考虑数值噪声的热-电耦合系统分析
|
摘要
由于仿真计算中数值噪声的影响,优化的设计函数常常是不光滑或不连续的,为多学科之间的解耦和优化计算带来较大困难。为此,借鉴全局优化的相关理论,提出了考虑数值噪声的热-电耦合系统分析方法。在解耦方法上,根据"同时分析和设计"(SAND)思想,将解耦问题转化为一个优化问题,在学科层引入Kriging替代模型以便过滤数值噪声,并采用极大似然估计法确定新增样本点的位置,较大程度上减少了解耦分析所需的重分析次数,通过一个典型的热-电耦合算例验证了模型和方法的有效性。
One of the difficulties in multidisciplinary design optimization for electronic cabinets is that the design functions are often not smooth or even discontinuous due to numerical noises. In order to solve this problem,a global optimization strategy for multidisciplinary systems was developed. Firstly,the system analysis problem was transformed into an optimization problem according to the idea of SAND( simultaneous analysis and design). Kriging models were introduced as surrogate models for the output variables of each subsystem in order to filter the numerical noises. The initial Kriging models were built by using sparse sample points. The location of next samples was determined by an "infill sampling criterion"which was derived by the maximum likelihood estimation. When the simulation tools exhibit large numerical noises,this method can greatly reduce the number of subsystem simulations needed in system analysis compared with other methods,such as the fixed point iteration method. Lastly,a typical thermal-electric coupling problem was taken as an example for demonstration of the effectiveness of the proposed method.
One of the difficulties in multidisciplinary design optimization for electronic cabinets is that the design functions are often not smooth or even discontinuous due to numerical noises. In order to solve this problem,a global optimization strategy for multidisciplinary systems was developed. Firstly,the system analysis problem was transformed into an optimization problem according to the idea of SAND( simultaneous analysis and design). Kriging models were introduced as surrogate models for the output variables of each subsystem in order to filter the numerical noises. The initial Kriging models were built by using sparse sample points. The location of next samples was determined by an "infill sampling criterion"which was derived by the maximum likelihood estimation. When the simulation tools exhibit large numerical noises,this method can greatly reduce the number of subsystem simulations needed in system analysis compared with other methods,such as the fixed point iteration method. Lastly,a typical thermal-electric coupling problem was taken as an example for demonstration of the effectiveness of the proposed method.
引文
[1]RENAUD J E,GABRIELE G A.Approximation in nonhierarchic system optimization[J].AIAA Journal,1994,32(1):198-205.
[2]ARIAN E.Convergence estimates for multidisciplinary analysis and optimization:NASA/CR-201752[R].ICASE Report,1997:97-57.
[3]HAN Yongzhi,GAO Hangshan,LI Lizhou.Kriging modelbased multidisciplinary design optimization for turbine blade[J].Journal of Aerospace Power,2007,22(7):1055-1059.
[4]KOCH P N,SIMPSON T W,ALLEN J K,et al.Statistical approximations for multidisciplinary design optimization:the problem of size[J].Journal of Aircraft,1999,36(1):275-286.
[5]JANG B S,YANG Y S,JUNG H S,et al.Managing approximation models in collaborative optimization[J].Structural&Multidisciplinary Optimization,2005,30(1):11-26.
[6]BAI Xiaotao,LI Weiji.Application of collaborative optimization based on approximate methods in wing design optimization[J].Acta Aeronautica et Astronautica Sinica,2006,27(5):847-850.
[7]韩永志,高行山,李立州,等.基于Kriging模型的涡轮叶片多学科优化设计[J].航空动力学报,2007,22(7):1055-1059.HAN Yongzhi,GAO Hangshan,LI Lizhou,et al.Kriging model-based multidisciplinary design optimization for turbine blade[J].Journal of Aerospace Power,2007,22(7):1055-1059.
[8]白小涛,李为吉.基于近似技术的协同优化方法在机翼设计优化中的应用[J].航空学报,2006,27(5):847-850.BAI Xiaotao,LI Weiji.Application of collaborative optimization based on approximate methods in wing design optimization[J].Acta Aeronautica et Astronautica Sinica,2006,27(5):847-850.
[9]CRAMER E J,DENNIS J E,FRANK P D,et al.Problem formulation for multidisciplinary optimization[J].SIAM Journal on Optimization,1994,4(4):754-776.
[10]BALLING R J,SOBIESZCZANSKI-SOBIESKI J.Optimization of coupled system:A critical overview of approaches[C]//Proceeding of the 5th AIAA/NASA/USAF/ISSMO Symposium of Multidisciplinary Analysis and Optimization.Panama:AIAA,1994:697-707.
[11]PADULA S L,ALEXANDROV N M,GREEN L L.MDO test suite at NASA langley research center[C]//Proceedings of the Sixth AIAA/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization.Bellevue:AIAA1996:4-6.
[12]VUGRIN K E,BORGGAARD J,CHAIR G,et al.On the effect of numerical noise in simulation-based optimization.master of science in mathematics[J].Journal of Interprofessional Care,2003,11(3):333-335.
[13]TIMOTHY W S,FARROKH M.Kriging models for global approximation in simulation-based multidisciplinary design optimization[J].AIAA Journal,2001,39(12):54-61.
[14]王彦.基于改进EGO算法的黑箱函数全局最优化[D].北京:北京工业大学,2014.
[15]杨晓涛,谷正气,杨振东,等.汽车乘员舱多层吸声材料的多目标优化[J].振动与冲击,2013,32(4):21-25.YANG Xiaotao,GU Zhengqi,YANG Zhendong,et al.Multitarget optimization of multilayer sound absorption material combinations in passenger compartment of a car[J].Journal of Vibration and Shock,2013,32(4):21-25.
[16]郭旺柳,宋文萍,许建华,等.旋翼桨尖气动/降噪综合优化设计研究[J].西北工业大学学报,2012,30(1):73-79.GUO Wangliu,SONG Wenping,XU Jianhua,et al.An effective aerodynamics/acoustic optimization of blade tip planform for helicopter rotors[J].Journal of Northwestern Polytechnical University,2012,30(1):73-79.
[17]匡玲.基于近似模型的两级集成系统协同优化方法研究[D].武汉:华中科技大学,2012.
[18]张勇.基于近似模型的汽车轻量化优化设计方法[D].湖南:湖南大学,2008.
[19]黎凯,杨旭静,郑娟.基于参数和代理模型不确定性的冲压稳健性设计优化[J].振动与冲击,2015,26(23):234-239.LI Kai,YANG Xujing,ZHENG Juan.Robust design optimization for stamping based on parametric and metamodel uncertainty[J].Journal of Vibration and Shock,2015,26(23):234-239.
[20]高海洋.基于振动特征指标与Kriging模型的结构损伤识别方法研究[D].大连:大连理工大学,2013.
[21]张晓琳.基于二次外罚函数和Kriging模型的目标级联方法研究[D].武汉:华中科技大学,2013.
[22]左曙光,韦开君,吴旭东,等.采用Kriging模型的离心压缩机叶轮多目标参数优化[J].农业工程学报,2016,32(2):77-83.ZUO Shuguang,WEI Kaijun,WU Xudong,et al.Multiobjective parameter optimization of centrifugal compressor impeller with kriging model[J].Transactions of the Chinese Society of Agricultural Engineering,2016,32(2):77-83.
[23]高月华.基于Kriging代理模型的优化设计方法及其在注塑成型中的应用[D].大连:大连理工大学,2009.
[24]HOERL A E,KENNARD R W.Ridge regression:biased estimation for nonorthogonal problems[J].Technometrics,1970,12(1):55-67.
[25]TIKHONOV A N,ARSENIN V Y.Solutions of Ill-posed problems[J].Mathematics of Computation,1978,32(144):491.
[26]JONES D R.A taxonomy of global optimization methods based on response surfaces[J].Journal of Global Optimization,2001,21(4):345-383.
[27]FORRESTER A I J.Efficient global optimization using expensive CFD simulations[D].Southampton:University of Southampton,2004.
[28]FORRESTER A I J,KEANE A J,BRESSLOFF N W.Design and analysis of“noisy”computer experiments[J].AIAA Journal,2006,44(10):2331-2339.
[29]MICHAEL J S.Flexibility and efficiency enhancements for constrained global design optimization with Kriging approximations[D].Michigan:University of Michigan,2002.
[2]ARIAN E.Convergence estimates for multidisciplinary analysis and optimization:NASA/CR-201752[R].ICASE Report,1997:97-57.
[3]HAN Yongzhi,GAO Hangshan,LI Lizhou.Kriging modelbased multidisciplinary design optimization for turbine blade[J].Journal of Aerospace Power,2007,22(7):1055-1059.
[4]KOCH P N,SIMPSON T W,ALLEN J K,et al.Statistical approximations for multidisciplinary design optimization:the problem of size[J].Journal of Aircraft,1999,36(1):275-286.
[5]JANG B S,YANG Y S,JUNG H S,et al.Managing approximation models in collaborative optimization[J].Structural&Multidisciplinary Optimization,2005,30(1):11-26.
[6]BAI Xiaotao,LI Weiji.Application of collaborative optimization based on approximate methods in wing design optimization[J].Acta Aeronautica et Astronautica Sinica,2006,27(5):847-850.
[7]韩永志,高行山,李立州,等.基于Kriging模型的涡轮叶片多学科优化设计[J].航空动力学报,2007,22(7):1055-1059.HAN Yongzhi,GAO Hangshan,LI Lizhou,et al.Kriging model-based multidisciplinary design optimization for turbine blade[J].Journal of Aerospace Power,2007,22(7):1055-1059.
[8]白小涛,李为吉.基于近似技术的协同优化方法在机翼设计优化中的应用[J].航空学报,2006,27(5):847-850.BAI Xiaotao,LI Weiji.Application of collaborative optimization based on approximate methods in wing design optimization[J].Acta Aeronautica et Astronautica Sinica,2006,27(5):847-850.
[9]CRAMER E J,DENNIS J E,FRANK P D,et al.Problem formulation for multidisciplinary optimization[J].SIAM Journal on Optimization,1994,4(4):754-776.
[10]BALLING R J,SOBIESZCZANSKI-SOBIESKI J.Optimization of coupled system:A critical overview of approaches[C]//Proceeding of the 5th AIAA/NASA/USAF/ISSMO Symposium of Multidisciplinary Analysis and Optimization.Panama:AIAA,1994:697-707.
[11]PADULA S L,ALEXANDROV N M,GREEN L L.MDO test suite at NASA langley research center[C]//Proceedings of the Sixth AIAA/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization.Bellevue:AIAA1996:4-6.
[12]VUGRIN K E,BORGGAARD J,CHAIR G,et al.On the effect of numerical noise in simulation-based optimization.master of science in mathematics[J].Journal of Interprofessional Care,2003,11(3):333-335.
[13]TIMOTHY W S,FARROKH M.Kriging models for global approximation in simulation-based multidisciplinary design optimization[J].AIAA Journal,2001,39(12):54-61.
[14]王彦.基于改进EGO算法的黑箱函数全局最优化[D].北京:北京工业大学,2014.
[15]杨晓涛,谷正气,杨振东,等.汽车乘员舱多层吸声材料的多目标优化[J].振动与冲击,2013,32(4):21-25.YANG Xiaotao,GU Zhengqi,YANG Zhendong,et al.Multitarget optimization of multilayer sound absorption material combinations in passenger compartment of a car[J].Journal of Vibration and Shock,2013,32(4):21-25.
[16]郭旺柳,宋文萍,许建华,等.旋翼桨尖气动/降噪综合优化设计研究[J].西北工业大学学报,2012,30(1):73-79.GUO Wangliu,SONG Wenping,XU Jianhua,et al.An effective aerodynamics/acoustic optimization of blade tip planform for helicopter rotors[J].Journal of Northwestern Polytechnical University,2012,30(1):73-79.
[17]匡玲.基于近似模型的两级集成系统协同优化方法研究[D].武汉:华中科技大学,2012.
[18]张勇.基于近似模型的汽车轻量化优化设计方法[D].湖南:湖南大学,2008.
[19]黎凯,杨旭静,郑娟.基于参数和代理模型不确定性的冲压稳健性设计优化[J].振动与冲击,2015,26(23):234-239.LI Kai,YANG Xujing,ZHENG Juan.Robust design optimization for stamping based on parametric and metamodel uncertainty[J].Journal of Vibration and Shock,2015,26(23):234-239.
[20]高海洋.基于振动特征指标与Kriging模型的结构损伤识别方法研究[D].大连:大连理工大学,2013.
[21]张晓琳.基于二次外罚函数和Kriging模型的目标级联方法研究[D].武汉:华中科技大学,2013.
[22]左曙光,韦开君,吴旭东,等.采用Kriging模型的离心压缩机叶轮多目标参数优化[J].农业工程学报,2016,32(2):77-83.ZUO Shuguang,WEI Kaijun,WU Xudong,et al.Multiobjective parameter optimization of centrifugal compressor impeller with kriging model[J].Transactions of the Chinese Society of Agricultural Engineering,2016,32(2):77-83.
[23]高月华.基于Kriging代理模型的优化设计方法及其在注塑成型中的应用[D].大连:大连理工大学,2009.
[24]HOERL A E,KENNARD R W.Ridge regression:biased estimation for nonorthogonal problems[J].Technometrics,1970,12(1):55-67.
[25]TIKHONOV A N,ARSENIN V Y.Solutions of Ill-posed problems[J].Mathematics of Computation,1978,32(144):491.
[26]JONES D R.A taxonomy of global optimization methods based on response surfaces[J].Journal of Global Optimization,2001,21(4):345-383.
[27]FORRESTER A I J.Efficient global optimization using expensive CFD simulations[D].Southampton:University of Southampton,2004.
[28]FORRESTER A I J,KEANE A J,BRESSLOFF N W.Design and analysis of“noisy”computer experiments[J].AIAA Journal,2006,44(10):2331-2339.
[29]MICHAEL J S.Flexibility and efficiency enhancements for constrained global design optimization with Kriging approximations[D].Michigan:University of Michigan,2002.