大跨度斜拉桥静动力可靠度分析
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摘要
优美的造型和良好的结构性能等特点,使得斜拉桥成为大跨度桥梁极具竞争性的桥型之一。目前大跨度斜拉桥的设计和建设基本采用确定性方法,这与斜拉桥实际上受多种随机因素的影响不符,确定性的分析方法难以揭示出结构材料参数、几何形状和外荷载等的变异对斜拉桥安全性的内在影响。作为高次超静定柔性结构,大跨度斜拉桥结构响应复杂。基于概率理论的可靠度分析方法研究随机因素作用下的斜拉桥结构安全可靠性,为大跨度斜拉桥的设计、建设和养护提供更合理的依据。斜拉桥结构的体系可靠度和抗震可靠度分析是工程实践中亟待解决的问题之一。本文以建成的三座斜拉桥为工程背景,开展了斜拉桥结构的体系和抗震可靠度研究工作,取得了以下成果：
(1)由虚功方程建立了平面梁单元T.L.列式的增量平衡方程,推导了平面梁与桁架单元的的弹性刚度矩阵和几何刚度矩阵,采用分段分块变刚度法计算梁单元的弹塑性刚度矩阵；推导了直接微分法计算结构响应梯度的公式；将有限元法与一次可靠度方法结合,建立了杆系结构的非线性有限元可靠度分析方法,采用Fortran90语言编制了基于直接微分法的有限元可靠度分析计算程序,并采用数值算例验证了所编程序的正确性和精度。
(2)考虑随机场的影响,研究了超大跨度斜拉桥在正常使用状态下的可靠度,进行了随机变量分布参数敏感性分析,识别了对斜拉桥结构可靠度指标有较大影响的主要随机变量；总结了随机场离散变量的分布参数对斜拉桥结构可靠度指标的敏感性规律。
(3)研究了超大跨度斜拉桥主塔、主梁和斜拉索承载能力极限状态下的可靠度,并对典型构件单元进行了随机变量分布参数敏感性分析,识别出对主塔、主梁和斜拉索不同单元可靠度指标影响最大的随机变量；总结了随机场离散变量分布参数对主塔、主梁和斜拉索等不同单元可靠度指标的敏感性规律。
(4)考虑几何非线性的影响,基于p约界法搜索了斜拉桥结构的主要失效模式,然后将斜拉桥结构的失效等效为一个串并联系统,研究了超大跨度斜拉桥承载能力极限状态下的2级体系可靠度问题。
(5)研究了基于神经网络和支持向量机的响应面可靠度分析方法,对传统的基于二次多项式的响应面法进行了改进,推导了神经网络和支持向量机响应面对随机参数的一阶和二阶导数,利用神经网络和支持向量机良好的泛化能力,解决多设计验算点的可靠度问题,并将神经网络和支持向量机方法应用于高度非线性极限状态曲面的可靠度计算问题。
(6)从模式识别的角度,将Monte Carlo模拟等概率变换为一个二分类问题,研究了基于神经网络和支持向量机的模式识别可靠度分析方法,数值算例的结果表明,基于多层前向网和支持向量机的模式识别可靠度分析方法能有效提高Monte Carlo模拟的计算效率,而径向基函数神经网络不适合于模式识别可靠度分析方法。
(7)分别从响应面拟合和模式识别不同角度研究了基于神经网络和支持向量机的重要抽样法,提出了改进的重要抽样(ISM)计算方法,大大提高了重要抽样法的计算效率。通过数值算例分析,验证了基于神经网络和支持向量机的重要抽样法的准确性和有效性；算例结果也说明,径向基函数神经网络不适合于模式识别重要抽样法。
(8)九江大桥斜拉桥正常使用状态下可靠度的计算结果表明,基于神经网络和支持向量机的可靠度分析方法的计算效率和精度较好,可用于实际工程结构的可靠度分析,具有较高的实用价值。
(9)将一次可靠度分析方法推广到大跨度斜拉桥的首次超越问题研究,针对设计验算点激励搜索困难的问题,提出基于神经网络的验算点激励法,为搜索精确的验算点激励提供了一个较好的初值；基于FORM首次超越概率分析方法研究了珠江黄埔大桥主塔关键截面的抗震可靠性。
(10)将首次超越概率问题由一个动力可靠度问题转化为静力可靠度问题,研究了基于神经网络响应面法的动力可靠性分析方法,分析计算了珠江黄埔大桥主塔关键截面水平地震激励下的抗震可靠度。
With the prominently esthetic feature and excellently structural beahavior performance, cable-stayed bridges are one of the most competitive bridges for long-span bridges. Until now the design and construction of modern long-span cable-stayed bridge are basically adopted the deterministic method, which is not accordance with the structural behavior. The responses of cable-stayed bridge under environmental effects are essentially affected by many random factors such as external loadings, material parameters and geometry factors of the cable-stayed bridges. As a highly indeterminate and flexible structure, the structural responses of long-span cable-stayed bridges are complex. It is difficult to use the deterministic method to demonstrate the substantial influence on the cable-stayed bridge's security which results from the stochastic variations of structural material parameters, geometry factors and external loadings. The reliability analysis of structures provides some solutions for the structural security of long-span cable-stayed bridges which is under the effect of random factors, and the reliability analysis method also provides the design, construction and maintainence of long-span cable-stayed bridges with a more rational basis. And the systematic and seismic reliability analysis is one of problems which are needed to be solved for the design and construction of long-span cable-stayed bridges. With three completed cable-stayed bridges as the engineering background, the systematic and seismic reliability of long-span cable-stayed bridges were investigated and presented in this dissertation. The theoretical innovations and main technological results are summarized as follows:
(1) Based on the incremental virtual work equation of 2-D continuum, the incremental equilibrium equations of a plane beam and truss element in T.L. formulation was developed. The elastic and geometric stiffness matrix were deduced, and the elasto-plastic stiffness matrix of the beam element was calculated with the fiber model. The formula of response gradients in Direct Differentiation Method was deduced. A nonlinear FEM/FORM reliability approach was proposed and a stochastic finite element program written in FORTRAN was developed. Several numerical examples were computed to validate the accuracy and high efficiency of the proposed approach and program.
(2) Considering the influence of random fields, the reliability of the long-span cable-stayed bridge under the serviceability limit-state was studied, and the sensitivities of the reliability index with respect to the means and the standard deviations of the random variables were computed. The most sensitive random variables on the reliability index were distinguished. The rules of the sensitivity which results from the distributed parameters of the discrete random variables in the random field to the reliability index were summarized.
(3) The element reliability indices of the pylons and the main girder and the cables of the long-span cable-stayed bridge under the ultimate limit-state were calculated, and the sensitivities of the random variable's distributed parameter about the typical component units are engaged. The random variables which have the greatest impact on the reliability index of different units about the pylons and the main girder and the cables of the long-span cable-stayed bridge were found out. The rules of the sensitivity in which the distributed parameters of the discrete random variables in random fields to the reliability index of different units about the tower and the girder and the cables were concluded.
(4) With considering the influence of geometrical nonlinearity, the system reliability at level 2 of the long-span cable-stayed bridge was analyzed. The (3-unzipping method was used to search the main failure modes of the cable-stayed bridge which is regarded as a series-parallel system in the end.
(5) The artificial neural network-based (ANN) Response Surface Method and the support vector machines-based (SVM) Response Surface Method were proposed to make some improvement about the traditional quadratic Response Surface Method. The first-order and the second-order gradients of the response based on ANN and SVM with respect to random variables are derived. The generalizing ability of ANN and SVM was used to resolve the problems with multiple design points in the limit state function and the highly nonlinear limit state function.
(6) The ANN-based and SVM-based pattern recognition reliability methods were studied by transforming the Monte Carlo simulation to a two classification problem in the same probability. The results of the numerical examples showed that the MLP-based and SVM-based pattern recognition reliability methods can enhance the computational efficiency of Monte Carlo simulation. The radial basis function network is not suited for the pattern recognition reliability method.
(7) The Important Sampling Method is improved by ANN-based and SVM-based important sampling methods from the viewpoints of the RSM and pattern recognition. The accuracy and efficiency of the ANN-based and SVM-base important sampling methods were verified by the results of the numerical examples. The radial basis function network can not be used as a classifier in the pattern recognition important sampling method.
(8) The results of the reliability analysis of the Jiujiang Cable-Stayed bridge under the serviceability limit-state indicate that the accuracy and efficiency of the ANN-based and SVM-base reliability methods are verified. These methods can be used in structural reliability analysis of practical long-span bridges.
(9) The first-order reliability method was used to study the first excursion question of long-span cable-stayed bridges. It is very difficult to determine the exact design point excitation. The artificial neural network-based design-point excitation method was suggested to give a favorable starting point to obtain the exact design point excitation. The first excursion probability of the crucial section of the tower in the Pearl River Huangpu Bridge was investigated by the first-order reliability method.
(10) The first excursion question was converted from the dynamic reliability problem to a static reliability problem, and the artificial neural network-based response surface method was discussed. The method was used to investigate the seismic reliability of the crucial section of the tower of the Pearl River Huangpu Bridge under the ground motion excitation.
(1)由虚功方程建立了平面梁单元T.L.列式的增量平衡方程,推导了平面梁与桁架单元的的弹性刚度矩阵和几何刚度矩阵,采用分段分块变刚度法计算梁单元的弹塑性刚度矩阵；推导了直接微分法计算结构响应梯度的公式；将有限元法与一次可靠度方法结合,建立了杆系结构的非线性有限元可靠度分析方法,采用Fortran90语言编制了基于直接微分法的有限元可靠度分析计算程序,并采用数值算例验证了所编程序的正确性和精度。
(2)考虑随机场的影响,研究了超大跨度斜拉桥在正常使用状态下的可靠度,进行了随机变量分布参数敏感性分析,识别了对斜拉桥结构可靠度指标有较大影响的主要随机变量；总结了随机场离散变量的分布参数对斜拉桥结构可靠度指标的敏感性规律。
(3)研究了超大跨度斜拉桥主塔、主梁和斜拉索承载能力极限状态下的可靠度,并对典型构件单元进行了随机变量分布参数敏感性分析,识别出对主塔、主梁和斜拉索不同单元可靠度指标影响最大的随机变量；总结了随机场离散变量分布参数对主塔、主梁和斜拉索等不同单元可靠度指标的敏感性规律。
(4)考虑几何非线性的影响,基于p约界法搜索了斜拉桥结构的主要失效模式,然后将斜拉桥结构的失效等效为一个串并联系统,研究了超大跨度斜拉桥承载能力极限状态下的2级体系可靠度问题。
(5)研究了基于神经网络和支持向量机的响应面可靠度分析方法,对传统的基于二次多项式的响应面法进行了改进,推导了神经网络和支持向量机响应面对随机参数的一阶和二阶导数,利用神经网络和支持向量机良好的泛化能力,解决多设计验算点的可靠度问题,并将神经网络和支持向量机方法应用于高度非线性极限状态曲面的可靠度计算问题。
(6)从模式识别的角度,将Monte Carlo模拟等概率变换为一个二分类问题,研究了基于神经网络和支持向量机的模式识别可靠度分析方法,数值算例的结果表明,基于多层前向网和支持向量机的模式识别可靠度分析方法能有效提高Monte Carlo模拟的计算效率,而径向基函数神经网络不适合于模式识别可靠度分析方法。
(7)分别从响应面拟合和模式识别不同角度研究了基于神经网络和支持向量机的重要抽样法,提出了改进的重要抽样(ISM)计算方法,大大提高了重要抽样法的计算效率。通过数值算例分析,验证了基于神经网络和支持向量机的重要抽样法的准确性和有效性；算例结果也说明,径向基函数神经网络不适合于模式识别重要抽样法。
(8)九江大桥斜拉桥正常使用状态下可靠度的计算结果表明,基于神经网络和支持向量机的可靠度分析方法的计算效率和精度较好,可用于实际工程结构的可靠度分析,具有较高的实用价值。
(9)将一次可靠度分析方法推广到大跨度斜拉桥的首次超越问题研究,针对设计验算点激励搜索困难的问题,提出基于神经网络的验算点激励法,为搜索精确的验算点激励提供了一个较好的初值；基于FORM首次超越概率分析方法研究了珠江黄埔大桥主塔关键截面的抗震可靠性。
(10)将首次超越概率问题由一个动力可靠度问题转化为静力可靠度问题,研究了基于神经网络响应面法的动力可靠性分析方法,分析计算了珠江黄埔大桥主塔关键截面水平地震激励下的抗震可靠度。
With the prominently esthetic feature and excellently structural beahavior performance, cable-stayed bridges are one of the most competitive bridges for long-span bridges. Until now the design and construction of modern long-span cable-stayed bridge are basically adopted the deterministic method, which is not accordance with the structural behavior. The responses of cable-stayed bridge under environmental effects are essentially affected by many random factors such as external loadings, material parameters and geometry factors of the cable-stayed bridges. As a highly indeterminate and flexible structure, the structural responses of long-span cable-stayed bridges are complex. It is difficult to use the deterministic method to demonstrate the substantial influence on the cable-stayed bridge's security which results from the stochastic variations of structural material parameters, geometry factors and external loadings. The reliability analysis of structures provides some solutions for the structural security of long-span cable-stayed bridges which is under the effect of random factors, and the reliability analysis method also provides the design, construction and maintainence of long-span cable-stayed bridges with a more rational basis. And the systematic and seismic reliability analysis is one of problems which are needed to be solved for the design and construction of long-span cable-stayed bridges. With three completed cable-stayed bridges as the engineering background, the systematic and seismic reliability of long-span cable-stayed bridges were investigated and presented in this dissertation. The theoretical innovations and main technological results are summarized as follows:
(1) Based on the incremental virtual work equation of 2-D continuum, the incremental equilibrium equations of a plane beam and truss element in T.L. formulation was developed. The elastic and geometric stiffness matrix were deduced, and the elasto-plastic stiffness matrix of the beam element was calculated with the fiber model. The formula of response gradients in Direct Differentiation Method was deduced. A nonlinear FEM/FORM reliability approach was proposed and a stochastic finite element program written in FORTRAN was developed. Several numerical examples were computed to validate the accuracy and high efficiency of the proposed approach and program.
(2) Considering the influence of random fields, the reliability of the long-span cable-stayed bridge under the serviceability limit-state was studied, and the sensitivities of the reliability index with respect to the means and the standard deviations of the random variables were computed. The most sensitive random variables on the reliability index were distinguished. The rules of the sensitivity which results from the distributed parameters of the discrete random variables in the random field to the reliability index were summarized.
(3) The element reliability indices of the pylons and the main girder and the cables of the long-span cable-stayed bridge under the ultimate limit-state were calculated, and the sensitivities of the random variable's distributed parameter about the typical component units are engaged. The random variables which have the greatest impact on the reliability index of different units about the pylons and the main girder and the cables of the long-span cable-stayed bridge were found out. The rules of the sensitivity in which the distributed parameters of the discrete random variables in random fields to the reliability index of different units about the tower and the girder and the cables were concluded.
(4) With considering the influence of geometrical nonlinearity, the system reliability at level 2 of the long-span cable-stayed bridge was analyzed. The (3-unzipping method was used to search the main failure modes of the cable-stayed bridge which is regarded as a series-parallel system in the end.
(5) The artificial neural network-based (ANN) Response Surface Method and the support vector machines-based (SVM) Response Surface Method were proposed to make some improvement about the traditional quadratic Response Surface Method. The first-order and the second-order gradients of the response based on ANN and SVM with respect to random variables are derived. The generalizing ability of ANN and SVM was used to resolve the problems with multiple design points in the limit state function and the highly nonlinear limit state function.
(6) The ANN-based and SVM-based pattern recognition reliability methods were studied by transforming the Monte Carlo simulation to a two classification problem in the same probability. The results of the numerical examples showed that the MLP-based and SVM-based pattern recognition reliability methods can enhance the computational efficiency of Monte Carlo simulation. The radial basis function network is not suited for the pattern recognition reliability method.
(7) The Important Sampling Method is improved by ANN-based and SVM-based important sampling methods from the viewpoints of the RSM and pattern recognition. The accuracy and efficiency of the ANN-based and SVM-base important sampling methods were verified by the results of the numerical examples. The radial basis function network can not be used as a classifier in the pattern recognition important sampling method.
(8) The results of the reliability analysis of the Jiujiang Cable-Stayed bridge under the serviceability limit-state indicate that the accuracy and efficiency of the ANN-based and SVM-base reliability methods are verified. These methods can be used in structural reliability analysis of practical long-span bridges.
(9) The first-order reliability method was used to study the first excursion question of long-span cable-stayed bridges. It is very difficult to determine the exact design point excitation. The artificial neural network-based design-point excitation method was suggested to give a favorable starting point to obtain the exact design point excitation. The first excursion probability of the crucial section of the tower in the Pearl River Huangpu Bridge was investigated by the first-order reliability method.
(10) The first excursion question was converted from the dynamic reliability problem to a static reliability problem, and the artificial neural network-based response surface method was discussed. The method was used to investigate the seismic reliability of the crucial section of the tower of the Pearl River Huangpu Bridge under the ground motion excitation.
引文
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