基于灵敏度分析的区间不确定性稳健设计
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摘要
针对机电产品优化设计中存在的大量不确定性因素,在灵敏度分析的基础上提出了区间不确定性稳健设计方法。首先探讨了灵敏度分析理论,借用Sobol'法筛选出对系统影响较大的因素并将不灵敏项进行固化;然后根据区间不确定性因素的特性,分析了不确定因素在某一区间变化时对系统整体的影响;最后给出了基于灵敏度分析的区间不确定性稳健设计优化模型。工程实例证明了该方法的有效性。
In order to solve the uncertain factors in the design optimization of mechanical and electrical products, a robust design method for interval uncertainty was proposed based on sensitivity analysis. Firstly, discussed the Sobol' method of the sensitivity analysis theory, the factors which had great influences on the system were selected. Secondly, by using the characteristics of interval uncertainty factors and the effects of uncertain factors on the whole system were analyzed in a certain interval. Finally, a robust design optimization model for interval uncertainty was given based on sensitivity analysis. The effectiveness of the proposed method was proved by an engineering examples.
In order to solve the uncertain factors in the design optimization of mechanical and electrical products, a robust design method for interval uncertainty was proposed based on sensitivity analysis. Firstly, discussed the Sobol' method of the sensitivity analysis theory, the factors which had great influences on the system were selected. Secondly, by using the characteristics of interval uncertainty factors and the effects of uncertain factors on the whole system were analyzed in a certain interval. Finally, a robust design optimization model for interval uncertainty was given based on sensitivity analysis. The effectiveness of the proposed method was proved by an engineering examples.
引文
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[23] BASTIN F.Nonlinear Stochastic Programming[D].Namur:University of Namur,2004.
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[25] 赵子衡.区间不确定性优化的若干高效算法研究及应用[D].长沙:湖南大学,2012.ZHAO Ziheng.Research and Application of Some Efficient Algorithms for Interval Uncertainty Optimization [D].Changsha:Hunan University,2012.
[26] 邱志平.不确定参数结构静力响应和特征值问题的区间分析方法[D].长春:吉林工业大学,吉林大学,1994.QIU Zhiping.Interval Analysis Method for Static Response and Eigenvalue Problems of Uncertain Parameter Structures [D].Changchun:Jilin Industrial University,Jilin University,1994.
[27] 姜潮.基于区间的不确定性优化理论与算法[D].长沙:湖南大学,2008.JIANG Chao.Interval Based Uncertainty Optimization Theory and Algorithm [D].Changsha:Hunan University,2008.
[28] 张鑫.基于可靠性的汽车转向机构稳健优化设[D].南昌:华东交通大学,2012.ZHANG Xin.Robust Optimization of Vehicle Steering Mechanism Based on Reliability [D].Nanchang:East China Jiaotong University,2012.
[2] GU X,RENAUD J E,PENNINGER C L.Implicit Uncertainty Propagation for Robust Collaborative Optimization[J].ASME J.Mech.Des.,2006,128(4):1001-1013.
[3] DU X,CHEN W.Efficient Uncertainty Analysis Methods for Multidisciplinary Robust Design[J].AIAA Journal,2002,40(3):545-552.
[4] DU X,CHEN W.Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design[J].ASME J.Mech.Des.,2004,126(2):225-233.
[5] DU X,CHEN W.Collaborative Reliability Analysis Under the Framework of Multidisciplinary Systems Design[J].Optim.Eng.,2005,6(1):63-84.
[6] LIU H,CHEN W,KOKKOLARAS M,et al.Probabilistic Analytical Target Cascading:a Moment Matching Formulation for Multilevel Optimization under Uncertainty[J].ASME J.Mech.Des.,2006,128(4):991-1000.
[7] DU X,CHEN W.Efficient Uncertainty Analysis Methods for Multidisciplinary Robust Design[J].AIAA Journal,2002,40(3):545-552.
[8] DU X,CHEN W.Collaborative Reliability Analysis under the Framework of Multidisciplinary Systems Design[J].Optim.Eng.,2005,6(1):63-84.
[9] SUES R H,CESARE M A,PAGEAU S S,et al.Reliability-based Optimization Considering Manufacturing and Operational Uncertainties[J].J.Aerosp.Eng.,2001,14(4):166-174.
[10] WU W D,RAO S S.Uncertainty Analysis and Allocation of Joint Tolerances in Robot Manipulators Based on Interval Analysis[J].Reliab.Eng.Syst.Saf.,2007,92(1):54-64.
[11] FERSON S,GINZBURG L R.Different Methods are Needed to Propagate Ignorance and Variability[J].Reliab.Eng.Syst.Saf.,1996,54(2/3):133-144.
[12] LI M,AZARM S.Multi-objective Collaborative Robust Optimization with Interval Uncertainty and Interdisciplinary Uncertainty Propagation[J].ASME J.Mech.Aug.,2008,130(8):1402.1-1402.11.
[13] LI M.Robust Optimization and Sensitivity Analysis with Multi-objective Genetic Algorithms:Single-and Multidisciplinary Applications[D].Maryland:University of Maryland,2007.
[14] CANNAVó F.Sensitivity Analysis for Volcanic Source Modeling Quality Assessment and Model Selection[J].Computers & Geosciences,2012,44(13):52-59.
[15] 阮文斌,吕震宙,安军,等.不确定条件下复合材料结构的全局灵敏度分析[J].复合材料学报,2014,31(3):699-706.RUAN Wenbin,LYU Zhenzhou,AN Jun,et al.Global Sensitivity Analysis of Composite Structure under Uncertain Conditions [J].Composite Journal,2014,31 (3):699-706.
[16] 张义民,刘巧伶,闻邦椿.单自由度非线性随机参数振动系统的可靠性灵敏度分析[J].固体力学学报,2003,24(1):61-67.ZHANG Yimin,LIU Qiaoling,WEN Bangchun.The Reliability Sensitivity of Single Degree of Freedom Nonlinear Vibration Systems with Random Parameters [J].Journal of Solid Mechanics Analysis,2003,24 (1):61-67.
[17] CANNAVó F.Sensitivity Analysis for Volcanic Source Modeling Quality Assessment and Model Selection[J].Computers & Geosciences,2012,44(13):52-59.
[18] HAMEL J,LI M,AZARM S.Design Improvement by Sensitivity Analysis under Interval Uncertainty Using Multi-Objective Optimization[J].Journal of Mechanical Design,2010,132(8):841-852.
[19] 邱志平,王晓军.结构灵敏度分析的区间方法[J].兵工学报,2005,26(6):798-802.QIU Zhiping,WANG Xiaojun.Method of Interval Structure Sensitivity Analysis [J].Acta Armamentarii,2005,26 (6):798-802.
[20] HALL J W,BOYCE S A,WANG Y,et al.Sensitivity Analysis for Hydraulic Models[J].Journal of Hydraulic Engineering-ASCE,2009,135(11):959-969.
[21] TIAN W.A Review of Sensitivity Analysis Methods in Building Energy Analysis[J].Renewable and Sustainable Energy Reviews,2013,20:411-419.
[22] CAMPOLONGO F,TARANTOLA S,SALTELLI A.Tackling Quantitatively Large Dimensionality Problems [J].Computer Physics Communications,1999,117(1):75-85.
[23] BASTIN F.Nonlinear Stochastic Programming[D].Namur:University of Namur,2004.
[24] INUIGUCHI M,RAMIíK J.Possibilistic Linear Programming:a Brief Review of Fuzzy Mathematical Programming and a Comparison with Stochastic Programming in Portfolio Selection Problem [J].Fuzzy Sets & Systems,2000,111(1):3-28.
[25] 赵子衡.区间不确定性优化的若干高效算法研究及应用[D].长沙:湖南大学,2012.ZHAO Ziheng.Research and Application of Some Efficient Algorithms for Interval Uncertainty Optimization [D].Changsha:Hunan University,2012.
[26] 邱志平.不确定参数结构静力响应和特征值问题的区间分析方法[D].长春:吉林工业大学,吉林大学,1994.QIU Zhiping.Interval Analysis Method for Static Response and Eigenvalue Problems of Uncertain Parameter Structures [D].Changchun:Jilin Industrial University,Jilin University,1994.
[27] 姜潮.基于区间的不确定性优化理论与算法[D].长沙:湖南大学,2008.JIANG Chao.Interval Based Uncertainty Optimization Theory and Algorithm [D].Changsha:Hunan University,2008.
[28] 张鑫.基于可靠性的汽车转向机构稳健优化设[D].南昌:华东交通大学,2012.ZHANG Xin.Robust Optimization of Vehicle Steering Mechanism Based on Reliability [D].Nanchang:East China Jiaotong University,2012.
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