结构动力可靠度计算的区域分解法和重要抽样法
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摘要
Lambros Katafygiotis提出的区域分解法和S.K.Au提出的重要抽样法,被用来计算受高斯随机过程作用的线性动力体系的失效概率。在以上两种方法的基础上,给出了非平稳随机地震作用下,单自由度线性体系动力可靠度的区域分解法和重要抽样法的计算步骤,对以上两种方法补充给出了选取失效域下标的措施;其中区域分解法将结构反应用离散脉冲响应函数表示,补充给出了极限状态函数系数的具体确定方法。通过算例对比分析了区域分解法和重要抽样法的计算效率,结果表明当计算小失效概率时,区域分解法的计算效率同重要抽样法一样高效,而对比Monte-Carlo法有显著提高,且两种方法的计算精度接近。
Domain decomposition method proposed by Lambros Katafygiotis and importance sampling method proposed by S.K.Au were used for calculating failure probability of linear dynamic structure subjected to Gauss random process.The calculation procedures of these two methods for single degree-of-freedom linear structure subjected to nonstationary earthquake were proposed.Method for selecting the indices of failure domains was suggested for both methods.Describing the response with discrete impulse response function for domain decomposition method,the specific method for determining coefficients of limit state functions was suggested.Through an example,calculation efficiency was compared between domain decomposition method and importance sampling method.The results show that these two methods have the same calculation efficiency for small failure probability,and their efficiency is much higher than Monte-Carlo method.The coefficient of variance obtained by domain decomposition method approximately equals to that obtained by importance sampling method.
Domain decomposition method proposed by Lambros Katafygiotis and importance sampling method proposed by S.K.Au were used for calculating failure probability of linear dynamic structure subjected to Gauss random process.The calculation procedures of these two methods for single degree-of-freedom linear structure subjected to nonstationary earthquake were proposed.Method for selecting the indices of failure domains was suggested for both methods.Describing the response with discrete impulse response function for domain decomposition method,the specific method for determining coefficients of limit state functions was suggested.Through an example,calculation efficiency was compared between domain decomposition method and importance sampling method.The results show that these two methods have the same calculation efficiency for small failure probability,and their efficiency is much higher than Monte-Carlo method.The coefficient of variance obtained by domain decomposition method approximately equals to that obtained by importance sampling method.
引文
[1]Ka-Veng Yuen,Lambros S.Katafygiotis.An efficient simula-tion method for reliability analysis of linear dynamical systems using simple additive rules of probability[J].Probabilistic Engineering Mechanics,2005,20,109—114.
[2]Veit Bayer,Christian Bucher.Importance sampling for first passage problems of nonlinear structures[J].Probabilistic Engineering Mechanics,1999,14:27—32.
[3]Au S K,Beck J L.First excursion probabilities for linear sys-tems by very efficient importance sampling[J].Probabilistic Engineering Mechanics,2001,16,193—207.
[4]吴斌,欧进萍,张纪刚.结构动力可靠度的重要抽样法[J].计算力学学报,2001,18(4):478—482.
[5]陆立新.结构可靠度的重要抽样法及其在耗能减震结构中的应用[D].哈尔滨:哈尔滨工业大学,2002.
[6]Lambros Katafygiotis,Sai Hung Cheung.Domain decomposi-tion method for calculating the failure probability of linear dy-namic systems subjected to Gaussian stochastic loads[J].Journal of Engineering Mechanics,2006,475—486.
[7]Lambros Katafygiotis,Sai Hung Cheung.Wedge simulation method for calculating the reliability of linear dynamical sys-tems[J].Probabilistic Engineering Mechanics,2004,19:229—238.
[8]Pradlwater HJ,Schueller G I.Assessment of lowprobability events of dynamical systems by controlled Monte Carlo simula-tion[J].Probabilistic Engineering Mechanics,1999,14:213—227.
[9]Siu-Kui Au,James L.Beck.Estimation of small failure prob-abilities in high dimensions by subset simulation[J].Proba-bilistic Engineering Mechanics,2001,16:263—277.
[10]Ching J,Beck J L,Au S K.Hybrid subset simulation method for reliability estimation of dynamic systems subjected to sto-chastic excitation[J].Probabilistic Engineering Mechanics,2005,20:199—214.
[11]Ching J,Au S K,Beck J L.Reliability estimation for dynam-ical systems subjected to stochastic excitation using subset simulation with splitting[J].Computer Methods in Applied Mechanics and Engineering,2005,194:1557—1579.
[12]薛素铎,王雪生,曹资.基于新抗震规范的地震动随机模型参数研究[J].土木工程学报,2003,36(5):5—10.
[2]Veit Bayer,Christian Bucher.Importance sampling for first passage problems of nonlinear structures[J].Probabilistic Engineering Mechanics,1999,14:27—32.
[3]Au S K,Beck J L.First excursion probabilities for linear sys-tems by very efficient importance sampling[J].Probabilistic Engineering Mechanics,2001,16,193—207.
[4]吴斌,欧进萍,张纪刚.结构动力可靠度的重要抽样法[J].计算力学学报,2001,18(4):478—482.
[5]陆立新.结构可靠度的重要抽样法及其在耗能减震结构中的应用[D].哈尔滨:哈尔滨工业大学,2002.
[6]Lambros Katafygiotis,Sai Hung Cheung.Domain decomposi-tion method for calculating the failure probability of linear dy-namic systems subjected to Gaussian stochastic loads[J].Journal of Engineering Mechanics,2006,475—486.
[7]Lambros Katafygiotis,Sai Hung Cheung.Wedge simulation method for calculating the reliability of linear dynamical sys-tems[J].Probabilistic Engineering Mechanics,2004,19:229—238.
[8]Pradlwater HJ,Schueller G I.Assessment of lowprobability events of dynamical systems by controlled Monte Carlo simula-tion[J].Probabilistic Engineering Mechanics,1999,14:213—227.
[9]Siu-Kui Au,James L.Beck.Estimation of small failure prob-abilities in high dimensions by subset simulation[J].Proba-bilistic Engineering Mechanics,2001,16:263—277.
[10]Ching J,Beck J L,Au S K.Hybrid subset simulation method for reliability estimation of dynamic systems subjected to sto-chastic excitation[J].Probabilistic Engineering Mechanics,2005,20:199—214.
[11]Ching J,Au S K,Beck J L.Reliability estimation for dynam-ical systems subjected to stochastic excitation using subset simulation with splitting[J].Computer Methods in Applied Mechanics and Engineering,2005,194:1557—1579.
[12]薛素铎,王雪生,曹资.基于新抗震规范的地震动随机模型参数研究[J].土木工程学报,2003,36(5):5—10.
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