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The paper aims to apply numerical optimization to the aircraft design procedures applied in the airspace industry.

It is harder than ever to achieve competitive construction. This is why numerical optimization is becoming a standard tool during the design process. Although optimization procedures are becoming more mature, yet in the industry practice, fairly simple examples of optimization are present. The more complicated is the task to solve, the harder it is to implement automated optimization procedures. This paper presents practical examples of optimization in aerospace sciences. The methodology is discussed in the article in great detail.

Encountered problems related to the numerical optimization are presented. Different approaches to the solutions of the problems are shown, which have impact on the time of optimization computations and quality of the obtained optimum. Achieved results are discussed in detail with relation to the used settings.

Investigated different aspects of handling optimization problems, improving quality of the obtained optimum or speeding-up optimization by parallel computations can be directly applied in the industry optimization practice. Lessons learned from multidisciplinary optimization can bring industry products to higher level of performance and quality, i.e. more advanced, competitive and efficient aircraft design procedures, which could be applied in the industry practice. This can lead to the new approach of aircraft design process.

Introduction of numerical optimization methods in aircraft design process. Showing how to solve numerical optimization problems related to advanced cases of conceptual and preliminary aircraft design.

The overall pressure drop in an axisymmetric contraction is minimised using two different grid sizes. The transition region was parameterised with only two design variables to make it possible to create surface plots of the objective function in the design space, which were based on 121 CFD calculations for each grid. The coarse grid showed to have significant numerical noise in the objective function while the finer grid had less numerical noise. The optimisation was performed with two methods, a Response Surface Model (RSM) and a gradient‐based method (the Method of Feasible Directions) to study the influence from numerical noise. Both optimisation methods were able to find the global optimum with the two different grid sizes (the search path for the gradient‐based method on the coarse grid was able to avoid the region in the design space containing local minima). However, the RSM needed fewer iterations in reaching the optimum. From a grid convergence study at two points in the design space the level of noise appeared to be sufficiently low, when the relative step size is 10^–4 for the finite difference calculations, to not influence the convergence if the errors are below 5 per cent for this contraction geometry.

Trusses constitute a fertile field to demonstrate the application of optimization techniques because of the possibility of several different configurations. Using such techniques allows the search for designs that minimize the use of material to safely comply with the imposed loads. Truss optimization can be classified into three categories: cross-section, shape, and topology. The purpose of this paper is to present a numerical and experimental study developed to minimize the weight of aluminum trusses, taking both the cross-sectional dimensions of the elements and the nodal coordinates as design variables.

Initially, several numerical computer simulations were performed with an optimization program developed by combining the displacement method and a simulated annealing optimization method. Subsequently, two aluminum trusses were selected and built in order to validate the numerical results obtained.

Experimental tests verified the excellent performance of the optimized model.

In addition, it was concluded that significant savings could be obtained from the application of the proposed formulation.

Compliant mechanism has been receiving a great interest in precision engineering. However, analytical methods involving their behavior analysis is still a challenge because there are unclear kinematic behaviors. Especially, design optimization for compliant mechanisms becomes an important task when the problem is more and more complex. Therefore, the purpose of this study is to design a new hybrid computational method. The hybridized method is an integration of statistics, numerical method, computational intelligence and optimization.

A tensural bistable compliant mechanism is used to clarify the efficiency of the developed method. A pseudo model of the mechanism is designed and simulations are planned to retrieve the data sets. Main contributions of design variables are analyzed by analysis of variance to initialize several new populations. Next, objective functions are transformed into the desirability, which are inputs of the fuzzy inference system (FIS). The FIS modeling is aimed to initialize a single-combined objective function (SCOF). Subsequently, adaptive neuro-fuzzy inference system is developed to modeling a relation of the main geometrical parameters and the SCOF. Finally, the SCOF is maximized by lightning attachment procedure optimization algorithm to yield a global optimality.

The results prove that the present method is better than a combination of fuzzy logic and Taguchi. The present method is also superior to other algorithms by conducting non-parameter tests. The proposed computational method is a usefully systematic method that can be applied to compliant mechanisms with complex structures and multiple-constrained optimization problems.

The novelty of this work is to make a new approach by combining statistical techniques, numerical method, computational intelligence and metaheuristic algorithm. The feasibility of the method is capable of solving a multi-objective optimization problem for compliant mechanisms with nonlinear complexity.

The purpose of this study is to propose a framework for expedited antenna optimization with numerical derivatives involving gradient variation monitoring throughout the optimization run and demonstrate it using a benchmark set of real-world wideband antennas. A comprehensive analysis of the algorithm performance involving multiple starting points is provided. The optimization results are compared with a conventional trust-region (TR) procedure, as well as the state-of-the-art accelerated TR algorithms.

The proposed algorithm is a modification of the TR gradient-based algorithm with numerical derivatives in which a monitoring of changes of the system response gradients is performed throughout the algorithm run. The gradient variations between consecutive iterations are quantified by an appropriately developed metric. Upon detecting stable patterns for particular parameter sensitivities, the costly finite differentiation (FD)-based gradient updates are suppressed; hence, the overall number of full-wave electromagnetic (EM) simulations is significantly reduced. This leads to considerable computational savings without compromising the design quality.

Monitoring of the antenna response sensitivity variations during the optimization process enables to detect the parameters for which updating the gradient information is not necessary at every iteration. When incorporated into the TR gradient-search procedures, the approach permits reduction of the computational cost of the optimization process. The proposed technique is dedicated to expedite direct optimization of antenna structures, but it can also be applied to speed up surrogate-assisted tasks, especially solving sub-problems that involve performing numerous evaluations of coarse-discretization models.

The introduced methodology opens up new possibilities for future developments of accelerated antenna optimization procedures. In particular, the presented routine can be combined with the previously reported techniques that involve replacing FD with the Broyden formula for directions that are satisfactorily well aligned with the most recent design relocation and/or performing FD in a sparse manner based on relative design relocation (with respect to the current search region) in consecutive algorithm iterations.

Benchmarking against a conventional TR procedure, as well as previously reported methods, confirms improved efficiency and reliability of the proposed approach. The applications of the framework include direct EM-driven design closure, along with surrogate-based optimization within variable-fidelity surrogate-assisted procedures. To the best of the authors’ knowledge, no comparable approach to antenna optimization has been reported elsewhere. Particularly, it surmounts established methodology by carrying out constant supervision of the antenna response gradient throughout successive algorithm iterations and using gathered observations to properly guide the optimization routine.

A method to solve shape and size optimisation problems with linear and non‐linear responses has been studied taking advantage of statistical methodologies. A nested optimisation procedure has been fixed. The global optimisation problem is decomposed in several subproblems where each non‐linear response is locally approximated with a first degree polynomial function identified by the definition and execution of an experimental plan. The approximating functions so obtained are used to evaluate the design sensitivity coefficients required by the optimisation procedure. The numerical results obtained during the optimisation process to verify exactly the value of the non‐linear responses are used to verify and to improve the approximating function accuracy. The non‐linear design sensitivity analysis method so defined has been used to solve a multidisciplinary shape optimisation problem involving a real 3D automotive structure.

In pure material design, the previous research has indicated that lots of optimization factors such as used algorithm and parameters have influence on the optimal solution. In other words, there are multiple local minima for the topological design of materials for extreme properties. Therefore, the purpose of this study is to attempt different or more concise algorithms to find much wider possible solutions to material design. As for the design of material microstructures for macro-structural performance, the previous studies test algorithms on 2D porous or composite materials only, it should be demonstrated for 3D problems to reveal numerical and computational performance of the used algorithm.

The presented paper is an attempt to use the strain energy method and the bi-directional evolutionary structural optimization (BESO) algorithm to tailor material microstructures so as to find the optimal topology with the selected objective functions. The adoption of the strain energy-based approach instead of the homogenization method significantly simplifies the numerical implementation. The BESO approach is well suited to the optimal design of porous materials, and the generated topology structures are described clearly which makes manufacturing easy.

As a result, the presented method shows high stability during the optimization process and requires little iterations for convergence. A number of interesting and valid material microstructures are obtained which verify the effectiveness of the proposed optimization algorithm. The numerical examples adequately consider effects of initial guesses of the representative unit cell (RUC) and of the volume constraints of solid materials on the final design. The presented paper also reveals that the optimized microstructure obtained from pure material design is not the optimal solution any more when considering the specific macro-structural performance. The optimal result depends on various effects such as the initial guess of RUC and the size dimension of the macrostructure itself.

This paper presents a new topology optimization method for the optimal design of 2D and 3D porous materials for extreme elastic properties and macro-structural performance. Unlike previous studies, the presented paper tests the proposed optimization algorithm for not only 2D porous material design but also 3D topology optimization to reveal numerical and computational performance of the used algorithm. In addition, some new and interesting material microstructural topologies have been obtained to provide wider possible solutions to the material design.

The present paper aims to address the description of a numerical optimization procedure, based on mesh morphing, and its application for the improvement of the aerodynamic performance of an industrial glider which suffers of a large separation occurring in the wing–fuselage junction region at high incidence angles.

Shape variations were applied to the baseline configuration through a mesh morphing technique founded on the mathematical framework of radial basis functions (RBF). The aerodynamic solutions were obtained coupling an RANS code with the mesh morphing tool RBF Morph™. Two shape modifiers were set up to generate a parametric numerical model. An optimization procedure, based on a design of experiment sampling, was set up implementing the fully automated workflow within a high performance computing (HPC) environment. The optimal candidates maximizing the aerodynamic efficiency were identified by means of a cubic RBF response surface approach.

The separation was significantly reduced, modifying the local geometry of fuselage and fairing and maintaining the wing aerofoil unchanged. A relevant aerodynamic efficiency improvement was finally gained.

The developed procedure proved to be a very powerful and efficient tool in facing aerodynamic design problems. However, it might be computationally very expensive if a large number of design variables are adopted and, in those cases, the method can be suitably used only within the HPC environment.

Such an optimization study is part of an explorative set of analyses that focused on better addressing the numerical strategies to be used in the development of the EU FP7 Project RBF4AERO.

In this work, the authors deal with topology optimization in electromagnetism using solid isotropic material with penalization (SIMP) method associated with a gradient-based algorithm. The purpose of this study is to propose and investigate the impact of new generalized material interpolation scheme (MIS) used in SIMP approaches.

The variable domains of this kind of electromagnetism design problem are decomposed into small squares which represent a material point (iron here) or void. A least square function where the magnetic field in a target zone has to be as close as possible to a fixed one is minimized. Then the binary optimization problem is relaxed to a continuous one. By using the adjoint variable method, the gradient is provided. By penalizing the objective function using MIS, gradient-based algorithms can then be directly applied to provide efficient solutions close to the binary ones.

In this work, new general MISs are proposed. It is shown on numerous numerical instances that the so-obtained design solutions are more precise to define the zones with or without materials.

Only the linearity of the materials is addressed because the associated adjoint method needs this assumption. However, the new penalization approaches are not dependent directly on this assumption.

The new MISs are efficiently applied to design of a hall effect thruster (HET) magnetic circuits. Furthermore, these schemes are generic and can then be applied to other topology optimization applications in electromagnetism as well as and in mechanism.

The purpose of this paper is to improve the hydraulic efficiency without changing the overall dimension. The blade profile optimization design of the aero-centrifugal pump based on the biharmonic equation surrogate model has been studied.

First of all, Bezier curves and linear function are used to control the annular angle distribution and the stacking angle of blade profile under the MATLAB platform. Grid independence analysis has been studied to find the finest mesh scheme. After the precision comparison of test data and computation fluid dynamics 15 sets of design parameters are carried out as the boundary condition of the biharmonic equation. The efficiency surrogate model of the biharmonic equation is constructed via iteratively solving of a discrete difference equation. The other two surrogate models of response surface model (RSM) and radial basis function neural network surrogate model (RBFNNSM) are compared with the biharmonic equation surrogate model by the standard of modified complex correlation coefficient R² and root mean square deviation (RSME). Finally, the artificial fish swarm algorithm has been used to find the global optimal design parameters with the objective function of highest efficiency.

The results show that the design parameters code conversion method can reduce the number of optimization parameters from five to three, makes the design space become a cube, and compared with RSM and RBFNNSM, the biharmonic equation surrogate model has higher precision with R² is 0.8958, RSME is 0.1382. The final optimum result of AFSA is at the point of [1 −1 −1]. The internal flow field analysis shows that after optimization the outlet relative velocity becomes more uniform and the wake effect has been significantly decreased. The hydraulic efficiency of the optimized pump is about 59.45 per cent increasing 5.4 per cent compared with a prototype pump.

This study developed a new method to optimize the design parameters of aero-centrifugal pump impeller based on biharmonic equation surrogate model, which had a good agreement with experimental values within just 15 sets of the original design. The optimization results shows that the method can improve the hydraulic efficiency significantly.