基于代理模型的高效全局低音爆优化设计方法

研究发展高效实用的低音爆优化设计方法,对于新一代低音爆超声速客机的研制具有重要的理论意义和应用价值。目前国内外发展的低音爆优化方法主要包括遗传算法（GA）和基于Adjoint的梯度优化。遗传算法虽然具有较强的全局优化能力,但其优化效率较低,无法很好满足实际应用的需要;而梯度优化虽然优化效率高,但易陷入局部最优。将最新发展的代理优化算法与音爆预测方法相结合,发展了一种具有全局优化能力的高效低音爆优化设计方法。首先,概述了所采用的线性音爆预测方法,并用NASA超声速圆锥体模型进行验证,表明其计算效率高、预测精度可满足飞行器初步设计的需要。其次,对所采用的代理优化（SBO）方法进行了概述,包括试验设计、代理模型建模、优化加点准则和收敛标准等。再次,运用所发展的方法开展了NASA多段圆锥体模型的低音爆优化设计算例研究,并与遗传算法和梯度优化的结果进行了比较,表明其优化效率比遗传算法提高了2个量级以上,且优化结果优于梯度方法。最后,将所发展的方法应用于AIAA音爆预测大会提供的翼身组合体外形（69°后掠三角翼）的低音爆优化设计,将远场音爆N型波峰值减少了27.4%,表明所发展的方法在复杂外形低音爆优化设计中具有很好的应用潜力。     

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。     

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。     

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.     

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.     

A hierarchical updating method for finite element model of airbag buffer system under landing impact

In this paper, we propose an impact finite element(FE) model for an airbag landing buffer system. First, an impact FE model has been formulated for a typical airbag landing buffer system. We use the independence of the structure FE model from the full impact FE model to develop a hierarchical updating scheme for the recovery module FE model and the airbag system FE model.Second, we define impact responses at key points to compare the computational and experimental results to resolve the inconsistency between the experimental data sampling frequency and experimental triggering. To determine the typical characteristics of the impact dynamics response of the airbag landing buffer system, we present the impact response confidence factors(IRCFs) to evaluate how consistent the computational and experiment results are. An error function is defined between the experimental and computational results at key points of the impact response(KPIR)to serve as a modified objective function. A radial basis function(RBF) is introduced to construct updating variables for a surrogate model for updating the objective function, thereby converting the FE model updating problem to a soluble optimization problem. Finally, the developed method has been validated using an experimental and computational study on the impact dynamics of a classic airbag landing buffer system.     

临近空间固体动力飞行器发动机与轨迹一体化设计优化

针对临近空间多级固体动力飞行器发动机与轨迹一体化设计优化问题,提出一种基于序列代理优化的高效设计方法。为了准确计算发动机的性能特性,对发动机进行了几何参数化建模,并针对复杂装药的燃面计算,提出了基于移动四面体的燃面计算算法。为了准确评估飞行器的最大航程能力,采用自适应Legendre-Gauss-Radau伪谱法获得给定发动机设计方案下的最大航程。为了提高发动机与轨迹一体化设计优化效率,提出了基于Kriging代理模型的多采样点高效全局代理优化算法,并进行了数值验证。计算结果表明：该优化方法收敛速度快,相比传统参数优化算法可以显著减少耗时目标函数和约束函数的计算次数,并能够有效地实现临近空间多级固体动力飞行器发动机与轨迹一体化设计优化。     

Recent advances in surrogate-based optimization

The evaluation of aerospace designs is synonymous with the use of long running and computationally intensive simulations. This fuels the desire to harness the efficiency of surrogate-based methods in aerospace design optimization. Recent advances in surrogate-based design methodology bring the promise of efficient global optimization closer to reality. We review the present state of the art of constructing surrogate models and their use in optimization strategies. We make extensive use of pictorial examples and, since no method is truly universal, give guidance as to each method's strengths and weaknesses.     

一种确定模型误差位置的方法

本文首先由解析有限元模型的模态矩阵,得到未测量自由度与已测量自由度模态之间的变换关系,利用该关系对解析模型进行缩聚。然后针对缩聚后的特征方程,利用解析刚度矩阵和质量矩阵以及实测的模态参数确定模型误差位置。模拟结果表明,该方法可行。     

Hierarchical model updating strategy of complex assembled structures with uncorrelated dynamic modes

In structural simulation and design, an accurate computational model directly determines the effectiveness of performance evaluation. To establish a high-fidelity dynamic model of a complex assembled structure, a Hierarchical Model Updating Strategy(HMUS) is developed for Finite Element(FE) model updating with regard to uncorrelated modes. The principle of HMUS is first elaborated by integrating hierarchical modeling concept, model updating technology with proper uncorrelated mode treatment, and...     

Global aerodynamic design optimization based on data dimensionality reduction

In aerodynamic optimization, global optimization methods such as genetic algorithms are preferred in many cases because of their advantage on reaching global optimum. However, for complex problems in which large number of design variables are needed, the computational cost becomes prohibitive, and thus original global optimization strategies are required. To address this need, data dimensionality reduction method is combined with global optimization methods, thus forming a new global optimization system, aiming to improve the efficiency of conventional global optimization. The new optimization system involves applying Proper Orthogonal Decomposition (POD) in dimensionality reduction of design space while maintaining the generality of original design space. Besides, an acceleration approach for samples calculation in surrogate modeling is applied to reduce the computational time while providing sufficient accuracy. The optimizations of a transonic airfoil RAE2822 and the transonic wing ONERA M6 are performed to demonstrate the effectiveness of the proposed new optimization system. In both cases, we manage to reduce the number of design variables from 20 to 10 and from 42 to 20 respectively. The new design optimization system converges faster and it takes 1/3 of the total time of traditional optimization to converge to a better design, thus significantly reducing the overall optimization time and improving the efficiency of conventional global design optimization method.     

An alternative numerical approach for full scale characterisation for riveted joint design

This paper describes a pure numerical methodology (FE database) to improve the representativeness of joint equivalent models for airframe crashworthiness. This method is based on material constitutive models and failure criterion in accurate 3D FE simulations. The interest of FE simulations is to define the dynamic strength of many types of riveted joints with a reduced cost compared to a pure experimental way. The FE database method is carried out on elementary riveted joints to predict and to analyse: first the post-riveting initial strain and stress state, and second several kinds of joint failure (e.g., crack propagation, rivet shearing or pull-out). The aim of the first step is to start the mechanical strength simulations with a correct deformed shape and post-riveting state. The responses of 3D riveted joint simulations can then be considered as reference and be used to optimise the mechanical properties of equivalent joint elements. A new equivalent joint element is developed to improve the representativeness of an airframe crash simulation.     

基于梯度增强型Kriging模型的气动反设计方法

基于Kriging模型的代理优化算法目前在气动优化设计中得到了广泛应用。但在高维(设计变量大于30个)气动优化中,计算量过大的问题对其进一步发展产生了严重制约。将翼型和机翼气动反设计问题转化为优化问题,采用Adjoint方法进行快速梯度求解,利用基于梯度增强型Kriging(GEK)模型的代理优化算法分别开展了18、36和108个设计变量的气动反设计。首先,通过采用在设计空间局部建立GEK模型的方法成功地将基于代理优化算法的气动反设计问题的维度拓展到了100维以上。其次,研究了梯度计算精度对基于GEK模型的反设计的影响,发现梯度精度越高,反设计的最终效果越好,同时效率相当。最后,通过不同维度的气动反设计算例,比较了改进拟牛顿法(BFGS)、基于GEK模型和Kriging模型的代理气动反设计方法,结果表明基于GEK模型的代理优化算法的效率大幅度高于基于Kriging模型的代理优化算法,并且维度越高,效率优势越明显;同时,基于GEK模型的代理优化算法在优化效果及分析程序调用次数上相比于BFGS方法也略有优势。     

Nonlinear uncertainty quantification of the impact of geometric variability on compressor performance using an adjoint method

Manufactured blades are inevitably different from their design intent, which leads to a deviation of the performance from the intended value. To quantify the associated performance uncertainty, many approaches have been developed. The traditional Monte Carlo method based on a Computational Fluid Dynamics solver(MC-CFD) for a three-dimensional compressor is prohibitively expensive. Existing alternatives to the MC-CFD, such as surrogate models and secondorder derivatives based on the adjoint metho...     

Dynamic parametric modeling-based model updating strategy of aeroengine casings

For accurate Finite Element (FE) modeling for the structural dynamics of aeroengine casings, Parametric Modeling-based Model Updating Strategy (PM-MUS) is proposed based on efficient FE parametric modeling and model updating techniques regarding uncorrelated/correlated mode shapes. Casings structure is parametrically modeled by simplifying initial structural FE model and equivalently simulating mechanical characteristics. Uncorrelated modes between FE model and experiment are reasonably handled by adopting an objective function to recognize correct correlated modes pairs. The parametrized FE model is updated to effectively describe structural dynamic characteristics in respect of testing data. The model updating technology is firstly validated by the detailed FE model updating of one fixed–fixed beam structure in light of correlated/uncorrelated mode shapes and measured mode data. The PM-MUS is applied to the FE parametrized model updating of an aeroengine stator system (casings) which is constructed by the proposed parametric modeling approach. As revealed in this study, (A) the updated models by the proposed updating strategy and dynamic test data is accurate, and (B) the uncorrelated modes like close modes can be effectively handled and precisely identify the FE model mode associated the corresponding experimental mode, and (C) parametric modeling can enhance the dynamic modeling updating of complex structure in the accuracy of mode matching. The efforts of this study provide an efficient dynamic model updating strategy (PM-MUS) for aeroengine casings by parametric modeling and experimental test data regarding uncorrelated modes.     

Experimental,analytical and numerical investigation on tensile behavior of twisted fiber yarns

Stitched composite materials are emerging as a promising material due to their high interlaminar strength, combined performance and light weight. The mechanical properties of stitch yarns are very essential for stitched composite structures. In this study, the tensile behaviors of the twisted fiber yarn in stitched composites were investigated experimentally, analytically and numerically. Two kinds of cross-sectional area of twisted yarn are proposed and discussed. The paper presents an intersecting circle model to describe the cross-section of twisted fiber yarns, and a physics-based theoretical model to predict the effective tensile moduli. The numerical models take into account the cross-sectional characteristic and the twist architecture. The investigation shows that: the sum of each fiber area should be used for experimental analysis; and the cross-sectional area surrounded by the yarn profile should be used for theoretical predictions and finite element (FE) simulations. The relative errors of the prediction method and the FE simulation are less than 2% and 1%, respectively. The friction between the fibers is derived, and the effect of friction on mechanical properties is discussed. The investigation method will serve as a fundamental component of twisted fiber bundle/yarn analysis.     

适用于气动弹性的小波非定常气动力降阶方法

发展非定常气动力模型降阶技术旨在缩减计算耗费并且使得计算流体力学信息能够应用于气动伺服弹性以及设计优化当中。采用小波方法建立基于Volterra级数的非定常气动力降阶模型。在模型识别过程中,激励是光滑连续的且以零阶保持方式进行离散,采样频率选择二的整数幂次。近似的一阶Volterra核基于Haar尺度函数族展开,鉴于Volterra核在系统响应中的衰减特性,可在合适的有限时长截断一阶核。为了获得一阶核的各项展开系数,需要求解由输入/输出数据组成的超定方程,其中涉及到奇异值分解算法。为了验证小波方法的有效性,算例选取了二维的NACA64a010翼型。数值仿真结果表明该方法能够比较准确地预测结构小扰动引起的非定常气动力响应且能描述一定的非线性现象。     

基于均匀化方法的缝纫层压板拉伸弹性模量有限元预测

利用均匀化方法研究缝纫复合材料层压板的弹性性能，给出了相应的数学分析模型。建立了有限元分析的单胞模型，并进行求解。计算结果表明，利用这种半解析模型可以得到缝纫层压板的弹性模量的上下限，其平均值与实验结果平均值吻合得很好。     

计及不确定性因素的结合面参数识别

结合面参数识别是复杂结构动力学建模的关键问题。由于连接结构的接触面的大小、摩擦系数，以及安装预应力等相关参数存在不确定性，本文提出把连接结构的接触刚度及接触阻尼作为随机分布参数处理，并使用基于响应面法的模型修正方法和分布代数方法进行识别，方法可行，便于实际工程应用。研究表明，连接结构参数具有正态分布或近似正态分布的特点；用线性有限元模型加上具有正态分布的接触刚度、接触阻尼模型可以描述真实结构的动态特性。     

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.