桥梁结构抗震可靠性分析方法研究
发布时间：2019-06-24 09:32
【摘要】：论文针对桥梁结构在地震作用下的随机振动和可靠度问题,探讨了一系列分析该类问题的方法。对于线性结构体系,论文主要研究了多点激励反应谱。对于非线性结构体系,论文在结构可靠度理论框架内主要研究了尾部等效线性化法,并提出了高效的设计点搜索算法。此外针对高维可靠度问题的挑战论文改进了正交平面抽样法,并提出了一种基于交叉熵的重要性抽样方法。论文主要工作内容如下：(1)论文简要回顾了多点激励反应谱(Multiple-support response spectrum/MSRS)以及一个考虑了高阶模态贡献的引申形式(Extended-MSRS),并介绍了基于力的里兹向量(Load-dependent Ritz vector/LDR vector)的概念及生成方法。根据结构动力学的基本原理探讨了LDR向量的力学意义,随后提出了基于里兹向量的多点激励反应谱(LDR-MSRS)。为了在LDR-MSRS分析中提前确定所需LDR向量的数目,论文提出了适用于LDR向量的模态截断准则。针对多维地震动激励问题的MSRS分析,论文提出了两种生成LDR向量的思路。第一种思路是将所有方向的荷载分布集合在影响矩阵中求得一组LDR向量,对每个方向的MSRS分析都利用这一组LDR向量；第二种思路是针对每个方向分别求解一组LDR向量,对各方向的MSRS分析仅利用与之相对应的LDR向量。最后通过两座连续刚构桥的算例分析比较了MSRS、Extended-MSRS和两种LDR-MSRS的效率和精度。(2)论文讨论了设计点搜索算法的基本概念并回顾了常用的i-HLRF算法,紧接着提出了一种针对求解系列设计点问题的高效算法,称作λ算法。λ算法将设计点问题转化为求解系列非线性方程组问题,并通过指定与可靠度指标相关的参数λ和利用Broyden's good method进行设计点搜索。(3)根据尾部等效线性化法(Tail-equivalent linearization method/TELM)的原理,针对结构受多点地震动激励的随机振动与动力可靠度问题推导了尾部等效线性化体系(Tail-equivalent linear system/TELS)的计算方法。另外在多点地震动激励过程的随机变量表达式推导中,引入了谱分解法,从而可利用各激励点地震动过程的统计相关性减少随机变量数目。通过算例验证了TELM对桥梁结构多点地震动激励问题的适用性。(4)论文介绍了高维可靠度问题的特点,探讨了正交平面抽样法(Orthogonal-plane sampling/OPS)在构件高维可靠度问题中的几何意义,根据该几何意义提出了改进的正交平面抽样法。另外论文提出了一种在特定半径的超球面上抽样的重要性抽样策略。根据该抽样策略以及利用基于交叉熵的重要性抽样(Cross-entropy based adaptive importance sampling/CE-AIS)理论,引入von Mises-Fisher mixture/vMFM分布模型构建了利用vMFM分布模型的基于交叉熵的重要性抽样法,称作CE-AIS-vMFM。根据最终抽样方式的不同,论文提出了两种CE-AIS-vMFM抽样策略。第一种方法将抽样域固定在一超球面上,该方法最终只能得到失效概率的近似值,但一般随着问题维度的增加,该近似值逼近于真实值。第二种方法允许抽样域变化,该方法在理论上可以得到失效概率的真实值。CE-AIS-vMFM是一种泛用性的抽样方法,它既可用于仅存在单个连续失效域的构件可靠度问题,也可用于存在多个离散失效域的系统可靠度问题。论文通过算例验证了OPS,改进的OPS和两种CE-AIS-vMFM在桥梁结构的高维动力可靠度分析中的精度和效率。(5)论文最后分别利用尾部等效线性化法(TELM)、正交平面抽样法(OPS)以及它的改进形式(MOPS)、采用von Mise-Fisher Mixture/vMFM分布模型的基于交叉熵的重要性抽样法(CE-AIS-vMFM)对一座四跨预应力混凝土连续刚构桥进行了多点地震动激励下的非线性随机振动和动力可靠度分析,并根据该算例的计算结果总结了各种分析方法的特点。
[Abstract]:In view of the random vibration and reliability of the bridge structure under the action of earthquake, a series of methods for analyzing such problems are discussed. For the linear structure system, the multi-point excitation reaction spectrum is mainly studied in this paper. For the nonlinear structure system, the tail equivalent linearization method is mainly studied in the framework of the structural reliability theory, and an efficient design point search algorithm is proposed. In addition, the orthogonal plane sampling method is improved for the challenge paper of high-dimensional reliability problem, and an importance sampling method based on cross entropy is proposed. The main contents of this paper are as follows: (1) The paper briefly reviews the multiple-support response spectrum/ MSRS and the extended-MSRS which takes into account the high-order mode contribution, and introduces the concept and the generation method of the load-dependent Ritz vector/ LDR vector based on the force. The mechanical meaning of LDR vector is discussed according to the basic principle of structural dynamics, and a multi-point excitation response spectrum (LDR-MSRS) based on the Ritz vector is proposed. In order to determine the number of LDR vectors in advance in the LDR-MSRS analysis, the modal truncation criterion for LDR vector is proposed. In order to solve the problem of multi-dimensional seismic excitation, two approaches to generate LDR vector are proposed. the first idea is to obtain a set of LDR vectors in the influence matrix in the load distribution set of all directions, and the set of LDR vectors is used for the MSRS analysis of each direction; the second idea is to solve a set of LDR vectors for each direction, The msrrs analysis for each direction only uses the ldr vector corresponding thereto. At last, the efficiency and precision of the MSRS, Extended-MSRS and the two LDR-MSRS are compared by an example of two continuous rigid frame bridges. (2) The basic concept of the design point search algorithm is discussed and the commonly used i-HLRF algorithm is reviewed, and a high-efficiency algorithm for solving the problem of a series of design points is proposed. The design point problem is transformed into a series of non-linear equations, and the design point search is carried out by specifying the parameters related to the reliability index and using the Broyden's good method. (3) According to the principle of Tail-equivalent linear method/ TLM, the calculation method of the tail-equivalent linear system (TALS) is derived for the problem of the random vibration and the dynamic reliability of the multi-point vibration excitation of the structure. In addition, in the derivation of the random variable expression of the multi-point vibration excitation process, the spectral decomposition method is introduced, so that the number of random variables can be reduced by the statistical correlation of the vibration process of each excitation point. The applicability of the TLM to the multi-point vibration excitation of the bridge structure is verified by an example. (4) The paper introduces the characteristics of high-dimensional reliability, and discusses the geometric significance of the orthogonal plane sampling (OPS) in the high-dimensional reliability of the component. The improved orthogonal plane sampling method is proposed according to the geometric significance. In addition, a sampling strategy of the importance of sampling on the super-sphere of a certain radius is proposed. Based on the sampling strategy and the cross-entropy based importance sampling (CE-AIS) theory, the importance sampling method based on the cross-entropy of the vMFM distribution model, called CE-AIS-vMFM, is constructed by introducing the von Mises-Fisher mixture/ vMFM distribution model. According to the different sampling methods, two CE-AIS-vMFM sampling strategies are proposed. In the first method, the sampling field is fixed on a superspherical surface, and the method can only get the approximate value of the failure probability, but generally with the increase of the problem dimension, the approximate value is approximate to the real value. The second method allows the sampling domain to be changed, and the method can theoretically obtain the true value of the failure probability. CE-AIS-vMFM is a general sampling method, which can be used to solve the reliability problem of the component with only a single continuous failure field, but also can be used to solve the reliability problem of the system with a plurality of discrete failure domains. The accuracy and efficiency of OPS, improved OPS and two CE-AIS-vMFM in high-dimensional dynamic reliability analysis of bridge structure are verified by an example. (5) The paper finally uses the tail equivalent linearization method (TLM), the orthogonal plane sampling method (OPS) and its modified form (MOPS). The non-linear random vibration and dynamic reliability of a four-span pre-stressed concrete continuous rigid frame are analyzed by using the cross-entropy-based importance sampling method (CE-AIS-vMFM) of the von Mise-Fisher Mixes/ vMFM distribution model. The characteristics of various analytical methods are summarized according to the calculated results.
【学位授予单位】：西南交通大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：U442.55
本文编号：2504952
[Abstract]:In view of the random vibration and reliability of the bridge structure under the action of earthquake, a series of methods for analyzing such problems are discussed. For the linear structure system, the multi-point excitation reaction spectrum is mainly studied in this paper. For the nonlinear structure system, the tail equivalent linearization method is mainly studied in the framework of the structural reliability theory, and an efficient design point search algorithm is proposed. In addition, the orthogonal plane sampling method is improved for the challenge paper of high-dimensional reliability problem, and an importance sampling method based on cross entropy is proposed. The main contents of this paper are as follows: (1) The paper briefly reviews the multiple-support response spectrum/ MSRS and the extended-MSRS which takes into account the high-order mode contribution, and introduces the concept and the generation method of the load-dependent Ritz vector/ LDR vector based on the force. The mechanical meaning of LDR vector is discussed according to the basic principle of structural dynamics, and a multi-point excitation response spectrum (LDR-MSRS) based on the Ritz vector is proposed. In order to determine the number of LDR vectors in advance in the LDR-MSRS analysis, the modal truncation criterion for LDR vector is proposed. In order to solve the problem of multi-dimensional seismic excitation, two approaches to generate LDR vector are proposed. the first idea is to obtain a set of LDR vectors in the influence matrix in the load distribution set of all directions, and the set of LDR vectors is used for the MSRS analysis of each direction; the second idea is to solve a set of LDR vectors for each direction, The msrrs analysis for each direction only uses the ldr vector corresponding thereto. At last, the efficiency and precision of the MSRS, Extended-MSRS and the two LDR-MSRS are compared by an example of two continuous rigid frame bridges. (2) The basic concept of the design point search algorithm is discussed and the commonly used i-HLRF algorithm is reviewed, and a high-efficiency algorithm for solving the problem of a series of design points is proposed. The design point problem is transformed into a series of non-linear equations, and the design point search is carried out by specifying the parameters related to the reliability index and using the Broyden's good method. (3) According to the principle of Tail-equivalent linear method/ TLM, the calculation method of the tail-equivalent linear system (TALS) is derived for the problem of the random vibration and the dynamic reliability of the multi-point vibration excitation of the structure. In addition, in the derivation of the random variable expression of the multi-point vibration excitation process, the spectral decomposition method is introduced, so that the number of random variables can be reduced by the statistical correlation of the vibration process of each excitation point. The applicability of the TLM to the multi-point vibration excitation of the bridge structure is verified by an example. (4) The paper introduces the characteristics of high-dimensional reliability, and discusses the geometric significance of the orthogonal plane sampling (OPS) in the high-dimensional reliability of the component. The improved orthogonal plane sampling method is proposed according to the geometric significance. In addition, a sampling strategy of the importance of sampling on the super-sphere of a certain radius is proposed. Based on the sampling strategy and the cross-entropy based importance sampling (CE-AIS) theory, the importance sampling method based on the cross-entropy of the vMFM distribution model, called CE-AIS-vMFM, is constructed by introducing the von Mises-Fisher mixture/ vMFM distribution model. According to the different sampling methods, two CE-AIS-vMFM sampling strategies are proposed. In the first method, the sampling field is fixed on a superspherical surface, and the method can only get the approximate value of the failure probability, but generally with the increase of the problem dimension, the approximate value is approximate to the real value. The second method allows the sampling domain to be changed, and the method can theoretically obtain the true value of the failure probability. CE-AIS-vMFM is a general sampling method, which can be used to solve the reliability problem of the component with only a single continuous failure field, but also can be used to solve the reliability problem of the system with a plurality of discrete failure domains. The accuracy and efficiency of OPS, improved OPS and two CE-AIS-vMFM in high-dimensional dynamic reliability analysis of bridge structure are verified by an example. (5) The paper finally uses the tail equivalent linearization method (TLM), the orthogonal plane sampling method (OPS) and its modified form (MOPS). The non-linear random vibration and dynamic reliability of a four-span pre-stressed concrete continuous rigid frame are analyzed by using the cross-entropy-based importance sampling method (CE-AIS-vMFM) of the von Mise-Fisher Mixes/ vMFM distribution model. The characteristics of various analytical methods are summarized according to the calculated results.
【学位授予单位】：西南交通大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：U442.55
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相关期刊论文 前3条
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