基于自适应点估计和最大熵原理的结构体系多构件可靠度分析
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摘要
准确而高效地求解结构体系中多个构件的可靠度水准对结构维护和优化具有重要意义,目前已有学者将蒙特卡洛法和响应面法用于此类可靠度分析。然而,蒙特卡洛法所需结构分析次数取决于失效概率的量级,通常计算成本较高。而响应面法的所需结构分析次数取决于杆件数量,当其数量较多时同样有较高的成本。鉴于此,该文提出了一种基于自适应点估计和最大熵原理的结构体系多构件可靠度分析方法,其所需的结构重分析次数上限与杆件数量无关,计算过程简便无需迭代。首先,通过引入自适应交叉项判定和双变量降维近似模型求解各杆件的前四阶矩;然后,根据各杆件的前四阶矩,采用最大熵原理求解各杆件的可靠度指标;最后,通过多个算例对比了蒙特卡洛法、响应面法和建议方法的精度和效率。结果表明建议方法所需的结构重分析次数远少于蒙特卡洛法和响应面法,实现过程简便,且精度能够满足工程要求。
It is important to analyze the reliability level of multi-components in a structural system accurately and efficiently. Monte Carlo method and response surface method are usually used in such reliability analysis.However, the number of structural analysis in Monte Carlo method depends on the value of the reliability index,which usually requires large computation cost. The number of structural analysis in response surface method depends on the number of components, which also needs significant computation cost when the number of components is large. A reliability method for multi-components in a structural system based on the adaptive point estimate method and the principle of maximum entropy is proposed. In this method, the upper limit of the required number of structural analysis is irrelevant to the number of components, and the computation process is easy to implement without iterations. Firstly, the first four moments of each component are calculated based on the combination of adaptive delineation of cross terms and bivariate dimensional decomposition. Then, the principle of maximum entropy is induced to evaluate the reliability index of each component according to the first four moments. Finally, several cases are investigated to compare the accuracy and efficiency of the Monte Carlo method, the response surface method and the proposed method. The results demonstrate that the proposed method has significant advantages in efficiency when compared with Monte Carlo method and response surface method,and can be implemented with satisfactory accuracy for engineering problems.
It is important to analyze the reliability level of multi-components in a structural system accurately and efficiently. Monte Carlo method and response surface method are usually used in such reliability analysis.However, the number of structural analysis in Monte Carlo method depends on the value of the reliability index,which usually requires large computation cost. The number of structural analysis in response surface method depends on the number of components, which also needs significant computation cost when the number of components is large. A reliability method for multi-components in a structural system based on the adaptive point estimate method and the principle of maximum entropy is proposed. In this method, the upper limit of the required number of structural analysis is irrelevant to the number of components, and the computation process is easy to implement without iterations. Firstly, the first four moments of each component are calculated based on the combination of adaptive delineation of cross terms and bivariate dimensional decomposition. Then, the principle of maximum entropy is induced to evaluate the reliability index of each component according to the first four moments. Finally, several cases are investigated to compare the accuracy and efficiency of the Monte Carlo method, the response surface method and the proposed method. The results demonstrate that the proposed method has significant advantages in efficiency when compared with Monte Carlo method and response surface method,and can be implemented with satisfactory accuracy for engineering problems.
引文
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[17]杨绿峰,袁彦华,余波.基于等概率近似变换的向量型层递响应面法分析结构可靠度[J].工程力学,2014,31(7):185―191.Yang Lüfeng,Yuan Yanhua,Yu Bo.Vector cooperative response surface method for structural reliability analysis based on approximately equivalent probability transformations[J].Engineering Mechanics,2014,31(7):185―191.(in Chinese)
[18]Rosenblatt M.Remarks on a multivariate transformation[J].The Annals of Mathematical Statistics,1952,23(3):470―472.
[19]Liu P L,Der Kiureghian A.Multivariate distribution models with prescribed marginals and covariances[J].Probabilistic Engineering Mechanics,1986,1(2):105―112.
[20]Xu H,Rahman S.A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics[J].International Journal of Numerical Methods in Engineering,2004,61(12):1992―2019.
[21]Fan W L,Wei J H,Ang H S,et al.Adaptive estimation of statistical moments of the responses of random systems[J].Probabilistic Engineering Mechanics,2016,43:50―67.
[22]Shannon C E.A mathematical theory of communication[J].Bell System Technical Journal,1948,27:379―423.
[2]张明.结构可靠度分析-方法与程序[M].北京:科学出版社,2009:89―93.Zhang Ming.Structural reliability analysis-methods and procedures[M].Beijing:Science Press,2009:89―93.(in Chinese)
[3]余波,陈冰,吴然立.剪切型钢筋混凝土柱抗剪承载力计算的概率模型[J].工程力学,2017,34(7):136―145.Yu Bo,Chen Bing,Wu Ranli.Probabilistic model for shear strength of shear-critical reinforced concrete columns[J].Engineering Mechanics,2017,34(7):136―145.(in Chinese)
[4]羡丽娜,何政,张延泰.考虑年均倒塌概率的结构倒塌安全储备可接受值[J].工程力学,2017,34(4):88―100.Xian Lina,He Zheng,Zhang Yantai.Acceptable structural collapse safety margin ratios based on annual collapse probability[J].Engineering Mechanics,2017,34(4):88―100.(in Chinese)
[5]Shayanfar M A,Barkhordari M A,Barkhori M,et al.An adaptive directional importance sampling method for structural reliability analysis[J].Structural Safety,2018,70:14―20.
[6]GB/50068-2001,建筑结构可靠度统一标准[S].北京:中国建筑工业出版社,2000.GB/50068-2001,Unified Standard for Reliability Design of Building Structures[S].Beijing:China Architecture Industry Press,2000.(in Chinese)
[7]Grooteman F.Adaptive radial-based importance sampling method for structural reliability[J].Structural Safety,2008,30(6):533―542.
[8]吕大刚,贾明明,李刚.结构可靠度分析的均匀设计响应面法[J].工程力学,2011,28(7):109―116.LüDagang,Jia Mingming,Li Gang.Uniform design response surface method for structural reliability analysis[J].Engineering Mechanics,2011,28(7):109―116.(in Chinese)
[9]Xuan S N,Sellier A,Duprat F,et al.Adaptive response surface method based on a double weighted regression technique[J].Probabilistic Engineering Mechanics,2009,24(2):135―143.
[10]Gavin H P,Yau S C.High-order limit state functions in the response surface method for structural reliability analysis[J].Structural Safety,2008,30(2):162―179.
[11]Guimar?es H,Matos J C,Henriques A A.An innovative adaptive sparse response surface method for structural reliability analysis[J].Structural Safety,2018,73:12―28.
[12]Sch?bi R,Sudret B.Structural reliability analysis for p-boxes using multi-level meta-models[J].Probabilistic Engineering Mechanics,2017,48:27―38.
[13]刘春城,孙显鹤,牟雪峰,等.高压输电塔覆冰荷载作用下可靠度分析[J].水电能源科学,2011(5),29(5):156―158.Liu Chuncheng,Sun Xianhe,Mu Xuefeng,et al.Reliability analysis of high voltage transmission tower under icing load[J].Water Resources and Power,2011(5),29(5):156―158.(in Chinese)
[14]熊铁华,侯建国,安旭文.覆冰、风荷载作用下南方某输电铁塔可靠度分析[J].武汉大学学报(工学版).2011,44(2):207―210.Xiong Tiehua,Hou Jianguo,An Xuwen.Reliability analysis of transmission tower under the wind load and icing load[J].Engineering Journal of Wuhan University.2011,44(2):207―210.(in Chinese)
[15]杨绿峰,李朝阳.结构随机分析的向量型层递响应面法[J].工程力学,2012,29(11):58―64.Yang Lüfeng,Li Zhaoyang.Vectorial hierarchical response surface method for analysis of stochastic structures[J].Engineering Mechanics,2012,29(12):58―64.(in Chinese)
[16]杨绿峰,李朝阳,杨显峰.结构可靠度分析的向量型层递响应面法[J].土木工程学报,2012(7):105―110.Yang Lüfeng,Li Zhaoyang,Yang Xianfeng.Vectorial cooperative response surface method for structural reliability[J].China Civil Engineering Journal,2012,45(7):105―110.(in Chinese)
[17]杨绿峰,袁彦华,余波.基于等概率近似变换的向量型层递响应面法分析结构可靠度[J].工程力学,2014,31(7):185―191.Yang Lüfeng,Yuan Yanhua,Yu Bo.Vector cooperative response surface method for structural reliability analysis based on approximately equivalent probability transformations[J].Engineering Mechanics,2014,31(7):185―191.(in Chinese)
[18]Rosenblatt M.Remarks on a multivariate transformation[J].The Annals of Mathematical Statistics,1952,23(3):470―472.
[19]Liu P L,Der Kiureghian A.Multivariate distribution models with prescribed marginals and covariances[J].Probabilistic Engineering Mechanics,1986,1(2):105―112.
[20]Xu H,Rahman S.A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics[J].International Journal of Numerical Methods in Engineering,2004,61(12):1992―2019.
[21]Fan W L,Wei J H,Ang H S,et al.Adaptive estimation of statistical moments of the responses of random systems[J].Probabilistic Engineering Mechanics,2016,43:50―67.
[22]Shannon C E.A mathematical theory of communication[J].Bell System Technical Journal,1948,27:379―423.