复杂装备精密产品Grey-PCE多质量特性稳健优化设计
|
摘要
为了解决柔顺复杂装备精密产品在不确定性结构参数情形下,其多质量特性波动与冲突的工程难题,提出一种灰色关联多项式混沌扩展(grey-polynomial chaos expansion,Grey-PCE)稳健优化设计新方法来解决这一工程难题。该方法基于多项式混沌扩展方法,建立柔顺复杂装备精密产品多质量特性代理模型;在此基础上,采用6σ稳健优化设计建模方法,构建了柔顺复杂装备精密产品多质量特性PCE稳健优化设计模型,通过NSGA-Ⅱ算法获得多质量特性解集;并采用接近度灰色关联分析法对多质量特性解集排序分析,获取了最佳稳健设计方案;最后,柔顺复杂装备精密产品算例验证了所提出方法的有效性和稳健性。
To deal with the multi-quality characteristics variation and conflict of the complex equipment products of compliant mechanism under the uncertain engineering conditions,a novel grey-polynomial chaos expansion(PCE)robust optimization design method is proposed which combines the grey relational analysis approach with the PCE robust optimization design approach.Firstly,the PCE approach is adopted to construct multi-quality characteristics surrogate models of the complex equipment products.Then,the PCE six sigma robust optimization design model of the complex equipment products is built by using six sigma robust design method.The solutions set of multi-quality characteristics is acquired from the NSGA-Ⅱalgorithm.Afterward,the grey relational analysis approach is adopt to sequential analyze the solutions set for obtaining the most satisfactory robustness design.Finally,the numerical example of the complex equipment products is provided to illustrate the effectiveness and robustness of the proposed method.
To deal with the multi-quality characteristics variation and conflict of the complex equipment products of compliant mechanism under the uncertain engineering conditions,a novel grey-polynomial chaos expansion(PCE)robust optimization design method is proposed which combines the grey relational analysis approach with the PCE robust optimization design approach.Firstly,the PCE approach is adopted to construct multi-quality characteristics surrogate models of the complex equipment products.Then,the PCE six sigma robust optimization design model of the complex equipment products is built by using six sigma robust design method.The solutions set of multi-quality characteristics is acquired from the NSGA-Ⅱalgorithm.Afterward,the grey relational analysis approach is adopt to sequential analyze the solutions set for obtaining the most satisfactory robustness design.Finally,the numerical example of the complex equipment products is provided to illustrate the effectiveness and robustness of the proposed method.
引文
[1]LI Y P,LIU S F,XU L,et al.Decision target adjustment quality function deployment network with an uncertain multi-level programming model for a complex product[J].Journal of Grey System,2015,27(3):132-150.
[2]李亚平,刘思峰,方志耕,等.多质量特性产品参数设计灰靶模型[J].中国机械工程,2016,27(8):1078-1083.LI Y P,LIU S F,FANG Z G,et al.Grey target model for parameter design of multi quality characteristic products[J].China Mechanical Engineering,2016,27(8):1078-1083.
[3]孙光永,李光耀,闫晓磊,等.多目标稳健优化设计方法在车身设计制造中的应用研究[J].固体力学学报,2011,32(2):186-196.SUN G Y,LI G Y,YAN X L,et al.Application research of multi-objective robust optimization for design and manufacture in vehicle body[J].Acta Mechanica Solida Sinica,2011,32(2):186-196.
[4]谢展,于德介,李蓉,等.汽车发动机悬置系统的多目标稳健优化设计[J].汽车工程,2013,35(10):893-897.XIE Z,YU D J,LI R,et al.Multi-objective robust optimization design of vehicle engine mount systems[J].Automotive Engineering,2013,35(10):893-897.
[5]CHEN D,FANG Z G,LIU X Q.Research on multiple-objective weighted grey target reliability optimization model of complex product[J].Journal of Grey System,2015,27(3):11-22.
[6]LI H,GU J,WANG M,et al.Multi-objective optimization of coronary stent using Kriging surrogate model[J].Biomedical Engineering Online,2016,15(2):148.
[7]FANG J,GAO Y,SUN G,et al.Multi objective robust design optimization of fatigue life for a truck cab[J].Reliability Engineering&System Safety,2015,135(135):1-8.
[8]LI F,SUN G,HUANG X,et al.Multiobjective robust optimization for crashworthiness design of foam filled thin-walled structures with random and interval uncertainties[J].Engineering Structures,2015,88(1):111-124.
[9]AKHTAR T,SHOEMAKER C A.Multi-objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection[J].Journal of Global Optimization,2016,64(1):1-16.
[10]MACKMAN T J,ALLEN C B,GHOREYSHI M,et al.Comparison of adaptive sampling methods for generation of surrogate aero-dynamic models[J].AIAA Journal,2014,51(4):797-808.
[11]ALIBRANDI U,ALANI A M,RICCIARDI G.A new sampling strategy for SVM-based response surface for structural reliability analysis[J].Probabilistic Engineering Mechanics,2015,41:1-12.
[12]GASPAR B,TEIXEIRA A P,SOARES C G.Assessment of the efficiency of Kriging surrogate models for structural reliability analysis[J].Probabilistic Engineering Mechanics,2014,37(4):24-34.
[13]KERSAUDY P,SUDRET B,VARSIER N,et al.A new surrogate modeling technique combining Kriging and polynomial chaos expansions-application to uncertainty analysis in computational dosimetry[J].Journal of Computational Physics,2015,286:103-117.
[14]FORRESTER D I A J,SOBESTER D A,KEANE A J.Engineering design via surrogate modelling:apractical guide[M].London:Antony Rowe,2008.
[15]FORRESTER A I J,KEANE A J.Recent advances in surrogate-based optimization[J].Progress in Aerospace Sciences,2009,45(1/3):50-79.
[16]WORTMAN T,COSTA A,NANNICINI G,et al.Advantages of surrogate models for architectural design optimization[J].Ai Edam Artificial Intelligence for Engineering Design Analysis&Manufacturing,2015,29(4):471-481.
[17]LI X,QIU H,CHEN Z,et al.A local Kriging approximation method using MPP for reliability-based design optimization[J].Computers&Structures,2016,162(C):102-115.
[18]欧阳林寒.模型不确定下的稳健参数设计研究[D].南京:南京理工大学,2016.OUYANG L H.Robust parameter design with model uncertainty[D].Nanjing:Nanjing University of Science and Technology,2016.
[19]韦东来.汽车覆盖件成形工艺的稳健优化与容差分析[D].上海:上海交通大学,2009.WEI D L.Robust optimization and tolerance analysis of autobody panel stamping[D].Shanghai:Shanghai Jiaotong University,2009.
[20]HOWELL L L.Compliant mechanisms[M].New York:Wiley,2001.
[21]万良琪.考虑设计参数不确定性的6σ稳健优化设计方法及工程应用[D].赣州:江西理工大学,2016.WAN L Q.The optimization and engineering application of 6σrobust based on uncertain design parameter[D].Ganzhou:Jiangxi University of Science and Technology,2016.
[22]SARMA P,XIE J.Efficient and robust uncertainty quantification in reservoir simulation with polynomial chaos expansions and non-intrusive spectral projection[C]∥Proc.of the SPE Reservoir Simulation Symposium,2011.
[23]CHEN Y,JAKEMAN J,GITTELSON C,et al.Local polynomial chaos expansion for linear differential equations with high dimensional random inputs[J].SIAM Journal on Scientific Computing,2015,37(1):79-102.
[24]FRANCIOSA P,GERBINO S,CEGLAREK D.Fixture capability optimization for early-stage design of assembly system with compliant parts using nested polynomial chaos expansion[J].Procedia CIRP,2016,41:87-92.
[25]HAMPTON J,DOOSTAN A.Compressive sampling of polynomial chaos expansions:convergence analysis and sampling strategies[J].Journal of Computational Physics,2014,280:363-386.
[26]STROUD A H.Approximate calculation of multiple integrals[M].Englewood Cliffs,NJ:Prentice-Hall,1971.
[27]WEBSTER M D,TATANG M A,MCRAE G J.Application of the probabilistic collocation method for an uncertainty analysis of a simple ocean model[J].MIT Joint Program on the Science and Policy of Global Change,1996,4:1-21.
[28]ACHARJEE S,ZABARAS N.Uncertainty propagation in finite deformations-a spectral stochastic Lagrangian approach[J].Computer Methods in Applied Mechanics&Engineering,2006,195(19/22):2289-2312.
[29]XIONG F,XUE B,YAN Z,et al.Polynomial chaos expansion based robust design optimization[J].International Conference on Quality,Reliability,Risk,Maintenance,&Safety Engineering,2011,412(8):868-873.
[30]SINGH T,SINGLA P,KONDA U.Polynomial chaos based design of robust input shapers[J].Journal of Dynamic Systems Measurement&Control,2010,132(5):626-634.
[31]徐贵阳.基于响应面法的微操作平台设计与性能综合[D].赣州:江西理工大学,2015.XU G Y.Design and performance synthesis of micro-manipulation stage based on response surface method[D].Ganzhou:Jiangxi University of Science and Technology,2015.
[2]李亚平,刘思峰,方志耕,等.多质量特性产品参数设计灰靶模型[J].中国机械工程,2016,27(8):1078-1083.LI Y P,LIU S F,FANG Z G,et al.Grey target model for parameter design of multi quality characteristic products[J].China Mechanical Engineering,2016,27(8):1078-1083.
[3]孙光永,李光耀,闫晓磊,等.多目标稳健优化设计方法在车身设计制造中的应用研究[J].固体力学学报,2011,32(2):186-196.SUN G Y,LI G Y,YAN X L,et al.Application research of multi-objective robust optimization for design and manufacture in vehicle body[J].Acta Mechanica Solida Sinica,2011,32(2):186-196.
[4]谢展,于德介,李蓉,等.汽车发动机悬置系统的多目标稳健优化设计[J].汽车工程,2013,35(10):893-897.XIE Z,YU D J,LI R,et al.Multi-objective robust optimization design of vehicle engine mount systems[J].Automotive Engineering,2013,35(10):893-897.
[5]CHEN D,FANG Z G,LIU X Q.Research on multiple-objective weighted grey target reliability optimization model of complex product[J].Journal of Grey System,2015,27(3):11-22.
[6]LI H,GU J,WANG M,et al.Multi-objective optimization of coronary stent using Kriging surrogate model[J].Biomedical Engineering Online,2016,15(2):148.
[7]FANG J,GAO Y,SUN G,et al.Multi objective robust design optimization of fatigue life for a truck cab[J].Reliability Engineering&System Safety,2015,135(135):1-8.
[8]LI F,SUN G,HUANG X,et al.Multiobjective robust optimization for crashworthiness design of foam filled thin-walled structures with random and interval uncertainties[J].Engineering Structures,2015,88(1):111-124.
[9]AKHTAR T,SHOEMAKER C A.Multi-objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection[J].Journal of Global Optimization,2016,64(1):1-16.
[10]MACKMAN T J,ALLEN C B,GHOREYSHI M,et al.Comparison of adaptive sampling methods for generation of surrogate aero-dynamic models[J].AIAA Journal,2014,51(4):797-808.
[11]ALIBRANDI U,ALANI A M,RICCIARDI G.A new sampling strategy for SVM-based response surface for structural reliability analysis[J].Probabilistic Engineering Mechanics,2015,41:1-12.
[12]GASPAR B,TEIXEIRA A P,SOARES C G.Assessment of the efficiency of Kriging surrogate models for structural reliability analysis[J].Probabilistic Engineering Mechanics,2014,37(4):24-34.
[13]KERSAUDY P,SUDRET B,VARSIER N,et al.A new surrogate modeling technique combining Kriging and polynomial chaos expansions-application to uncertainty analysis in computational dosimetry[J].Journal of Computational Physics,2015,286:103-117.
[14]FORRESTER D I A J,SOBESTER D A,KEANE A J.Engineering design via surrogate modelling:apractical guide[M].London:Antony Rowe,2008.
[15]FORRESTER A I J,KEANE A J.Recent advances in surrogate-based optimization[J].Progress in Aerospace Sciences,2009,45(1/3):50-79.
[16]WORTMAN T,COSTA A,NANNICINI G,et al.Advantages of surrogate models for architectural design optimization[J].Ai Edam Artificial Intelligence for Engineering Design Analysis&Manufacturing,2015,29(4):471-481.
[17]LI X,QIU H,CHEN Z,et al.A local Kriging approximation method using MPP for reliability-based design optimization[J].Computers&Structures,2016,162(C):102-115.
[18]欧阳林寒.模型不确定下的稳健参数设计研究[D].南京:南京理工大学,2016.OUYANG L H.Robust parameter design with model uncertainty[D].Nanjing:Nanjing University of Science and Technology,2016.
[19]韦东来.汽车覆盖件成形工艺的稳健优化与容差分析[D].上海:上海交通大学,2009.WEI D L.Robust optimization and tolerance analysis of autobody panel stamping[D].Shanghai:Shanghai Jiaotong University,2009.
[20]HOWELL L L.Compliant mechanisms[M].New York:Wiley,2001.
[21]万良琪.考虑设计参数不确定性的6σ稳健优化设计方法及工程应用[D].赣州:江西理工大学,2016.WAN L Q.The optimization and engineering application of 6σrobust based on uncertain design parameter[D].Ganzhou:Jiangxi University of Science and Technology,2016.
[22]SARMA P,XIE J.Efficient and robust uncertainty quantification in reservoir simulation with polynomial chaos expansions and non-intrusive spectral projection[C]∥Proc.of the SPE Reservoir Simulation Symposium,2011.
[23]CHEN Y,JAKEMAN J,GITTELSON C,et al.Local polynomial chaos expansion for linear differential equations with high dimensional random inputs[J].SIAM Journal on Scientific Computing,2015,37(1):79-102.
[24]FRANCIOSA P,GERBINO S,CEGLAREK D.Fixture capability optimization for early-stage design of assembly system with compliant parts using nested polynomial chaos expansion[J].Procedia CIRP,2016,41:87-92.
[25]HAMPTON J,DOOSTAN A.Compressive sampling of polynomial chaos expansions:convergence analysis and sampling strategies[J].Journal of Computational Physics,2014,280:363-386.
[26]STROUD A H.Approximate calculation of multiple integrals[M].Englewood Cliffs,NJ:Prentice-Hall,1971.
[27]WEBSTER M D,TATANG M A,MCRAE G J.Application of the probabilistic collocation method for an uncertainty analysis of a simple ocean model[J].MIT Joint Program on the Science and Policy of Global Change,1996,4:1-21.
[28]ACHARJEE S,ZABARAS N.Uncertainty propagation in finite deformations-a spectral stochastic Lagrangian approach[J].Computer Methods in Applied Mechanics&Engineering,2006,195(19/22):2289-2312.
[29]XIONG F,XUE B,YAN Z,et al.Polynomial chaos expansion based robust design optimization[J].International Conference on Quality,Reliability,Risk,Maintenance,&Safety Engineering,2011,412(8):868-873.
[30]SINGH T,SINGLA P,KONDA U.Polynomial chaos based design of robust input shapers[J].Journal of Dynamic Systems Measurement&Control,2010,132(5):626-634.
[31]徐贵阳.基于响应面法的微操作平台设计与性能综合[D].赣州:江西理工大学,2015.XU G Y.Design and performance synthesis of micro-manipulation stage based on response surface method[D].Ganzhou:Jiangxi University of Science and Technology,2015.