基于离散伴随方程的三维雷达散射截面几何敏感度计算

针对有限差分法计算雷达散射截面（RCS）梯度效率低，采用高精度雷达散射截面评估时计算代价高的问题，提出了一种基于麦克斯韦积分方程离散伴随方程的RCS梯度高效计算方法。基于伴随方程的梯度计算可以通过一次雷达散射截面求解、一次伴随方程求解获得RCS关于所有设计变量的梯度。其中麦克斯韦积分方程离散伴随方程的形式与原方程基本一致，可以采用矩量法（MOM）及多层快速多极子算法（MLFMA）求解。伴随方程求解计算量与直接雷达散射截面评估基本一致，存储量在直接雷达散射截面评估的基础上增加不明显。通过双椎体模型、导弹模型对基于矩量法、多层快速多极子算法的伴随梯度进行验证，证明了基于伴随方法的RCS梯度计算可以实现复杂外形中RCS梯度的高效、高精度求解，为基于梯度的高精度气动/隐身一体化优化提供了基础。     

Adjoint-based robust optimization design of laminar flow wing under flight condition uncertainties

It is an inherent uncertainty problem that the application of laminar flow technology to the wing of large passenger aircraft is affected by flight conditions. In order to seek a more robust natural laminar flow control effect, it is necessary to develop an effective optimization design method. Meanwhile, attention must be given to the impact of crossflow(CF) instability brought on by the sweep angle. This paper constructs a robust optimization design framework based on discrete adjoint methods ...     

Sealing reliability modeling of aviation seal based on interval uncertainty method and multidimensional response surface

Many variables affect the sealing performance, and their distribution characteristics are difficult to obtain with probabilistic methods owing to the high cost involved. Numerous problems in engineering are similar due to the appearance of small-sample parameters. In this study, the sealing reliability of an aviation seal was defined as the research object, and an interval uncertainty method and multidimensional response surface were proposed to calculate the sealing reliability.Based on this, we first analyzed the failure mechanism of the aviation seal and established a leakage rate model. Then, based on the non-probabilistic interval model, an interval uncertainty method was proposed to construct the analytical model. With reference to the limit state equation from the structural reliability theory, the multidimensional response surface was used for fast calculation.Then, we chose the single-cylinder gas steering gear used in aircraft as the case study, its sealing reliability in working and non-working statuses were calculated, and the results were verified with the actual maintenance records. By analyzing the sensitivity of some variables, we can improve the sealing reliability of the aviation seal by improving the surface roughness only if the cost allows.Finally, we consider that the method proposed in this study realizes the application of smallsample uncertainty analysis in reliability analysis, and could provide a feasible way to solve the similar problems in engineering with multidimensional and small-sample parameters.     

基于网格变形的伴随方法在翼型优化中的应用

进行了基于网格变形的伴随方法在翼型气动优化设计中应用的研究。随着集成了伴随方法的流场求解器的普及和效率的不断提高,采用梯度法进行翼型气动优化设计的主要计算花费逐渐由计算梯度对流场变量的敏感度（或流场敏感度）转变为计算梯度对网格变形的敏感度（或网格敏感度）,后者的求解通常采用有限差分方法,计算花费较高。在传统伴随方法（或流场伴随方法）的基础上,引入了基于网格变形的伴随方法（或网格伴随方法）,采用网格伴随方法计算梯度,可以大幅度减少梯度计算花费,提高翼型气动优化设计的效率。     

基于伴随方法的单级低速压气机气动设计优化

采用梯度方法对某型4.5级压气机最后级进行气动设计优化研究，梯度由连续伴随方法计算确定，多排伴随方程采用伴随掺混面模型进行数值求解。首先，采用基于经验修正的初步设计方法设计带进口导叶的4.5级低速、低压缩比压气机的原始气动外形。之后，在压气机近失速工况对最后级静子叶片进行伴随气动设计优化，通过优化叶型和安装角降低流动损失，目标函数定义为加权求和形式的熵增和流量偏差，优化中对流量进行约束。最后，开展基于伴随方法的多工况气动设计优化研究，改善两个不同转速条件下最后级的气动性能。优化结果表明，基于伴随方法的多排气动设计优化可以通过改变叶片气动外形提升多排全工况气动性能。     

A novel robust aerodynamic optimization technique coupled with adjoint solvers and polynomial chaos expansion

Uncertainty is common in the life cycle of an aircraft, and Robust Aerodynamic Optimization (RAO) that considers uncertainty is important in aircraft design. To avoid the curse of dimensionality in surrogate-based optimization, this study proposes an adjoint RAO technique called “R-Opt”. Polynomial Chaos Expansion (PCE) is coupled with the R-Opt technique to quantify uncertainty in the responses of the target (including its mean and standard deviation). Only one process of PCE model construction is required in each iteration, and the gradients of uncertainty can be inferred via chain rules. The proposed method is more efficient than prevalent methods, and avoids the problem of a disagreement over the best PCE basis from among a number of PCE models (especially in case of sparse PCE). It also supports the application of sparse PCE. Two benchmark tests and two airfoil cases were used to verify R-Opt, and the optimal solutions were deemed to be robust. It improved the mean aerodynamic performance and reduced the standard deviation of the target.     

大展弦比前掠翼气动隐身多目标优化

前掠翼布局优越的气动性能为无人机气动布局设计提供了一条新的方向。采用CST方法对翼型几何外形进行参数化描述,实现前掠翼气动和隐身多学科优化设计模型的参数化描述。建立了基于N-S方程的计算流体力学方法的前掠翼气动分析模型和基于矩量法的计算电磁学方法的前掠翼隐身分析模型。提出了基于Kriging模型的前掠翼气动隐身多目标优化方法,采用拉丁超方试验设计方法获取样本点,建立前掠翼气动和隐身的Kriging代理模型。将Pareto多目标遗传算法与Kriging代理模型结合进行大展弦比前掠翼的气动隐身多目标优化设计。研究结果表明,所建立的分析模型是合理的,所提出的多目标优化设计方法是可行的,能够有效提高大展弦比前掠翼性能与优化效率。     

Adjoint boundary sensitivity method to assess the effect of nonuniform boundary conditions

The performance of turbomachinery is largely affected by the nonuniform boundary conditions caused by the coupling between neighboring parts, such as the inlet distortion and hot streak. Existing works study this problem by comparing the flow fields with uniform and nonuniform boundary conditions, which is cost extensive. In this work a new and efficient method is developed by computing the sensitivities of arbitrary performance metric relative to the boundary conditions and this method quantita...     

一种基于共轭方程法求解黏性反问题的简化方法

 对于给定压力分布的黏性气动反问题,考虑到壁面微小扰动造成的压力变化主要由势流作用引起,因此可以简化用以获得目标函数对设计变量敏感性导数的共轭方程。将黏性流场插值到粗网格中作为彻体力模型方程的解,则其相应的共轭方程将以简单的源项取代原方程中复杂的黏性项。由于在粗网格中求解,网格数减少,同时收敛速度加快,简化的共轭方程计算时间可以减少到黏性方程的十分之一。典型的算例结果表明,对于附着的边界层流动简化方法计算得到的敏感性导数具有较高的精度,能够有效完成反问题设计且减少总的计算耗时。     

A model-based prognostics method for fatigue crack growth in fuselage panels

This paper proposes a model-based prognostics method that couples the Extended Kalman Filter (EKF) and a new developed linearization method. The proposed prognostics method is developed in the context of fatigue crack propagation in fuselage panels where the model parameters are unknown and the crack propagation is affected by different types of uncertainties. The coupled method is composed of two steps. The first step employs EKF to estimate the unknown model parameters and the current damage state. In the second step, the proposed efficient linearization method is applied to compute analytically the statistical distribution of the damage evolution path in some future time. A numerical case study is implemented to evaluate the performance of the proposed method. The results show that the coupled EKF-linearization method provides satisfactory results: the EKF algorithm well identifies the model parameters, and the linearization method gives comparable prediction results to Monte Carlo (MC) method while leading to very significant computational cost saving. The proposed prognostics method for fatigue crack growth can be used for developing predictive maintenance strategy for an aircraft fleet, in which case, the computational cost saving is significantly meaningful.     

考虑多工况性能可靠性的航空发动机循环设计方法

为实现航空发动机总体性能设计方法由传统的确定性设计向不确定性概率设计转变，提出基于分布式协同响应面法思想的航空发动机多工况性能可靠性循环优化设计方法:建立了引入非确定性部件性能的航空发动机性能仿真模型，通过试验设计、非设计点性能仿真试验等步骤，构建了各典型工况下发动机推力与耗油率性能可靠度关于设计点循环参数的分布式响应面模型，并以此构建多工况性能协同响应面模型进行循环参数优化设计，最终获得循环参数非劣解集并通过随机试验进行验证。结果表明，通过多工况性能可靠性循环优化设计方法获得的循环参数非劣解集均能使发动机在多个典型工况下的总体性能同时达到不低于97.5%的高可靠度，为设计人员根据实际情况选取循环参数提供依据。      

基于控制理论和NS方程的气动设计方法研究

研究了基于控制理论和NS方程的气动设计方法,针对给定的目标函数表达形式,应用该设计理论在计算坐标下详细推导了相应的共轭方程及边界条件具体表达形式,以及梯度方程求解表达式,通过合理的数学变换,导出了共轭方程在笛卡尔坐标系下的直观表达形式,发展了有效的共轭方程数值求解方法,通过流动控制方程数值求解、共轭方程数值求解、目标函数对设计变量的梯度求解和优化算法等方面的有效结合,研究与发展了一种新的气动设计方法,以二维机翼气动设计为例,成功进行了亚、跨音速情形下的相关设计算例研究,研究结果表明应用控制理论和NS方程的气动设计方法在设计理论、适用性以及时间花费等方面都有着很好的特色和优点,且设计结果也更为可靠.     

面向多级加筋壳的高效变保真度代理模型

多级加筋壳结构作为一种新颖的航空航天薄壁结构,具有轻质、高承载的优势。由于其加筋结构复杂,导致基于高保真度模型的多级加筋壳后屈曲分析耗时较长,提高其后屈曲分析及优化效率对于多级加筋壳快速设计具有重要的意义。变保真度模型在复杂工程问题的设计与优化过程中得到了广泛的应用,其通过桥函数连接高保真度模型和低保真度模型,具有预测精度高和计算成本低的优点。首先建立了多级加筋壳结构的高保真度模型和低保真度模型,并基于高斯过程回归构建了多级加筋壳结构的变保真度模型,然后基于变保真度模型的最大均方根误差方法开展自适应加点。结果表明,在达到同样的较高预测精度水平时,基于提出方法构建的变保真度模型比直接采用高保真度模型构建的代理模型节约了60%的计算成本,表现出优异的效率优势。同时,还探讨了不同类型低保真度模型对于多级加筋壳结构变保真度模型预测精度的影响。分析结果表明,对于多级加筋壳承载力评估这类典型的后屈曲问题,建立可捕捉后屈曲特性的低保真度模型能有效提升变保真度模型的精度。     

基于控制理论的Euler方程翼型减阻优化设计

在Jameson的控制论气动优化设计思想下，应用Euler方程研究了翼型的反设计和减阻问题。设计过程中的梯度是通过求解一个伴随偏微分方程而得到的，每个设计迭代只需求解一次Euler方程和一次伴随方,一与设计变量数无关。在具体数值执行中：①利用分部积分将目标函数变分的计算转化成了类似于计算Euler方程残值的形式，节省了机器时间；②根据控制理论的要求，将减阻问题转化成了相应地修改伴随方程的物面边界条件和目标函数的变分表达，使问题得到了简化；③利用特征不变量分析法，处理了伴承方程的物面和远场边界条件。设计算例证明了本文方法可靠性好、收敛快、大大节约设计时间。     

Shape preserving topology optimization for structural radar cross section control

The purpose of this paper is to present a shape preserving topology optimization method to prevent the adverse effects of the mechanical deformation on the Radar Cross Section(RCS).The optimization will suppress the variation of RCS on the perfect conductor surface by structural design. On the one hand, the physical optics method is utilized to calculate the structural RCS,which is based on the surface displacement field obtained from the finite element analysis of the structure. The correspondi...     

Reliability estimation of mechanical seals based on bivariate dependence analysis and considering model uncertainty

The reliability estimation of mechanical seals is of crucial importance due to their wide applications in pumps in various mechanical systems. Failure of mechanical seals might cause leakage, and might lead to system failure and other relevant consequences. In this study, the reliability estimation for mechanical seals based on bivariate dependence analysis and considering model uncertainty is proposed. The friction torque and leakage rate are two degradation performance indicators of mechanical seals that can be described by the Wiener process, Gamma process, and inverse Gaussian process. The dependence between the two indicators can be described by different copula functions. Then the model uncertainty is considered in the reliability estimation using the Bayesian Model Average (BMA) method, while the unknown parameters in the model are estimated by Bayesian Markov Chain Monte Carlo (MCMC) method. A numerical simulation study and fatigue crack study are conducted to demonstrate the effectiveness of the BMA method to capture model uncertainty. A degradation test of mechanical seals is conducted to verify the proposed model. The optimal stochastic process models for two performance indicators and copula function are determined based on the degradation data. The results show the necessity of using the BMA method in degradation modeling.     

基于共轭方程法的跨声速机翼阻力优化设计

机翼的气动特性从根本上决定了飞机巡航状态下的气动特性,经过良好设计的机翼会明显地提升全机的气动特性。连续共轭方程方法由于其求解梯度的计算量与设计变量数目无关,可以对复杂构型进行有效的优化设计。本文采用连续共轭方程方法对粘性条件下的机翼气动外形进行了优化设计。采用有限体积法进行流动控制方程和共轭方程的数值空间离散,多步Runge-Kutta方法进行时间推进,对于某三维机翼进行了有效的气动优化设计。     

基于分解策略的涡轮叶片可靠性及多学科设计优化

将反一阶可靠性分析方法与多学科可行方法相结合,提出了一种适用于涡轮叶片复杂结构的可靠性及多学科设计优化方法.在优化过程中使用Kriging近似模型并不断提高模型精度,解决了多学科可行方法反复调用仿真程序进行多学科分析,计算量较大的问题.该方法将可靠性分析与多学科优化过程分离,提高了优化计算效率.以某型涡轮叶片的设计优化为例,对该方法进行了验证并与传统双循环方法进行了对比.结果表明,优化结果满足可靠性的要求,与双循环方法相比优化效率提高63.8%,证明了该方法在工程应用中的可行性和有效性.      

适用于非周期流固耦合问题的时间谱方法

针对非定常流固耦合设计、分析问题所面临的计算效率与精度、鲁棒性之间的矛盾,采取将Chebyshev谱方法与基于非定常面元和几何非线性梁有限元模型的流固耦合分析方法相结合的方式,建立了针对大展弦比机翼非定常流固耦合优化设计问题的,可与伴随方法相结合的时间谱方法。Chebyshev谱方法直接对流固耦合的控制方程进行处理,利用Chebyshev算子替换系统状态变量,将非定常问题转化为Chebyshev控制点处耦合的定常问题。通过这种方式建立的流固耦合时间谱方法具有较高的计算精度、效率和足够的鲁棒性。验证算例及Goland机翼颤振速度计算实例表明,Chebyshev谱方法的计算精度随着Chebyshev控制点个数的增加而不断增大。只需选取较少的控制点,Chebyshev谱方法便可以达到满足精度要求的计算结果。与此同时,建立的流固耦合时间谱方法不仅适用于周期性非定常问题还适用于非周期性非定常问题。     

Automated design methodology of turbulent internal flow using discrete adjoint formulation

An optimal shape design approach is presented for a subsonic S-shaped intake geometry using aerodynamic sensitivity analysis. Sensitivity analysis is performed for the three-dimensional Navier–Stokes equations coupled with two-equation turbulence models using a discrete adjoint method. For code validation, the result of the flow solver is compared with experimental data and other computational results. Through the study on turbulence models and grid refinement, results from several turbulence models are compared and the minimal number of grid points yielding an accurate numerical solution is obtained. And, the adjoint sensitivity code is also validated by the comparison with complex step derivative results. To obtain a sufficient and flexible design space, NURBS equations are employed as a geometric representation and a new grid modification technique, Least Square NURBS Grid Approximation is applied. With the verified flow solver, sensitivity analysis code and geometric modification technique, the optimization of the S-shaped intake is carried out and the enhancement of overall intake performance is achieved. In addition, the off-design performance of a designed S-shaped intake is tested to confirm the robustness of the current design approach. As a result, the capability and efficiency of the present design tools are successfully demonstrated in three-dimensional high Reynolds subsonic intake design.