Optimum blank design for sheet metal forming based on the interaction of high- and low-fidelity FE models

This paper deals with an optimization methodology for the design of the sheet-metal-forming process. In this study, a new design optimization system is developed which employs an iterative optimization technique and numerical simulation of a sheet-metal-forming process. The main feature of this new optimization method is that it is based on the interaction of high- and low-fidelity simulation models in order to reduce overall computing time. In the iterative optimization procedure, only the corrected low-fidelity model is used. The high-fidelity model, which requires much longer computing time, is used only for the correction of the low-fidelity analysis and validation of the final solution. To demonstrate the developed optimization method on a practical application, it is applied to the optimum blank design for deep-drawing process of a rectangular box. In deep-drawing, the flange of the drawn product is usually trimmed off to obtain the desired product geometry, and the trimmed material is wasted. Therefore, the formulation of the optimization problem is to determine the optimum initial blank geometry which minimizes the amount of the trimmed material, that is, the waste of material. It is confirmed that the blank design was optimized successfully in remarkably short computing time by the developed optimization method.     

基于自适应多可信度多项式混沌-Kriging模型的高效气动优化方法

多可信度代理模型已经成为提高基于代理模型的优化算法效率和可信度水平最有效的手段之一.然而目前流行的co-Kriging和分层Kriging (HK)等多可信度代理模型泛化能力不足,缺乏对高阶/高非线性建模问题的适应性,难以广泛应用.文章基于发展的自适应多可信度多项式混沌-Kriging (MF-PCK)代理模型,在提高建模效率和对高阶/高非线性问题近似准确率的同时,建立了基于该自适应MF-PCK模型的高效全局气动优化方法.在发展的方法中,提出了基于MF-PCK模型的新型变可信度期望改进加点方法,使代理优化算法效率进一步提高.为了验证发展方法的全面表现,将其应用在经典的数值函数算例以及多个跨音速气动外形的确定性优化和稳健优化设计中,并与基于Kriging和HK模型的代理优化算法进行了全面比较.结果表明,发展的新型多可信度全局气动优化方法其优化效率相对于基于Kriging和HK模型的优化效率显著提高,结果更好也更加可靠,并且稳健优化设计效率和结果也更符合工程应用需求,证明了其相对于基于Kriging和HK模型的代理优化算法的显著优势.     

Active flutter suppression control law design method based on balanced proper orthogonal decomposition reduced order model

Active control for nonlinear aeroelastic structures is an attractive innovative technology. The design of classic active flutter controllers has often been based on low-fidelity and low-accuracy linear aerodynamic models. Multi-physics high-fidelity reduced order model (ROM) was used to design active control laws. In order to provide a lower-order model for controllers design, a balanced proper orthogonal decomposition ROM (POD-BT/ROM) was investigated. A state-space aeroservoelastic model and the active flutter suppression control law design method based on POD-BT/ROM were proposed. The effectiveness of the proposed method was then demonstrated by NACA 0012 airfoil, AGARD 445.6 wing and the Goland wing+ aeroelastic model.     

Multi-fidelity surrogate reduced-order modeling of steady flow estimation

A multi-fidelity reduced-order model (ROM), which incorporates low-fidelity data to improve the prediction of high-fidelity results, is proposed for the reconstruction of steady flow field at different conditions. The spatial basis functions of low-fidelity and high-fidelity data, which are generated for all training sets are extracted separately by proper orthogonal decomposition. Then a surrogate model is used to construct mappings between the mode coefficients obtained from low-fidelity and the high-fidelity data. In the online stage, both the low-fidelity flow at the predicted state and the surrogate model are needed to predict the mode coefficients of the high-fidelity flow, and the high-fidelity flow field is subsequently reconstructed. This method differs from existing surrogate-based reduced-order modeling method because it allows the use of partial physical information for flow estimation, which is coming from the low-fidelity data instead of adopting a black-box mapping between system state and the projection coefficients. Numerical studies are presented for a lid-driven cavity problem and transonic flow past a NACA0012 airfoil. Two low-fidelity models, with either a coarse mesh or a lower numerical order, are considered respectively. Results show that the proposed multi-fidelity ROM predicts the flow field accurately and outperforms the traditional methods in both interpolated and extrapolated conditions.     

高速列车气动外形优化研究进展

随着运行速度的提升, 高速列车对气动外形的要求也越来越高, 追求性能优异、美观大方的气动外形是新型高速列车研发的一个重要方向. 基于当前高速列车外形研发的思路, 可以将气动外形优化概括为基于流场机理的改型优化和基于优化算法的外形优化两类. 本文简要回顾了当前国内外在这两类优化途径上的系列工作, 着重介绍了作者所在团队近年来做过的一系列气动外形优化工作. 在基于流场机理的改型优化上, 着重从"和谐号"和"复兴号"这两款主力车型的外形研发上探讨其改型优化的思路, 主要探讨了空调导流罩、受电弓平台、风挡和转向架裙板几类对列车阻力影响较为明显的部件的优化设计,并介绍了其相对于上一代车型在气动性能上的提升. 基于优化算法的外形优化方法,则因循气动外形优化流程, 在列车外形已经具有较好性能的基础上,以高速列车头型流线型为主要优化对象,分别从高速列车参数化方法、替代模型开发以及优化算法改进三个方面进行介绍.其中,高速列车参数化方法主要介绍了局部型函数法、修正车辆造型函数法和类别/形状函数法三类;替代模型开发介绍了最优化替代模型和基于交叉验证的Kriging模型; 在优化算法的改进上介绍了改进的非劣分类多目标粒子群算法和连续域混沌蚁群算法两方面的内容.基于上述三个方面介绍了气动外形优化策略在典型工程上的应用案例.      

涡波一体乘波飞行器宽速域气动优化设计研究

涡波一体宽速域乘波飞行器通过在低速引入涡效应,显著改善了传统乘波体在低速状态下的升阻特性,具有在未来宽速域空天飞行器总体气动设计当中得到广泛应用的巨大潜力.但是,该设计方法的研究尚不完善,特别是在基准流场建立过程中忽略了三维效应、低速效应、黏性效应以及头部/前缘的钝化效应,因此其高低速气动特性均有优化设计的空间.针对此问题,本文结合高保真RANS求解器、自由变形参数化方法、鲁棒的结构网格变形方法、离散伴随方法以及序列二次规划算法,发展了基于离散伴随的宽速域飞行器气动优化设计方法.基于上述方法,针对涡波一体乘波飞行器开展了兼顾低速与高超声速气动性能的三维整机气动优化设计研究,获得了宽速域优化构型并对其进行了流动机理分析.结果表明,相较于初始构型,宽速域优化构型可以将飞行器高超声速状态下升阻特性略微提升的同时,显著增强低速状态飞行器背风面的旋涡效应,进而使飞行器低速状态的升力和升阻比均提升10%以上,改善了涡波一体宽速域乘波飞行器的高低速气动性能.     

Aero-thermal optimization of in-flight electro-thermal ice protection systems in transient de-icing mode

Even if electro-thermal ice protection systems (IPS) consume less energy when operating in de-icing mode than in anti-icing mode, they still need to be optimized for energy usage. The optimization, however, should also take into account the effect of the de-icing system on the aerodynamic performance. The present work offers an optimization framework in which both thermal and aerodynamic viewpoints are taken into account in formulating various objective and constraint functions by considering the energy consumption, the thickness, the volume, the shape and the location of the accreted ice on the surface as the key parameters affecting the energy usage and the aerodynamic performance. The design variables include the power density and the activation time of the electric heating blankets. A derivative-free technique, called the mesh adaptive direct search (MADS) method, is used to carry out the optimization process, which would normally need a large number of unsteady conjugate heat transfer (CHT) calculations for the IPS simulation. To avoid such prohibitive computations, reduced-order modeling (ROM) is used to construct simplified low-dimensional CHT models. The approach is illustrated through several test cases, in which different combinations of objective and constraint functions, design variables and cycling sequence patterns are examined. In these test cases, the energy consumption is significantly reduced compared to the experiments by improving the spatial and temporal distribution of the thermal energy usage. The results show the benefits of the approach in bringing energy, safety and aerodynamic considerations together in designing de-icing systems.     

融入压力分布信息的气动力建模方法

气动外形优化设计与飞行器性能分析中, 直接运用数值模拟或风洞实验获取气动力的成本高, 构建代理模型是提高外形优化和性能分析效率的重要途径. 然而, 构建模型的过程中, 研究者只关注积分后的气动力和力矩信息. 本文通过充分利用采样过程中所产生的压力分布信息, 来提高建模的精度和泛化性, 进而降低样本获取的成本. 提出了一种小样本框架下融入压力分布信息的气动力建模方法, 首先通过数值模拟或风洞试验获得不同流动参数状态下翼型表面的压力分布信息和气动系数, 其次通过本征正交分解技术对压力分布信息进行特征提取, 获取不同输入参数状态下压力分布信息对应的POD系数, 之后结合输入参数通过Kriging算法对压力分布信息进行建模, 将压力分布信息积分得到低精度气动系数的预测模型, 最后低精度气动系数结合输入参数通过Kriging算法构造高精度的气动系数预测模型. 通过同状态变翼型算例以及CAS350翼型变状态算例进行验证, 该方法相比于传统的克里金模型直接预测气动力, 有效提高了气动力的预测精度和模型的鲁棒性, 同时缩小了学习样本的数据量.      

Improving vortex models via optimal control theory

Low-order inviscid point vortex models have demonstrated success in capturing the qualitative behavior of aerodynamic forces resulting from unsteady lifting surface maneuvers. However, the quantitative agreement is often lacking for separated flows as a result of the ambiguity in the edge conditions in this fundamentally unsteady process. In this work, we develop a model reduction framework in which such models can be systematically improved with empirical results. We consider the low-order impulse matching vortex model in which, in its original form, Kutta conditions are applied at both edges to determine the strengths of single point vortices shed from each edge. Here, we relax the Kutta condition imposed at the plate׳s edges and instead seek the time rate of change of the vortex strengths that minimize the discrepancy between the model-predicted and high-fidelity simulation force histories, while the vortex positions adhere to the dynamics of the low-order model. A constrained minimization problem is constructed within an optimal control framework and solved by means of variational principles. The optimization approach is demonstrated on several unsteady wing maneuvers, including pitch-up and impulsive translation at a fixed angle of attack. Additionally, a stitching technique is introduced for extending the time interval over which the model is optimized.     

AERODYNAMIC OPTIMIZATION OF HIGH-SPEED TRAIN BASED ON RBF MESH DEFORMATION

基于局部型函数三维参数化方法、改进的蚁群算法和改进的克里金（Kriging）代理模型,开展了列车头型的三维气动减阻优化设计研究。为了避免复杂几何外形大变形情况下千万量级网格的重复生成,提高高速列车头型优化设计的效率,引入了缩减控制点的径向基函数网格变形技术。优化结果表明：径向基函数网格变形技术在不降低网格质量的情况下可以有效缩短网格变形的时间消耗,能够用于复杂几何外形的气动优化设计;在给定的设计空间内,控制鼻锥外形的6个关键设计参数对列车气动阻力的影响呈单调递增关系;优化后,在满足约束条件的情况下,简化外形列车的整车气动阻力减小5.41%,头尾车减阻效果明显,中间车气动阻力基本不变。     

基于离散共轭方法的高超声速导弹气动外形优化设计

开展了离散共轭方法在高超声速气动外形优化设计中的应用研究。构建了基于NURBS方法的几何外形参数化方法,完成了一种简单高效的动网格方法,建立了基于Euler方程的离散共轭方法,并将这些方法与优化算法等集成起来够构建了适合复杂外形的高超声速气动外形优化设计系统。利用该系统对一种导弹的前体进行了优化设计研究,使其升阻比提高了11.2%,优化后导弹前体形状接近双锥外形,说明双锥形前体有利于减小阻力。算例表明,离散共轭方法在高超声速气动外形优化设计中具有良好的应用前景。     

Efficient shape optimization for fluid–structure interaction problems

An approach for the shape optimization of fluid–structure interaction (FSI) problems is presented. It is based on a partitioned solution procedure for fluid–structure interaction, a shape representation with NURBS, and sequential quadratic programming approach for optimization within a parallel environment with MPI as direct coupling tool. The optimization procedure is accelerated by employing reduced order models based on a proper orthogonal decomposition method with snapshots and Kriging. After the verification of the FSI optimization, the functionality and efficiency of the reduced order modeling as well as the corresponding optimization procedure are investigated.     

Aerodynamic shape optimization on overset grids using the adjoint method

This paper deals with the use of the continuous adjoint equation for aerodynamic shape optimization of complex configurations with overset grids methods. While the use of overset grid eases the grid generation process, the non‐trivial task of ensuring communication between overlapping grids needs careful attention. This need is effectively addressed by using a practically useful technique known as the implicit hole cutting (IHC) method. The method depends on a simple cell selection process based on the criterion of cell size, and all grid points including interior points and fringe points are treated indiscriminately in the computation of the flow field. This paper demonstrates the simplicity of the IHC method for the adjoint equation. Similar to the flow solver, the adjoint equations are solved on conventional point‐matched and overlapped grids within a multi‐block framework. Parallel computing with message passing interface is also used to improve the overall efficiency of the optimization process. The method is successfully demonstrated in several two‐ and a three‐dimensional shape optimization cases for both external and internal flow problems. Copyright © 2009 John Wiley & Sons, Ltd.     

Optimization of 3D wings based on Navier-Stokes solutions and genetic algorithms

The problem of the aerodynamic shape optimization to minimum drag, subject to geometrical and aerodynamic constraints, is considered. An accurate and computationally efficient approach to the multiobjective constrained design of 3D aerodynamic wings is proposed. The optimization is driven by full Navier-Stokes computations and Genetic Algorithms (GAs). The verification results include a variety of optimization cases for a classical test-case of ONERA M6 wing in transonic flight conditions. The method allows to significantly reduce the total drag of optimized wings, while exhibiting high robustness and keeping CFD computational volume to an acceptable level.     

Piezoelectric energy harvesting from morphing wing motions for micro air vehicles

Wing flapping and morphing can be very beneficial to managing the weight of micro air vehicles through coupling the aerodynamic forces with stability and control. In this letter, harvesting energy from the wing morphing is studied to power cameras, sensors, or communication devices of micro air vehicles and to aid in the management of their power. The aerodynamic loads on flapping wings are simulated using a three-dimensional unsteady vortex lattice method. Active wing shape morphing is considered to enhance the performance of the flapping motion. A gradient-based optimization algorithm is used to pinpoint the optimal kinematics maximizing the propellent efficiency. To benefit from the wing deformation, we place piezoelectric layers near the wing roots. Gauss law is used to estimate the electrical harvested power. We demonstrate that enough power can be generated to operate a camera. Numerical analysis shows the feasibility of exploiting wing morphing to harvest energy and improving the design and performance of micro air vehicles.     

Design optimization of unsteady airfoils with continuous adjoint method

In this paper, a new unsteady aerodynamic design method is presented based on the Navier-Stokes equations and a continuous adjoint approach. A basic framework of time-accurate unsteady airfoil optimization which adopts time-averaged aerodynamic coefficients as objective functions is presented. The time-accurate continuous adjoint equation and its boundary conditions are derived. The flow field and the adjoint equation are simulated numerically by the finite volume method (FVM). Feasibility and accuracy of the approach are perfectly validated by the design optimization results of the plunging NACA0012 airfoil.     

CFD‐based optimization of aerofoils using radial basis functions for domain element parameterization and mesh deformation

A novel domain element shape parameterization method is presented for computational fluid dynamics‐based shape optimization. The method is to achieve two aims: (1) provide a generic ‘wrap‐around’ optimization tool that is independent of both flow solver and grid generation package and (2) provide a method that allows high‐fidelity aerodynamic optimization of two‐ and three‐dimensional bodies with a low number of design variables. The parameterization technique uses radial basis functions to transfer domain element movements into deformations of the design surface and corresponding aerodynamic mesh, thus allowing total independence from the grid generation package (structured or unstructured). Independence from the flow solver (either inviscid, viscous, aeroelastic) is achieved by obtaining sensitivity information for an advanced gradient‐based optimizer (feasible sequential quadratic programming) by finite‐differences. Results are presented for two‐dimensional aerofoil inverse design and drag optimization problems. Inverse design results demonstrate that a large proportion of the design space is feasible with a relatively low number of design variables using the domain element parameterization. Heavily constrained (in lift, volume, and moment) two‐dimensional aerofoil drag optimization has shown that significant improvements over existing designs can be achieved using this method, through the use of various objective functions. Copyright © 2008 John Wiley & Sons, Ltd.     

考虑气动参数扰动的再入轨迹快速优化方法

针对传统再入轨迹优化方法收敛速度慢、对初值敏感程度高等的局限性,提出了一种基于序列凸优化的再入轨迹快速求解方法.该方法以倾侧角的变化率作为控制量,改进了现有凸化策略,考虑到抑制数值优化过程中由于数值离散方式带来的锯齿化现象,采用 B 样条曲线离散控制量,同时为避免算法在初始猜想值附近出现伪不可行的问题,增加额外虚拟控制量,通过一种"回溯直线"搜索的方法,提高算法的稳定性、快速性和寻优结果的光滑性.为研究飞行器再入过程中的气动参数扰动问题,采用采样点少、易于实现,计算效率高的广义混沌多项式理论研究方法,建立了基于广义混沌多项式和凸优化相结合的再入轨迹鲁棒优化模型,该模型在优化过程中考虑气动参数扰动对寻优结果的影响作用,避免了传统轨迹与制导律的复杂迭代设计环节,可有效降低优化轨迹对气动参数扰动的敏感程度,在气动参数不确定条件的干扰下,依然可以保证飞行器顺利安全的完成飞行任务.最后,以美国某可重复使用飞行器的再入任务为例,验证了基于序列凸优化的再入轨迹优化方法的快速性以及鲁棒优化模型对气动参数扰动的抗干扰性能力,表明了该方法具有一定的工程应用性.      

FAST OPTIMIZATION METHOD OF REENTRY TRAJECTORY CONSIDERING AERODYNAMIC PARAMETER PERTURBATION

针对传统再入轨迹优化方法收敛速度慢、对初值敏感程度高等的局限性,提出了一种基于序列凸优化的再入轨迹快速求解方法.该方法以倾侧角的变化率作为控制量,改进了现有凸化策略,考虑到抑制数值优化过程中由于数值离散方式带来的锯齿化现象,采用 B 样条曲线离散控制量,同时为避免算法在初始猜想值附近出现伪不可行的问题,增加额外虚拟控制量,通过一种"回溯直线"搜索的方法,提高算法的稳定性、快速性和寻优结果的光滑性.为研究飞行器再入过程中的气动参数扰动问题,采用采样点少、易于实现,计算效率高的广义混沌多项式理论研究方法,建立了基于广义混沌多项式和凸优化相结合的再入轨迹鲁棒优化模型,该模型在优化过程中考虑气动参数扰动对寻优结果的影响作用,避免了传统轨迹与制导律的复杂迭代设计环节,可有效降低优化轨迹对气动参数扰动的敏感程度,在气动参数不确定条件的干扰下,依然可以保证飞行器顺利安全的完成飞行任务.最后,以美国某可重复使用飞行器的再入任务为例,验证了基于序列凸优化的再入轨迹优化方法的快速性以及鲁棒优化模型对气动参数扰动的抗干扰性能力,表明了该方法具有一定的工程应用性.     

Domain versus boundary computation of flow sensitivities with the continuous adjoint method for aerodynamic shape optimization problems

This paper considers the computation of flow sensitivities that arise in the context of design optimization. The scheme is based on the solution of a continuous adjoint problem, for which two complementary, although analytically equivalent, approaches have been routinely used for some time now, yielding expressions for the sensitivities that contain, respectively, boundary and domain integrals. These concepts are clarified in a unified framework and their equivalence at the continuous level is demonstrated through appropriate algebraic manipulations. Equivalence at the discrete level is assessed through numerical testing for various aerodynamic shape‐optimization problems. Copyright © 2011 John Wiley & Sons, Ltd.