Multidisciplinary Shape Optimization Research Articles

Hierarchical variable fidelity evolutionary optimization methods and their applications in aerodynamic shape design

This paper proposes two hierarchical evolutionary optimization methods based on variable fidelity analysis and search space contraction for aerodynamic shape design, i.e. hierarchical evolutionary Pareto and Nash games. One of these techniques is used in the optimization process, namely the advantages of high and low fidelity flow simulation. The high-fidelity model provides solution accuracy while the low-fidelity model reduces the computational cost. Especially, the search space contraction and the population size reduction are introduced in the process of transition from the optimization on low fidelity simulation to the optimization on high fidelity simulation, so that the optimization based on high fidelity simulation can get the high-precision optimal solution with a relatively less Central Processing Unit(CPU) cost. They are applied to the single objective natural laminar wing shape design at transonic flow and the multidisciplinary shape optimization of a hypersonic air-breathing vehicle respectively. The optimization results show that regardless of a single objective or multi-objective/multidisciplinary optimization problem, the new hierarchical optimization methods proposed in this paper can improve the optimization efficiency by 5-10 times.

$$\lambda $$-DNNs and their implementation in conjugate heat transfer shape optimization

A data-driven two-branch deep neural network (DNN), to be referred to as $$\lambda $$ -DNN, used to predict scalar fields is presented. The network architecture consists of two separate branches (input layers) connected to the main one towards its output. In multi-disciplinary shape optimization problems, such as those this paper is dealing with, the input to the $$\lambda $$ -DNN contains data relevant to the geometrical shape and the case itself. Herein, the $$\lambda $$ -DNN is used in conjugate heat transfer (CHT) analysis and shape optimization problems, synergistically with codes simulating flows over the fluid domain and solving the heat conduction equations over the solid one. It is used to optimize a duct and an internally cooled turbine blade-airfoil surrounded by hot gas. The $$\lambda $$ -DNNs, after being trained on fields computed using the CHT solver, are used as surrogates for either the heat conduction equation solver of the solid domain, replicating either one out of the two disciplines of the problem or the coupled CHT solver.

Multidisciplinary free-form optimization of solid structures for mean compliance minimization and time-dependent temperature control

A parameter-free free-form optimization method to solve multidisciplinary shape optimization problems of solid structures is presented in this paper. The design objective is both to minimize the mean compliance of linear elastic structures and to control the temperature at arbitrary locations and time periods for arbitrary loadings and under volume constraint, simultaneously. The multidisciplinary design problem is formulated as a distributed-parameter shape optimization problem based on the variational method, and the global objective function is defined using an original normalized weighted sum method. The shape gradient density functions with respect to the shape variation are derived based on the material derivative and the adjoint variable methods. The shape gradient density functions theoretically derived are applied to the H1 gradient method, a gradient method in the function space, to obtain the optimal shape while maintaining the smoothness of the shape. Numerical examples are considered to demonstrate the validity and the effectiveness of the developed optimization method.

Multidisciplinary Shape Optimization of Missile Fin Configuration Subject to Aerodynamic Heating

The main goal of this paper is to expand previously conducted study and consequently to upgrade the proposed multimodular numerical framework developed for fluid–structure interaction simulation (FSI) and multidisciplinary design optimization (MDO) purposes, in a manner that thermal–structure interaction is observed and implemented into the established numerical framework. The upgraded and considerably improved algorithm was used for MDO of the short-range ballistic missile (SRBM) model. Because of its high-speed regimes, this aircraft model was selected for the purpose of numerical modeling and optimization of aerodynamically heated structure. The present study is concerned with a broader observation of critical multipoint flight conditions and represents a more realistic scenario, which indicates this study as one contribution more in a scope of fluid–thermal–structure interaction (FTSI) numerical modeling and optimization. With respect to predefined objectives and constraints, multidisciplinary shape optimization of the fin structure resulted in overall improvement of the missile initial performances. Also, aerothermally induced critical responses of the fin structure were prevented. Numerical modeling of FSI/FTSI and MDO within an industry-accepted design tool resulted in powerful monolithic environment, which, with adopted multipoint regimes and multicriteria settings, was used for aerodynamic–thermal/structural optimization. The obtained results were compared with the results from the previous study conducted without thermal effects.

Multidisciplinary shape optimization of ductile iron castings by considering local microstructure and material behaviour

During the casting process and solidification of ductile iron castings, a heterogeneous microstructure is formed throughout the casting. This distribution is strongly influenced by the item geometry and the process related factors, as chemical composition and local solidification conditions. Geometrical changes to the geometry of the casting thus alters the local mechanical behavior and properties, as well as the distribution of stresses and strains when the casting is subjected to load. In order to find an optimal geometry, e.g. with reduced weight and increased load-bearing capacity, this interdependency between geometry and local material behavior needs to be considered and integrated into the optimization method. In this contribution, recent developments in the multidisciplinary integration of casting process simulation, solidification and microstructure modelling, microstructure-based material characterization, finite element structural analyses with local material behavior and structural optimization techniques are presented and discussed. The effect and relevance of considering the local material behavior in shape optimization of ductile iron castings is discussed and evidenced by an industrial application. It is shown that by adopting a multidisciplinary optimization approach by integration of casting simulation and local material behavior into shape optimization, the potential of the casting process to obtain components with high performance and reliability can be enabled and utilized.

AESOP—a numerical platform for aerodynamic shape optimization

Aerodynamic shape optimization based on Computational Fluid Dynamics can automatically improve the design of aircraft components. In order to obtain the best computational efficiency, the adjoint method is applied on the complete mapping, from the parameters of design to the evaluation of the cost function or constraints. The mapping considered here includes the parameterization, the mesh deformation, the primal-to-dual mesh transformation and the flow equations solved by the unstructured flow solver Edge distributed by FOI. The numerical platform AESOP integrates the flow and adjoint flow solver, mesh deformation schemes, algorithms of shape parameterization and algorithms for gradient-based optimization. The result is a portable and efficient implementation for large scale aerodynamic shape optimization and future applications in multidisciplinary shape optimization. The structure of the program is outlined and examples of applications are presented. The method of shape parameterization using Radial Basis Functions is discussed in more details because it is expected to play a major role in the development of multidisciplinary optimization.

A surrogate-model based multidisciplinary shape optimization method with application to a 2D subsonic airfoil

A surrogate-model based shape optimization method is presented and applied to the case of the multidisciplinary shape optimization of a 2D NACA subsonic airfoil. The cost function is designed so that both the far-field radiated noise and the aerodynamic forces are controlled. The surrogate model is based on the Kriging optimal interpolation technique. In order to increase the efficiency of the method, a dynamic Kriging method is developed, which can be interpreted as an Adaptive Mesh Refinement method in the shape optimization parameters.

Multidisciplinary and multiple operating points shape optimization of three-dimensional compressor blades

The recent progress in simulation technologies in several fields such as computational fluid dynamics, structures, thermal analysis, and unsteady flow combined with the emergence of improved optimization algorithms makes it now possible to develop and use automatic optimization software and methodologies to perform complex multidisciplinary shape optimization process. In the present applications, the MAX optimization software developed at CENAERO is used to perform the optimization. This software allows performing derivative free optimization with very few calls to the computer intensive simulation software. The method employed in this paper combines the use of a genetic algorithm (with real coding of the variables) to an approximate (or meta) model to accelerate significantly the optimization process. The performance of this optimization methodology is illustrated on the optimization of three-dimensional turbomachinery blades for multiple operating points and multidisciplinary objectives and constraints. The NASA rotor 67 geometry is used to demonstrate the capabilities of the method. The aim is to find the optimal shape for three different operating conditions: one at a near peak efficiency point, one at choked mass flow, and one near the stall flow. The three points are analyzed at the same blade rotational speed but with different mass flows. A finite element structural mechanics software is used to compute the static and dynamic mechanical responses of the blade. A Navier–Stokes solver is used to calculate the aerodynamic performance. High performance computers (HPC) are used in this application. Cenaero’s HPC infrastructure contains a Linux cluster with 170 3.06 GHz Xeon processors. The optimization algorithm is parallelized using MPI.

定量的な車体骨格構想検討のための全体最適化技術の開発

This paper reports on a new multi-disciplinary shape optimization approach, which is aimed to use in conceptual design stage and enable quick reviews of numerous design alternatives with body in white (BIW) vehicle model. In the proposed method, shape model of BIW consist, of design lines of body frame and its cross-section, and does not needs CAD drawings fully controlled by optimization technology. Basis function method is used for representing the cross-section geometries and change them. Major difference between proposal method and conventional one is, in our method, the bases are reformulated based on contribution of performance characteristics before they are used in optimization. Due to the reformulation, each basis has physical meaning (ex. better for stiffness, better for crashworthiness and so on). Also it significantly decreases DOF of problem, because it describes problems in the space of performance characteristics. Finally, we will apply the proposal approach to a BIW model of real Honda vehicle and show its validity and effective ness comparing with current design with canonical optimization approach.

Survey of Shape Parameterization Techniques for High-Fidelity Multidisciplinary Shape Optimization

A survey is provided of shape parameterization techniques formultidisciplinary optimization, and some emerging ideas are highlighted. The survey focuses on the suitability of available techniques for multidisciplinary applications of complex cone gurations using high-e delity analysis tools such as computational e uid dynamics and computational structural mechanics. The suitability criteria are based on the efe ciency, effectiveness, ease of implementation, and availability of analytical sensitivities for geometry and grids. A section on sensitivity analysis, grid regeneration, and grid deformation techniques is also provided.

Survey of shape parameterization techniques for high-fidelity multidisciplinary shape optimization

Survey of shape parameterization techniques for high-fidelity multidisciplinary shape optimization

Multidisciplinary shape optimization in aerodynamics and electromagnetics using genetic algorithms

SUMMARY A multiobjective multidisciplinary design optimization (MDO) of two-dimensional airfoil is presented. In this paper, an approximation for the Pareto set of optimal solutions is obtained by using a genetic algorithm (GA). The first objective function is the drag coefficient. As a constraint it is required that the lift coefficient is above a given value. The CFD analysis solver is based on the finite volume discretization of the inviscid Euler equations. The second objective function is equivalent to the integral of the transverse magnetic radar cross section (RCS) over a given sector. The computational electromagnetics (CEM) wave field analysis requires the solution of a two-dimensional Helmholtz equation which is obtained using a fictitious domain method. Numerical experiments illustrate the above evolutionary methodology on an IBM SP2 parallel computer. Copyright © 1999 John Wiley & Sons, Ltd.

Multidisciplinary shape optimization in aerodynamics and electromagnetics using genetic algorithms

A multiobjective multidisciplinary design optimization (MDO) of two-dimensional airfoil is presented. In this paper, an approximation for the Pareto set of optimal solutions is obtained by using a genetic algorithm (GA). The first objective function is the drag coefficient. As a constraint it is required that the lift coefficient is above a given value. The CFD analysis solver is based on the finite volume discretization of the inviscid Euler equations. The second objective function is equivalent to the integral of the transverse magnetic radar cross section (RCS) over a given sector. The computational electromagnetics (CEM) wave field analysis requires the solution of a two-dimensional Helmholtz equation which is obtained using a fictitious domain method. Numerical experiments illustrate the above evolutionary methodology on an IBM SP2 parallel computer. Copyright © 1999 John Wiley & Sons, Ltd.