基于改进的动态Kriging模型的结构可靠度算法
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摘要
对于复杂航空航天机械产品,极限状态方程往往表现出隐式、高度非线性的特点,而且通常需要调用有限元分析,从而耗费大量时间。将混合粒子群-模拟退火(PSOSA)算法应用到Kriging模型中相关参数的寻优过程,提高了预测精度。同时结合动态更新机制,逐渐加入样本点,尽可能减少函数的调用次数,从而提高了计算效率,并将该算法应用到结构可靠性分析中。通过案例分析,和传统蒙特卡罗模拟方法、响应面等经典方法进行对比,所提算法与蒙特卡罗模拟方法计算结果更加接近,计算时间大大缩短,效率和精度都明显改进。
For complex aerospace machinery products,the limit state functions are often implicit and highly nonlinear,and the reliability calculation usually requires time-consuming finite element analysis.In this paper,the particle swarm optimization-simulated annealing(PSOSA) algorithm is applied to the optimization of the correlation parameters of the dynamic Kriging model,which improves the prediction accuracy.At the same time,with the dynamic update mechanism,sample points are gradually added to reduce the number of function callsas much as possible,thereby improving the calculation efficiency.The algorithm is applied to the structural reliability analysis.The Monte Carlo method,response surface and other classic algorithms are compared,and the results of the proposed algorithm are closer to those of Monte Carlo method,and the calculation time is greatly shortened,which shows that the efficiency and accuracy of the algorithm are improved significantly.
For complex aerospace machinery products,the limit state functions are often implicit and highly nonlinear,and the reliability calculation usually requires time-consuming finite element analysis.In this paper,the particle swarm optimization-simulated annealing(PSOSA) algorithm is applied to the optimization of the correlation parameters of the dynamic Kriging model,which improves the prediction accuracy.At the same time,with the dynamic update mechanism,sample points are gradually added to reduce the number of function callsas much as possible,thereby improving the calculation efficiency.The algorithm is applied to the structural reliability analysis.The Monte Carlo method,response surface and other classic algorithms are compared,and the results of the proposed algorithm are closer to those of Monte Carlo method,and the calculation time is greatly shortened,which shows that the efficiency and accuracy of the algorithm are improved significantly.
引文
[1]DITLEVSEN O,MADSEN H O.Structural reliability methods[M].Chichester:John Wiley&Sons Ltd,2007.
[2]PELLISSETTI M F,SCHU LLER G I.On general purpose software in structural reliability-An overview[J].Structural Safety,2006,28(1-2):3-16.
[3]REH S,BELEY J D,MUKHERJEE S,et al.Probabilistic finite element analysis using ANSYS[J].Steel Construction,2008,28(1):17-43.
[4]SCHU LLER G I,PRADLWARTER H J,KOUTSOURELAKISP S.A critical appraisal of reliability estimation procedures for high dimensions[J].Probabilistic Engineering Mechanics,2004,19(4):463-474.
[5]ZHAO W,QIU Z.An efficient response surface method and its application to structural reliability and reliability-based optimization[J].Finite Elements in Analysis&Design,2013,67(5):34-42.
[6]CHERKASSKY V,MA Y.Practical selection of SVM parameters and noise estimation for SVM regression[J].Neural Networks the Official Journal of the International Neural Network Society,2004,17(1):113-126.
[7]GOMES H M,AWRUCH A M.Comparison of response surface and neural network with other methods for structural reliability analysis[J].Structural Safety,2004,26(1):49-67.
[8]MATHERON G.Principles of geostatistics[J].Economic Geology,1963,58(8):1246-1266.
[9]韩忠华.Kriging模型及代理优化算法研究进展[J].航空学报,2016,37(11):3197-3225.HAN Z H.Kriging surrogate model and its application to design optimization:A review of recent progress[J].Acta Aeronautica et Astronautica Sinica,2016,37(11):3197-3225(in Chinese).
[10]ZHANG J,ZHANG L M,TANG W H.Kriging numerical models for geotechnical reliability analysis[J].Soils and Foundations,2011,51(6):1169-1177.
[11]LIU H,CUI W M,HE B,et al.The contact reliability analysis of gear rack based on the Kriging and RSM method[C]∥Proceedings of the 2015 International Conference on Applied Science and Engineering Innovation.Paris:Atlantis Press,2015:279-284.
[12]刘瞻,张建国,王灿灿,等.基于优化Kriging模型和重要抽样法的结构可靠度混合算法[J].航空学报,2013,34(6):1347-1355.LIU Z,ZHANG J G,WANG C C,et al.Hybrid structure reliability method combining optimized Kriging model and importance sampling[J].Acta Aeronautica et Astronautica Sinica,2013,34(6):1347-1355(in Chinese).
[13]陈志英,任远,白广忱,等.粒子群优化的Kriging近似模型及其在可靠性分析中的应用[J].航空动力学报,2011,26(7):1522-1530.CHEN Z Y,REN Y,BAI G C,et al.Particle swarm optimized Kriging approximate model and its application to reliability analysis[J].Journal of Aerospace Power,2011,26(7):1522-1530(in Chinese).
[14]MA J G,REN Z Y,ZHAO G X,et al.A new reliability analysis method combining adaptive Kriging with weight index Monte Carlo simulation[J].IEEE Transactions on Magnetics,2018,54(3):7001904.
[15]LI X K,QIU H B,CHEN Z Z,et al.A local Kriging approximation method using MPP for reliability-based design optimization[J].Computers&Structures,2016,162:102-115.
[16]ECHARD B,GAYTON N,LEMAIRE M.A Kriging improvement of the Monte Carlo simulation:AK-MCS method[M].Boca Raton:CRC Press-Taylor&Francis Group,2011:679-686.
[17]XIA B,REN Z Y,KOH C S.A novel reliability-based optimal design of electromagnetic devices based on adaptive dynamic Taylor Kriging[J].IEEE Transactions on Magnetics,2017,53(6):7201504.
[18]佟操,孙志礼,杨丽,等.一种基于Kriging和Monte Carlo的主动学习可靠度算法[J].航空学报,2015,36(9):2992-3001.TONG C,SUN Z L,YANG L,et al.An active learning reliability method based on Kriging and Monte Carlo[J].Acta Aeronautica et Astronautica Sinica,2015,36(9):2992-3001(in Chinese).
[2]PELLISSETTI M F,SCHU LLER G I.On general purpose software in structural reliability-An overview[J].Structural Safety,2006,28(1-2):3-16.
[3]REH S,BELEY J D,MUKHERJEE S,et al.Probabilistic finite element analysis using ANSYS[J].Steel Construction,2008,28(1):17-43.
[4]SCHU LLER G I,PRADLWARTER H J,KOUTSOURELAKISP S.A critical appraisal of reliability estimation procedures for high dimensions[J].Probabilistic Engineering Mechanics,2004,19(4):463-474.
[5]ZHAO W,QIU Z.An efficient response surface method and its application to structural reliability and reliability-based optimization[J].Finite Elements in Analysis&Design,2013,67(5):34-42.
[6]CHERKASSKY V,MA Y.Practical selection of SVM parameters and noise estimation for SVM regression[J].Neural Networks the Official Journal of the International Neural Network Society,2004,17(1):113-126.
[7]GOMES H M,AWRUCH A M.Comparison of response surface and neural network with other methods for structural reliability analysis[J].Structural Safety,2004,26(1):49-67.
[8]MATHERON G.Principles of geostatistics[J].Economic Geology,1963,58(8):1246-1266.
[9]韩忠华.Kriging模型及代理优化算法研究进展[J].航空学报,2016,37(11):3197-3225.HAN Z H.Kriging surrogate model and its application to design optimization:A review of recent progress[J].Acta Aeronautica et Astronautica Sinica,2016,37(11):3197-3225(in Chinese).
[10]ZHANG J,ZHANG L M,TANG W H.Kriging numerical models for geotechnical reliability analysis[J].Soils and Foundations,2011,51(6):1169-1177.
[11]LIU H,CUI W M,HE B,et al.The contact reliability analysis of gear rack based on the Kriging and RSM method[C]∥Proceedings of the 2015 International Conference on Applied Science and Engineering Innovation.Paris:Atlantis Press,2015:279-284.
[12]刘瞻,张建国,王灿灿,等.基于优化Kriging模型和重要抽样法的结构可靠度混合算法[J].航空学报,2013,34(6):1347-1355.LIU Z,ZHANG J G,WANG C C,et al.Hybrid structure reliability method combining optimized Kriging model and importance sampling[J].Acta Aeronautica et Astronautica Sinica,2013,34(6):1347-1355(in Chinese).
[13]陈志英,任远,白广忱,等.粒子群优化的Kriging近似模型及其在可靠性分析中的应用[J].航空动力学报,2011,26(7):1522-1530.CHEN Z Y,REN Y,BAI G C,et al.Particle swarm optimized Kriging approximate model and its application to reliability analysis[J].Journal of Aerospace Power,2011,26(7):1522-1530(in Chinese).
[14]MA J G,REN Z Y,ZHAO G X,et al.A new reliability analysis method combining adaptive Kriging with weight index Monte Carlo simulation[J].IEEE Transactions on Magnetics,2018,54(3):7001904.
[15]LI X K,QIU H B,CHEN Z Z,et al.A local Kriging approximation method using MPP for reliability-based design optimization[J].Computers&Structures,2016,162:102-115.
[16]ECHARD B,GAYTON N,LEMAIRE M.A Kriging improvement of the Monte Carlo simulation:AK-MCS method[M].Boca Raton:CRC Press-Taylor&Francis Group,2011:679-686.
[17]XIA B,REN Z Y,KOH C S.A novel reliability-based optimal design of electromagnetic devices based on adaptive dynamic Taylor Kriging[J].IEEE Transactions on Magnetics,2017,53(6):7201504.
[18]佟操,孙志礼,杨丽,等.一种基于Kriging和Monte Carlo的主动学习可靠度算法[J].航空学报,2015,36(9):2992-3001.TONG C,SUN Z L,YANG L,et al.An active learning reliability method based on Kriging and Monte Carlo[J].Acta Aeronautica et Astronautica Sinica,2015,36(9):2992-3001(in Chinese).