机翼颤振控制与不确定性优化问题研究
|
摘要
飞机气动弹性及其优化设计是飞机研制中的重要内容之一。已有工作主要基于传统的确定性方法,而实际工程中,不确定性因素无处不在,且不确定程度参差不一,将直接导致其实际性能和设计值相差较远。而气动弹性优化方案更需要具有稳健性,并能在设计阶段就将各种系统参数不确定因素纳入设计范围。
本文在全面回顾了传统气动弹性颤振优化分析方法的基础上,对包含不确定性的机翼气动弹性优化方法进行了系统性的研究和探索。分别研究了包含随机不确定因素的颤振优化设计和包含区间不确定因素的颤振优化设计。采用响应面法实现了基于随机不确定性的机翼结构颤振优化设计分析,和基于区间不确定性的机翼结构不确定性分析。数值算例证明了方法的可行性和高效性。
本文主要贡献和创新包括如下几个方面:
1、根据模糊控制不依赖于被控对象的精确模型,对参数变化不敏感,具有很强鲁棒性的特点,提出一种模糊逻辑控制器,对包含间隙的二元机翼极限环振荡进行控制,并对其响应机理进行探讨和研究。数值仿真结果表明,模糊控制器能够有效抑制非线性极限环振动,使系统迅速达到稳定,提高系统颤振速度。
2、考虑气动弹性系统设计参数的随机不确定性,提出一种基于响应面法,以机翼结构的颤振性能为设计目标的可靠性优化方法,并用复合材料层合板翼模型验证其可行性和正确性。该方法能够高效率地对包含随机不确定性的机翼颤振问题进行优化。
3、考虑气动弹性系统参数随机不确定性,提出一种基于神经网络代理模型的机翼结构颤振可靠性优化设计方法。该法效率高,节约计算成本,能够有效解决复杂机翼结构不确定性颤振优化问题。
4、针对工程问题中不确定因素统计数据信息不完备、待设计目标不具备函数表达式问题,提出了基于Kriging代理模型、包含区间不确定性参数的机翼结构稳健性优化设计方法。该方法给出了稳健性优化模型,并将其转换为易于实现确定性形式。该方法不需要考虑不确定性参数的分布型式,也不要求目标函数或约束函数连续性、可导性等,对数学模型要求不高;更方便工程设计人员选择对目标稳健性和约束稳健性的设计偏好。
最后对本文工作进行了总结,并展望了未来研究方向。
One of the most important steps in airplane design process is aerodynamic analysis and optimization on wing structures. Now most of work which had been researched is based on traditional deterministic optimization methods. But in real engineering projects, uncertainty exists everywhere inevitably. This directly leads to the performance of products are far from design. The aeroelastic design schemes of aeroelastic systems should have robust stability, and all kinds of uncertainties should be taken into consideration from the beginning of optimization design process.
Based on systematic review of the traditional optimization design methods for aeroelastic design, research and exploration on the optimization methods about aeroelastic design containing uncertain parameters is performed in this thesis. The research work on optimization methods for aeroelasic problems of wing structures which contain interval uncertainties and random uncertainties is performed separately. Numerical examples show the feasibility and efficiency of those methods. The main work of this thesis is listed as follows:
1. Fuzzy controller has good robustness, which is not sensitive to uncertainty of disturbance, without the requirement of the exact mathematic model. Based on such characteristics, a novel controller based on fuzzy control strategy is designed to suppress the LCO vibration of typical wing section with control surface freeplay. Simulation results indicate that this method is valid and the fuzzy controller has good performance.
2. Considering various random uncertainties exist in aeroelastic system, a novel reliability-based method, using the response surface method, is developed to perform optimization of wing structures with the object of maximum flutter speed. An example of plane composite material wing structure is presented. The results show the validity and correctness of this method. This method can complete the optimization of wing flutter problem containing uncertain parameters efficiently.
3. A novel robust optimization method is developed which is based on neural network surrogate model for flutter optimization problem including random uncertain parameters. The method can solve the wing structure flutter optimization problem with high efficiency and economizes computational cost.
4. For engineering problems which lack of statistics information of uncertainty and without explicit formulation of design objects, a novel robust design optimization method using interval analysis is present based on Kriging surrogate model of wing structures. The robust optimization model is built based on the method of non probability robust optimization theory, and is changed to the deterministic form which is suitable for using the traditional optimization methods. This method has the advantages that it has less requirements on uncertainty and mathematical. This method is very convenient for engineering analysist to show their preference whether on objective performance or constains performances.
At last, the research work of this dissertation is summarized and the prospective of further research is discussed.
本文在全面回顾了传统气动弹性颤振优化分析方法的基础上,对包含不确定性的机翼气动弹性优化方法进行了系统性的研究和探索。分别研究了包含随机不确定因素的颤振优化设计和包含区间不确定因素的颤振优化设计。采用响应面法实现了基于随机不确定性的机翼结构颤振优化设计分析,和基于区间不确定性的机翼结构不确定性分析。数值算例证明了方法的可行性和高效性。
本文主要贡献和创新包括如下几个方面:
1、根据模糊控制不依赖于被控对象的精确模型,对参数变化不敏感,具有很强鲁棒性的特点,提出一种模糊逻辑控制器,对包含间隙的二元机翼极限环振荡进行控制,并对其响应机理进行探讨和研究。数值仿真结果表明,模糊控制器能够有效抑制非线性极限环振动,使系统迅速达到稳定,提高系统颤振速度。
2、考虑气动弹性系统设计参数的随机不确定性,提出一种基于响应面法,以机翼结构的颤振性能为设计目标的可靠性优化方法,并用复合材料层合板翼模型验证其可行性和正确性。该方法能够高效率地对包含随机不确定性的机翼颤振问题进行优化。
3、考虑气动弹性系统参数随机不确定性,提出一种基于神经网络代理模型的机翼结构颤振可靠性优化设计方法。该法效率高,节约计算成本,能够有效解决复杂机翼结构不确定性颤振优化问题。
4、针对工程问题中不确定因素统计数据信息不完备、待设计目标不具备函数表达式问题,提出了基于Kriging代理模型、包含区间不确定性参数的机翼结构稳健性优化设计方法。该方法给出了稳健性优化模型,并将其转换为易于实现确定性形式。该方法不需要考虑不确定性参数的分布型式,也不要求目标函数或约束函数连续性、可导性等,对数学模型要求不高;更方便工程设计人员选择对目标稳健性和约束稳健性的设计偏好。
最后对本文工作进行了总结,并展望了未来研究方向。
One of the most important steps in airplane design process is aerodynamic analysis and optimization on wing structures. Now most of work which had been researched is based on traditional deterministic optimization methods. But in real engineering projects, uncertainty exists everywhere inevitably. This directly leads to the performance of products are far from design. The aeroelastic design schemes of aeroelastic systems should have robust stability, and all kinds of uncertainties should be taken into consideration from the beginning of optimization design process.
Based on systematic review of the traditional optimization design methods for aeroelastic design, research and exploration on the optimization methods about aeroelastic design containing uncertain parameters is performed in this thesis. The research work on optimization methods for aeroelasic problems of wing structures which contain interval uncertainties and random uncertainties is performed separately. Numerical examples show the feasibility and efficiency of those methods. The main work of this thesis is listed as follows:
1. Fuzzy controller has good robustness, which is not sensitive to uncertainty of disturbance, without the requirement of the exact mathematic model. Based on such characteristics, a novel controller based on fuzzy control strategy is designed to suppress the LCO vibration of typical wing section with control surface freeplay. Simulation results indicate that this method is valid and the fuzzy controller has good performance.
2. Considering various random uncertainties exist in aeroelastic system, a novel reliability-based method, using the response surface method, is developed to perform optimization of wing structures with the object of maximum flutter speed. An example of plane composite material wing structure is presented. The results show the validity and correctness of this method. This method can complete the optimization of wing flutter problem containing uncertain parameters efficiently.
3. A novel robust optimization method is developed which is based on neural network surrogate model for flutter optimization problem including random uncertain parameters. The method can solve the wing structure flutter optimization problem with high efficiency and economizes computational cost.
4. For engineering problems which lack of statistics information of uncertainty and without explicit formulation of design objects, a novel robust design optimization method using interval analysis is present based on Kriging surrogate model of wing structures. The robust optimization model is built based on the method of non probability robust optimization theory, and is changed to the deterministic form which is suitable for using the traditional optimization methods. This method has the advantages that it has less requirements on uncertainty and mathematical. This method is very convenient for engineering analysist to show their preference whether on objective performance or constains performances.
At last, the research work of this dissertation is summarized and the prospective of further research is discussed.
引文
[1] Bisplinghoff R L. Aeroelasticity. Addison-Wesley,1955.
[2] Garrick I E, Read R D III, Historical Development of Aircraft Flutter, Journal of Aircraft, 1981,Vol.18(11):897-912.
[3]赵永辉.气动弹性力学与控制.科学出版社. 2007.
[4]伏欣H W.气动弹性力学原理.沈克杨译.上海科学技术文献出版社,1982.
[5] Theodorsen T. General Theory of Aerodynamic Instability and the Mechanism of Flutter, NACA Report NO. 496,1935.
[6] Albano E, Rodden W P. A doublet-lattice method for calculating lift distributions of oscillating surface in surbsonic flow. AIAA Journal,1969,7(20:279-285.
[7] Razani R. The Behavior of the Fully Stessed Design of Structures and its Relationship to Minimum Weight Design. AIAA Journal. 1965, 3(12):p2262-2268.
[8] Miura H. An Improved Fully Stressed Design Algorithm for Plate/Shell Structures. Structural Optimization. 1990,2:p233-237.
[9] Gary L, Giles. Simultaneous Calculation of Aircraft Design Loads and Strucutral Member Sizes. AIAA Journal. 1975, 75-965.
[10] Wilkinson K, Lerner E. Practical Design of Minimum weight Aircraft Structures for Strength and Flutter Requirements. AIAA 6th Aircraft Design Flight Test and Operations Meeting. 1974.
[11]张挂江.飞行器复合材料结构气动弹性刚度剪裁优化设计研究,[硕士学位论文].西安:西北工业大学,2006.
[12] Corso L M, Popelka D A, Nixon M W. Design, analysis and test of a composite tailored tiltrotor wing. Aemerican Helicopter Socety. 53rd Annual Forum Proceedings, Vols 1 and 2209-219 19997.
[13] Santini P, Gasbari P, Altobelli M, Rossi A. A comparative overview of strain actuated surfaces' design. Journal of Reinforced Plastics and Composites.1997, 16 (6):519-536.
[14] Chattopadhyay A, Seeley C E, Jha R. Aeroelastic tailoring using piezoelectric actuation and hybrid optimization. SPIE Conference on Smart Structures and Integrated Systems. Mar 02-05,1998.
[15] Eastep F E, Tischler V A, Venkayya V B et al. Aeroelastic tailoring of composite structures. Journal of Aricraft. 1999, 36 (6):1041-1047 .
[16] Weisshaar T A, Duke D K, Dobbins A. Active aeroelastic tailoring with adaptive continuous control surfaces. AIAA/ASME/ASCE/AHS/ASC 41st Structures, Structural Dynamics, and Materials Conference. APR 03-06, 2000.
[17] Cesnik C, Ortega M, Patil M J. Active aeroelastic tailoring of high aspect ratio composite wings. AIAA/ASME/ASCE/AHS/ASC 41st Structures, Structural Dynamics, and Materials Conference. APR 03-06, 2000.
[18] Tischler V A, Venkayya V B, Sensburg O. Aeroelastic tailoring of empennage structures. AIAA/ASME/ASCE/AHS/ASC 41st Structures, Structural Dynamics, and Materials Conference, APR 03-06, 2000.
[19] Gern F H, Librescu L. Aeroelastic tailoring of composite wings exhibiting nonclassical effects and carrying external stores. Journal of Aircraft.2000, (6):1097-1104.
[20] Librescu L, Qin Z M, Ambur D R. Implications of warping restraint on statics and dynamics of elastically tailored thin-walled composite beams. International Journal Journal of Mechanical sciences .2003.45 (8):1247-1267.
[21] Arizono H, Isogai K. Application of genetic algorithm for aeroelastic tailoring of a cranked arrow wing. Journal of aircraft. 2005,42 (2):493-499.
[22] Weisshaar T A, Duke D K. Induced drag reduction using aeroelastic tailoring with adaptive control surfaces. Journal of Aircraft.2006,43 (1):157-164.
[23] Guo S J, Cheng W Y, Cui D G. Aeroelastic tailoring of composite wing structures by laminate layup optimization. AIAA Journal .2006. 44 (12):3146-3150.
[24] Kim D H, Oh S W, Lee I, Kweon J H, et ta. Weight optimization of composite flat and curved wings satisfying both flutter and divergence constrains. Advances in Composite Materials and Structures, Pts 1 and 2 334-335477-480 2007.
[25] Manan A, Vio G A, Harmin M Y, Cooper J E. Optimization of aeroelastic composite structures using evolutionary algorithms. Engineering Optimization. 2010,42 (2):171-184.
[26] Mccormick D J. Distributed Uncertainty Analysis Techniques for Conceptual Launch Vechicle Dsign. Georgia Institute of Technology,2001.
[27] Kirby M R. A Mehodology for Technology Identification Evaluation and Selection in Conceptual and Preliminary Aircraft Design. Georgia Institute of Technology,2001.
[28] Padmanabhan D. Reliability-based Optimization for Multidisciplinary System Design. Aerospace and Mechanical Engineering Notre Mame,2003.
[29] Du X P. Efficient Methods for Engineerin Design Under Uncertainty. University ofIllinois,2002.
[30] Jin R, Chen R, Simpson T W. Comparative Studies of Metamodeling Techniques under Multiple Modeling Criteria. AIAA 2000-4801.
[31] Lin Y. An Efficient Robust Concept Exploration Method and Sequential Exploratory Experimental Design. Georgai Institute of Technology,2004.
[32] Oberkampf W L, Helton J C, Sentz K. Mathematical Representation of Uncertainty. AIAA 2001-1645.
[33] Oberkampf W L, Deland S M, Rutherford B M. Estimation of Total Uncertainty in Modeling and Simulation. Sandia National Laboratories, SAND 2000-0824.
[34] Thomas A Z, Hemsch M J, HIlberger M W, et ta. Needs and Opportunities for Uncertainty-based Multidisciplinary Design Methods for Aerospace Vehicles. NASA/TM-2002-211462.
[35] Ben-Haim Y. Roubust Reliability in the Mathmatical Science. Berlin:Springer-Verlag,1996.
[36] Ben-Haim Y , Elishakoff I. Convex Models of Uncertainty in Applied Mechanics. Amsterdam: Elsevier,1990.
[37]扎德.模糊集合、语言变量及模糊逻辑.北京:科学出版社,1982.
[38] Senthil M, Ranjan G, Dineshkumar H. Robust Aeroelastic Optimization of Composite Helicopter Rotor. International Conference on Engineering Optimization. Rio de Janeiro,Brazil,01-05 June 2008.
[39] Sharon L., Padula, Clyde R. Gumbert, Wu Li. Aerospace Application of Optimization Under Uncertainty. Optim Eng.2006,7:317-328.
[40] Enevoldsen I, Sorensen J. Relaibiltiy based optimization in structural engineering. Structural Safty, 15:169,1994.
[41] Chandu S, Grandhi R. General purpose procedure for reliability based structural optimization under parametric uncertainties. Advances in Engineering Software, 23:7-14,1995.
[42] Pettit C,Grandhi R. Multidisciplinary optimization of aerospace structures with high reliability. In 8th Joint Space Conference on Probability Mechanics and Structural Reliability, South Bend, IN. ASCE,July 2000.
[43] Pettit C L, Candield R A, Ghanem R. Stochastic analysis of an aeroelastic system. In 15th ASCE Engineering Mechanics Conference, June 2-5,2002, Columbia University, New York, 2002.
[44] Zink P, Raveh D, Mavris D. Robust structural design for active aeroelastic wing withaerodynamic uncertainties. In 41st Stucctures, Structural Dynamics, and Materials conference and Exhibit, Atlanta, GA. AIAA/ASME/ASCE/AHS/ACS, April 2000.
[45] Pettit C,Grandhi R. Preliminary weight optimization of a wing structures for gust response and aileron effectiveness reliability. International Conference on computational Engineering Sciences, August ,2000, Los Angeles, CA, 2000.
[46] Pettit C,Grandhi R. Reliability optimization of aerospace structures for gust response and aileron effectiveness. In 8th International Conference on Structural Safety and Reliability, June 2001, Newport Beach, CA,2001.
[47] Kuttenkeuler J, Ringertz U. Aeroelastic tailoring considering uncertainties in material properties. Structural Optimization, 1998, 15(3-4):157-162
[48] Zingales M, Elishakoff I. Hybrid aeroelastic optimization and antioptimization. AIAA Journal. 2001, 39(1):161-175.
[49] Moulin B, Idan M, Karpel M. Aeroservoelastic structural and control optimization using robust design schemes. Journal of Guidance Control and Dynamics, and Materials Conference. 2000, APR 0.3-06.
[50] Borglund D. Robust aeroelasticity stability analysis considering frequency domain aerodynamic uncertainty. Journal of Aircraft. 2003, 40(1):189-193.
[51] Karpel M, Moulin B, Idan M. Robust aeroservo elastic design with structural variations and modeling uncertainties. 2003,Journal of Aircraft, 2003, 946-954.
[52] Pettit C L. Uncertainty quantification in aeroelasticity: Recent and research challenges. Journal of Aircraft. 2004, 41(5):1217-1229.
[53] Buschek H, Calise A J. Uncertainty modeling and fixed order controller design for a hypersonic vehicle model. Journal of Guidance Control and Dynamics. 1997,20(1):42-48.
[54] Zeng Y M, Singh S N. Output feedback variable structure adaptive control of an aeroelastic system. Journal of Guidance Control and Dynamics. 1998, 21(6):830-837.
[55] Xing W H, Singh, S N. Adaptive output feedback control of a nonlinear aeroelastic structure. AIAA Guidance ,Navigation, and Control Conference. 1999, VOLS 1-31675-1685.
[56] Vipperman J S, Barker J M, Clark R L, et al. Comparison of mu and H-2-synthesis controllers on an experimental typical section. Journal of Guidance Control and Dynamics. 1999, 22(2):278-285.
[57] Lind R, Brenner M. Incorporating flight data into robust aeroelastic model. Journal of Aircraft. 1998, 35(3):470-477.
[58] Lind R, Brenner M. Flutterometer: An on-line tool to predict robust flutter margins[J]. Journal of Aircraft. 2000, 37(6):1105-1112.
[59] Degaki T, Suzuki S. Sliding mode control application for two dimensional active flutter suppression. Transactions of the Japan Society for Aeronautical and Space Sciences. 2001, 43 (142) : 174-181.
[60] Ghosh D, Ghanem R, Pettit C. Stochastic buckling analysis of a joined wing[R]. Advances in Stochastic Structural Dynamics. 2003, 133-140.
[61] Millman D R, King P I, Maple RC et al. Estimatino the probability of failure of a nonlinear aeroelastic system. Journal of Aircraft. 2006, 43(2):504-516.
[62] Lindsley N J, Petti C L, Beran PS. Nonlinear plate aeroelastic response with uncertain stiffness and boundary conditions. Structures and Infrastructure Engineering. 2006, 2(3-4):201-220.
[63] Attar P J, Dowell E H. Stochastic analysis of a nonlinear aeroelastic model using the response surface method. Journal of Aircraft. 2006,43(4):1044-1052.
[64] Wu Z G, Yang C. Approach for Aeroelastic Robust Stability Analysis. Chinese Journal of Aeronautics. 2008, 21(5):417-422.
[65] Borglund D. Robust Eigenvalue Analysis Using the Structured Singular Value: The mu-p method. AIAA Journal. 2008, 46(11):2806-2813.
[66] Murugan S, Harursampath D, Ganguli R. Material uncertainty propagation in helicopter nonlinear aeroelastic response and vibration analysis. AIAA Journal. 2008, 46(9):2332-2344.
[67] Yun H W, Han J L. Match point solution for robust flutter analysis in constant Mach Prediction. Chinese Journal of Aeronautics. 2008, 21(2):105-114.
[68] Castravete S C, Ibrahim R A. Effect of stiffness uncertainties on the flutter of a cantilever wing. AIAA Journal, 2008,46(4):925-935.
[69] Caracoglia L. Influence of uncertainty in selected aerodynamic and structural parameters on the buffeting response of long span bridges. Journal of Wind Engineering and Industrial Aerodynamics. 2008, 96(3):327-344.
[70] Song S F, Lu Z Z, Zhang W W et al. Reliability and Sesitivity Analysis of Transonic Flutter Using Improved Line Sampling Technique. Chinese Journal of Aeronautics. 2009, 22(5):513-519.
[71] Wang X J, Qiu Z P. Nonprobabilistic Interval Reliability Analysis of Wing Flutter. AIAA Journal. 2009, 47(3): 743-748.
[72] Anthony A. Giunta. Perspectives on Optimization Under Uncertainty: Algorithms andApplications. 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 30 August-1 September 2004,Albany, New York.
[73] Phadke M S. Quality Engineering Using Robust Design. Prentice Hall, Englewood Cliffs, NJ,1989.
[74] Chen S, Nikolaidis E, Cudney H H, Rosca R, and R T Haftka. Comparison of probabilistic and fuzzy set methods for designing under uncertainty. In Proceedings of the 40th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, 1999.
[75] Nikolaidis E, Haftka R, Rosca R. Comparison of probabilistic and possibility-based methods for design against catastrophic failure under uncertainty. Nsf report, University of Florida, Gainesville, FL, 1998.
[76] MSC. corporation, NASTRAN Encyclopedia V70.5
[77]冉玉国. NASTRAN气弹程序的二次开发[硕士论文].南京:南京航空航天大学,2006.
[78] Rodden, W P , Love J R, Equations of Motion of Quasisteady Flight Vehicle Utilizing Restrained Static Aeroelastic Characteristics, Journal of Aircraft. Vol 22(9) ,September 1995, pp802-809.
[79] Johnson E H,Venkayya V B. ASTROS Theoretical Manual, AFWAL-TR-88-3028, December 1988.
[80] Mukhopadhyay V. Historical perspective on analysis and control of aeroelastic response[J]. Journal of Guidance, Control, and Dynamics, 2003, 26 (5):673-684.
[81]任勇生等.飞行器非线性气动弹性和颤振主动控制研究进展.力学季刊,2003,24(4): 534-540.
[82] Wazak M, Srinathkumar S. Flutter suppression for the active flexible wing control system design and experimental validation. AIAA J,1992,138-145.
[83] Conner M D, Tang D M, Dowell E H et al. Nonlinear behaviors of a typical airfoil section with a control surface freeplay: a numerical and experimental study. Journal of Fluids and Structures,1997, 11:89-109.
[84]赵永辉,胡海岩.具有操纵间隙非线性二维翼段的气动弹性分析.航空学报,2003,24(6):521-525.
[85]李道春向锦武.间隙非线性气动弹性颤振控制[J].北京航空航天大学学报, 2007,33(6):640-643.
[86] Ko J, Kurdila A J, Strganac T W. Nonlinear control of a proto typical wing section withtorsional nonlinearity. Journal of Guidance, Control, and Dynamics, 1997,20(6):1181-1189.
[87] Ko J, Strganac T W, Kurdila A J. Stability and control of a structurally nonlinear Aeroelastic system. Journal of Guidance,Control,and Dynamics,1998,21(5):718-725.
[88] Behal A, Marzocca P, Rao V M, Nonlinear adaptive control of an aeroelastic two-dimensional lifting surface. Journal of Guidance, Control, and Dynamics, 2006,29(2):382-390.
[89] Xing W and Singh S N, Adaptive Output Feedback Control of a nonlinear Aeroelastic Stucture. Journal of Guidance,Control,and Dynamics, 2000,23(6):1109-1116.
[90] Kanellakopoulos I, Kokotovic P V, Morse A S. Systematic Design of Adaptive Controllers for Feedback Linearizable System. IEEE Transactions on Automatic Control,1991, 36(11):1241-1253.
[91] Zhang R and Singh S N. Adaptive output Feedback Control of an Aeroelastic System with Unstructured uncertainty.Journal of Guidance,Control,and Dynamics,2001,24(3):503-509.
[92] Ko J, Strganac T W, Junkins J L et al. Structured model reference adaptive control for a wing section with structural nonlinearity. Journal of Vibration and Control,2002,8.
[93] Strganac TW, Ko J,Thompson DE et al. Investigations of Limit Cycle Oscillations in Aeroelastic Systems[R]. CEAS/ AIAA/ICASE/NASA Langley, International Forum on Aeroelasticity, Williamsburg, Virginia, 1999.
[94] Akella MR. Structured Adaptive Control Theory and Applications to Trajectory Tracking In Aerospace Systems[D]. Department of Aerospace Engineering,Texas A&M Unibversity,1998.
[95]于明礼.基于超声电机作动器的二维翼段颤振主动抑制[博士论文].南京:南京航空航天大学,2006.
[96] Theodorsen T, General theory of aerodynamic instability and mechanism of flutter, NACA Report No. 496,1935.
[97]穆雪峰.多学科设计优化代理模型技术的研究应用[硕士论文].南京:南京航空航天大学,2006.
[98]项可风,吴启光.实验设计与数据分析.上海:上海科学技术出版社,1989:p469-475.
[99]张铁茂,丁建国.设计实验与数据处理.北京:兵器工业出版社,1990:p190-195.
[100] Hard R L. Multiquadric Equations of Topography and Other Irregular Surfaces. Journal of Geophysical Research, 1971(76):1905-1915.
[101] M J D Powell, Radial Basis Functions for Multivarible Interpolation: A Review, Oxford University press,New York,1987.
[102] Matheron G. Principles of Geostatistics. Economic Geology, 1963(58):1246-1266.
[103]王晓锋,席光.基于Kriging模型的翼型气动性能优化设计.航空学报,2005,26(5):545-549.
[104]刘克农,姚卫星,穆雪锋.基于Kriging代理模型的结构形状优化方法研究.计算力学学报,2006,23(3):344-347.
[105] Sakata S, Ashida F, ZaKo M. An efficient algorithm for Kriging approximation and optimization with large scale sampling data. Computer Methods in Applied Mechanics and Engineering, 2004, 193:385-404.
[106]谢延敏,于沪平,陈军,等.基于Kriging模型的可靠度计算.上海交通大学学报, 2007,41(2):177-180.
[107] S Haykin, Neural Networks: A Comprehensive Foundation, Prentice-Hall, NJ, 1999.
[108] W Shyy, P K Tucker, R Vaidyanathan, Response Surface and Neural Network Techniques for Rocket Engine Injector Optimization, AIAA 99-2455.
[109] Kurkova, K, 1995. Kolmogorov’s Theorem. The Handbook of Brain Theory and Neural Networks, ed. M. A.A.rbib,MIT Press,pp.501-502.
[110] Varadarajan S, Chen W, Pelka C. Robust Concept Exploration Method of Propulsion Systems with Enhanced Model Approximation Capabilities, Engineering Optimization, 32(3), 309-334,2000.
[111] C M Bishop. Pattern Recognition and Machine Learning. Springer,2006.
[112] M Sugiyama and H Ogawa. Optimal Design of Regularization Term and Regularizatoin Parameter by Subspace Information Criterion. Neural Networks, 15(3):349-361,2002.
[113] C Cornell. A probability based structural code. Journal of American Concrete institute, 66(12):974-985,1969.
[114] Hasofer A and Lind N. Exact and invariant second moment code format. Journal of Engineering Mechanics, 100:111-121,1974.
[115]秦权.结构可靠度随机有限元理论及其工程应用.清华大学出版社. 2006.
[116] Breitung K. Asymptotic approximation for multinormal integrals. Journal of Engineering Mechanics, 1984,110(30:357-366.
[117] Huang B, Du X. Analytical robustness assessment for robust design. Structural and Multidisciplinary Optimization. 34(2):123-137,2007.
[118] Jung D H, Lee B C. Development of a simple and efficient method for robust optimization. Int J Number Methods Eng, 2002,53(9):2201-2215.
[119] Du X, Chen W. Towards a better understanding of modeling feasibility robustness in engineering design. ASME J of Mechanical Design, 2000,122(4):385-394.
[120] Parkinson A, Sorensen C, Pourhassan N. A general approach for robust optional desing.ASME J of Mechanical Design, 1993,115(1):74-80.
[121] Sangmun Shin, Byung Rae Cho. Bias specified robust design optimization and its analytical solutions. Computers and Industrial Engineering,2005,48:129-140.
[122] Khalid AI Widyan, Jorge Angeles. A Model Based Formulation of Robust Design. J Mech Design Trans ASME, 2005, 127:388-396.
[123] Tu J, K K, and Park, Y H, A New study on reliability based design optimization, Trans of ASME, Journal of Mech Design,1999,121,557-564.
[124] Tu J,Choi K K. A New Study on Reliability Based Design Optimication. J Mech Des ASME. 1999, 121(4):557-564.
[125] Der Kiureghian, Zhang Y, Li C C. Inverse Reliabiltiy Problem[J]. ASME Journal of Engineering Mechanics. 1994, 120(5):1154-1156.
[126] Li H, Foschi R O. An Inverse Reliability method and its application. Structural Safty. 1998,20:257-270.
[127] Lee T W, Kwak B M. A Relaibiltiy Based Optimal Design Using Advanced First Order Second Moment Method. Mech Struct Mach. 1987-88, 15(4):523-542.
[128] Kirjner-Neto C, Polak E, Kiureghian A D. An outer approximations approach to reliability optimal design of structures. Journal of Optimization Theory and Applications. 1998, 98(1) :1-16.
[129] Youn B D, Choi K K, Park Y H. Hybird Analysis for Reliability Based Design Optimization . J Mech Des , ASME, 2003,125(2):221-232.
[130] Youn B D, Choi K K, An Investigatin of Nonlinearity of Reliability-Based Design Optimization Approaches. Journal of Mechanical Design. 2004, 126:403-411.
[131] Ong YS, Nair PB, Kaene AJ. Evolutionary optimization of computationally expensive problems via surrogate modeling. AIAA Journal. 2003, 41(4):687-696.
[132] Forrester AIJ, Sobester A, Keane AJ. Multi fidelity optimization via serrate modeling. Proceedings of The Royal Society A-mathematical Physical and Engineering Sciences. 2007, 4633251-3269.
[133] Zhang K S, Han Z H, Li W J, Song WP. Coupled Aerodynamic/Structural Optimization of a Subsomic Transport Wing Using a Surrogate Model. Journal of Aircraft. 2008, 45(6):2167-2171.
[134] Robinson T D, Eldred M S, Willcox K E et al. Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping. AIAAJournal. 2008, 46(11): 2814-2822.
[135] Coelho R F, Breitkopf P, Knopf Lenoir C, et al. Bi-Level model reduction for coupled problems. Structural and Multidisciplinary Optimization. 2009, 39(4):401-418.
[136] Hu T Y, Y X Q, Aerodynamic/Stealthy/Structural Multidisciplinary Design Optimization of Unmanned Combat Air Vehicle. Chinese Journal of Aeronautics. 2009, 22(4):380-386.
[137] Forrester A IJ. Bolack-box Calibration for Complex-System Simulation. Philosophical Transactions of The Royal Society A-Mathematical Physical and Engineering Sciences. 2009, 368 (192- 4 ) :3567-3579.
[138] Paiva R M, Carvalho ARD, Crawford C, Suleman A. Comparison of Surrogate Models in a Multidisciplinary Optimization Framwork for Wing Design. 2010, 48(5): 995-1006.
[139] Du X P, Chen Wei. Efficient Uncertainty Analysis Methods for Multidisciplinary Robust Design. AIAA Journal. 2002, 40(3):545-552.
[140] Mavris D N, Oliver B, Delaurentis D A. Robust Design Simulaton :a Probabilistic Approach to Multidisciplinary Design Journal of Aircraft.1999,36(1):398-407.
[141] Koch P N, Simpson T W, Allen J K, et al. Statistical Approximation for Multidisciplinary Design Optimization : the Problem of Size. Journal of Aircraft.1999,36(1):275-286.
[142] Du X P, Chen W. An Efficient Approach to Probabilistic Uncertainty Analysis in Simulation-Based Multidisciplinary Design. AIAA 2000-0423.
[143] Balling R J, Free J C, and Parkinson A R. Consideration of Worst Case Manufacturing Tolerances in Design Optimization. Trans of the ASME ,Journal of Mech Design. 1986,108,438-411.
[144] Sundaresan S, Lshii K, and Houser D R. A Robust Optimization Procedure with Variations on Design Variable and Constraints. Advances in Design Automation, 1993,69(1),379-386.
[145] Majumder L, Rao S S. Interval Based Muti Objective Optimization of Aircraft Wings Under Gust Loads. AIAA Journal,2009,47(3):563-575.
[146] Li F Y, Li G Y. Interval-Based Uncertain Multi-Objective Optimization Design of Vehicle Crashworthiness. CMC-Composites Materials & Continua. 2010,15(3):199-219.
[147] Han X,Jiang C,Gong S,Huang YH. Transient Waves in Composite-Laminated Plates with Uncertain Load and Material Property. International Journal for Numerical Methods in Engineering. 2008. 75(3):253-274.
[148] Ge R,Chen J Q,Wei JH. Reliability-Based Design of Composites Under the Mixed Uncertainties and the Optimization Algorithm. ACTA MECHANICA SOLIDA SINICA.2008,21(1):19-27.
[149] Adali S, Sadek IS, Bruch JC, Sloss JM, Cagdas IU. Optimal Sizing of Piezo-actuators for Minimum-deflection of Frames Under Uncertain Loads. Journal of the Franklin Institute-Engineering and Applied Matthematics. 2007, 344698-710.
[150] Adali S, Sadek I S, Bruch J C, Sloss J M. Optimization of Composite Plates with Piezoelectric Stiffener-actuators Under in-plane Compressive Loads. Composite Structures.2005, 71(3-4):293-301.
[151]黄波.不确定机械结构区间非概率可靠性关键技术研究[硕士论文].西安:电子科技大学.2009.
[152] Moore R E. Methods and Applications of Interval Analysis. London: Prentice-Hall Inc., 1979.
[153] Averbakh I, Lebedev V. On the Complexity of Minimax Regret Linear Programming. European Journal of Operational Research. 2005,160(1):227-231.
[154] Hansen E. Global Optimization Using Interval Analysis. New York:Mareel Dekkef,1992.
[155] Inuiguchi M. Sakawa M. Minimax Regret Solution to Linear Programming Problems with an Interval Objective Function. European Jouranl of Operational Research, 1995,86(3):526-536.
[156]张兴芳,张兴伟.区间数的排序及其在系统决策中的应用.系统工程理论与实践,1999,19(7):112-115.
[157]郭书祥,吕震宙,冯元生.基于区间分析的结构非概率可靠性模型.计算力学学报,2001,18(1):55-60.
[158] Inuiguchi M, Sakawa M. Minimax Regret Analysis in Linear Programs with an Interval Objective Function. Proceedings of IWSCI’96, 1996,208-317.
[159] Nakahara Y, Sasaki Gen M. On the Linear Programming Problems with Interval Coefficients. Int J Comput Indust Eng. 1992,23(1-4):301-4.
[160]徐泽水,达庆利.区间数排序的可能度法及其应用.系统工程学报.2003,18(1):67-70.
[2] Garrick I E, Read R D III, Historical Development of Aircraft Flutter, Journal of Aircraft, 1981,Vol.18(11):897-912.
[3]赵永辉.气动弹性力学与控制.科学出版社. 2007.
[4]伏欣H W.气动弹性力学原理.沈克杨译.上海科学技术文献出版社,1982.
[5] Theodorsen T. General Theory of Aerodynamic Instability and the Mechanism of Flutter, NACA Report NO. 496,1935.
[6] Albano E, Rodden W P. A doublet-lattice method for calculating lift distributions of oscillating surface in surbsonic flow. AIAA Journal,1969,7(20:279-285.
[7] Razani R. The Behavior of the Fully Stessed Design of Structures and its Relationship to Minimum Weight Design. AIAA Journal. 1965, 3(12):p2262-2268.
[8] Miura H. An Improved Fully Stressed Design Algorithm for Plate/Shell Structures. Structural Optimization. 1990,2:p233-237.
[9] Gary L, Giles. Simultaneous Calculation of Aircraft Design Loads and Strucutral Member Sizes. AIAA Journal. 1975, 75-965.
[10] Wilkinson K, Lerner E. Practical Design of Minimum weight Aircraft Structures for Strength and Flutter Requirements. AIAA 6th Aircraft Design Flight Test and Operations Meeting. 1974.
[11]张挂江.飞行器复合材料结构气动弹性刚度剪裁优化设计研究,[硕士学位论文].西安:西北工业大学,2006.
[12] Corso L M, Popelka D A, Nixon M W. Design, analysis and test of a composite tailored tiltrotor wing. Aemerican Helicopter Socety. 53rd Annual Forum Proceedings, Vols 1 and 2209-219 19997.
[13] Santini P, Gasbari P, Altobelli M, Rossi A. A comparative overview of strain actuated surfaces' design. Journal of Reinforced Plastics and Composites.1997, 16 (6):519-536.
[14] Chattopadhyay A, Seeley C E, Jha R. Aeroelastic tailoring using piezoelectric actuation and hybrid optimization. SPIE Conference on Smart Structures and Integrated Systems. Mar 02-05,1998.
[15] Eastep F E, Tischler V A, Venkayya V B et al. Aeroelastic tailoring of composite structures. Journal of Aricraft. 1999, 36 (6):1041-1047 .
[16] Weisshaar T A, Duke D K, Dobbins A. Active aeroelastic tailoring with adaptive continuous control surfaces. AIAA/ASME/ASCE/AHS/ASC 41st Structures, Structural Dynamics, and Materials Conference. APR 03-06, 2000.
[17] Cesnik C, Ortega M, Patil M J. Active aeroelastic tailoring of high aspect ratio composite wings. AIAA/ASME/ASCE/AHS/ASC 41st Structures, Structural Dynamics, and Materials Conference. APR 03-06, 2000.
[18] Tischler V A, Venkayya V B, Sensburg O. Aeroelastic tailoring of empennage structures. AIAA/ASME/ASCE/AHS/ASC 41st Structures, Structural Dynamics, and Materials Conference, APR 03-06, 2000.
[19] Gern F H, Librescu L. Aeroelastic tailoring of composite wings exhibiting nonclassical effects and carrying external stores. Journal of Aircraft.2000, (6):1097-1104.
[20] Librescu L, Qin Z M, Ambur D R. Implications of warping restraint on statics and dynamics of elastically tailored thin-walled composite beams. International Journal Journal of Mechanical sciences .2003.45 (8):1247-1267.
[21] Arizono H, Isogai K. Application of genetic algorithm for aeroelastic tailoring of a cranked arrow wing. Journal of aircraft. 2005,42 (2):493-499.
[22] Weisshaar T A, Duke D K. Induced drag reduction using aeroelastic tailoring with adaptive control surfaces. Journal of Aircraft.2006,43 (1):157-164.
[23] Guo S J, Cheng W Y, Cui D G. Aeroelastic tailoring of composite wing structures by laminate layup optimization. AIAA Journal .2006. 44 (12):3146-3150.
[24] Kim D H, Oh S W, Lee I, Kweon J H, et ta. Weight optimization of composite flat and curved wings satisfying both flutter and divergence constrains. Advances in Composite Materials and Structures, Pts 1 and 2 334-335477-480 2007.
[25] Manan A, Vio G A, Harmin M Y, Cooper J E. Optimization of aeroelastic composite structures using evolutionary algorithms. Engineering Optimization. 2010,42 (2):171-184.
[26] Mccormick D J. Distributed Uncertainty Analysis Techniques for Conceptual Launch Vechicle Dsign. Georgia Institute of Technology,2001.
[27] Kirby M R. A Mehodology for Technology Identification Evaluation and Selection in Conceptual and Preliminary Aircraft Design. Georgia Institute of Technology,2001.
[28] Padmanabhan D. Reliability-based Optimization for Multidisciplinary System Design. Aerospace and Mechanical Engineering Notre Mame,2003.
[29] Du X P. Efficient Methods for Engineerin Design Under Uncertainty. University ofIllinois,2002.
[30] Jin R, Chen R, Simpson T W. Comparative Studies of Metamodeling Techniques under Multiple Modeling Criteria. AIAA 2000-4801.
[31] Lin Y. An Efficient Robust Concept Exploration Method and Sequential Exploratory Experimental Design. Georgai Institute of Technology,2004.
[32] Oberkampf W L, Helton J C, Sentz K. Mathematical Representation of Uncertainty. AIAA 2001-1645.
[33] Oberkampf W L, Deland S M, Rutherford B M. Estimation of Total Uncertainty in Modeling and Simulation. Sandia National Laboratories, SAND 2000-0824.
[34] Thomas A Z, Hemsch M J, HIlberger M W, et ta. Needs and Opportunities for Uncertainty-based Multidisciplinary Design Methods for Aerospace Vehicles. NASA/TM-2002-211462.
[35] Ben-Haim Y. Roubust Reliability in the Mathmatical Science. Berlin:Springer-Verlag,1996.
[36] Ben-Haim Y , Elishakoff I. Convex Models of Uncertainty in Applied Mechanics. Amsterdam: Elsevier,1990.
[37]扎德.模糊集合、语言变量及模糊逻辑.北京:科学出版社,1982.
[38] Senthil M, Ranjan G, Dineshkumar H. Robust Aeroelastic Optimization of Composite Helicopter Rotor. International Conference on Engineering Optimization. Rio de Janeiro,Brazil,01-05 June 2008.
[39] Sharon L., Padula, Clyde R. Gumbert, Wu Li. Aerospace Application of Optimization Under Uncertainty. Optim Eng.2006,7:317-328.
[40] Enevoldsen I, Sorensen J. Relaibiltiy based optimization in structural engineering. Structural Safty, 15:169,1994.
[41] Chandu S, Grandhi R. General purpose procedure for reliability based structural optimization under parametric uncertainties. Advances in Engineering Software, 23:7-14,1995.
[42] Pettit C,Grandhi R. Multidisciplinary optimization of aerospace structures with high reliability. In 8th Joint Space Conference on Probability Mechanics and Structural Reliability, South Bend, IN. ASCE,July 2000.
[43] Pettit C L, Candield R A, Ghanem R. Stochastic analysis of an aeroelastic system. In 15th ASCE Engineering Mechanics Conference, June 2-5,2002, Columbia University, New York, 2002.
[44] Zink P, Raveh D, Mavris D. Robust structural design for active aeroelastic wing withaerodynamic uncertainties. In 41st Stucctures, Structural Dynamics, and Materials conference and Exhibit, Atlanta, GA. AIAA/ASME/ASCE/AHS/ACS, April 2000.
[45] Pettit C,Grandhi R. Preliminary weight optimization of a wing structures for gust response and aileron effectiveness reliability. International Conference on computational Engineering Sciences, August ,2000, Los Angeles, CA, 2000.
[46] Pettit C,Grandhi R. Reliability optimization of aerospace structures for gust response and aileron effectiveness. In 8th International Conference on Structural Safety and Reliability, June 2001, Newport Beach, CA,2001.
[47] Kuttenkeuler J, Ringertz U. Aeroelastic tailoring considering uncertainties in material properties. Structural Optimization, 1998, 15(3-4):157-162
[48] Zingales M, Elishakoff I. Hybrid aeroelastic optimization and antioptimization. AIAA Journal. 2001, 39(1):161-175.
[49] Moulin B, Idan M, Karpel M. Aeroservoelastic structural and control optimization using robust design schemes. Journal of Guidance Control and Dynamics, and Materials Conference. 2000, APR 0.3-06.
[50] Borglund D. Robust aeroelasticity stability analysis considering frequency domain aerodynamic uncertainty. Journal of Aircraft. 2003, 40(1):189-193.
[51] Karpel M, Moulin B, Idan M. Robust aeroservo elastic design with structural variations and modeling uncertainties. 2003,Journal of Aircraft, 2003, 946-954.
[52] Pettit C L. Uncertainty quantification in aeroelasticity: Recent and research challenges. Journal of Aircraft. 2004, 41(5):1217-1229.
[53] Buschek H, Calise A J. Uncertainty modeling and fixed order controller design for a hypersonic vehicle model. Journal of Guidance Control and Dynamics. 1997,20(1):42-48.
[54] Zeng Y M, Singh S N. Output feedback variable structure adaptive control of an aeroelastic system. Journal of Guidance Control and Dynamics. 1998, 21(6):830-837.
[55] Xing W H, Singh, S N. Adaptive output feedback control of a nonlinear aeroelastic structure. AIAA Guidance ,Navigation, and Control Conference. 1999, VOLS 1-31675-1685.
[56] Vipperman J S, Barker J M, Clark R L, et al. Comparison of mu and H-2-synthesis controllers on an experimental typical section. Journal of Guidance Control and Dynamics. 1999, 22(2):278-285.
[57] Lind R, Brenner M. Incorporating flight data into robust aeroelastic model. Journal of Aircraft. 1998, 35(3):470-477.
[58] Lind R, Brenner M. Flutterometer: An on-line tool to predict robust flutter margins[J]. Journal of Aircraft. 2000, 37(6):1105-1112.
[59] Degaki T, Suzuki S. Sliding mode control application for two dimensional active flutter suppression. Transactions of the Japan Society for Aeronautical and Space Sciences. 2001, 43 (142) : 174-181.
[60] Ghosh D, Ghanem R, Pettit C. Stochastic buckling analysis of a joined wing[R]. Advances in Stochastic Structural Dynamics. 2003, 133-140.
[61] Millman D R, King P I, Maple RC et al. Estimatino the probability of failure of a nonlinear aeroelastic system. Journal of Aircraft. 2006, 43(2):504-516.
[62] Lindsley N J, Petti C L, Beran PS. Nonlinear plate aeroelastic response with uncertain stiffness and boundary conditions. Structures and Infrastructure Engineering. 2006, 2(3-4):201-220.
[63] Attar P J, Dowell E H. Stochastic analysis of a nonlinear aeroelastic model using the response surface method. Journal of Aircraft. 2006,43(4):1044-1052.
[64] Wu Z G, Yang C. Approach for Aeroelastic Robust Stability Analysis. Chinese Journal of Aeronautics. 2008, 21(5):417-422.
[65] Borglund D. Robust Eigenvalue Analysis Using the Structured Singular Value: The mu-p method. AIAA Journal. 2008, 46(11):2806-2813.
[66] Murugan S, Harursampath D, Ganguli R. Material uncertainty propagation in helicopter nonlinear aeroelastic response and vibration analysis. AIAA Journal. 2008, 46(9):2332-2344.
[67] Yun H W, Han J L. Match point solution for robust flutter analysis in constant Mach Prediction. Chinese Journal of Aeronautics. 2008, 21(2):105-114.
[68] Castravete S C, Ibrahim R A. Effect of stiffness uncertainties on the flutter of a cantilever wing. AIAA Journal, 2008,46(4):925-935.
[69] Caracoglia L. Influence of uncertainty in selected aerodynamic and structural parameters on the buffeting response of long span bridges. Journal of Wind Engineering and Industrial Aerodynamics. 2008, 96(3):327-344.
[70] Song S F, Lu Z Z, Zhang W W et al. Reliability and Sesitivity Analysis of Transonic Flutter Using Improved Line Sampling Technique. Chinese Journal of Aeronautics. 2009, 22(5):513-519.
[71] Wang X J, Qiu Z P. Nonprobabilistic Interval Reliability Analysis of Wing Flutter. AIAA Journal. 2009, 47(3): 743-748.
[72] Anthony A. Giunta. Perspectives on Optimization Under Uncertainty: Algorithms andApplications. 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 30 August-1 September 2004,Albany, New York.
[73] Phadke M S. Quality Engineering Using Robust Design. Prentice Hall, Englewood Cliffs, NJ,1989.
[74] Chen S, Nikolaidis E, Cudney H H, Rosca R, and R T Haftka. Comparison of probabilistic and fuzzy set methods for designing under uncertainty. In Proceedings of the 40th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, 1999.
[75] Nikolaidis E, Haftka R, Rosca R. Comparison of probabilistic and possibility-based methods for design against catastrophic failure under uncertainty. Nsf report, University of Florida, Gainesville, FL, 1998.
[76] MSC. corporation, NASTRAN Encyclopedia V70.5
[77]冉玉国. NASTRAN气弹程序的二次开发[硕士论文].南京:南京航空航天大学,2006.
[78] Rodden, W P , Love J R, Equations of Motion of Quasisteady Flight Vehicle Utilizing Restrained Static Aeroelastic Characteristics, Journal of Aircraft. Vol 22(9) ,September 1995, pp802-809.
[79] Johnson E H,Venkayya V B. ASTROS Theoretical Manual, AFWAL-TR-88-3028, December 1988.
[80] Mukhopadhyay V. Historical perspective on analysis and control of aeroelastic response[J]. Journal of Guidance, Control, and Dynamics, 2003, 26 (5):673-684.
[81]任勇生等.飞行器非线性气动弹性和颤振主动控制研究进展.力学季刊,2003,24(4): 534-540.
[82] Wazak M, Srinathkumar S. Flutter suppression for the active flexible wing control system design and experimental validation. AIAA J,1992,138-145.
[83] Conner M D, Tang D M, Dowell E H et al. Nonlinear behaviors of a typical airfoil section with a control surface freeplay: a numerical and experimental study. Journal of Fluids and Structures,1997, 11:89-109.
[84]赵永辉,胡海岩.具有操纵间隙非线性二维翼段的气动弹性分析.航空学报,2003,24(6):521-525.
[85]李道春向锦武.间隙非线性气动弹性颤振控制[J].北京航空航天大学学报, 2007,33(6):640-643.
[86] Ko J, Kurdila A J, Strganac T W. Nonlinear control of a proto typical wing section withtorsional nonlinearity. Journal of Guidance, Control, and Dynamics, 1997,20(6):1181-1189.
[87] Ko J, Strganac T W, Kurdila A J. Stability and control of a structurally nonlinear Aeroelastic system. Journal of Guidance,Control,and Dynamics,1998,21(5):718-725.
[88] Behal A, Marzocca P, Rao V M, Nonlinear adaptive control of an aeroelastic two-dimensional lifting surface. Journal of Guidance, Control, and Dynamics, 2006,29(2):382-390.
[89] Xing W and Singh S N, Adaptive Output Feedback Control of a nonlinear Aeroelastic Stucture. Journal of Guidance,Control,and Dynamics, 2000,23(6):1109-1116.
[90] Kanellakopoulos I, Kokotovic P V, Morse A S. Systematic Design of Adaptive Controllers for Feedback Linearizable System. IEEE Transactions on Automatic Control,1991, 36(11):1241-1253.
[91] Zhang R and Singh S N. Adaptive output Feedback Control of an Aeroelastic System with Unstructured uncertainty.Journal of Guidance,Control,and Dynamics,2001,24(3):503-509.
[92] Ko J, Strganac T W, Junkins J L et al. Structured model reference adaptive control for a wing section with structural nonlinearity. Journal of Vibration and Control,2002,8.
[93] Strganac TW, Ko J,Thompson DE et al. Investigations of Limit Cycle Oscillations in Aeroelastic Systems[R]. CEAS/ AIAA/ICASE/NASA Langley, International Forum on Aeroelasticity, Williamsburg, Virginia, 1999.
[94] Akella MR. Structured Adaptive Control Theory and Applications to Trajectory Tracking In Aerospace Systems[D]. Department of Aerospace Engineering,Texas A&M Unibversity,1998.
[95]于明礼.基于超声电机作动器的二维翼段颤振主动抑制[博士论文].南京:南京航空航天大学,2006.
[96] Theodorsen T, General theory of aerodynamic instability and mechanism of flutter, NACA Report No. 496,1935.
[97]穆雪峰.多学科设计优化代理模型技术的研究应用[硕士论文].南京:南京航空航天大学,2006.
[98]项可风,吴启光.实验设计与数据分析.上海:上海科学技术出版社,1989:p469-475.
[99]张铁茂,丁建国.设计实验与数据处理.北京:兵器工业出版社,1990:p190-195.
[100] Hard R L. Multiquadric Equations of Topography and Other Irregular Surfaces. Journal of Geophysical Research, 1971(76):1905-1915.
[101] M J D Powell, Radial Basis Functions for Multivarible Interpolation: A Review, Oxford University press,New York,1987.
[102] Matheron G. Principles of Geostatistics. Economic Geology, 1963(58):1246-1266.
[103]王晓锋,席光.基于Kriging模型的翼型气动性能优化设计.航空学报,2005,26(5):545-549.
[104]刘克农,姚卫星,穆雪锋.基于Kriging代理模型的结构形状优化方法研究.计算力学学报,2006,23(3):344-347.
[105] Sakata S, Ashida F, ZaKo M. An efficient algorithm for Kriging approximation and optimization with large scale sampling data. Computer Methods in Applied Mechanics and Engineering, 2004, 193:385-404.
[106]谢延敏,于沪平,陈军,等.基于Kriging模型的可靠度计算.上海交通大学学报, 2007,41(2):177-180.
[107] S Haykin, Neural Networks: A Comprehensive Foundation, Prentice-Hall, NJ, 1999.
[108] W Shyy, P K Tucker, R Vaidyanathan, Response Surface and Neural Network Techniques for Rocket Engine Injector Optimization, AIAA 99-2455.
[109] Kurkova, K, 1995. Kolmogorov’s Theorem. The Handbook of Brain Theory and Neural Networks, ed. M. A.A.rbib,MIT Press,pp.501-502.
[110] Varadarajan S, Chen W, Pelka C. Robust Concept Exploration Method of Propulsion Systems with Enhanced Model Approximation Capabilities, Engineering Optimization, 32(3), 309-334,2000.
[111] C M Bishop. Pattern Recognition and Machine Learning. Springer,2006.
[112] M Sugiyama and H Ogawa. Optimal Design of Regularization Term and Regularizatoin Parameter by Subspace Information Criterion. Neural Networks, 15(3):349-361,2002.
[113] C Cornell. A probability based structural code. Journal of American Concrete institute, 66(12):974-985,1969.
[114] Hasofer A and Lind N. Exact and invariant second moment code format. Journal of Engineering Mechanics, 100:111-121,1974.
[115]秦权.结构可靠度随机有限元理论及其工程应用.清华大学出版社. 2006.
[116] Breitung K. Asymptotic approximation for multinormal integrals. Journal of Engineering Mechanics, 1984,110(30:357-366.
[117] Huang B, Du X. Analytical robustness assessment for robust design. Structural and Multidisciplinary Optimization. 34(2):123-137,2007.
[118] Jung D H, Lee B C. Development of a simple and efficient method for robust optimization. Int J Number Methods Eng, 2002,53(9):2201-2215.
[119] Du X, Chen W. Towards a better understanding of modeling feasibility robustness in engineering design. ASME J of Mechanical Design, 2000,122(4):385-394.
[120] Parkinson A, Sorensen C, Pourhassan N. A general approach for robust optional desing.ASME J of Mechanical Design, 1993,115(1):74-80.
[121] Sangmun Shin, Byung Rae Cho. Bias specified robust design optimization and its analytical solutions. Computers and Industrial Engineering,2005,48:129-140.
[122] Khalid AI Widyan, Jorge Angeles. A Model Based Formulation of Robust Design. J Mech Design Trans ASME, 2005, 127:388-396.
[123] Tu J, K K, and Park, Y H, A New study on reliability based design optimization, Trans of ASME, Journal of Mech Design,1999,121,557-564.
[124] Tu J,Choi K K. A New Study on Reliability Based Design Optimication. J Mech Des ASME. 1999, 121(4):557-564.
[125] Der Kiureghian, Zhang Y, Li C C. Inverse Reliabiltiy Problem[J]. ASME Journal of Engineering Mechanics. 1994, 120(5):1154-1156.
[126] Li H, Foschi R O. An Inverse Reliability method and its application. Structural Safty. 1998,20:257-270.
[127] Lee T W, Kwak B M. A Relaibiltiy Based Optimal Design Using Advanced First Order Second Moment Method. Mech Struct Mach. 1987-88, 15(4):523-542.
[128] Kirjner-Neto C, Polak E, Kiureghian A D. An outer approximations approach to reliability optimal design of structures. Journal of Optimization Theory and Applications. 1998, 98(1) :1-16.
[129] Youn B D, Choi K K, Park Y H. Hybird Analysis for Reliability Based Design Optimization . J Mech Des , ASME, 2003,125(2):221-232.
[130] Youn B D, Choi K K, An Investigatin of Nonlinearity of Reliability-Based Design Optimization Approaches. Journal of Mechanical Design. 2004, 126:403-411.
[131] Ong YS, Nair PB, Kaene AJ. Evolutionary optimization of computationally expensive problems via surrogate modeling. AIAA Journal. 2003, 41(4):687-696.
[132] Forrester AIJ, Sobester A, Keane AJ. Multi fidelity optimization via serrate modeling. Proceedings of The Royal Society A-mathematical Physical and Engineering Sciences. 2007, 4633251-3269.
[133] Zhang K S, Han Z H, Li W J, Song WP. Coupled Aerodynamic/Structural Optimization of a Subsomic Transport Wing Using a Surrogate Model. Journal of Aircraft. 2008, 45(6):2167-2171.
[134] Robinson T D, Eldred M S, Willcox K E et al. Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping. AIAAJournal. 2008, 46(11): 2814-2822.
[135] Coelho R F, Breitkopf P, Knopf Lenoir C, et al. Bi-Level model reduction for coupled problems. Structural and Multidisciplinary Optimization. 2009, 39(4):401-418.
[136] Hu T Y, Y X Q, Aerodynamic/Stealthy/Structural Multidisciplinary Design Optimization of Unmanned Combat Air Vehicle. Chinese Journal of Aeronautics. 2009, 22(4):380-386.
[137] Forrester A IJ. Bolack-box Calibration for Complex-System Simulation. Philosophical Transactions of The Royal Society A-Mathematical Physical and Engineering Sciences. 2009, 368 (192- 4 ) :3567-3579.
[138] Paiva R M, Carvalho ARD, Crawford C, Suleman A. Comparison of Surrogate Models in a Multidisciplinary Optimization Framwork for Wing Design. 2010, 48(5): 995-1006.
[139] Du X P, Chen Wei. Efficient Uncertainty Analysis Methods for Multidisciplinary Robust Design. AIAA Journal. 2002, 40(3):545-552.
[140] Mavris D N, Oliver B, Delaurentis D A. Robust Design Simulaton :a Probabilistic Approach to Multidisciplinary Design Journal of Aircraft.1999,36(1):398-407.
[141] Koch P N, Simpson T W, Allen J K, et al. Statistical Approximation for Multidisciplinary Design Optimization : the Problem of Size. Journal of Aircraft.1999,36(1):275-286.
[142] Du X P, Chen W. An Efficient Approach to Probabilistic Uncertainty Analysis in Simulation-Based Multidisciplinary Design. AIAA 2000-0423.
[143] Balling R J, Free J C, and Parkinson A R. Consideration of Worst Case Manufacturing Tolerances in Design Optimization. Trans of the ASME ,Journal of Mech Design. 1986,108,438-411.
[144] Sundaresan S, Lshii K, and Houser D R. A Robust Optimization Procedure with Variations on Design Variable and Constraints. Advances in Design Automation, 1993,69(1),379-386.
[145] Majumder L, Rao S S. Interval Based Muti Objective Optimization of Aircraft Wings Under Gust Loads. AIAA Journal,2009,47(3):563-575.
[146] Li F Y, Li G Y. Interval-Based Uncertain Multi-Objective Optimization Design of Vehicle Crashworthiness. CMC-Composites Materials & Continua. 2010,15(3):199-219.
[147] Han X,Jiang C,Gong S,Huang YH. Transient Waves in Composite-Laminated Plates with Uncertain Load and Material Property. International Journal for Numerical Methods in Engineering. 2008. 75(3):253-274.
[148] Ge R,Chen J Q,Wei JH. Reliability-Based Design of Composites Under the Mixed Uncertainties and the Optimization Algorithm. ACTA MECHANICA SOLIDA SINICA.2008,21(1):19-27.
[149] Adali S, Sadek IS, Bruch JC, Sloss JM, Cagdas IU. Optimal Sizing of Piezo-actuators for Minimum-deflection of Frames Under Uncertain Loads. Journal of the Franklin Institute-Engineering and Applied Matthematics. 2007, 344698-710.
[150] Adali S, Sadek I S, Bruch J C, Sloss J M. Optimization of Composite Plates with Piezoelectric Stiffener-actuators Under in-plane Compressive Loads. Composite Structures.2005, 71(3-4):293-301.
[151]黄波.不确定机械结构区间非概率可靠性关键技术研究[硕士论文].西安:电子科技大学.2009.
[152] Moore R E. Methods and Applications of Interval Analysis. London: Prentice-Hall Inc., 1979.
[153] Averbakh I, Lebedev V. On the Complexity of Minimax Regret Linear Programming. European Journal of Operational Research. 2005,160(1):227-231.
[154] Hansen E. Global Optimization Using Interval Analysis. New York:Mareel Dekkef,1992.
[155] Inuiguchi M. Sakawa M. Minimax Regret Solution to Linear Programming Problems with an Interval Objective Function. European Jouranl of Operational Research, 1995,86(3):526-536.
[156]张兴芳,张兴伟.区间数的排序及其在系统决策中的应用.系统工程理论与实践,1999,19(7):112-115.
[157]郭书祥,吕震宙,冯元生.基于区间分析的结构非概率可靠性模型.计算力学学报,2001,18(1):55-60.
[158] Inuiguchi M, Sakawa M. Minimax Regret Analysis in Linear Programs with an Interval Objective Function. Proceedings of IWSCI’96, 1996,208-317.
[159] Nakahara Y, Sasaki Gen M. On the Linear Programming Problems with Interval Coefficients. Int J Comput Indust Eng. 1992,23(1-4):301-4.
[160]徐泽水,达庆利.区间数排序的可能度法及其应用.系统工程学报.2003,18(1):67-70.