高效低噪的二维翼型优化设计

针对传统的气动优化设计未考虑气动噪声影响的局限性,开展了基于噪声预测模型的气动优化设计方法在二维翼型中的应用研究。建立了由几何外形参数化方法、径向基函数(Radial Basis Function,RBF)动网格技术、改进粒子群优化算法、气动分析方法、气动噪声预测方法等五大模块构成的优化设计系统,且各模块均采用标模算例进行验证。通过对二维SC(2)-0714超临界翼型进行了单点多目标优化设计。通过对比翼型几何形状、压力系数分布以及在不同迎角下的气动力系数曲线与总声压级的关系可得,翼型头部半径、厚度影响其头部压力峰值、压力恢复、逆压梯度等特性,从而影响升阻比和总声压级,逆压梯度越小,翼型的总声压级越小。优化结果表明,在设计状态下显著提高了升阻比、降低气动噪声,考虑气动噪声的二维翼型优化设计系统可在实际的工程设计中进行应用。     

鲁棒优化设计方法在结构动力学中的应用

在传统的静力学鲁棒优化设计基础上,考虑时间t参数,通过优化系统目标函数和约束条件的鲁棒性,将鲁棒优化设计方法运用在动力学问题中。通过一个主系统的质量和刚度均有微小波动的二自由度模型减振器设计算例,与传统的优化设计方法相比,显示了鲁棒优化设计的优越性,能使结构具有更稳定的性能。     

不确定情景下应急物资储备库选址问题研究

针对在地震等自然灾害发生时受灾点以及应急需求均为不确定的情况,研究了灾前预置应急物资储备库的选址问题。通过设计多个需求情景来描述受灾点与应急需求的不确定性,建立了有最大运输距离限制的鲁棒优化模型,并设计了鲁棒优化方法。通过数值计算比较分析鲁棒优化方法和随机优化方法的计算结果,表明鲁棒优化解受不确定因素产生的偏差要比随机优化解小,鲁棒优化方法能够有效地减弱不确定性因素对选址方案的影响,并且能降低由预测偏差带来的风险。     

结构动力鲁棒优化设计方法综述

如何提高结构动力学性能的鲁棒性,以减小各种不确定性因素对设计结果的影响是当前学术界和工程界研究和关注的热点问题之一。该文阐述了结构动力鲁棒优化设计的基本概念,从基于Taguchi的方法、基于多目标优化的方法和基于响应面建模的方法三个方面对结构动力鲁棒优化设计的研究进行了综述。以双转子为例,从结构的动力响应要求出发,采用响应面建模、多目标优化的方法进行了设计并与采用Taguchi方法得到的结果进行比较。结果表明,基于响应面建模、多目标优化的方法能够获得多个具有鲁棒性的设计方案,在处理具有不确定性的结构动力学问题时有着很大的应用潜力。最后,对当前方法和后续研究内容作了简要总结和展望。     

汽车动力总成悬置系统鲁棒优化算法

应用鲁棒优化设计理论,考虑设计变量的不确定性对优化设计结果的影响,建立鲁棒优化模型。以动力总成悬置系统能量解耦为目标,悬置刚度参数为设计变量,考虑设计目标的均值和标准差,建立动力总成悬置系统的鲁棒优化模型。针对粒子群算法求解容易陷入局部最优解的问题,采用混合粒子群算法对动力总成悬置系统的悬置刚度参数进行鲁棒优化,并用Monte Carlo方法进行分析,以考察设计值的变化对目标函数的影响。结果表明,优化方法可以有效提高悬置系统的鲁棒性。     

基于中弧线-厚度函数的翼型形状解析构造法

复杂翼型几何形状的解析表达对叶片的优化设计有重要的意义,文章研究了用解析函数构造复杂翼型形状的方法。通过对儒科夫斯基翼型函数的简化,得到用中弧线-厚度函数表示翼型型线的解析表达式,对式中的相关系数和指数进行重新定义和变换,构造出包括儒科夫斯基翼型的一般翼型型线的解析表达式;通过进一步分离上、下型线并进行重新组合的方法可构造出更复杂翼型的形状;再通过增加一个独立的厚度函数项的方法,可构造出具有光滑尾缘形状的翼型。研究表明,复杂翼型的几何形状可通过有限个参数的解析函数表达,这些参数不仅具有明确的几何意义,而且使用方便,便于调整翼型的局部形状。文中给出了用翼型、弦长和扭角函数构造风力机叶片解析函数的应用示例。     

手术持续时间不确定的手术排程鲁棒优化

针对病人手术持续时间有较大范围不确定性的手术排程问题,综合考虑医院成本和病人满意度,采用绝对鲁棒优化策略,构建了手术持续时间不确定的手术排程优化模型,并设计了将单亲遗传算法和内点法相结合的两层混合优化算法,外层的单亲遗传算法确定病人在不同手术台的手术顺序,内层的内点法确定在给定的手术顺序下实现最差性能的手术持续时间.通过对大量随机算例进行仿真实验,并与基于期望值的确定性优化策略进行对比,结果验证了所提绝对鲁棒优化策略的有效性.     

结构-声场耦合系统区间鲁棒优化设计

以工程中普遍存在的结构-声场耦合系统为研究对象,充分考虑系统本身及外载荷的不确定性,基于区间理论建立了含有非概率不确定参数的区间有限元分析方法及区间鲁棒优化模型。首先,利用区间对不确定性参数进行定量化描述,借助泰勒展式提出了求解耦合系统响应范围的区间有限元分析方法。然后,引入鲁棒优化设计的思想,基于区间序关系和区间可能度,分别建立了含区间参数目标函数和约束条件的转换模型,原区间不确定性优化问题就转化为确定性的多目标优化问题。最后通过数值算例,进一步说明了本文所建立鲁棒优化设计模型及算法的有效性。     

复杂产品的多学科鲁棒协同设计优化方法研究

为了处理好复杂产品各子系统之间的耦合关系以及各子系统的异构性问题,以协同优化(CO)算法为基础,结合系统不确定分析(SUA)方法和近似不确定传播(IUP)方法,构建了多学科鲁棒协同设计优化算法框架.在设计变量的不确定性能够被概率分布函数描述的情况下,此算法框架能够解决复杂产品的设计优化问题.通过对梳齿式微加速度计的多学科鲁棒协同优化设计算例的计算,验证了此算法在输入参数存在微小扰动的情况下能够有效提高设计解的鲁棒性.     

非线性气动弹性系统的鲁棒稳定性分析

基于结构奇异值理论和特征多项式的值域方法,研究了带有结构和气动参数不确定性的非线性二元机翼的鲁棒稳定性问题.机翼模型包括非线性的扭转弹簧和能够反映失速效应的非线性气动模型.针对零摄动,使用肛方法分析线性化系统在平衡点的鲁棒稳定性.针对非零摄动,将平衡点位置看作关于不确定参数的函数并展开为泰勒级数,从而在μ方法的框架下考虑平衡点的不确定性.此外,计算不确定特征多项式的值域范围,并使用除零条件来判断其鲁棒稳定性.仿真数值结果给出了鲁棒颤振速度的上下界,表明了方法的有效性.     

Response surface approach to aerodynamic optimization design of helicopter rotor blade

This paper describes a hovering rotor blade design through the suitable combination of flow analysis and optimization technique. It includes a parametric study concerned with the influence of design variables and different design conditions such as objective functions and constraints on the rotor performance. Navier–Stokes analysis is employed to compute the hovering rotor performance in subsonic and transonic operating conditions. Response surface method based on D‐optimal 3‐level factorial design and genetic algorithm are applied to obtain the optimum solution of a defined objective function including the penalty terms of constraints. The designs of the rotor airfoil geometry and the rotor tip shape are performed in subsonic and transonic conditions, and it is observed that the new rotor blades optimized by various objective functions and constraints have better aerodynamic characteristics than the baseline rotor blade. The influence of design variables and their mutual interactions on the rotor performance is also examined through the optimization process. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust design using Bayesian Monte Carlo

In this paper, we propose an efficient strategy for robust design based on Bayesian Monte Carlo simulation. Robust design is formulated as a multiobjective problem to allow explicit trade‐off between the mean performance and variability. The proposed method is applied to a compressor blade design in the presence of manufacturing uncertainty. Process capability data are utilized in conjunction with a parametric geometry model for manufacturing uncertainty quantification. High‐fidelity computational fluid dynamics simulations are used to evaluate the aerodynamic performance of the compressor blade. A probabilistic analysis for estimating the effect of manufacturing variations on the aerodynamic performance of the blade is performed and a case for the application of robust design is established. The proposed approach is applied to robust design of compressor blades and a selected design from the final Pareto set is compared with an optimal design obtained by minimizing the nominal performance. The selected robust blade has substantial improvement in robustness against manufacturing variations in comparison with the deterministic optimal blade. Significant savings in computational effort using the proposed method are also illustrated. Copyright © 2007 John Wiley & Sons, Ltd.     

An adaptive geometry parametrization for aerodynamic shape optimization

An adaptive geometry parametrization is presented to represent aerodynamic configurations during shape optimization. This geometry parametrization technique is constructed by integrating the classical B-spline formulation with a knot insertion algorithm. It is capable of inserting control points into a given parametrization without modifying the geometry. Taking advantage of this technique, a shape optimization problem can be solved as a sequence of optimizations from the basic parametrization to more refined parametrizations. Additional control points are inserted based on criteria incorporating sensitivity analysis and geometric constraints. Example problems involving airfoil optimization and induced drag minimization demonstrate the effectiveness of the proposed approach in comparison to uniformly refined parametrizations.     

Aerospace applications of optimization under uncertainty

The Multidisciplinary Optimization (MDO) Branch at NASA Langley Research Center develops new methods and investigates opportunities for applying optimization to aerospace vehicle design. This paper describes MDO Branch experiences with three applications of optimization under uncertainty: (1) improved impact dynamics for airframes, (2) transonic airfoil optimization for low drag, and (3) coupled aerodynamic and structures optimization of a 3-D wing. For each case, a brief overview of the problem and references to previous publications are provided. The three cases are aerospace examples of the challenges and opportunities presented by optimization under uncertainty. The present paper will illustrate a variety of needs for this technology, summarize promising methods, and uncover fruitful areas for new research.     

Uncertainty‐based robust aerodynamic optimization of rotor blades

The aerodynamic performance of a compressor is highly sensitive to uncertain working conditions. This paper presents an efficient robust aerodynamic optimization method on the basis of nondeterministic computational fluid dynamic (CFD) simulation and multi‐objective genetic algorithm (MOGA). A nonintrusive polynomial chaos method is used in conjunction with an existing well‐verified CFD module to quantify the uncertainty propagation in the flow field. This method is validated by comparing with a Monte Carlo method through full 3D CFD simulations on an axial compressor (National Aeronautics and Space Administration rotor 37). On the basis of the validation, the nondeterministic CFD is coupled with a surrogate‐based MOGA to search for the Pareto front. A practical engineering application is implemented to the robust aerodynamic optimization of rotor 37 under random outlet static pressure. Two curve angles and two sweep angles at tip and hub are used as design variables. Convergence analysis shows that the surrogate‐based MOGA can obtain the Pareto front properly. Significant improvements of both mean and variance of the efficiency are achieved by the robust optimization. The comparison of the robust optimization results with that of the initial design, and a deterministic optimization demonstrate that the proposed method can be applied to turbomachinery successfully. Copyright © 2012 John Wiley & Sons, Ltd.     

Design optimization using multiple dominance relations

A challenge in engineering design is to choose suitable objectives and constraints from many quantities of interest, while ensuring an optimization is both meaningful and computationally tractable. We propose an optimization formulation that can take account of more quantities of interest than existing formulations, without reducing the tractability of the problem. This formulation searches for designs that are optimal with respect to a binary relation within the set of designs that are optimal with respect to another binary relation. We then propose a method of finding such designs in a single optimization by defining an overall ranking function to use in optimizers, reducing the cost required to solve this formulation. In a design under uncertainty problem, our method obtains the most robust design that is not stochastically dominated faster than a multiobjective optimization. In a car suspension design problem, our method obtains superior designs according to a k-optimality condition than previously suggested multiobjective approaches to this problem. In an airfoil design problem, our method obtains designs closer to the true lift/drag Pareto front using the same computational budget as a multiobjective optimization.     

Aerothermodynamic shape optimization of hypersonic blunt bodies

The aim of this study is to develop a reliable and efficient design tool that can be used in hypersonic flows. The flow analysis is based on the axisymmetric Euler/Navier–Stokes and finite-rate chemical reaction equations. The equations are coupled simultaneously and solved implicitly using Newton's method. The Jacobian matrix is evaluated analytically. A gradient-based numerical optimization is used. The adjoint method is utilized for sensitivity calculations. The objective of the design is to generate a hypersonic blunt geometry that produces the minimum drag with low aerodynamic heating. Bezier curves are used for geometry parameterization. The performances of the design optimization method are demonstrated for different hypersonic flow conditions.     

High-Fidelity Computational Optimization for 3-D Flexible Wings: Part II—Effect of Random Geometric Uncertainty on Design

The effect of geometric uncertainty due to statistically independent, random, normally distributed shape parameters is demonstrated in the computational design of a 3-D flexible wing. A first-order second-moment statistical approximation method is used to propagate the assumed input uncertainty through coupled Euler CFD aerodynamic/finite element structural codes for both analysis and sensitivity analysis. First-order sensitivity derivatives obtained by automatic differentiation are used in the input uncertainty propagation. These propagated uncertainties are then used to perform a robust design of a simple 3-D flexible wing at supercritical flow conditions. The effect of the random input uncertainties is shown by comparison with conventional deterministic design results. Sample results are shown for wing planform, airfoil section, and structural sizing variables.     

Virtual Stackelberg game coupled with the adjoint method for aerodynamic shape optimization

In this article, a Virtual Stackelberg Game (VSG) is proposed for aerodynamic shape optimization, where the design variables are divided into two categories to optimize the same objective function, one acts as a leader, and the other ones as followers react independently and selfishly relative to the leader's strategy. During each Stackelberg strategy cycle, the Gradient-Based Method (GBM) with the adjoint method in Stanford University Unstructured (SU²) is applied in the optimization of each player. Firstly, parametric studies of VSG by two simple cases are conducted to assess the impact of critical parameters on aerodynamic shape optimization, including the design cycle, the split of design variables and role (leader and follower) assignment. Based on the criterion from parametric studies, two typical numerical cases under transonic flow are applied—the drag reduction design of a 2D airfoil and a 3D wing. It is found that, compared to the original GBM method, VSG can provide better optimization results with less computational cost.     

A Classifiers Based Optimization Technique for Designing Turbine Airfoils

The primary focus of this work is in the development of an evolutionary optimization technique which gets progressively 'smarter' during the optimization process by learning from computed domain knowledge. In the approach, the influence of the design variables on the problem solution is recognized, and the knowledge learned is then generalized to dynamically create or change design rules during optimization. This technique, when applied to a constrained optimization problem, shows progressive improvement in convergence of search, as successive generations of rules evolve by learning from the environment. This method is applied to a complex aerodynamic optimization problem involving turbine airfoil design. In this investigation, the 3D geometry of an airfoil is optimized by simultaneously optimizing multiple 2D slices of the airfoil. Results from the optimization of a low pressure turbine nozzle are presented in the paper. Results obtained using standard numerical optimization techniques are also presented for comparison purposes.