基于多重子域代理模型的结构可靠性分析
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摘要
基于合理子域概念,构建多重代理模型。多重代理模型在合理子域内采用经典响应面模型,在合理子域外采用经典Kriging模型,能够充分利用两种经典模型各自的优势。多重代理模型能够合理规避经典响应面模型中响应函数采取事先假定形式带来的可靠度评估风险,同时能够有效避免经典Kriging模型中试验点组合爆炸的问题。相比经典响应面模型,多重代理模型所需试验点数量并未增加,计算效率与经典响应面模型大体相同。算例表明,本文方法的计算结果与MCS的计算结果几乎一致,具有较好的计算精度。
A multiple surrogate model is constructed based on the concept of reasonable sub-region in this study.The classical response surface model is used inside of the reasonable sub-region,and the classical Kriging model is used outside of the reasonable sub-region.The multiple-surrogate model can make full use of the advantages of both classical models,reasonably avoid the reliability evaluation risk brought by the assumed response function in the classical response surface model,and effectively avoid the problem of combination explosion of experiment points in the classical Kriging model.Compared with the classical response surface model,the number of experiment points constructed the multiple-Kriging model surrogate model does not increase,and thus the computational efficiency is roughly the same as that of the classical response surface model.The numerical results indicated that the proposed method has the similar accuracy as Monte Carlo simulation,and thus is satisfactory.
A multiple surrogate model is constructed based on the concept of reasonable sub-region in this study.The classical response surface model is used inside of the reasonable sub-region,and the classical Kriging model is used outside of the reasonable sub-region.The multiple-surrogate model can make full use of the advantages of both classical models,reasonably avoid the reliability evaluation risk brought by the assumed response function in the classical response surface model,and effectively avoid the problem of combination explosion of experiment points in the classical Kriging model.Compared with the classical response surface model,the number of experiment points constructed the multiple-Kriging model surrogate model does not increase,and thus the computational efficiency is roughly the same as that of the classical response surface model.The numerical results indicated that the proposed method has the similar accuracy as Monte Carlo simulation,and thus is satisfactory.
引文
[1] Kang S C,Koh H M,Choo J F.An efficient response surface method using moving least squares approximation for structural reliability analysis[J].Probabilistic Engineering Mechanics,2010,25(4):365-371.
[2] Gavin H P,Yau S C.High-order limit state functions in the response surface method for structural reliabi-lity analysis[J].Structural Safety,2008,30(2):162-179.
[3] 刘成立,吕震宙.结构可靠性分析中考虑高次项修正的组合响应面法[J].航空学报,2006,27(4):594-599.(LIU Cheng-li ,Lü Zhen-zhou.Response surface combination improved by high order term for structural reliability analysis[J].Acta Aeronautica et Astronautica Sinica,2006,27(4):594-599.(in Chinese))
[4] 洪飞,吴剑国.可靠性分析的改进加权响应面法[J].浙江工业大学学报,2012,40(1):106-110.(HONG Fei,WU Jian-guo.An improved response surface method based on weighted regression for reliability analysis[J].Journal of Zhejiang Univer-sity of Technology,2012,40(1):106-110.(in Chinese))
[5] 张崎,李兴斯.基于Kriging模型的结构可靠性分析[J].计算力学学报,2006,23(2):175-179.(ZHANG Qi,LI Xing-si.Analysis of structural reliability based on Kriging model[J].Chinese Journal of Computational Mechanics,2006,23(2):175-179.(in Chinese))
[6] 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 Zhong-hua.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))
[7] 赵维涛,邱志平.基于合理子域的改进响应面方法[J].力学学报,2014,46(3):409-416.(ZHAO Wei-tao,QIU Zhi-ping.An improved response surface method based on the reasonable subdomain[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(3):409-416.(in Chinese))
[8] Zhao W T,Shi X Y,Tang K.A response surface method based on sub-region of interest for structural reliability analysis[J].Structural Engineering and Mechanics,2016,57(4):587-602.
[9] Bucher C G,Bourgund U.A fast and efficient response surface approach for structural reliability problems[J].Structural Safety,1990,7(1):57-66.
[10] Guan X L,Melchers R E.Effect of response surface parameter variation on structural reliability estimates[J].Structural Safety,2001,23(4):429-444.
[11] 李洪双,吕震宙.结构可靠性分析的支持向量机响应面法[J].计算力学学报,2009,26(2):199-203.(LI Hong-shuang,Lü Zhen-zhou.A support vector machine response surface method for structural reliability analysis[J].Chinese Journal of Computational Mechanics,2009,26(2):199-203.(in Chinese))
[12] 程晔,周翠英,黄林冲,等.基于缩减样本窗口的响应面重构方法[J].计算力学学报,2011,28(5):699-704.(CHENG Ye,ZHOU Cui-ying,HUANG Lin-chong,et al.Sequential response surface reconstructing method based on reducing sampling windows[J].Chinese Journal of Computational Mechanics,2011,28(5):699-704.(in Chinese))
[13] Hadidi A,Azar B F,Rafiee A.Efficient response surface method for high-dimensional structural reliability analysis[J].Structural Safety,2017,68:15-27.
[14] Roussouly N,Petitjean F,Salaun M.A new adaptive response surface method for reliability analysis[J].Probabilistic Engineering Mechanics,2013,32:103-115.
[2] Gavin H P,Yau S C.High-order limit state functions in the response surface method for structural reliabi-lity analysis[J].Structural Safety,2008,30(2):162-179.
[3] 刘成立,吕震宙.结构可靠性分析中考虑高次项修正的组合响应面法[J].航空学报,2006,27(4):594-599.(LIU Cheng-li ,Lü Zhen-zhou.Response surface combination improved by high order term for structural reliability analysis[J].Acta Aeronautica et Astronautica Sinica,2006,27(4):594-599.(in Chinese))
[4] 洪飞,吴剑国.可靠性分析的改进加权响应面法[J].浙江工业大学学报,2012,40(1):106-110.(HONG Fei,WU Jian-guo.An improved response surface method based on weighted regression for reliability analysis[J].Journal of Zhejiang Univer-sity of Technology,2012,40(1):106-110.(in Chinese))
[5] 张崎,李兴斯.基于Kriging模型的结构可靠性分析[J].计算力学学报,2006,23(2):175-179.(ZHANG Qi,LI Xing-si.Analysis of structural reliability based on Kriging model[J].Chinese Journal of Computational Mechanics,2006,23(2):175-179.(in Chinese))
[6] 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 Zhong-hua.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))
[7] 赵维涛,邱志平.基于合理子域的改进响应面方法[J].力学学报,2014,46(3):409-416.(ZHAO Wei-tao,QIU Zhi-ping.An improved response surface method based on the reasonable subdomain[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(3):409-416.(in Chinese))
[8] Zhao W T,Shi X Y,Tang K.A response surface method based on sub-region of interest for structural reliability analysis[J].Structural Engineering and Mechanics,2016,57(4):587-602.
[9] Bucher C G,Bourgund U.A fast and efficient response surface approach for structural reliability problems[J].Structural Safety,1990,7(1):57-66.
[10] Guan X L,Melchers R E.Effect of response surface parameter variation on structural reliability estimates[J].Structural Safety,2001,23(4):429-444.
[11] 李洪双,吕震宙.结构可靠性分析的支持向量机响应面法[J].计算力学学报,2009,26(2):199-203.(LI Hong-shuang,Lü Zhen-zhou.A support vector machine response surface method for structural reliability analysis[J].Chinese Journal of Computational Mechanics,2009,26(2):199-203.(in Chinese))
[12] 程晔,周翠英,黄林冲,等.基于缩减样本窗口的响应面重构方法[J].计算力学学报,2011,28(5):699-704.(CHENG Ye,ZHOU Cui-ying,HUANG Lin-chong,et al.Sequential response surface reconstructing method based on reducing sampling windows[J].Chinese Journal of Computational Mechanics,2011,28(5):699-704.(in Chinese))
[13] Hadidi A,Azar B F,Rafiee A.Efficient response surface method for high-dimensional structural reliability analysis[J].Structural Safety,2017,68:15-27.
[14] Roussouly N,Petitjean F,Salaun M.A new adaptive response surface method for reliability analysis[J].Probabilistic Engineering Mechanics,2013,32:103-115.