橋梁結構抗震可靠性分析方法研究
發布時間：2019-06-24 09:32
【摘要】：論文針對橋梁結構在地震作用下的隨機振動和可靠度問題,探討了一系列分析該類問題的方法。對于線性結構體系,論文主要研究了多點激勵反應譜。對于非線性結構體系,論文在結構可靠度理論框架內主要研究了尾部等效線性化法,并提出了高效的設計點搜索算法。此外針對高維可靠度問題的挑戰論文改進了正交平面抽樣法,并提出了一種基于交叉熵的重要性抽樣方法。論文主要工作內容如下：(1)論文簡要回顧了多點激勵反應譜(Multiple-support response spectrum/MSRS)以及一個考慮了高階模態貢獻的引申形式(Extended-MSRS),并介紹了基于力的里茲向量(Load-dependent Ritz vector/LDR vector)的概念及生成方法。根據結構動力學的基本原理探討了LDR向量的力學意義,隨后提出了基于里茲向量的多點激勵反應譜(LDR-MSRS)。為了在LDR-MSRS分析中提前確定所需LDR向量的數目,論文提出了適用于LDR向量的模態截斷準則。針對多維地震動激勵問題的MSRS分析,論文提出了兩種生成LDR向量的思路。第一種思路是將所有方向的荷載分布集合在影響矩陣中求得一組LDR向量,對每個方向的MSRS分析都利用這一組LDR向量；第二種思路是針對每個方向分別求解一組LDR向量,對各方向的MSRS分析僅利用與之相對應的LDR向量。最后通過兩座連續剛構橋的算例分析比較了MSRS、Extended-MSRS和兩種LDR-MSRS的效率和精度。(2)論文討論了設計點搜索算法的基本概念并回顧了常用的i-HLRF算法,緊接著提出了一種針對求解系列設計點問題的高效算法,稱作λ算法。λ算法將設計點問題轉化為求解系列非線性方程組問題,并通過指定與可靠度指標相關的參數λ和利用Broyden's good method進行設計點搜索。(3)根據尾部等效線性化法(Tail-equivalent linearization method/TELM)的原理,針對結構受多點地震動激勵的隨機振動與動力可靠度問題推導了尾部等效線性化體系(Tail-equivalent linear system/TELS)的計算方法。另外在多點地震動激勵過程的隨機變量表達式推導中,引入了譜分解法,從而可利用各激勵點地震動過程的統計相關性減少隨機變量數目。通過算例驗證了TELM對橋梁結構多點地震動激勵問題的適用性。(4)論文介紹了高維可靠度問題的特點,探討了正交平面抽樣法(Orthogonal-plane sampling/OPS)在構件高維可靠度問題中的幾何意義,根據該幾何意義提出了改進的正交平面抽樣法。另外論文提出了一種在特定半徑的超球面上抽樣的重要性抽樣策略。根據該抽樣策略以及利用基于交叉熵的重要性抽樣(Cross-entropy based adaptive importance sampling/CE-AIS)理論,引入von Mises-Fisher mixture/vMFM分布模型構建了利用vMFM分布模型的基于交叉熵的重要性抽樣法,稱作CE-AIS-vMFM。根據最終抽樣方式的不同,論文提出了兩種CE-AIS-vMFM抽樣策略。第一種方法將抽樣域固定在一超球面上,該方法最終只能得到失效概率的近似值,但一般隨著問題維度的增加,該近似值逼近于真實值。第二種方法允許抽樣域變化,該方法在理論上可以得到失效概率的真實值。CE-AIS-vMFM是一種泛用性的抽樣方法,它既可用于僅存在單個連續失效域的構件可靠度問題,也可用于存在多個離散失效域的系統可靠度問題。論文通過算例驗證了OPS,改進的OPS和兩種CE-AIS-vMFM在橋梁結構的高維動力可靠度分析中的精度和效率。(5)論文最后分別利用尾部等效線性化法(TELM)、正交平面抽樣法(OPS)以及它的改進形式(MOPS)、采用von Mise-Fisher Mixture/vMFM分布模型的基于交叉熵的重要性抽樣法(CE-AIS-vMFM)對一座四跨預應力混凝土連續剛構橋進行了多點地震動激勵下的非線性隨機振動和動力可靠度分析,并根據該算例的計算結果總結了各種分析方法的特點。
[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.
【學位授予單位】：西南交通大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：U442.55
本文編號：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.
【學位授予單位】：西南交通大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：U442.55
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