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。     

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。     

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.     

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.     

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.     

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%).     

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.     

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。     

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.      

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.     

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.     

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.      

基于概率方法的航天器姿态控制系统参数设计

针对传统航天器控制系统参数设计方法中存在的设计保守、主观经验性较强等缺点,使用概率分布对参数不确定性进行量化描述,采用概率指标代替确定性指标,对参数随机分布的系统进行概率分析,并使用可行域图对设计空间进行表征。在此基础上,应用概率优化方法对控制器参数进行优化设计。最后,通过实例对提出的方法进行仿真验证。仿真结果表明,概率分析方法能够放宽参数的设计空间,通过概率优化方法可以得到满足概率指标要求的设计结果,提高了设计效率。     

基于可靠性的飞机风挡抗鸟撞优化设计

传统的飞机风挡设计通常在确定的工况下进行,未能充分考虑实际鸟撞风挡过程中不确定性因素的影响,导致飞机鸟撞风挡的故障多发。综合考虑鸟撞飞机风挡过程中鸟体材料参数、质量、撞击速度等不确定因素的影响,以飞机风挡抗鸟撞的可靠度为约束,风挡质量为目标,基于双循环方法和近似技术建立了风挡抗鸟撞可靠性优化设计系统,利用一阶矩法进行可靠性分析,对某飞机风挡进行了基于可靠性的优化设计。实例分析证明所建风挡抗鸟撞可靠性优化设计系统可行有效。     

面向控制的高超声速飞行器总体优化设计方法

从前期高超声速飞行器基础理论以及关键技术的研究到现今的飞行试验可以看出,高超声速飞行器在总体设计阶段过晚考虑飞行器动力学特性和控制性能会给后期控制系统设计带来极大的困难。在对两类高超声速飞行器试飞与控制相关问题分析的基础上,提出了面向控制的高超声速飞行器总体优化设计方法,给出了面向控制的总体优化设计研究方法、思路和模块框架。     

太阳能无人机高效螺旋桨气动设计

太阳能无人机“超高空、超长航时”的设计方向给螺旋桨的气动设计带来了极大挑战。本文根据某太阳能无人机总体方案,使用多点多目标优化方法改进设计了桨叶翼型,合理布置叶宽分布与桨距,设计出低雷诺数工作环境下的高效螺旋桨,并且在全包线范围内保持较高的气动效率。利用叶素理论对该设计方案进行了性能评估,结果显示在巡航状态下,该螺旋桨的工作效率达到85%以上,各项指标满足设计要求。     

垂直起降运载火箭返回轨迹不确定性优化

针对垂直起降运载火箭一子级在返回着陆的过程中存在的参数不确定性,提出了一种基于非侵入式多项式混沌展开的序列优化和可靠度评估的返回轨迹不确定性优化方法。首先,建立了返回多飞行段轨迹在确定性条件下的优化模型。然后,为同时兼顾轨迹的鲁棒性和可靠性,建立了由鲁棒最优目标函数、基于可靠度的路径约束和鲁棒等式约束组成的不确定性返回轨迹优化模型。最后,基于非侵入式多项式混沌展开方法对鲁棒目标函数和等式约束进行量化处理,将原随机鲁棒优化问题转化为高维状态空间中的等价确定性优化问题;为提高路径约束的可靠度评估效率,基于非侵入式多项式混沌展开方法对最可能点法进行改进,进一步发展了序列优化和可靠度评估策略。数值仿真结果表明,所提出的不确定性优化方法具有较好的鲁棒性,可以满足工程可靠性指标要求,同时还具有较高的精度和计算效率。