径向基函数参数化翼型的气动力降阶模型优化

基于小扰动和弱非线性假设,提出了一种基于气动力降阶模型和径向基函数参数化的翼型优化方法.其主要方法是用径向基函数参数化翼型扰动;通过CFD辨识参数扰动对翼型气动力影响的降阶模型核函数;基于叠加法建立了参数变化对翼型气动力影响的降阶模型;最后基于该气动力降阶模型计算并优化翼型升阻特性.NACA0012翼型优化的结果表明基于气动力降阶模型的优化方法是可行的,可以极大地提高翼型优化速度.     

基于谐波平衡法的尾流激励的叶片振动降阶模型方法

在航空发动机中下游叶片在上游尾流的作用下易发生受迫振动,严重影响叶片的颤振和疲劳性能.对于这种尾流作用下复杂的流固耦合情况需要一种有效的方法来分析.针对这一问题,提出了基于谐波平衡法的尾流激励的叶片振动降阶模型方法.该方法首先将上游尾流Fourier(傅立叶)分解为若干尾流谐波,并计算各尾流谐波下叶片气动力谐波的振幅,得到尾流引起的叶片气动力;再通过叶片的结构运动方程和气动力降阶模型的耦合分析尾流激励下叶片的振动.算例结果表明,该方法可以快速准确地分析尾流激励下叶片的振动特性.     

C-Bézier曲线降阶的B网扰动和约束优化法

基于B网扰动和约束优化方法,对n次C-Bézier曲线控制多边形顶点进行扰动,并找到其退化为n-1次次C-Bézier曲线的条件.在满足退化条件的约束下,使n次C-Bézier曲线控制多边形顶点扰动量最小,由此找到降阶为n-1次的C-Bézier曲线,同时也研究了在C~0,C~1连续条件下对n次C-Bézier曲线降阶的B网扰动和约束优化方法.给出了扰动显示格式计算方法和降阶逼近的误差估计式.     

基于等价输入扰动的空间桁架振动控制的研究(英文)

基于等价输入扰动(EID)的方法,通过对抑制外界未知扰动(匹配的或者非匹配的),实现了对空间桁架的振动控制.首先利用有限元分析(FEA),计算空间桁架的质量矩阵,阻尼矩阵,刚度矩阵及输入矩阵,进而建立空间桁架的模型.为了便于分析和设计,利用模态降阶的方法对模型进行降阶处理.在降阶的模型的基础上,设计等价输入扰动观测器观测外部未知扰动.基于观测的结果,进一步地设计了空间桁架的振动控制方法.最后给出数值仿真,以证实所提方法的有效性.     

基于降阶模型和数据驱动的动态结构数字孪生方法北大核心CSCD

针对受动载荷作用的结构,提出了一种基于降阶模型库和机器学习数据驱动的数字孪生构建方法.首先根据物理结构服役过程中可能出现的损伤状态,采用有限单元法建立高保真有限元模型.其次采用Krylov子空间模型降阶方法对模型进行降阶,建立了物理结构各种状态下的降阶模型,形成模型库.最后利用随机森林机器学习算法训练获得模型选择器,通过物理结构上传感器的数据推断当前物理结构的状态,驱动数字孪生体跟随物理结构一同演化.设计制作了一个框架结构物理模型,模拟了结构不同位置损伤及不同损伤程度,验证了提出的数字孪生构建方法.     

基于Mori-Zwanzig格式和偏最小二乘的非线性模型降阶

本征正交分解及Galerkin投影是解决复杂非线性系统模型降阶问题常用的方法.然而,该方法在构造降阶系统过程中只截取基函数的部分模态,这通常会使得降阶系统不准确.针对该问题,提出了对降阶系统误差进行快速校正的方法.首先应用Mori-Zwanzig格式对降阶系统的误差进行分析,理论上得到误差模型的形式和有效预测变量.再通过偏最小二乘方法构造预测变量和系统误差的多元回归模型,建立误差预测模型.将所构造的误差预测模型直接嵌入到原降阶系统,得到新的降阶系统在形式上等价于对原模型的右端采用Petrov-Galerkin投影.最后给出了新的降阶系统的误差估计.数值结果进一步说明了所提方法能有效地提高降阶系统的稳定性和准确性,且具有较高计算效率.     

基于卷积神经网络模型数值求解双曲型偏微分方程的研究

人工神经网络近年来得到了快速发展,将此方法应用于数值求解偏微分方程是学者们关注的热点问题.相比于传统方法其具有应用范围广泛（即同一种模型可用于求解多种类型方程）、网格剖分条件要求低等优势,并且能够利用训练好的模型直接计算区域中任意点的数值.该文基于卷积神经网络模型,对传统有限体积法格式中的权重系数进行优化,以得到在粗粒度网格下具有较高精度的新数值格式,从而更适用于复杂问题的求解.该网络模型可以准确、有效地求解Burgers方程和level set方程,数值结果稳定,且具有较高数值精度.     

一种面向图像识别的神经网络通用扰动生成算法

近年来,基于深度神经网络的图像识别技术表现出良好的性能,然而研究表明神经网络容易受到对抗扰动攻击而发生分类错误,施加一个小的通用扰动就能使神经网络在整个数据集上失效.为构建更加健壮的神经网络,对通用扰动生成的研究显得至关重要.通用扰动生成问题要求得到一个扰动向量对整个数据集产生指定扰动率的攻击效果,相较于单张图片扰动生成问题其约束条件更严格,计算难度更大.目前已有算法得到的通用扰动范数较大,容易被人眼识别.文章基于优化理论提出新的通用扰动生成算法,在达到指定扰动率的同时能产生更小的通用扰动.算法结合PCA降维思想克服了问题的规模性带来的困难;然后利用单张对抗扰动向量的均值叠加随机噪声,得到满足扰动率的初始通用扰动;最后改进梯度下降方法在保证扰动率的同时得到更小的通用扰动.实验表明,该方法可有效攻击各类先进神经网络:在达到相同扰动率的情况下,所得通用扰动的范数较Uni.Perturbation算法的结果平均降低了54%.     

基于分数阶GM(1,1)与BP神经网络的电力负荷预测

传统的灰色GM(1,1)和BP神经网络模型存在对原始序列依赖高,收敛速度慢等缺点.将分数阶累加的思想引入GM(1,1)模型,再用逐层训练算法改进传统的BP神经网络.基于我国2010-2014年的电力数据,构建分数阶GM(1,1)与BP神经网络组合模型,预测2015年和2016年的总发电量.实证结果表明,该组合模型比GM(1,1)模型,分数阶GM(1,1)模型以及GM(1,1)与BP神经网络组合模型具有更好的数据拟合效果,更高的预测精度.     

一种基于奇异摄动理论的鲁棒自适应非仿射非线性控制方法

文章针对一类具有参数不确定性和未知扰动项的非仿射非线性系统,提出了一种基于奇异摄动理论的鲁棒自适应控制方法.首先,通过控制输入构建了一个快变子系统,为原系统引入时标分离特性,使闭环系统可以在快变和慢变时间尺度上分解为两个降阶子系统:边界层子系统和降阶慢变子系统.在快时间尺度上,通过设计边界层子系统的结构使其在平衡点处指数稳定;在慢时间尺度上,针对含有参数不确定性和未知扰动项的降阶慢变子系统设计鲁棒自适应控制器.根据奇异摄动理论,闭环系统的跟踪性能可由降阶慢变子系统近似.文章提出的控制方法同时考虑了参数不确定性和未知扰动项的影响,在不忽略非仿射结构的前提下实现控制目标,不依赖于原系统的时标分离特性,且避免了反步法中的“复杂性爆炸”问题.两组与参考文献控制方法的对比仿真结果验证了文章控制方法的有效性.     

Aerodynamic Optimization of Airfoils Using Adaptive Parameterization and Genetic Algorithm

A new method for airfoil shape parameterization is presented, and its influences on the optimum design and convergence of the evolutionary optimization process are investigated. An online adaptive method is used that alters the airfoil parametric function during the process of optimization. A geometric inverse design is carried out, and the capability of the method for producing general airfoil shapes is assessed. The performance of the method is then evaluated by aerodynamic shape optimization. The result indicates that the proposed method improves the optimum design airfoil significantly. In addition, it reduces the total number of flow solver calls, which consequently reduces the required computational time.     

变可信度模型在气动优化中的应用

在气动外形优化中, 采用近似模型管理结构（AMF）方法,对变可信度模型进行组织和管理．这样能够充分利用低可信度模型,将主要计算量集中在低可信度模型的优化迭代过程中．同时,采用高可信度模型监控优化过程,使最终的优化解收敛到高可信度模型上．最后,设计了零阶变可信度气动特性优化管理结构与搜索算法,对某飞翼型无人机的翼型进行了气动优化．优化外形的气动性能与初始外形比有所提高．实际结果表明所提出的方法具有良好的可行性和适用性．     

Numerical bifurcation analysis of static stall of airfoil and dynamic stall under unsteady perturbation

By the finite element method combined with Arbitrary-Lagrangian-Eulerian (ALE) frame and explicit Characteristic Based Split Scheme (CBS), the complex flows around stationary and sinusoidal pitching airfoil are studied numerically. In particular, the static and dynamic stalls are analyzed in detail, and the natures of the static stall of NACA0012 airfoil are given from viewpoint of bifurcations. Following the bifurcation in Map, the static stall is proved to be the result from saddle-node bifurcation which involves both the hysteresis and jumping phenomena, by introducing a Map and its Floquet multiplier, which is constructed in the numerical simulation of flow field and related to the lift of the airfoil. Further, because the saddle-node bifurcation is sensitive to imperfection or perturbation, the airfoil is then subjected to a perturbation which is a kind of sinusoidal pitching oscillation, and the flow structure and aerodynamic performance are studied numerically. The results show that the large-scale flow separation at the static stall on the airfoil surface can be removed or delayed feasibly, and the ensuing lift could be enhanced significantly and also the stalling incidence could be delayed effectively. As a conclusion, it can be drawn that the proper external excitation can be considered as a powerful control strategy for the stall. As an unsteady aerodynamic behavior of high angle of attack, the dynamic stall can be investigated from viewpoint of nonlinear dynamics, and there exists a rich variety of nonlinear phenomena, which are related to the lift enhancement and drag reduction.     

Nonlinear dynamic analysis of a complex dual rotor-bearing system based on a novel model reduction method

In this paper, a dynamic model of a complex dual rotor-bearing system of an aero-engine is established based on the finite element method with three types of beam elements (rigid disc, cylindrical beam element and conical beam element), as well as taking into account the nonlinearities of all of the supporting rolling element bearings. To rapidly and accurately analyze dynamic behaviors of the complex dual rotor-bearing system, a two-level model order reduction (MOR) method is proposed by combining component mode synthesis (CMS) method and proper orthogonal decomposition (POD) technique. The first-level reduced-order model (ROM) of the dual rotors is obtained by CMS method with a high precision for the original system. Then, the POD method is applied to second-level model order reduction to further decrease the degrees of freedom (DOFs) of first-level ROM. Second-level ROM with mode expansion and direct second-level ROM are obtained, and the nonlinear displacement responses of the two ROMs are compared with the first-level ROM. The numerical results demonstrate that the proposed method has a higher computational efficiency and accuracy in terms of mode expansion than the direct model reduction by using POD method. In addition, the nonlinear vibration responses of the dual rotor-bearing system are studied by this second-level ROM in the case of different clearances of the inter-shaft bearing. The results indicate that the dynamic characteristics of the dual rotor-bearing system are very complicated for a large clearance.     

基于改进粒子群算法的翼型稳健型气动优化设计

基于标准粒子群算法,将位移变化作为影响微粒速度的变量,使得粒子群算法关于粒子位置为二阶精度函数,加快了收敛速度;进一步地在粒子速度更新公式中引入振荡环节,提高了群体多样性,改善了算法的全局收敛性．以改进粒子群算法为基础,结合气动分析程序、代理模型以及翼型参数化方法,构建了翼型稳健型气动优化设计系统．针对某型客机的基本翼型以及翼梢小翼翼型气动优化设计结果表明,优化后的翼型气动特性相对于初始翼型在较宽的设计范围内都有了大幅度提高．     

Natural laminar flow shape optimization in transonic regime with competitive Nash game strategy

The Natural Laminar Flow (NLF) airfoil/wing design optimization is an efficient method which can reduce significantly turbulence skin friction by delaying transition location at high Reynolds numbers. However, the reduction of the friction drag is competitively balanced with the increase of shock wave induced drag in transonic regime. In this paper, a distributed Nash Evolutionary Algorithms (EAs) is presented and extended to multi-level parallel computing, namely multi-level parallel Nash EAs. The proposed improved methodology is used to solve NLF airfoil shape design optimization problem. It turns out that the optimization method developed in this paper can easily capture a Nash Equilibrium (NE) between transition delaying and wave drag increasing. Results of numerical experiments demonstrate that both wave drag and friction drag performances of a NE are greatly improved. Moreover, performance of the NE is equivalent to that of cooperative Pareto-optimum solutions, but it is more efficient in terms of CPU time. The successful application validates efficiency of algorithms in solving complex aerodynamic optimization problem.     

Preconditioning the Pressure Tracking in Fluid Dynamics by Shape Hessian Information

Potential flow pressure matching is a classical inverse design aerodynamic problem. The resulting loss of regularity during the optimization poses challenges for shape optimization with normal perturbation of the surface mesh nodes. Smoothness is not enforced by the parameterization but by a proper choice of the scalar product based on the shape Hessian, which is derived in local coordinates for starshaped domains. Significant parts of the Hessian are identified and combined with an aerodynamic panel solver. The resulting shape Hessian preconditioner is shown to lead to superior convergence properties of the resulting optimization method. Additionally, preconditioning gives the potential for level independent convergence.     

Certified Nonlinear Parameter Optimization with Reduced Basis Surrogate Models

PDE-constrained parameter optimization problems suffer from the high dimensionality of the corresponding discretizations, which results in long optimization runtimes. One possible approach to solve such large scale optimization problems more rapidly is to replace the PDE constraint by a low-dimensional model constraint obtained via model reduction. We present a general technique for certification of such surrogate optimization results by a-posteriori error estimation based on Reduced Basis (RB) models. We allow arbitrary PDEs and optimization functionals, in particular cover nonlinear optimization problems. Experiments on a stationary heat-conduction problem demonstrate the applicability of the error bound. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)