Kriging模型在机翼气动外形优化中的应用

针对粒子群等随机优化算法计算量大的缺点,发展了基于Kriging模型的优化方法.采用改进的量子粒子群算法对Kriging模型的相关模型参数进行优化,以提高代理模型预测精度,并与具有双层结构的粒子群算法相结合.采用雷诺平均N-S方程流场求解器与多目标非线性适应值加权方法,对高维度多目标多约束的跨声速机翼进行了优化,设计的机翼具有理想的压力分布,降低了机翼阻力系数,并且有效控制了低头力矩和翼根弯矩,表明该方法具有较强的工程实用性.     

Application of a PCA-DBN-based surrogate model to robust aerodynamic design optimization

An efficient method employing a Principal Component Analysis (PCA)-Deep Belief Network (DBN)-based surrogate model is developed for robust aerodynamic design optimization in this study. In order to reduce the number of design variables for aerodynamic optimizations, the PCA technique is implemented to the geometric parameters obtained by parameterization method. For the purpose of predicting aerodynamic parameters, the DBN model is established with the reduced design variables as input and the aerodynamic parameters as output, and it is trained using the k-step contrastive divergence algorithm. The established PCA-DBN-based surrogate model is validated through predicting lift-to-drag ratios of a set of airfoils, and the results indicate that the PCA-DBN-based surrogate model is reliable and obtains more accurate predictions than three other surrogate models. Then the efficient optimization method is established by embedding the PCA-DBN-based surrogate model into an improved Particle Swarm Optimization (PSO) framework, and applied to the robust aerodynamic design optimizations of Natural Laminar Flow (NLF) airfoil and transonic wing. The optimization results indicate that the PCA-DBN-based surrogate model works very well as a prediction model in the robust optimization processes of both NLF airfoil and transonic wing. By employing the PCA-DBN-based surrogate model, the developed efficient method improves the optimization efficiency obviously.     

基于粒子群神经网络的轮盘优化

将粒子群算法(PSO)和BP神经网络相结合, 构建了一种新型智能结构优化算法.PSO方法除用于结构优化外, 还被用于BP神经网络的构造及网络训练, 使之可自适应调整优化.结构优化中, 以BP神经网络取代有限元方法, 通过设计变量来映射目标函数和约束, 从而大大提高了计算速度.将此方法用于轮盘结构优化, 使得轮盘体积减少了17.5%, 结果通过检验.该方法便捷、高效, 为解决工程结构优化问题提供了一个新途径.      

基于代理模型的结构外形优化

提出了一种将代理模型用于机翼结构外形优化的方法。重点介绍了建立结构分析代理模型的过程,包括确定设计变量及取值范围、生成试验设计点、建立参数化结构模型、有限元结构优化设计、提取结构特性并构造代理模型。最后通过一个简单的机翼结构优化算例验证了这种方法的可行性和有效性。     

Variable-fidelity optimization with design space reduction

Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task owing to the curse of dimensionality. This paper presents a new algorithm to reduce the size of a design space to a smaller region of interest allowing a more accurate surrogate model to be generated. The framework requires a set of models of different physical or numerical fidelities. The low-fidelity (LF) model provides physics-based approximation of the high-fidelity (HF) model at a fraction of the computational cost. It is also instrumental in identifying the small region of interest in the design space that encloses the high-fidelity optimum. A surrogate model is then constructed to match the low-fidelity model to the high-fidelity model in the identified region of interest. The optimization process is managed by an update strategy to prevent convergence to false optima. The algorithm is applied on mathematical problems and a two-dimen-sional aerodynamic shape optimization problem in a variable-fidelity context. Results obtained are in excellent agreement with high-fidelity results, even with lower-fidelity flow solvers, while showing up to 39% time savings.     

Aerodynamic design optimization of nacelle/pylon position on an aircraft

The arbitrary space-shape free form deformation (FFD) method developed in this paper is based on non-uniform rational B-splines (NURBS) basis function and used for the integral parameterization of nacelle-pylon geometry. The multi-block structured grid deformation technique is established by Delaunay graph mapping method. The optimization objects of aerodynamic characteristics are evaluated by solving NavierStokes equations on the basis of multi-block structured grid. The advanced particle swarm optimization (PSO) is utilized as search algorithm, which com-bines the Kriging model as surrogate model during optimization. The optimization system is used for optimizing the nacelle location of DLR-F6 wing-body-pylon-nacelle. The results indicate that the aerodynamic interference between the parts is significantly reduced. The optimization design system established in this paper has extensive applications and engineering value.     

Surrogate role of machine learning in motor-drive optimization for more-electric aircraft applications

Motor drives form an essential part of the electric compressors, pumps, braking and actuation systems in the More-Electric Aircraft (MEA). In this paper, the application of Machine Learning (ML) in motor-drive design and optimization process is investigated. The general idea of using ML is to train surrogate models for the optimization. This training process is based on sample data collected from detailed simulation or experiment of motor drives. However, the Surrogate Role (SR) of ML may vary for different applications. This paper first introduces the principles of ML and then proposes two SRs (direct mapping approach and correction approach) of the ML in a motor-drive optimization process. Two different cases are given for the method comparison and validation of ML SRs. The first case is using the sample data from experiments to train the ML surrogate models. For the second case, the joint-simulation data is utilized for a multi-objective motor-drive optimization problem. It is found that both surrogate roles of ML can provide a good mapping model for the cases and in the second case, three feasible design schemes of ML are proposed and validated for the two SRs. Regarding the time consumption in optimizaiton, the proposed ML models can give one motor-drive design point up to 0.044 s while it takes more than 1.5 mins for the used simulation-based models.     

Model parameters estimation of aero-engine based on hybrid optimization algorithm

A hybrid optimization algorithm for the time-domain identification of multivariable,state space model for aero-engine was presented in this paper.The optimization procedure runs particle swarm optimization (PSO) and least squares optimization (LSO) "in series".PSO starts from an initial population and searches for the optimum solution by updating generations.However,it can sometimes run into a suboptimal solution.Then LSO can start from the suboptimal solution of PSO,and get an optimum solution by conjugate gradient algorithm.The algorithm is suitable for the high-order multivariable system which has many parameters to be estimated in wide ranges.Hybrid optimization algorithm is applied to estimate the parameters of a 4-input 4-output state variable model (SVM) for aero-engine.The simulation results demonstrate the effectiveness of the proposed algorithm.      

Research on multi-fidelity aerodynamic optimization methods

 Constructing high approximation accuracy surrogate model with lower computational cost has great engineering significance. In this paper, using co-Kriging method, an efficient multifidelity surrogate model is constructed based on two independent high and low fidelity samples. Co-Kriging method can use a greater quantity of low-fidelity information to enhance the accuracy of a surrogate of the high-fidelity model by modeling the correlation between high and low fidelity model, thus computational cost of building surrogate model can be greatly reduced. A wing-body problem is taken as an example to compare characteristics of co-Kriging multi-fidelity (CKMF) model with traditional Kriging based multi-fidelity (KMF) model. A sampling convergence of the CKMF model and the KMF model is conducted, and an appropriate sampling design is selected through the sampling convergence analysis. The results indicate that CKMF model has higher approximation accuracy with the same high-fidelity samples, and converges at less high-fidelity samples. A wing-body drag reduction optimization design using genetic algorithm is implemented. Satisfying design results are obtained, which validate the feasibility of CKMF model in engineering design.     

Efficient aerodynamic shape optimization using variable-fidelity surrogate models and multilevel computational grids

A variable-fidelity method can remarkably improve the efficiency of a design optimization based on a high-fidelity and expensive numerical simulation, with assistance of lower-fidelity and cheaper simulation(s). However, most existing works only incorporate “two” levels of fidelity, and thus efficiency improvement is very limited. In order to reduce the number of high-fidelity simulations as many as possible, there is a strong need to extend it to three or more fidelities. This article proposes a novel variable-fidelity optimization approach with application to aerodynamic design. Its key ingredient is the theory and algorithm of a Multi-level Hierarchical Kriging (MHK), which is referred to as a surrogate model that can incorporate simulation data with arbitrary levels of fidelity. The high-fidelity model is defined as a CFD simulation using a fine grid and the lower-fidelity models are defined as the same CFD model but with coarser grids, which are determined through a grid convergence study. First, sampling shapes are selected for each level of fidelity via technique of Design of Experiments (DoE). Then, CFD simulations are conducted and the output data of varying fidelity is used to build initial MHK models for objective (e.g. C_D) and constraint (e.g. C_L, C_m) functions. Next, new samples are selected through infill-sampling criteria and the surrogate models are repetitively updated until a global optimum is found. The proposed method is validated by analytical test cases and applied to aerodynamic shape optimization of a NACA0012 airfoil and an ONERA M6 wing in transonic flows. The results confirm that the proposed method can significantly improve the optimization efficiency and apparently outperforms the existing single-fidelity or two-level-fidelity method.     

Kriging模型及代理优化算法研究进展

代理模型方法由于能显著提高工程优化设计问题的效率,在航空航天及其他领域得到了广泛重视,并逐渐发展成为一类优化算法,本文称其为代理优化（SBO）算法。在现有的代理模型方法中,如多项式响应面、径向基函数、神经网络、支持向量回归、多变量插值/回归、多项式混沌展开等,源于地质统计学的Kriging模型具有代表性,是一种非常具有应用潜力的代理模型方法。以飞行器设计领域的优化问题为背景,介绍了Kriging代理模型及应用于优化设计的理论和算法的最新研究进展。首先,概述了Kriging模型的基本理论和算法,并讨论了影响Kriging模型鲁棒性和效率的几个关键性问题。其次,回顾了Kriging模型理论和算法研究的3个最新研究进展,包括梯度增强型Kriging、CoKriging和分层Kriging模型。而后,分析提炼了基于Kriging模型的代理优化算法的优化机制和优化框架,给出了“优化加点准则”和“子优化”的概念,并介绍了目前常用的几种优化加点准则及其相应子优化问题的求解与约束处理;同时,还介绍了最新提出的局部EI加点准则以及代理优化的终止条件。最后,介绍了代理优化在标准测试函数算例验证、飞行器气动与多学科优化设计典型算例确认方面的研究进展,并对当前存在的一些关键科学问题以及未来研究方向进行了讨论。     

An efficient aerodynamic shape optimization of blended wing body UAV using multi-fidelity models

This paper presents a novel optimization technique for an efficient multi-fidelity model building approach to reduce computational costs for handling aerodynamic shape optimization based on high-fidelity simulation models. The wing aerodynamic shape optimization problem is solved by dividing optimization into three steps—modeling 3D(high-fidelity) and 2D(lowfidelity) models, building global meta-models from prominent instead of all variables, and determining robust optimizing shape associated with tuning local meta-models. The adaptive robust design optimization aims to modify the shape optimization process. The sufficient infilling strategy—known as adaptive uniform infilling strategy—determines search space dimensions based on the last optimization results or initial point. Following this, 3D model simulations are used to tune local meta-models. Finally, the global optimization gradient-based method—Adaptive Filter Sequential Quadratic Programing(AFSQP) is utilized to search the neighborhood for a probable optimum point. The effectiveness of the proposed method is investigated by applying it, along with conventional optimization approach-based meta-models, to a Blended Wing Body(BWB) Unmanned Aerial Vehicle(UAV). The drag coefficient is defined as the objective function, which is subjected to minimum lift coefficient bounds and stability constraints. The simulation results indicate improvement in meta-model accuracy and reduction in computational time of the method introduced in this paper.     

基于近似技术的高亚声速运输机机翼气动/结构优化设计

探索基于近似技术的高亚声速运输机机翼气动/结构多学科设计优化方法,建立了基于近似技术的多学科设计优化框架。气动学科采用全速势方程加黏性修正进行翼身组合体跨声速流动的气动计算,结构学科采用有限元分析方法进行应力与变形计算。采用均匀设计法给出若干样本点,分别采用二次响应面、Kriging模型和径向基神经网络等多种近似技术,构造气动学科和结构学科的近似分析模型,并对几种近似模型精度进行了分析和比较。研究发现,Kriging模型和二次响应面具有几乎等同的较高的近似精度,神经网络的近似精度则较差,由于二次响应面计算量更小,故最终选定为机翼设计优化的近似方法。以升阻比和结构重量为目标,考虑升力、机翼面积以及应力和应变约束条件,对运输机机翼4个外形参数和4个结构参数进行多目标、多约束优化设计。优化后的机翼具有较好的气动/结构综合性能,表明本文方法是可行的。     

基于自适应代理模型的气动优化方法

气动优化设计中,为了减少优化系统的计算周期,提高搜索效率,引入结构简单、计算量较小的代理模型,而运用有效的插值和选样方法(自适应选样)可以大大减少建立代理模型的时间。因此本文提出了一种基于自适应代理模型的气动优化方法。首先对自适应代理模型进行研究,建立了 Kriging 自适应代理模型和支持向量回归自适应代理模型,这两种自适应代理模型在相同样本点情况下比一般代理模型拥有更高的预测能力,然后将这其应用到翼型优化设计中,取得了良好的优化效果,从而表明这两种自适应代理模型不仅简单实用,而且明显提高了气动分析的计算效率。     

基于自适应随机优化的连续阵风关键载荷预测

连续阵风载荷是构成民用飞机设计工况的主要载荷之一，在设计阶段，任意一轮的模型更新都涉及到上万种载荷工况的计算，然而其中仅个别工况构成载荷包线，需进行强度校核。为此发展了一套阵风关键载荷的快速识别方法。首先，采用二水平全因子（2LFF）采样获取得到初始计算工况，基于已计算得到的载荷值，结合多元自适应回归样条（MARS）建立一个可靠的代理模型；然后，在此基础上，开创性地应用自适应随机优化技术，实现对阵风关键工况及载荷的主动搜索；最后，以适航条款规定的侧向连续阵风载荷进行方法验证及参数影响研究。计算结果表明，本文建立的方法可以高效且准确地实现连续阵风关键载荷的预测，针对本文算例，关键载荷的预测值与基准值相比误差小于1%。     

基于模拟退火算法与响应面模型的三维气动优化设计方法

提出了一套适用于高耗时三维气动设计问题的优化设计体系.其主要思想是采用改进拉丁超立方体试验设计选取样本点,应用自行开发的三维粘性流场求解程序进行流场计算建立数据库,采用二次响应面方法建立近似模型,再应用高效模拟退火算法进行全局寻优.以NASA rotor57为对象,在详细进行流场计算基础上采用所提出的优化体系对其进行了三维积叠优化设计.在对流量、效率加以严格约束的条件下,总压比可提高1.8%,对流场结构进行了分析.优化结果表明本优化方法省时,适于三维气动设计的特点.     

增广拉格朗日子集模拟优化方法

传统的工程结构优化设计方法在求解多设计变量、多约束条件的结构优化设计问题时,存在诸多不足,针对上述问题,基于增广拉格朗日约束处理方法和子集模拟优化方法发展一种新的结构优化设计方法——增广拉格朗日子集模拟优化方法(ALSSO).该方法首先利用拉格朗日乘子法处理多重约束条件,然后利用子集模拟优化方法对转化后的无约束优化问题进行求解;对罚函数因子的更新方法进行改进,以保证收敛过程的稳定性;利用两个算例对该方法的计算精度、稳健性以及计算效率进行验证,并与其他优化方法进行对比.结果表明:增广拉格朗日子集模拟优化方法具有非常优秀的寻优性能.     

考虑飞行条件变化和制造误差的气动优化方法

提出一种渐近全局代理模型方法以提高稳健优化中的代理模型的精度.基本思路是连续成批地在样本空间的全局和局部均加入新样本点,不断提高代理模型的全局拟合精度.将基于渐近全局代理模型稳健优化方法应用于高亚声速翼型设计,结果表明不仅目标值阻力系数具有稳健性,对飞行条件的小幅度变化和制造误差不敏感,而且力矩系数的约束也具有稳健性.     

Particle swarm optimization applied to hypersonic reentry trajectories

This paper presents the novel use of the particle swarm optimization(PSO)to generate the end-to-end trajectory for hypersonic reentry vehicles in a quite simple formulation.The velocitydependent bank angle profile is developed to reduce the search space of unknown parameters based on the constrained PSO algorithm.The path constraints are enforced by setting the fitness function to be infinite on condition that the particles violate the maximum allowable values.The PSO algorithm also provides a much easier means to satisfy the terminal conditions by adding penalty terms to the fitness function.Furthermore,the approximate reentry landing footprint is fast constructed by incorporating an interpolation model into the standardized bank angle profiles.Numerical simulations demonstrate that the PSO method is a feasible and flexible tool to generate the end-to-end trajectory and landing footprint for hypersonic reentry vehicles.     

Surrogate-based analysis and optimization

A major challenge to the successful full-scale development of modern aerospace systems is to address competing objectives such as improved performance, reduced costs, and enhanced safety. Accurate, high-fidelity models are typically time consuming and computationally expensive. Furthermore, informed decisions should be made with an understanding of the impact (global sensitivity) of the design variables on the different objectives. In this context, the so-called surrogate-based approach for analysis and optimization can play a very valuable role. The surrogates are constructed using data drawn from high-fidelity models, and provide fast approximations of the objectives and constraints at new design points, thereby making sensitivity and optimization studies feasible. This paper provides a comprehensive discussion of the fundamental issues that arise in surrogate-based analysis and optimization (SBAO), highlighting concepts, methods, techniques, as well as practical implications. The issues addressed include the selection of the loss function and regularization criteria for constructing the surrogates, design of experiments, surrogate selection and construction, sensitivity analysis, convergence, and optimization. The multi-objective optimal design of a liquid rocket injector is presented to highlight the state of the art and to help guide future efforts.