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result(s) for
"Shape optimization"
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Isoperimetric inequalities in unbounded convex bodies
We consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body
eBook
Robust optimization design of a flying wing using adjoint and uncertainty-based aerodynamic optimization approach
Robust optimization design is significant and urgently required for the fly wings, owing to its unique characteristics. However, there is a lack of efficient tools for performing shape optimization which considers multiple uncertainties. This is in part because implementing robust design in the widely used and very efficient adjoint-based optimization method is challenging. This paper addresses this need by developing an uncertainty-based optimization design framework where the gradient-enhanced polynomial chaos expansion and discrete, adjoint-based optimization framework are coupled to perform shape optimization under multiple uncertainties. The gradient information from adjoint equation is applied to improve the computation efficiency. The objective function is the statistic moment, consisting of mean and standard deviation. The gradients of the statistic moment are computed using the adjoint-based system and reconstructing a regression algorithm. A flying wing configuration with deterministic and two uncertainty-based optimizations is performed. The first uncertainty-based optimization considers flight conditions, Mach and angle of attack, and the second one added the planform uncertainty parameters, i.e., inner and outer wing sweep angle. The uncertainty-based optimizations gain reductions of statistic moments by 8.58% and 5.3%, respectively. Compared with the deterministic optimization, the uncertainty-based optimizations behave much better in robustness but sacrifice a small aerodynamic performance. The successful uncertainty-based optimization enables acceptable risks of fly wing design in the development process and indicates that our established framework can be applied for future aircraft robust optimization design.
Journal Article
Efficient aerodynamic shape optimization of transonic wings using a parallel infilling strategy and surrogate models
Surrogate models are used to dramatically improve the design efficiency of numerical aerodynamic shape optimization, where high-fidelity, expensive computational fluid dynamics (CFD) is often employed. Traditionally, in adaptation, only one single sample point is chosen to update the surrogate model during each updating cycle, after the initial surrogate model is built. To enable the selection of multiple new samples at each updating cycle, a few parallel infilling strategies have been developed in recent years, in order to reduce the optimization wall clock time. In this article, an alternative parallel infilling strategy for surrogate-based constrained optimization is presented and demonstrated by the aerodynamic shape optimization of transonic wings. Different from existing methods in which multiple sample points are chosen by a single infill criterion, this article uses a combination of multiple infill criteria, with each criterion choosing a different sample point. Constrained drag minimizations of the ONERA-M6 and DLR-F4 wings are exercised to demonstrate the proposed method, including low-dimensional (6 design variables) and higher-dimensional problems (up to 48 design variables). The results show that, for surrogate-based optimization of transonic wings, the proposed method is more effective than the existing parallel infilling strategies, when the number of initial sample points are in the range from
N
v
to
8N
v
(
N
v
here denotes the number of design variables). Each case is repeated 50 times to eliminate the effect of randomness in our results.
Journal Article
Topology and shape optimization methods using evolutionary algorithms: a review
Topology optimization has evolved rapidly since the late 1980s. The optimization of the geometry and topology of structures has a great impact on its performance, and the last two decades have seen an exponential increase in publications on structural optimization. This has mainly been due to the success of material distribution methods, originating in 1988, for generating optimal topologies of structural elements. Previous methods suffered from mathematical complexity and a limited scope for applicability, however with the advent of increased computational power and new techniques topology optimization has grown into a design tool used by industry. There are two main fields in structural topology optimization, gradient based, where mathematical models are derived to calculate the sensitivities of the design variables, and non gradient based, where material is removed or included using a sensitivity function. Both fields have been researched in great detail over the last two decades, to the point where structural topology optimization has been applied to real world structures. It is the objective of this review paper to present an overview of the developments in non gradient based structural topology and shape optimization, with a focus on evolutionary algorithms, which began as a non gradient method, but have developed to incorporate gradient based techniques. Starting with the early work and development of the popular algorithms and focusing on the various applications. The sensitivity functions for various optimization tasks are presented and real world applications are analyzed. The article concludes with new applications of topology optimization and applications in various engineering fields.
Journal Article
Topology and Size–Shape Optimization of an Adaptive Compliant Gripper with High Mechanical Advantage for Grasping Irregular Objects
This study presents an optimal design procedure including topology optimization and size–shape optimization methods to maximize mechanical advantage (which is defined as the ratio of output force to input force) of the synthesized compliant mechanism. The formulation of the topology optimization method to design compliant mechanisms with multiple output ports is presented. The topology-optimized result is used as the initial design domain for subsequent size–shape optimization process. The proposed optimal design procedure is used to synthesize an adaptive compliant gripper with high mechanical advantage. The proposed gripper is a monolithic two-finger design and is prototyped using silicon rubber. Experimental studies including mechanical advantage test, object grasping test, and payload test are carried out to evaluate the design. The results show that the proposed adaptive complaint gripper assembly can effectively grasp irregular objects up to 2.7 kg.
Journal Article
Technical review on design optimization in forging
Forging is a traditional and important manufacturing technology to produce various high strength products and is widely used in engineering fields such as automotive, aerospace and heavy industry. To produce highly accurate product, underfill that the material is not filled into the cavity should strongly avoided. For material saving and near-net product, flash should be minimized. To make the tool life long, it is preferable to produce product with low forging load. It is also preferable to uniformly deform the billet as much as possible for high strength product. Crack is a crucial defect and should strongly be avoided. Therefore, many requirements are taken into account in order to produce the forged product. To meet the requirements, design optimization in forging coupled with computer aided engineering (CAE) is an effective approach. This paper systematically reviews the related papers from the design optimization point of view. For the billet or die shape optimization, the papers are classified into four approaches. The process parameters optimization such as the billet temperature, the die temperature, the stroke length and the friction coefficient is conducted, and the related papers are also classified into four categories. The design variables and the objective function(s) used in the papers are clarified with the design optimization technique. The multi-stage forging including the hammer forging for producing complex product shape is also briefly reviewed. Finally, major performance indexes and the future outlook are summarized for the further development of design optimization in forging.
Journal Article
A deep reinforcement learning optimization framework for supercritical airfoil aerodynamic shape design
In the context of traditional aerodynamic shape optimization design methods, the necessity to re-execute the complete optimization process when the initial shape changes poses significant challenges in engineering applications. These challenges encompass problems like data wastage and restricted ability for experience learning. We propose a policy learning-based optimization method that can automatically learn optimization experience through interactions with the environment. This optimization framework is based on deep reinforcement learning and consists of the policy learning process and the policy execution process. The action network, trained during the policy learning process, serves as a black box model of optimization experience and can directly and efficiently participate in guiding the actual optimization process. The optimization framework is validated through two-dimensional Rosenbrock function optimization, demonstrating its exceptional performance in achieving high-precision optimal solutions. Then, the effectiveness of this optimization method is demonstrated in the multi-point optimization design of supercritical airfoils, which aims to improve the buffet onset lift within predefined design constraints while maintaining the cruise lift-drag ratio. With the datum-coupled state format, the optimization experience can be tailored to the optimization requirements of different initial states during the learning process, leading to an optimization success rate in the optimization space that can exceed 90%.
Journal Article
Ship Forebody Optimization Based on Rankine Source Method
The shape of the ship’s forebody has a greater impact on the ship’s resistance, and a reasonable optimization of the forebody can play a role in reducing the propulsion power and optimizing the resistance performance. Under the premise of Rankine source method of potential flow wave theory as the theoretical basis, SHIPFLOW software is used as the calculation tool, and CAESES software is used as the optimization tool to study the optimal design of the ship with minimum wave resistance. In the optimization process, a real ship is taken as the object, and the optimal solution of the rising wave resistance coefficient is calculated with the rising wave resistance coefficient as the objective function and the ship speed and displacement as the constraints. The real ship is selected as the mother ship, the parameters of the hull shape are taken as the design variables, and the shape of the forebody is optimized by the Lackenby shift method, so as to obtain a ship shape with less wave resistance at the same speed and within the displacement limit. The results show that the improved ship shape has obvious effect of reducing the wave resistance, which verifies the effectiveness and feasibility of this method for ship shape optimization
Journal Article
Modeling and optimization with Gaussian processes in reduced eigenbases
Parametric shape optimization aims at minimizing an objective function
f
(
x
) where
x
are CAD parameters. This task is difficult when
f
(⋅) is the output of an expensive-to-evaluate numerical simulator and the number of CAD parameters is large. Most often, the set of all considered CAD shapes resides in a manifold of lower effective dimension in which it is preferable to build the surrogate model and perform the optimization. In this work, we uncover the manifold through a high-dimensional shape mapping and build a new coordinate system made of eigenshapes. The surrogate model is learned in the space of eigenshapes: a regularized likelihood maximization provides the most relevant dimensions for the output. The final surrogate model is detailed (anisotropic) with respect to the most sensitive eigenshapes and rough (isotropic) in the remaining dimensions. Last, the optimization is carried out with a focus on the critical dimensions, the remaining ones being coarsely optimized through a random embedding and the manifold being accounted for through a replication strategy. At low budgets, the methodology leads to a more accurate model and a faster optimization than the classical approach of directly working with the CAD parameters.
Journal Article