Efficient aerodynamic shape optimization by structure exploitation

In this paper, we consider an optimization problem for the complete design chain of an airfoil. Starting with a parameter vector, one has to perform a three step procedure to evaluate the desired objective: Generate a grid around the airfoil, compute the flow around the airfoil, and compute the objective. Applying a gradient-based optimization method, one has to provide derivatives for this complex process. In the present paper, we propose the advanced use of automatic differentiation to compute the required gradient information. We report numerical results together with a mesh independency study and an analysis of the optimization process for an inviscid RAE2822 airfoil under transonic flight conditions.     

Multi-objective aerodynamic shape optimization of small livestock trailers

This article presents a formal optimization study of the design of small livestock trailers, within which the majority of animals are transported to market in the UK. The benefits of employing a headboard fairing to reduce aerodynamic drag without compromising the ventilation of the animals’ microclimate are investigated using a multi-stage process involving computational fluid dynamics (CFD), optimal Latin hypercube (OLH) design of experiments (DoE) and moving least squares (MLS) metamodels. Fairings are parameterized in terms of three design variables and CFD solutions are obtained at 50 permutations of design variables. Both global and local search methods are employed to locate the global minimum from metamodels of the objective functions and a Pareto front is generated. The importance of carefully selecting an objective function is demonstrated and optimal fairing designs, offering drag reductions in excess of 5% without compromising animal ventilation, are presented.     

Shape optimization using adaptive shape refinement

A large part of the computational effort in shape optimization problems is expended in the numerical computation of the gradients for sensitivity information. This effort increases dramatically with an increase in the number of variables used to represent the shape. An adaptation of the gradient projection algorithm for shape optimization problems is described here along with a method to reduce the intermediate size of the optimization problem by allowing adaptive refinement of the shape. The method is demonstrated with a simple representative test case.     

Virtual Stackelberg game coupled with the adjoint method for aerodynamic shape optimization

In this article, a Virtual Stackelberg Game (VSG) is proposed for aerodynamic shape optimization, where the design variables are divided into two categories to optimize the same objective function, one acts as a leader, and the other ones as followers react independently and selfishly relative to the leader's strategy. During each Stackelberg strategy cycle, the Gradient-Based Method (GBM) with the adjoint method in Stanford University Unstructured (SU²) is applied in the optimization of each player. Firstly, parametric studies of VSG by two simple cases are conducted to assess the impact of critical parameters on aerodynamic shape optimization, including the design cycle, the split of design variables and role (leader and follower) assignment. Based on the criterion from parametric studies, two typical numerical cases under transonic flow are applied—the drag reduction design of a 2D airfoil and a 3D wing. It is found that, compared to the original GBM method, VSG can provide better optimization results with less computational cost.     

An element-by-element strategy for non-linear shape optimization

A strategy for the efficient solution of non-linear shape optimization problems is developed. This strategy employs an integrated element-by-element approach to the solution of the governing partial differential equations, and, more particularly, to the computation of the necessary gradients of the objective function and constraints using an adjoint formulation. This proves to be a very efficient strategy and also is relatively easy to implement, because the local effect of design changes can be exploited. The method is tested with an application involving the design of the shape of electromagnet poles in order to obtain a desired field in the interpolar region.     

An adaptive response surface method for crashworthiness optimization

Response surface-based design optimization has been commonly used for optimizing large-scale design problems in the automotive industry. However, most response surface models are built by a limited number of design points without considering data uncertainty. In addition, the selection of a response surface in the literature is often arbitrary. This article uses a Bayesian metric to systematically select the best available response surface among several candidates in a library while considering data uncertainty. An adaptive, efficient response surface strategy, which minimizes the number of computationally intensive simulations, was developed for design optimization of large-scale complex problems. This methodology was demonstrated by a crashworthiness optimization example.     

Discrete shape sensitivity equations for aerodynamic problems

Intensive research and development in Computational Fluid Dynamics (CFD) has recently produced many powerful CFD codes to simulate complex aerodynamic phenomena. However, in order to enhance the usefulness of these CFD codes for design practice, development of design sensitivity equations compatible to these codes becomes very important. This paper represents a part of such an effort to develop a sensitivity analysts methodology that enables the sensitivity equations to be implemented into existing CFD codes with minimal code modification. The methodology is based upon a pre-elimination procedure which accounts for consistently linearized boundary conditions. Formulations of both the direct differentiation and the adjoint variable methods will be presented in the paper.     

A general methodology for structural shape optimization problems using automatic adaptive remeshing

The proposed methodology is based on the use of the adaptive mesh refinement (AMR ) techniques in the context of 2D shape optimization problems analysed by the finite element method. A suitable and very general technique for the parametrization of the optimization problem, using B-splines to define the boundary, is first presented. Then mesh generation, using the advancing frontal method, the error estimator and the mesh refinement criterion are studied in the context of shape optimization problems In particular, the analytical sensitivity analysis of the different items ruling the problem (B-splines. finite element mesh, structural behaviour and error estimator) is studied in detail. The sensitivities of the finite element mesh and error estimator permit their projection from one design to the next one leading to an a priori knowledge of the finite element error distribution on the new design without the necessity of any additional structural analysis. With this information the mesh refinement criterion permits one to build up a finite element mesh on the new design with a specified and controlled level of error. The robustness and reliability of the proposed methodology is checked by means of several examples.     

An adaptive direct multisearch method for black-box multi-objective optimization

Optimization and Engineering - At present, black-box and simulation-based optimization problems with multiple objective functions are becoming increasingly common in the engineering context. In...     

An adaptive metamodel-based global optimization algorithm for black-box type problems

In this article, an adaptive metamodel-based global optimization (AMGO) algorithm is presented to solve unconstrained black-box problems. In the AMGO algorithm, a type of hybrid model composed of kriging and augmented radial basis function (RBF) is used as the surrogate model. The weight factors of hybrid model are adaptively selected in the optimization process. To balance the local and global search, a sub-optimization problem is constructed during each iteration to determine the new iterative points. As numerical experiments, six standard two-dimensional test functions are selected to show the distributions of iterative points. The AMGO algorithm is also tested on seven well-known benchmark optimization problems and contrasted with three representative metamodel-based optimization methods: efficient global optimization (EGO), GutmannRBF and hybrid and adaptive metamodel (HAM). The test results demonstrate the efficiency and robustness of the proposed method. The AMGO algorithm is finally applied to the structural design of the import and export chamber of a cycloid gear pump, achieving satisfactory results.