大型管网系统考虑腐蚀影响的抗震可靠性分析与优化
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摘要
管网系统的抗震分析分为两个层次：单元层次和系统层次。单元层次的抗震分析主要是评价管网系统中的各结构单元(主要是管线)在地震作用下的性能，而系统层次则是评价整个管网系统在地震作用下的性能。抗震分析的最终目标，是指导工程系统的优化设计和系统改造，提高系统的抗震性能。本文从管网系统中腐蚀管线的抗震可靠度分析入手，实现了腐蚀管线的地震随机反应与抗震可靠度分析。在此基础上，发展了管网系统考虑腐蚀影响的抗震连通可靠度分析算法与抗震拓扑优化方法。具体内容包括：
1．基于带吸收壁的齐次马尔科夫链，提出了管线腐蚀发生时间的离散分布模型，并根据管线腐蚀线性发展模型，推导给出了随服役时间变化的管线腐蚀剩余有效面积概率分布。更深入一步，在齐次马尔科夫过程的基础上，提出了管线腐蚀发生时间的连续分布模型，结合管线腐蚀线性发展模型，推导给出了随服役时间变化时管线腐蚀剩余有效面积的概率密度函数。
2．利用弹性地基梁原理，结合管线腐蚀剩余有效面积的概率分布和概率密度函数，利用随机摄动理论推导给出了腐蚀管线在地震激励下位移和应力反应的均值和标准差。基于第三强度理论，给出了管线应力在地震作用下的极限状态方程，利用一次二阶矩方法研究了腐蚀管线的抗震可靠度。
3．介绍了网络系统连通可靠度分析的概念，对三种应用较广泛的网络系统连通可靠性分析算法进行了叙述。然后，提出了以系统结构函数递推分解为基本特征的结构函数递推分解算法来进行系统可靠度分析，并利用结构函数和路事件集合进行了严格的数学证明。在此基础上，利用结构函数递推分解重新诠释了网络抗震连通可靠性分析的最小路递推分解算法，并推导给出了计算效率更高的改进最小路递推分解算法。利用算例对最小路递推分解算法和改进最小路递推分解算法进行了对比分析。
4．提出了以系统互补结构函数递推分解为基本特征的互补结构函数递推分解算法来进行系统失效概率的分析，并进行了严格的数学证明。在此基础上，推导给出了可以计算网络失效概率的最小割递推分解算法和改进最小割递推分解算法。这类算法有效克服了最小路类递推分解算法在强震作用下网络系统计算结果收敛较慢的缺点。在此基础上，对最小路类递推分解算法和最小割类递推分解算法进行了对比分析，分析了两类算法具有不同适用范围的原因。
5．在管网系统抗震可靠性分析基础上，进行了生命线工程网络系统抗震优化设计研究。选用改进最小路递推分解算法作为管网系统抗震可靠度分析工具，以管网建设造价为目标函数，管网拓扑结构为优化途径，管网抗震性能为约束条件，形成基于系统连通可靠性寻求管网最优拓扑结构的优化模型。结合系统单元投资重要度分析，采用遗传—模拟退火混合算法对管网拓扑优化问题进行优化求解。
6．应用上述理论，对沈阳市天然气管网分别进行了不考虑腐蚀和考虑腐蚀作用的管线抗震可靠度分析、管网抗震连通可靠性分析与抗震拓扑优化研究。
7．利用Microsoft Visual C++6.0软件，开发了城市供气管网抗震可靠性分析和优化软件。软件实现了城市供气管网系统的建模、分析和结果显示功能，具有界面友好，操作简便的特点，为城市供气管网的抗震研究和抗震设计提供了有力的工具。
The seismic analysis of networks can be classified into two levels, elements and systems. Herein, the seismic analysis of elements means to evaluate the pipelines performance after the earthquake while the seismic analysis of systems is focused on whether the whole network can meet the consumers' requirements after the earthquake or not. Moreover, the goal of the seismic analysis of networks is to provide an optimization and design tool which is used to improve the network performance subject to seismic wave propagation. In this paper, an approach for calculating the stochastic seismic responses of buried pipeline with corrosions is presented. Several algorithms for seismic connectivity reliability analysis and optimization of networks is established. The content of this paper can be expressed as follows
1. Homogeneous Markov chain with absorbing barrier, an effect mathematics tool for simulating the evolution of system with discrete states, is used to simulate the occurrence of corrosion on the pipeline. Combining with linear corrosion development model, the probability distribution of the pipeline corroded section area, which is assumed as a discrete stochastic variable, is derived. Furthermore, homogeneous Markov process is used to model the occurrence of corrosion on the pipeline and the probability density function of pipeline corroded section area, which is assumed as a continuous stochastic variable, is derived.
2. On the basis of above two corrosion models of pipeline, elastic foundation beam method, a classical method for analyzing the seismic response of pipeline subject to seismic wave propagation, is used to express the seismic axial displacement and axial stress of pipeline as the function of the random variable, pipe segments section areas. Using random perturbation approach, the random seismic response of pipeline is simplified as the linear function of pipe segments section areas. Then the mean and covariance of the seismic response is derived. According to the third strength method, the limit state equation of the pipeline under earthquake is given and the seismic reliability of the pipeline is derived using first order method.
3. The concepts and three commonly used algorithms related to the network connectivity reliability analysis are introduced. Structural function recursive decomposition algorithm is presented to calculate the system reliability and several theorems are proved. On the basis of structural function recursive decomposition algorithm, the minimal path-based recursive decomposition algorithm(MPRDA) is explained from a new viewpoint. Furthermore, a modified minimal path-based recursive decomposition algorithm(MMPRDA) is derived. Also, MPRDA and MMPRDA are compared and the results indicate that MMPRDA owns higher efficiency than MPRDA.
4. From the complementary viewpoint, complementary structural function recursive decomposition algorithm is also presented to calculate the system failure probability. On the basis of complementary structural function recursive decomposition algorithm, a minimal cut-based recursive decomposition algorithm(MCRDA) and a modified minimal cut-based decomposition algorithm(MMCRDA) are derived. These two algorithms have the advantage over MPRDA and MMPRDA on calculating the connectivity reliability of networks under strong earthquake which own low reliability edges. Also, the efficiency of MMPRDA and MMCRDA are compared and the reasons that MMPRDA is more suitable for the networks owning high reliability edges while MMCRDA is more suitable for the networks owning low reliability are analyzed.
5. The goal of system connectivity reliability analysis is to guide network seismic optimization and design. In this paper, with network's cost and reliability as optimization object and restriction, a network topology optimization model is established. Combining with network elements investigation importance analysis, simulated annealing genetic algorithm are used to solve above optimization problem.
6 Using above methods, the seismic reliability and optimal topology of gas network in Shenyang City are calculated with two cases being considered respectively, without corrosions and with corrosions.
7 Using Microsoft Visual C+ +6.0 software, city gas system seismic reliability analysis and optimization software, is worked out. This soft-ware, owing friendly interface and convenient operation, can realize the modeling, analysis and displaying results of networks. The software provides powerful tool for the seismic research and design of gas network.
1．基于带吸收壁的齐次马尔科夫链，提出了管线腐蚀发生时间的离散分布模型，并根据管线腐蚀线性发展模型，推导给出了随服役时间变化的管线腐蚀剩余有效面积概率分布。更深入一步，在齐次马尔科夫过程的基础上，提出了管线腐蚀发生时间的连续分布模型，结合管线腐蚀线性发展模型，推导给出了随服役时间变化时管线腐蚀剩余有效面积的概率密度函数。
2．利用弹性地基梁原理，结合管线腐蚀剩余有效面积的概率分布和概率密度函数，利用随机摄动理论推导给出了腐蚀管线在地震激励下位移和应力反应的均值和标准差。基于第三强度理论，给出了管线应力在地震作用下的极限状态方程，利用一次二阶矩方法研究了腐蚀管线的抗震可靠度。
3．介绍了网络系统连通可靠度分析的概念，对三种应用较广泛的网络系统连通可靠性分析算法进行了叙述。然后，提出了以系统结构函数递推分解为基本特征的结构函数递推分解算法来进行系统可靠度分析，并利用结构函数和路事件集合进行了严格的数学证明。在此基础上，利用结构函数递推分解重新诠释了网络抗震连通可靠性分析的最小路递推分解算法，并推导给出了计算效率更高的改进最小路递推分解算法。利用算例对最小路递推分解算法和改进最小路递推分解算法进行了对比分析。
4．提出了以系统互补结构函数递推分解为基本特征的互补结构函数递推分解算法来进行系统失效概率的分析，并进行了严格的数学证明。在此基础上，推导给出了可以计算网络失效概率的最小割递推分解算法和改进最小割递推分解算法。这类算法有效克服了最小路类递推分解算法在强震作用下网络系统计算结果收敛较慢的缺点。在此基础上，对最小路类递推分解算法和最小割类递推分解算法进行了对比分析，分析了两类算法具有不同适用范围的原因。
5．在管网系统抗震可靠性分析基础上，进行了生命线工程网络系统抗震优化设计研究。选用改进最小路递推分解算法作为管网系统抗震可靠度分析工具，以管网建设造价为目标函数，管网拓扑结构为优化途径，管网抗震性能为约束条件，形成基于系统连通可靠性寻求管网最优拓扑结构的优化模型。结合系统单元投资重要度分析，采用遗传—模拟退火混合算法对管网拓扑优化问题进行优化求解。
6．应用上述理论，对沈阳市天然气管网分别进行了不考虑腐蚀和考虑腐蚀作用的管线抗震可靠度分析、管网抗震连通可靠性分析与抗震拓扑优化研究。
7．利用Microsoft Visual C++6.0软件，开发了城市供气管网抗震可靠性分析和优化软件。软件实现了城市供气管网系统的建模、分析和结果显示功能，具有界面友好，操作简便的特点，为城市供气管网的抗震研究和抗震设计提供了有力的工具。
The seismic analysis of networks can be classified into two levels, elements and systems. Herein, the seismic analysis of elements means to evaluate the pipelines performance after the earthquake while the seismic analysis of systems is focused on whether the whole network can meet the consumers' requirements after the earthquake or not. Moreover, the goal of the seismic analysis of networks is to provide an optimization and design tool which is used to improve the network performance subject to seismic wave propagation. In this paper, an approach for calculating the stochastic seismic responses of buried pipeline with corrosions is presented. Several algorithms for seismic connectivity reliability analysis and optimization of networks is established. The content of this paper can be expressed as follows
1. Homogeneous Markov chain with absorbing barrier, an effect mathematics tool for simulating the evolution of system with discrete states, is used to simulate the occurrence of corrosion on the pipeline. Combining with linear corrosion development model, the probability distribution of the pipeline corroded section area, which is assumed as a discrete stochastic variable, is derived. Furthermore, homogeneous Markov process is used to model the occurrence of corrosion on the pipeline and the probability density function of pipeline corroded section area, which is assumed as a continuous stochastic variable, is derived.
2. On the basis of above two corrosion models of pipeline, elastic foundation beam method, a classical method for analyzing the seismic response of pipeline subject to seismic wave propagation, is used to express the seismic axial displacement and axial stress of pipeline as the function of the random variable, pipe segments section areas. Using random perturbation approach, the random seismic response of pipeline is simplified as the linear function of pipe segments section areas. Then the mean and covariance of the seismic response is derived. According to the third strength method, the limit state equation of the pipeline under earthquake is given and the seismic reliability of the pipeline is derived using first order method.
3. The concepts and three commonly used algorithms related to the network connectivity reliability analysis are introduced. Structural function recursive decomposition algorithm is presented to calculate the system reliability and several theorems are proved. On the basis of structural function recursive decomposition algorithm, the minimal path-based recursive decomposition algorithm(MPRDA) is explained from a new viewpoint. Furthermore, a modified minimal path-based recursive decomposition algorithm(MMPRDA) is derived. Also, MPRDA and MMPRDA are compared and the results indicate that MMPRDA owns higher efficiency than MPRDA.
4. From the complementary viewpoint, complementary structural function recursive decomposition algorithm is also presented to calculate the system failure probability. On the basis of complementary structural function recursive decomposition algorithm, a minimal cut-based recursive decomposition algorithm(MCRDA) and a modified minimal cut-based decomposition algorithm(MMCRDA) are derived. These two algorithms have the advantage over MPRDA and MMPRDA on calculating the connectivity reliability of networks under strong earthquake which own low reliability edges. Also, the efficiency of MMPRDA and MMCRDA are compared and the reasons that MMPRDA is more suitable for the networks owning high reliability edges while MMCRDA is more suitable for the networks owning low reliability are analyzed.
5. The goal of system connectivity reliability analysis is to guide network seismic optimization and design. In this paper, with network's cost and reliability as optimization object and restriction, a network topology optimization model is established. Combining with network elements investigation importance analysis, simulated annealing genetic algorithm are used to solve above optimization problem.
6 Using above methods, the seismic reliability and optimal topology of gas network in Shenyang City are calculated with two cases being considered respectively, without corrosions and with corrosions.
7 Using Microsoft Visual C+ +6.0 software, city gas system seismic reliability analysis and optimization software, is worked out. This soft-ware, owing friendly interface and convenient operation, can realize the modeling, analysis and displaying results of networks. The software provides powerful tool for the seismic research and design of gas network.
引文
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