Hybrid uncertainty-based design optimization and its application to hybrid rocket motors for manned lunar landing

Design reliability and robustness are getting increasingly important for the general design of aerospace systems with many inherently uncertain design parameters. This paper presents a hybrid uncertainty-based design optimization (UDO) method developed from probability theory and interval theory. Most of the uncertain design parameters which have sufficient information or experimental data are classified as random variables using probability theory, while the others are defined as interval variables with interval theory. Then a hybrid uncertainty analysis method based on Monte Carlo simulation and Taylor series interval analysis is developed to obtain the uncer-tainty propagation from the design parameters to system responses. Three design optimization strategies, including deterministic design optimization (DDO), probabilistic UDO and hybrid UDO, are applied to the conceptual design of a hybrid rocket motor (HRM) used as the ascent propulsion system in Apollo lunar module. By comparison, the hybrid UDO is a feasible method and can be effectively applied to the general design of aerospace systems.     

考虑性能及成本的固体火箭发动机多学科设计优化

为综合考虑固体火箭发动机的燃烧室、药柱、内弹道、喷管及成本等学科影响,梳理学科间耦合关系,并建立了以总冲最大、成本最小为优化目标的固体火箭发动机多学科设计优化（MDO）模型。为降低MDO问题的计算成本,提出一种基于Kriging代理模型的多目标自适应优化方法（KRG-MAOM）。优化过程中,分别对目标与约束构建Kriging模型,并采用多目标优化算法求解,在伪Pareto解中综合考虑支配关系与分布特性选取新增样本点,引导优化快速收敛。算例结果表明,KRG-MAOM算法在全局收敛性与优化效率方面具有显著优势。最后,采用KRG-MAOM算法求解该MDO问题,得到可行的Pareto解集方案,与初始方案相比,同性能情况下成本节省约3.36%;同成本情况下性能提升约10.93%,从而验证MDO模型合理性与KRG-MAOM算法有效性。     

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。     

涡轮叶片多学科可靠性及稳健设计优化

为了得到一种适用于涡轮叶片复杂结构并同时考虑可靠性及稳健性的多学科设计优化方法,将6sig-ma可靠性及稳健设计优化方法与多学科可行方法(MDF)相结合,采用二阶Taylor展开法进行可靠性及稳健性分析,实现了涡轮叶片多学科6sigma可靠性及稳健设计优化。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计算量较大的问题。实例分析表明,与确定性多学科设计优化相比,采用该方法得到的涡轮叶片可靠性及稳健性均有大幅度提高,同时设计目标最优,满足工程应用的要求,验证了该方法在工程应用中的可行性。     

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。     

基于双循环的离心叶轮多学科可靠性优化设计

 针对传统多学科设计优化方法中未能考虑不确定因素的问题,开展基于可靠性的多学科设计优化(RBMDO)方法的研究。以离心式压气机叶轮为对象,综合考虑工作状况和材料参数等随机性因素的影响,利用改进的一次二阶矩(AFOSM)法进行可靠性分析,通过双循环策略将多学科可行优化方法与可靠性分析相结合,合理引入近似技术,建立了基于可靠性的多学科设计优化系统。对某离心叶轮进行多学科可靠性优化设计的算例表明,在满足所有可靠性指标的前提下,该方法可实现离心叶轮综合性能的提高,并有效地缩减设计周期。     

装药几何参数不确定性优化设计

1引言固体火箭发动机装药设计,一般要求在满足发动机内弹道性能和相关约束条件下,选择药型并确定其几何参数,同时综合考虑燃烧室壳体内部绝热层、衬层和人工脱粘层的设计要求。装药设计作为发动机设计的核心,其设计质量很大程度决定了发动机性能优劣。航天飞机固体助推火箭发动     

Robust design and analysis of a conformal expansion nozzle with inverse-design idea

This paper examines robust optimization design and analysis of a conformal expansion nozzle of flying wing Unmanned Aerial Vehicle(UAV) with the inverse-design idea.In view of flow features and stealth constraints, the inverse-design idea is described and the uncertainty-based robust design model is presented.A robust design system employs this model to combine deterministic optimization and robust optimization and is applied into design of a conformal expansion nozzle.The results indicate that design optimization can conform to the anticipation of the inversedesign idea and significantly improve the aerodynamic performance that meet the requirement of 6σ.The present method is a feasible nozzle design strategy that integrates robust optimization and inverse-design.     

Multi-disciplinary design optimization with fuzzy uncertainties and its application in hybrid rocket motor powered launch vehicle

In this paper, an Uncertainty-based Multi-disciplinary Design Optimization (UMDO) method combining with fuzzy theory and Multi-Discipline Feasible (MDF) method is developed for the conceptual design of a Hybrid Rocket Motor (HRM) powered Launch Vehicle (LV). In the method proposed, membership functions are used to represent the uncertain factors, the fuzzy statistical experiment is introduced to analyze the propagation of uncertainties, and means, standard deviations and credibility measures are used to delineate uncertain responses. A geometric programming problem is solved to verify the feasibility of the Fuzzy-based Multi-Discipline Feasible (F-MDF) method. A multi-disciplinary analysis of a three-stage HRM powered LV involving the disciplines of propulsion, structure, aerodynamics and trajectory is implemented, and the mathematical models corresponding to the F-MDF method and the MDF method are established. A two-phase optimization method is proposed for multi-disciplinary design optimization of the LV, including the orbital capacity optimization phase based on the Ziolkowski formula, and the scheme trajectory verification phase based on the 3-degree-of-freedom point trajectory simulation. The correlation coefficients and the quadratic Response Surface Method (RSM) based on Latin Hypercube Sampling (LHS) are adopted for sensitive analysis of uncertain factors, and the Multi-Island Genetic Algorithm (MIGA) is adopted as the optimization algorithm. The results show that the F-MDF method is applicable in LV conceptual design, and the design with the F-MDF method is more reliable and robust than that with the MDF method.     

Effect of Variable Selection on Multidisciplinary Design Optimization： a Flight Vehicle Example

Different multidisciplinary design optimization (MDO) problems are formulated and compared. Two MDO formulations are applied to a sounding rocket in order to optimize the performance of the rocket. In the MDO of the referred vehicle, three disciplines have been considered,which are trajectory, propulsion and aerodynamics. A special design structure matrix is developed to assist data exchange between disciplines. This design process uses response surface method (RSM) for multidisciplinary optimization of the rocket. The RSM is applied to the design in two categories: the propulsion model and the system level. In the propulsion model, RSM deter-mines an approximate mathematical model of the engine output parameters as a function of design variables. In the system level, RSM fits a surface of objective function versus design variables. In the first MDO problem formulation, two design variables are selected to form propulsion discipline. In the second one, three new design variables from geometry are added and finally, an optimization method is applied to the response surface in the system level in order to find the best result. Application of the first developed multidisciplinary design optimization procedure increased accessible altitude (performance index) of the referred sounding rocket by twenty five percents and the second one twenty nine.     

Six sigma robust design optimization for thermal protection system of hypersonic vehicles based on successive response surface method

Lightweight design is important for the Thermal Protection System(TPS) of hypersonic vehicles in that it protects the inner structure from severe heating environment. However, due to the existence of uncertainties in material properties and geometry, it is imperative to incorporate uncertainty analysis into the design optimization to obtain reliable results. In this paper, a six sigma robust design optimization based on Successive Response Surface Method(SRSM) is established for the TPS to improve the reliability and robustness with considering the uncertainties. The uncertain parameters related to material properties and thicknesses of insulation layers are considered and characterized by random variables following normal distributions. By employing SRSM, the values of objective function and constraints are approximated by the response surfaces to reduce computational cost. The optimization is an iterative process with response surfaces updating to find the true optimal solution. The optimization of the nose cone of hypersonic vehicle cabin is provided as an example to illustrate the feasibility and effectiveness of the proposed method.     

Multidisciplinary Design and Optimization of Multistage Ground-launched Boost Phase Interceptor Using Hybrid Search Algorithm

This article proposes a multidisciplinary design and optimization (MDO) strategy for the conceptual design of a multistage ground-based interceptor (GBI) using hybrid optimization algorithm, which associates genetic algorithm (GA) as a global optimizer with sequential quadratic programming (SQP) as a local optimizer. The interceptor is comprised of a three-stage solid propulsion system for an exoatmospheric boost phase intercept (BPI). The interceptor's duty is to deliver a kinetic kill vehicle (KKV) to the optimal position in space to accomplish the mission of intercept. The modules for propulsion, aerodynamics, mass properties and flight dynamics are integrated to produce a high fidelity model of the entire vehicle. The propulsion module comprises of solid rocket motor (SRM) grain design, nozzle geometry design and performance prediction analysis. Internal ballistics and performance prediction parameters are calculated by using lumped parameter method. The design objective is to minimize the gross lift off mass (GLOM) of the interceptor under the mission constraints and performance objectives. The proposed design and optimization methodology provide designers with an efficient and powerful approach in computation during designing interceptor systems.     

导弹/固体火箭发动机一体化设计

本文以两级推力固体火箭发动机为动力的某空-空导弹作为算例,研究了导弹/固体火箭发动机一体化设计的问题.为此,建立了固体火箭发动机的能量模型、质量模型和导弹与目标的数学模型.利用优化理论,成功地完成了九个设计变量的优化问题.优化结果表明,导弹的起飞质量减轻23.3kg(约占总重的9%).     

基于 Kriging模型机翼平面外形气动优化设计

使用基于Kriging模型的优化设计方法,进行了非常规布局机翼的平面外形多目标优化设计。利用CFD技术进行机翼升力系数和阻力系数的气动计算,通过拉丁超立方试验设计生成样本点,建立了Kriging代理模型,结合多目标遗传算法对机翼平面外形进行多点多目标优化设计,最终得到了Pareto最优解集。根据设计需求,从Pa-ret0前沿选取一个非劣解作为优化结果。结果表明：陆ging模型与cFD计算误差很小,可信度高;在不问设计状态下,机翼气动性能都得到了提高,表明优化设计方法具有可行性和高效性。     

Optimal air-launching rocket design using system trades and a multi-disciplinary optimization approach

Compared with the conventional ground rocket launching, air-launching has many advantages. However, a comprehensive and integrated system design approach is required because the physical geometry of air launch vehicle is quite dependent on the installation limitation of the mother plane. For the selection of the best system alternative, a trade study for the first stage engine type and launching speeds is performed using a sequential optimization technique, confirming the feasibility of the baseline air-launching rocket. Then, a system design has been performed using the multi-disciplinary feasible (MDF) design optimization method. Analysis modules include mission analysis, staging, propulsion analysis, configuration, weight analysis, aerodynamics analysis and trajectory analysis. As a result of multi-disciplinary system optimization, a supersonic air launching rocket with total mass of 1244.9 kg, total length of 6.36 m, outer diameter of 0.60 m has been successfully designed to launch a satellite of 7.5 kg to the 700 km circular orbit.     

改进粒子群优化算法在亚轨道飞行器固液混合发动机设计中的应用

针对粒子群优化算法在求解多维复杂优化问题时容易陷入局部最优的缺点,提出了动态目标粒子群优化算法,通过分析寻优过程中粒子与个体最优位置和全局最优位置之间存在的位置关系,建立了新的速度更新公式.最后,应用该算法对某型号亚轨道飞行器固液混合发动机进行了优化设计.仿真结果表明,改进算法搜索能力强、收敛速度快,能有效解决此类问题,可为亚轨道飞行器的发动机优化设计提供理论参考.      

一种高效的基于可靠性的多学科设计优化方法(英文)

Design for modem engineering system is becoming multidisciplinary and incorporates practical uncertainties; therefore, it is necessary to synthesize reliability analysis and the multidisciplinary design optimization （MDO） techniques for the design of complex engineering system. An advanced first order second moment method-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and the reliability analysis methods. It is seen through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.     

基于可靠性的涡轮叶片双循环多学科设计优化

提出一种适用于涡轮叶片复杂结构的基于可靠性多学科设计优化方法.使用多学科可行性优化方法解耦.根据实验设计结果,通过Kriging模型建立多学科分析过程的近似模型,并在计算过程中不断更新近似模型.将Hasofer-Lind Rackwitz-Fiessler(HL-RF)可靠性计算方法和优化算法以双循环可靠性优化方法相结合,实现基于可靠性的多学科设计优化模型.实例分析表明,在保证结构的可靠度要求条件下,设计结果满足性能最优.验证了基于可靠性多学科设计优化方法在工程实践中的应用是可行的.      

用于概念设计的离心泵叶轮多目标优化

用两种多目标优化方法对某型液体火箭发动机氧化剂泵叶轮进行多目标优化设计.在优化过程中, 以泵的扬程、效率和泵质量为优化目标, 对叶轮的主要几何参数进行优化.用NCGA(Neighborhood Culti-vation Genetic Algorithm)方法得到优化问题的Pareto前沿;用超传递近似法得到分目标的最佳权值, 进而采用评价函数法求出优化问题的最佳设计值.并分析了主要结构参数对泵性能参数的影响.      

民机机身下部结构耐撞性优化设计

 针对含多设计参数的典型民机机身下部结构耐撞性设计,提出了一种设计方法,该方法以最小化客舱地板的初始加速度峰值与最大化参考压溃状态的结构内能为优化双目标,通过Kriging模型对结构的冲击响应进行预测,采用非支配排序遗传算法II(NSGA-II)对双目标进行优化,进而由Nash-Pareto策略获得最优方案。为了得到最优设计方案,同时研究设计参数对机身结构耐撞性的影响,提出最大化期望提高与最大化预测方差同步加点准则建立代理模型。采用该设计方法,以典型民机机身下部结构设计问题为算例,对客舱地板支撑结构、货舱地板和泡沫构件形状参数进行优化。结果表明,相对原始设计客舱地板的加速度峰值降低约18.3%,次高加速度峰值也得到有效降低,改善了机身结构的耐撞性;Kriging模型预测响应与有限元分析结果误差小于1%,说明了设计方法的有效性。