基于序列代理模型的结构可靠性分析方法
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摘要
工程中部件或系统的性能函数通常是隐函数形式,该文提出基于高效代理模型的结构可靠性分析方法,构造新增样本点学习函数,并用于指导在序列迭代过程中的样本点选择。所提出的学习函数考虑了变量权重并保证所选的样本点相互之间有一定的距离且分布在极限状态方程周围。算例分析表明该方法有较好的精度和鲁棒性,不仅适用于性能函数为隐函数时的结构可靠性分析,而且也适用于现有的各种代理模型(神经网络、支持向量机、响应面等),为结构可靠性分析提供新途径与新方法。
Performance functions of components and structural systems are often given using implicit functions for many practical engineering. An efficient surrogate-models-based reliability analysis method is proposed in this paper, a new sample selection learning function is constructed as a guideline to adaptively select new sample point at each iteration. The proposed learning function considers the weights of variables and ensures that the selected sample points reside not only around the limit-state functions, but also far away each other. The numerical examples show that the proposed method is accuracy and robustness, thus it can be used for structural systems with implicit performance function and various existing surrogate models(e.g., neural networks, support vector machine, response surface model). The proposed method provides a novel method for structural reliability analysis.
Performance functions of components and structural systems are often given using implicit functions for many practical engineering. An efficient surrogate-models-based reliability analysis method is proposed in this paper, a new sample selection learning function is constructed as a guideline to adaptively select new sample point at each iteration. The proposed learning function considers the weights of variables and ensures that the selected sample points reside not only around the limit-state functions, but also far away each other. The numerical examples show that the proposed method is accuracy and robustness, thus it can be used for structural systems with implicit performance function and various existing surrogate models(e.g., neural networks, support vector machine, response surface model). The proposed method provides a novel method for structural reliability analysis.
引文
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[13]PAPADOPOULOS V,GIOVANIS D G,LAGAROS N D,et al.Accelerated subset simulation with neural networks for reliability analysis[J].Computer Methods in Applied Mechanics and Engineering,2012,223-224:70-80.
[14]ECHARD B,GAYTON N,LEMAIRE M.AK-MCS:an active learning reliability method combining Kriging and Monte Carlo simulation[J].Structural Safety,2011(33):145-154.
[15]HU Z,MAHADEVAN S.Global sensitivity analysisenhanced surrogate(GSAS)modeling for reliability analysis[J].Structural and Multidisciplinary Optimization,2016,53(3):501-521.
[16]ZHU Z F,DU X.Reliability analysis with Monte Carlo simulation and dependent Kriging predictions[J].ASMEJournal of Mechanical Design,2016,138:1214031-12140311.
[17]苏永华,罗正东,张盼凤,等.基于Kriging的边坡稳定可靠度主动搜索法[J].岩土工程学报,2013,35(10):1863-1869.SU Yong-hua,LUO Zheng-dong,ZHANG Pan-feng,et al.Active searching algorithm for slope stability reliability based on kriging model[J].Chinese Journal of Geotechnical Engineering,2013,35(10):1863-1869.
[18]GASPAR B,TEIXEIRA A P,GUEDES SOARES C.Assessment of the efficiency of kriging surrogate models for structural reliability analysis[J].Probabilistic Engineering Mechanics,2014,37:24-34.
[19]DUBOURG V,SUDRET B.Meta-model-based importance sampling for reliability sensitivity analysis[J].Structural Safety,2014(49):27-36.
[20]JIN R C,SUDJIANTO A,CHEN W.On sequential sampling for global metamodeling in engineering design[C]//Proceedings of DETC 2002.Canada:[s.n.],2002.
[21]DUAN L,XIAO N C,HU Z,et al.An efficient lightweight design strategy for body-in-white based on implicit parameterization technique[J].Structural and Multidisciplinary Optimization,2017,55(5):1927-1943.
[22]CANNAVO F.Sensitivity analysis for volcanic source modeling quality assessment and model selection[J].Computers and Geosciences,2012,44:52-59.
[23]XIAO N C,ZUO M J,ZHOU C.A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis[J].Reliability Engineering and System Safety,2018,169:330-338.
[2]LOW B K.FORM,SORM,and spatial modeling in geotechnical engineering[J].Structural Safety,2014(49):56-64.
[3]MELCHERS R E.Structural reliability analysis and prediction[M].2nd ed.New York:Wiley,1999.
[4]KAYMAZ I.Application of kriging method to structural reliability problems[J].Structural Safety,2005(27):133-151.
[5]EASON J,CREMASCHI S.Adaptive sequential sampling for surrogate model generation with artificial neural networks[J].Computers and Chemical Engineering,2014,68:220-232.
[6]GOSWAMI S,GHOSH S,CHAKRABORTY S.Reliability analysis of structures by iterative improved response surface method[J].Structural Safety,2016(60):56-66.
[7]BUCHER C G,BOURGUND U.A fast and efficient response surface approach for structural reliability problems[J].Structural Safety,1990,7(1):57-66.
[8]KAYMAZ I,MCMAHON C A.A response surface method based on weighted regression for structural reliability analysis[J].Probabilistic Engineering Mechanics,2005,20:11-17.
[9]NGUYEN X S,SELLIER A,DUPRAT F,et al.Adaptive response surface method based on a double weighted regression technique[J].Probabilistic Engineering Mechanics,2009,24:135-143.
[10]GOSWAMI S,GHOSH S,CHAKRABORTY S.Reliability analysis of structures by iterative improved response surface method[J].Structural Safety,2016(60):56-66.
[11]SUNDAR V S,SHIELDS M D.Surrogate-enhanced stochastic search algorithms to identify implicitly defined functions for reliability analysis[J].Structural Safety,2016(62):1-11.
[12]BOURINET J M.Rare-event probability estimation with adaptive support vector regression surrogates[J].Reliability Engineering and System Safety,2016,150:210-221.
[13]PAPADOPOULOS V,GIOVANIS D G,LAGAROS N D,et al.Accelerated subset simulation with neural networks for reliability analysis[J].Computer Methods in Applied Mechanics and Engineering,2012,223-224:70-80.
[14]ECHARD B,GAYTON N,LEMAIRE M.AK-MCS:an active learning reliability method combining Kriging and Monte Carlo simulation[J].Structural Safety,2011(33):145-154.
[15]HU Z,MAHADEVAN S.Global sensitivity analysisenhanced surrogate(GSAS)modeling for reliability analysis[J].Structural and Multidisciplinary Optimization,2016,53(3):501-521.
[16]ZHU Z F,DU X.Reliability analysis with Monte Carlo simulation and dependent Kriging predictions[J].ASMEJournal of Mechanical Design,2016,138:1214031-12140311.
[17]苏永华,罗正东,张盼凤,等.基于Kriging的边坡稳定可靠度主动搜索法[J].岩土工程学报,2013,35(10):1863-1869.SU Yong-hua,LUO Zheng-dong,ZHANG Pan-feng,et al.Active searching algorithm for slope stability reliability based on kriging model[J].Chinese Journal of Geotechnical Engineering,2013,35(10):1863-1869.
[18]GASPAR B,TEIXEIRA A P,GUEDES SOARES C.Assessment of the efficiency of kriging surrogate models for structural reliability analysis[J].Probabilistic Engineering Mechanics,2014,37:24-34.
[19]DUBOURG V,SUDRET B.Meta-model-based importance sampling for reliability sensitivity analysis[J].Structural Safety,2014(49):27-36.
[20]JIN R C,SUDJIANTO A,CHEN W.On sequential sampling for global metamodeling in engineering design[C]//Proceedings of DETC 2002.Canada:[s.n.],2002.
[21]DUAN L,XIAO N C,HU Z,et al.An efficient lightweight design strategy for body-in-white based on implicit parameterization technique[J].Structural and Multidisciplinary Optimization,2017,55(5):1927-1943.
[22]CANNAVO F.Sensitivity analysis for volcanic source modeling quality assessment and model selection[J].Computers and Geosciences,2012,44:52-59.
[23]XIAO N C,ZUO M J,ZHOU C.A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis[J].Reliability Engineering and System Safety,2018,169:330-338.