结构可靠度计算方法研究
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摘要
工程结构在施工建造及使用过程中,需要承受设备、人群、车辆等荷载的作用以及风、雨、雪等自然环境的作用;同时,工程结构还有建造费用高和使用周期长的特点,工程结构的安全可靠与否,不但影响着社会生产实践,而且还关系到人民的生命和财产安全。因此,工程结构应要求具有一定的可靠性,才能保证结构在规定的使用期内能够满足设计要求的各项使用功能。
结构可靠度理论是处理结构不确定性、进行结构性能评估的有力工具。现有基本的结构可靠度计算方法可分为一次二阶矩法、蒙特卡罗法和响应面法。一次二阶矩法可以方便用于功能函数为显式表达的情况,但对于可靠性要求较高的结构,其计算精度有时不能满足工程需要。蒙特卡罗法可应用于隐式功能函数情况下可靠度的计算,但该法往往需借助大量的样本试验,计算效率很低。响应面法利用响应面函数逼近真实的功能函数,是当前解决隐式功能函数情况下结构可靠度计算的有效方法,但是如何构造逼真、稳定、方便的响应面函数是该领域研究的重要内容。
本文总结了国内外结构可靠度的研究现状,在对现有结构可靠度计算方法进行深入研究的基础上,寻求计算精度和计算效率较高的结构可靠度计算方法,以期能将结构可靠度理论更好地应用于实际工程领域。
本文的主要工作包括:
(1)系统阐述显式结构功能函数的可靠度计算方法,并对这些方法的计算原理及其优缺点进行深入研究,为本文方法的提出打下理论基础。
(2)对于隐式功能函数的可靠度计算方法,本文着重阐述多项式响应面法、人工神经网络响应面法和支持向量机响应面法的计算原理及其优缺点,并对参数选取和取值进行讨论。
(3)借鉴二次二阶矩法,本文提出两种改进的响应面法,即二次多项式响应面—曲率拟合法和二次多项式响应面—拉普拉斯渐进积分方法。
本文的主要结论有:
(1)二次二阶矩法是以一次二阶矩法为基础,并对一次二阶矩法的计算结果进行二次修正,在多数情况下有着更好的计算精度。其中曲率拟合法的计算精度主要取决于二次多项式对结构功能函数的逼近程度,而拉普拉斯渐进积分方法的计算精度主要受验算点精度的影响。
(2)二次多项式响应面法对于大多数隐式功能函数,都能准确得到验算点,有较好的计算精度和计算效率,且原理简单,操作方便。但是对于一些特殊的高度非线性功能函数,二次多项式响应面法不能准确获得验算点或者无法收敛。支持向量机响应面法对于一些特殊高度非线性功能函数,在合适的参数取值下,能够准确获得验算点,不仅有良好的收敛性,而且有效减少了计算量,提高了计算效率。但是支持向量机响应面法原理较为复杂,而且理论上没有给出参数选取的依据,本文通过算例验证,给出了较通用的参数取值。在BP神经网络响应面法中,由于神经网络响应面函数为高度非线性的函数,改进一次二阶矩法很难准确获得验算点。同时初始样本点的选取对BP神经网络响应面法的计算结果影响较大,由于理论上也无法给出选取的依据,本文采用拉丁超立方体方法抽取样本点,并通过算例验证,给出了较通用的参数取值。
(3)传统响应面法在计算结构的可靠指标时需结合改进一次二阶矩法,当结构非线性程度较高时,计算误差较大。本文针对传统响应面法的缺点,提出了两种改进的响应面法,即二次多项式响应面—曲率拟合法和二次多项式响应面—拉普拉斯渐进积分方法。并通过算例分析表明,本文方法操作简便、在保证较高的计算效率前提下,有效地提高了计算精度。
During construction and service, structures are subjected to the various loads, such as the self weight, the weight of equipments, crowd, and vehicle and to the impact from natural environment such as wind, rain, snow and so on. Also, structures have characteristics of high construction cost and long working period, and their reliability not only influences on the production practice, but also relations to the safety of people's life and property. Therefore, structures must have certain reliability to make sure that they can satisfy each operational function in prescriptive period.
Structural reliability theory is a powerful tool to solve structure uncertainties and evaluate structural performance. The present usually reliability analysis method for engineering structures are Monte Carlo Simulate (MCS), First-order Second-moment method (FOSM) and Reliability Surface Method (RSM). FOSM is usually used for the explicit performance function, and the accuracy of FOSM can not satisfy the engineering requirement sometimes for the structures which have higher reliability requirement. MCS has to use a large number of sample test and the efficiency is low. The implicit performance function is approached with RSM, and it’s an effective way to solve the implicit performance function reliability analysis, and the key issue of RSM is how to construct a high-fidelity, stable, easy-used response surface function with fewer samples.
This thesis concludes domestic and foreign research present situation of the structure reliability. Based on a study of present reliability analysis methods, the main task of this thesis is to find a more efficient algorithm and try to apply it to engineering practice.
The main work of this thesis is as follows:
(1) On calculating methods of reliability for the explicit performance function, a clear understanding has been formed on the computation principle and the advantages and disadvantages of the present algorithms. It laid a good theoretical foundation for the algorithm proposed in the thesis.
(2) On calculating methods of reliability for the implicit performance function, this thesis firstly elaborates on the computation principle and the advantages and disadvantages of Polynomial Response Surface Method, Artificial Neural Networks Response Surface Method and Support Vector Regression Response Surface Method, and then discusses the selection of parameters.
(3) Two improved response surface method has been put forward which is named Quadratic Polynomial Response Surface-Curvature Fitting Method and Quadratic Polynomial Response Surface-Laplace integral Method.
The main conclusions obtained in this thesis are as follow:
(1) Based on FOSM, Second-order second-moment method modifies the results of FOSM, and has better calculation accuracy. The calculation accuracy of curvature fitting method depends on the degree of performance function fitted by quadratic polynomial. The calculation accuracy of laplace integral depends on the value of design point.
(2) Quadratic Polynomial Response Surface Method whose computation principle is simple can calculates the precise value of design point for most implicit performance function. But for some special highly nonlinear structure, Quadratic Polynomial Response Surface Method can’t get precise value of design point or can't be convergent. By contrast, Support Vector Regression Response Surface Method has good convergent, and it also reduce calculation amount. But the computation principle of Support Vector Regression Response Surface Method is complex, and the selection of its parameters isn’t proved in theory. The values of its parameters are given in this thesis. Because Artificial Neural Networks Response Surface functions is highly nonlinear function, so it’s difficult to get precise value of design point in theory. Because the selection of initially sample isn’t proved in theory, Latin Hypercube Sampling has been put forward in this thesis, and effective parameter values are proposed proved by numerical examples.
(3) Two improved response surface method has been put forward which is named Quadratic Polynomial Response Surface-Curvature Fitting Method and Quadratic Polynomial Response Surface-Laplace integral Method. Proved by numerical examples, these methods are easy to operate and effectively improve the calculation accuracy. Furthermore these methods apply to engineering practice well.
结构可靠度理论是处理结构不确定性、进行结构性能评估的有力工具。现有基本的结构可靠度计算方法可分为一次二阶矩法、蒙特卡罗法和响应面法。一次二阶矩法可以方便用于功能函数为显式表达的情况,但对于可靠性要求较高的结构,其计算精度有时不能满足工程需要。蒙特卡罗法可应用于隐式功能函数情况下可靠度的计算,但该法往往需借助大量的样本试验,计算效率很低。响应面法利用响应面函数逼近真实的功能函数,是当前解决隐式功能函数情况下结构可靠度计算的有效方法,但是如何构造逼真、稳定、方便的响应面函数是该领域研究的重要内容。
本文总结了国内外结构可靠度的研究现状,在对现有结构可靠度计算方法进行深入研究的基础上,寻求计算精度和计算效率较高的结构可靠度计算方法,以期能将结构可靠度理论更好地应用于实际工程领域。
本文的主要工作包括:
(1)系统阐述显式结构功能函数的可靠度计算方法,并对这些方法的计算原理及其优缺点进行深入研究,为本文方法的提出打下理论基础。
(2)对于隐式功能函数的可靠度计算方法,本文着重阐述多项式响应面法、人工神经网络响应面法和支持向量机响应面法的计算原理及其优缺点,并对参数选取和取值进行讨论。
(3)借鉴二次二阶矩法,本文提出两种改进的响应面法,即二次多项式响应面—曲率拟合法和二次多项式响应面—拉普拉斯渐进积分方法。
本文的主要结论有:
(1)二次二阶矩法是以一次二阶矩法为基础,并对一次二阶矩法的计算结果进行二次修正,在多数情况下有着更好的计算精度。其中曲率拟合法的计算精度主要取决于二次多项式对结构功能函数的逼近程度,而拉普拉斯渐进积分方法的计算精度主要受验算点精度的影响。
(2)二次多项式响应面法对于大多数隐式功能函数,都能准确得到验算点,有较好的计算精度和计算效率,且原理简单,操作方便。但是对于一些特殊的高度非线性功能函数,二次多项式响应面法不能准确获得验算点或者无法收敛。支持向量机响应面法对于一些特殊高度非线性功能函数,在合适的参数取值下,能够准确获得验算点,不仅有良好的收敛性,而且有效减少了计算量,提高了计算效率。但是支持向量机响应面法原理较为复杂,而且理论上没有给出参数选取的依据,本文通过算例验证,给出了较通用的参数取值。在BP神经网络响应面法中,由于神经网络响应面函数为高度非线性的函数,改进一次二阶矩法很难准确获得验算点。同时初始样本点的选取对BP神经网络响应面法的计算结果影响较大,由于理论上也无法给出选取的依据,本文采用拉丁超立方体方法抽取样本点,并通过算例验证,给出了较通用的参数取值。
(3)传统响应面法在计算结构的可靠指标时需结合改进一次二阶矩法,当结构非线性程度较高时,计算误差较大。本文针对传统响应面法的缺点,提出了两种改进的响应面法,即二次多项式响应面—曲率拟合法和二次多项式响应面—拉普拉斯渐进积分方法。并通过算例分析表明,本文方法操作简便、在保证较高的计算效率前提下,有效地提高了计算精度。
During construction and service, structures are subjected to the various loads, such as the self weight, the weight of equipments, crowd, and vehicle and to the impact from natural environment such as wind, rain, snow and so on. Also, structures have characteristics of high construction cost and long working period, and their reliability not only influences on the production practice, but also relations to the safety of people's life and property. Therefore, structures must have certain reliability to make sure that they can satisfy each operational function in prescriptive period.
Structural reliability theory is a powerful tool to solve structure uncertainties and evaluate structural performance. The present usually reliability analysis method for engineering structures are Monte Carlo Simulate (MCS), First-order Second-moment method (FOSM) and Reliability Surface Method (RSM). FOSM is usually used for the explicit performance function, and the accuracy of FOSM can not satisfy the engineering requirement sometimes for the structures which have higher reliability requirement. MCS has to use a large number of sample test and the efficiency is low. The implicit performance function is approached with RSM, and it’s an effective way to solve the implicit performance function reliability analysis, and the key issue of RSM is how to construct a high-fidelity, stable, easy-used response surface function with fewer samples.
This thesis concludes domestic and foreign research present situation of the structure reliability. Based on a study of present reliability analysis methods, the main task of this thesis is to find a more efficient algorithm and try to apply it to engineering practice.
The main work of this thesis is as follows:
(1) On calculating methods of reliability for the explicit performance function, a clear understanding has been formed on the computation principle and the advantages and disadvantages of the present algorithms. It laid a good theoretical foundation for the algorithm proposed in the thesis.
(2) On calculating methods of reliability for the implicit performance function, this thesis firstly elaborates on the computation principle and the advantages and disadvantages of Polynomial Response Surface Method, Artificial Neural Networks Response Surface Method and Support Vector Regression Response Surface Method, and then discusses the selection of parameters.
(3) Two improved response surface method has been put forward which is named Quadratic Polynomial Response Surface-Curvature Fitting Method and Quadratic Polynomial Response Surface-Laplace integral Method.
The main conclusions obtained in this thesis are as follow:
(1) Based on FOSM, Second-order second-moment method modifies the results of FOSM, and has better calculation accuracy. The calculation accuracy of curvature fitting method depends on the degree of performance function fitted by quadratic polynomial. The calculation accuracy of laplace integral depends on the value of design point.
(2) Quadratic Polynomial Response Surface Method whose computation principle is simple can calculates the precise value of design point for most implicit performance function. But for some special highly nonlinear structure, Quadratic Polynomial Response Surface Method can’t get precise value of design point or can't be convergent. By contrast, Support Vector Regression Response Surface Method has good convergent, and it also reduce calculation amount. But the computation principle of Support Vector Regression Response Surface Method is complex, and the selection of its parameters isn’t proved in theory. The values of its parameters are given in this thesis. Because Artificial Neural Networks Response Surface functions is highly nonlinear function, so it’s difficult to get precise value of design point in theory. Because the selection of initially sample isn’t proved in theory, Latin Hypercube Sampling has been put forward in this thesis, and effective parameter values are proposed proved by numerical examples.
(3) Two improved response surface method has been put forward which is named Quadratic Polynomial Response Surface-Curvature Fitting Method and Quadratic Polynomial Response Surface-Laplace integral Method. Proved by numerical examples, these methods are easy to operate and effectively improve the calculation accuracy. Furthermore these methods apply to engineering practice well.
引文
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[7]李建慧,李爱群,郭彤.斜拉桥不确定性参数随机分析研究[J].公路交通科技,2008,25(11):72-77
[8]张建仁,汪维安,余钱华.高墩大跨连续刚构桥收缩徐变效应的概率分析[J].长沙交通学院学报,2006,22(2):1-8
[9]王晓峰.降雨入渗对非饱和土边坡稳定性影响的研究[D].陕西:西安建筑科技大学,2003
[1] Wong F S.Slope reliability and response surface method[J].Journal of Geotch Engineering, 1985, 111(1): 32-53
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[8] Nello Cristianini,John Shawe-Taylor.支持向量机导论[M].北京:电子工业出版社,2004.
[9] Vapnik V N著,张学工译.统计学习理论的本质[M].北京:清华大学出版社,2000
[10]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1):32-42
[11] Wei G Z, Chen B G.Application of least squares support vector machine forregression to reliability analysis[J].Chinese Journal of Aeronautics, 2009, 22(2): 160-166
[12]金伟良,唐纯喜,陈进.基于SVM的结构可靠度分析响应面方法[J].计算力学学报,2007,24(6):713-718
[13]金伟良,袁雪霞.基于LS-SVM的结构可靠度响应面分析方法[J].浙江大学学报,2007,41(1):44-47
[14] Hurtado J E.An examination of methods for approximating implicit limit state functions from the viewpoint of statistical learning theory[J].Structural safety, 2004(26): 271-293
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[2.1]张建仁,刘扬,许福友等.结构可靠度理论及其在桥梁工程中的应用[M].北京:人民交通出版社,2003
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[1]吴世伟.结构可靠度分析[M].北京:人民交通出版社,1990
[2]丘晋文.大跨度桥梁空气静力可靠度研究[D].华南理工大学工学硕士学位论文,2007
[3] Rackwitz R, Fiessler B.Structural relizbility under combined random load sequences [J].Computers and Structures, 1978, 9(5): 489-494
[4]张建仁,刘扬,许福友等.结构可靠度理论及其在桥梁工程中的应用[M].北京:人民交通出版社,2003
[5]赵国藩,金伟良,贡金鑫.结构可靠度理论[M].北京:中国建筑工业出版社,2000
[6] Melchers R E.Search-based Importance Sampling[J].Structrual Safety, 1990, 9(2): 117-128
[7]李建慧,李爱群,郭彤.斜拉桥不确定性参数随机分析研究[J].公路交通科技,2008,25(11):72-77
[8]张建仁,汪维安,余钱华.高墩大跨连续刚构桥收缩徐变效应的概率分析[J].长沙交通学院学报,2006,22(2):1-8
[9]王晓峰.降雨入渗对非饱和土边坡稳定性影响的研究[D].陕西:西安建筑科技大学,2003
[1] Wong F S.Slope reliability and response surface method[J].Journal of Geotch Engineering, 1985, 111(1): 32-53
[2]苏永华,方祖烈,高谦.用响应面法分析特殊地下岩体空间的可靠性[J].岩石力学与工程学报,2000,19(1):55-58
[3]武清玺.基于界面元模型的响应面法及其在大型结构可靠度分析中的应用[D].河海大学工学博士学位论文,1999
[4]张明.结构可靠度分析——方法与程序[M].北京:科学出版社,2009
[5]黄靓,易伟建,汪优.基于RBF神经网络的结构可靠度分析方法[J].湘潭大学自然科学学报,2006,28(4):109-114
[6]董长虹.Matlab神经网络与应用[M].北京:国防工业出版社,2005
[7]姜绍飞.基于神经网络的结构优化与损伤识别[M].北京:科学出版社,2002
[8] Nello Cristianini,John Shawe-Taylor.支持向量机导论[M].北京:电子工业出版社,2004.
[9] Vapnik V N著,张学工译.统计学习理论的本质[M].北京:清华大学出版社,2000
[10]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1):32-42
[11] Wei G Z, Chen B G.Application of least squares support vector machine forregression to reliability analysis[J].Chinese Journal of Aeronautics, 2009, 22(2): 160-166
[12]金伟良,唐纯喜,陈进.基于SVM的结构可靠度分析响应面方法[J].计算力学学报,2007,24(6):713-718
[13]金伟良,袁雪霞.基于LS-SVM的结构可靠度响应面分析方法[J].浙江大学学报,2007,41(1):44-47
[14] Hurtado J E.An examination of methods for approximating implicit limit state functions from the viewpoint of statistical learning theory[J].Structural safety, 2004(26): 271-293
[1]丘晋文.大跨度桥梁空气静力可靠度研究[D].华南理工大学硕士学位论文, 2007 (导师:苏成)
[2]罗秀锋.大跨度桥梁静风响应与气静力稳定性可靠度研究[D].华南理工大学硕士学位论文, 2008 (导师:苏成)
[3]秦权,林道锦,梅刚.结构可靠度随机有限元——理论及工程应用[M].北京:清华大学出版社,2006
[4] Lars Tvedt.Distribution of quadratic forms in normal space-application to structural realiability[J].Journal of Engineering mechanics, 1990, 116(6): 1183-1197
[5] Zhao Y G, Tetsuro Ono.New Approximations for SORM: Part I[J].Journal of Engineering Menchanics, 1999, 125(1): 79-85
[6]赵国藩,金伟良,贡金鑫.结构可靠度理论[M].北京:中国建筑工业出版社,2000