结构极值响应估计方法的有效性研究
|
摘要
基于广义极值分布和移位广义对数正态分布的加速模拟方法能够有效估计随机荷载作用下结构响应的极值分布.为了调查这两种加速模拟方法在结构极值响应尾部分布估计中的效率,详细讨论了基于响应样本的广义极值分布和移位广义对数正态分布的参数估计过程,对比分析了这两种加速模拟方法在估计随机变量极值分布的尾部、线性结构随机响应极值分布的尾部和非线性结构随机响应极值分布的尾部中的计算费用和数值精度,给出了这两种加速模拟方法的相对特点和适用范围,为结构极值响应的估计提供方法选择方面的建议.
The accelerated simulation method based on generalized extreme value distribution and shift generalized lognormal distribution was proposed to effectively estimate the extreme value distribution of structural response under random loading.In order to investigate the efficiency of the two accelerated simulation methods in the estimation of the tail of the distribution of structural extreme response,the parameter estimation process of generalized extreme value distribution and shift generalized lognormal distribution based on simulated samples was discussed in detail in this paper.A comparative analysis of these two kinds of accelerated simulation method about computational cost and accuracy in the estimate of the tail of the extreme value distribution of the random variable,the tail of the extreme value distribution of the random response of the linear structure,and the tail of the extreme distribution of the stochastic response of the nonlinear structure was made.The characteristics and applicable scope of the two accelerated simulation methods were given.In the end,the suggestion on how to choose two accelerated simulation methods was given.
The accelerated simulation method based on generalized extreme value distribution and shift generalized lognormal distribution was proposed to effectively estimate the extreme value distribution of structural response under random loading.In order to investigate the efficiency of the two accelerated simulation methods in the estimation of the tail of the distribution of structural extreme response,the parameter estimation process of generalized extreme value distribution and shift generalized lognormal distribution based on simulated samples was discussed in detail in this paper.A comparative analysis of these two kinds of accelerated simulation method about computational cost and accuracy in the estimate of the tail of the extreme value distribution of the random variable,the tail of the extreme value distribution of the random response of the linear structure,and the tail of the extreme distribution of the stochastic response of the nonlinear structure was made.The characteristics and applicable scope of the two accelerated simulation methods were given.In the end,the suggestion on how to choose two accelerated simulation methods was given.
引文
[1]赵国藩.工程结构可靠性理论与应用[M].大连:大连理工大学出版社,1996.
[2]SHINOZUKA M.Monte Carlo solution of structural dynamics[J].Computers and Structures,1972,2:855-874.
[3]NAESS A,GAIDAI O.Monte Carlo methods for estimating the extreme response of dynamical systems[J].Journal of engineering mechanics,2008,134(8):628-636.
[4]BALESDENT M,MORIO J,MARZAT J.Krigingbased adaptive importance sampling algorithm for rare event estimation[J].Structural safety,2013,44:1-10.
[5]TAFLANDIS A A,CHEUNG S H.Stochastic sampling using moving least squares response surface approximations[J].Probabilistic engineering mechanics,2012,28:216-224.
[6]GRIGORIU M,SAMORODNITSKY G.Reliability of dynamic systems in random environment by extreme value theory[J].Probabilistic engineering mechanics,2014,38:54-69.
[7]HE J,GONG J H.Estimate of small first passage probabilities of nonlinear random vibration systems by using tail approximation of extreme distributions[J].Structural safety,2016,60:28-36.
[8]MICHAELOV G,LUTES LD,SARKANI S.Extreme value of response to nonstationary excitation[J].Journal of engineering mechanics,2001,127(4):352-63.
[9]HE J.Approximate method for estimating extreme value responses of nonlinear stochastic dynamic systems[J].Journal of engineering mechanics,2015,141(7):04015009.
[2]SHINOZUKA M.Monte Carlo solution of structural dynamics[J].Computers and Structures,1972,2:855-874.
[3]NAESS A,GAIDAI O.Monte Carlo methods for estimating the extreme response of dynamical systems[J].Journal of engineering mechanics,2008,134(8):628-636.
[4]BALESDENT M,MORIO J,MARZAT J.Krigingbased adaptive importance sampling algorithm for rare event estimation[J].Structural safety,2013,44:1-10.
[5]TAFLANDIS A A,CHEUNG S H.Stochastic sampling using moving least squares response surface approximations[J].Probabilistic engineering mechanics,2012,28:216-224.
[6]GRIGORIU M,SAMORODNITSKY G.Reliability of dynamic systems in random environment by extreme value theory[J].Probabilistic engineering mechanics,2014,38:54-69.
[7]HE J,GONG J H.Estimate of small first passage probabilities of nonlinear random vibration systems by using tail approximation of extreme distributions[J].Structural safety,2016,60:28-36.
[8]MICHAELOV G,LUTES LD,SARKANI S.Extreme value of response to nonstationary excitation[J].Journal of engineering mechanics,2001,127(4):352-63.
[9]HE J.Approximate method for estimating extreme value responses of nonlinear stochastic dynamic systems[J].Journal of engineering mechanics,2015,141(7):04015009.