最大熵法可靠度理论在工程应用中的改进
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摘要
地震作用下,工程结构响应的随机性无法用确定性方法反映,将最大熵法引入可靠度理论,能在少量的已知条件下求得事件的最小有偏概率分布函数。本文基于最大熵法可靠度理论,提出了既能解决收敛问题,又能保证函数精度的控制方法。分析了样本数量对概率密度函数、超越概率、可靠指标精度的影响,给出了保证工程应用精度的建议样本个数。
Under the action of earthquake,the definiteness method can't reflect the variability of structural response. Introducing the maximum entropy into reliability theory,the probability distribution junction is obtained with the minimum deviation under a small amount of known conditions.Then,based on the maximum entropy reliability theory,a control method which can guarantee the convergence and precision was put forward in this paper.To a deep extent,the influences of the sample number on probability density function,exceeding probability,reliable index are analyzed.In addition,the suggestion of sample number is proposed to ensure the accuracy of engineering application.
Under the action of earthquake,the definiteness method can't reflect the variability of structural response. Introducing the maximum entropy into reliability theory,the probability distribution junction is obtained with the minimum deviation under a small amount of known conditions.Then,based on the maximum entropy reliability theory,a control method which can guarantee the convergence and precision was put forward in this paper.To a deep extent,the influences of the sample number on probability density function,exceeding probability,reliable index are analyzed.In addition,the suggestion of sample number is proposed to ensure the accuracy of engineering application.
引文
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[11]Shohat J,Tamarkin J.The problem of moments[M].New York: American Mathematical society,1963.11 - 56
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[17]董聪,刘西拉.非线性结构系统可靠度理论及其模拟方法[J].土木工程学报,1998,31(1):33-43
[18]佟晓利,赵国藩.一种和结构可靠度分析几何法相结合的响应面方法[J].土木工程学报,1997,30(4):51-57
[2]E T Jaynes.Information theory and statistical Mechanics[J].Physical Reviews,1957,Vol.106(4):620 - 630
[3]Golan A,Judge G and Miller D.Maximum Entropy Econometrics:Robust Estimation With Limited Data[M].John Wiley＆Sors,1996.11 -23
[4]孟庆生.信息论[M].西安:西安交通大学出版社,1989.19-33
[5]韦征,叶继红,沈世钊.最大熵法可靠度理论在工程中的应用[J].振动与冲击,2007,26(6):146-148,151
[6]韦征.单层球壳在地震作用下基于最大熵法的破坏模式预测[D].南京:东南大学,2007.12-16
[7]郭海山,沈世钊.单层网壳结构动力稳定性分析方法[J].建筑结构学报,2003,Vol.24(3):1-9
[8]沈世钊,支旭东.球面网壳结构在强震下的失效机理[J].土木工程学报,2005,Vol.38(1):11-20
[9]苑宏宇,叶继红,沈世钊,单建.单层球面网壳在简单动荷载作用下的失效研究[J].工程抗震与加固改造,2006,Vol.28(4):10 -17
[10]Paul Penfield,Jr.Information and Entropy[M].Massachusetts Institute of Technology,2003.80 - 84
[11]Shohat J,Tamarkin J.The problem of moments[M].New York: American Mathematical society,1963.11 - 56
[12]Kapur JN,Kesavan HK.Entropy optimization principles with applications [M].London:Academic Press,1992.127 - 138
[13]Sobczyk K,Trebicki J.Maximum entropy principle in stochastic dynamics [J].Probab Engng Mech,1990,Vol.5(3):102 - 110
[14]Silvin G.Information theory with application[M].New York: MCGrawHill,1977.293 - 301
[15]张学文,马力.熵气象学[M].北京:气象出版社,1992.114- 125
[16]GB50068—2001,建筑结构可靠度设计统一标准[S].北京:中国建筑工业出版社,2001.2-3
[17]董聪,刘西拉.非线性结构系统可靠度理论及其模拟方法[J].土木工程学报,1998,31(1):33-43
[18]佟晓利,赵国藩.一种和结构可靠度分析几何法相结合的响应面方法[J].土木工程学报,1997,30(4):51-57
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