brief description of the different components of the framework. These include several algorithms for design and optimisation, a GUI and different modules for design, optimisation, mesh generation, CAD systems, post-processing and parallel computing. Hence we have within the framework, a complete set of numerical tools for analysing and optimising real world aeronautical and UAV problems.

The method is capable of identifying the trade- off between the multi-physics involved and provides classical aerodynamic shapes as well as alternative configurations from which the design team can choose.

It was observed that there was a computational gain on using a hierarchical topology of fidelity models as compared to a single model during the optimisation. Further research in this design environment using higher fidelity Navier-Stokes turbulent flow analysers with unstructured adapted meshes in the optimisation procedure is needed and applications of the method to more complex aerodynamic configurations are presently under investigation.

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References 1. Louis, Mo, Braum and P. Gage and I. Kroo and I. Thomas and A. Artificial Intelligence. Springer- Verlag, Oyama, M. Liou, and S. Parmee and A. Banzhaf, J. Daida, A. Eiben, M.

Garzon, V.

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