生命线工程网络抗震可靠性分析方法的比较研究

A Comparison Research on the Methods of Analyzing Lifeline Systems' Seismic Reliability

生命线工程网络抗震可靠性分析是进行生命线工程系统规划、设计、改造与优化的基础。因此 ,寻找一种高效的适应性强的系统可靠性分析方法对实际工程应用具有重要的意义。本文主要介绍两种高效的网络系统两终端连通可靠性分析方法———递推分解算法和有序二分决策图算法。首先 ,分别对两种算法的原理及实现过程进行了详细的论述和说明 ,并且用c语言编制了二分决策图算法的计算程序。然后 ,利用这两种方法及随机模拟算法对 2 0个以往研究中的经典算例和两个实际工程网络———河南省电力网和上海市浦西供水管网 ,进行了网络系统抗震连通可靠性分析。通过对实例分析结果的比较研究 ,得到了一些经验性的结论 ,以期为优化设计工程网络时选择系统可靠性的分析工具提供参考。研究表明 ,由于递推分解算法具有适应性强和能够求得问题近似解的优点 ,因此有良好的实际工程应用前景。

Reliability analysis of lifeline systems under seismic action is the basic problem in the lifeline systems' layout, design, rebuilding and optimization. Finding an efficient evaluating method for large lifeline systems' reliability is a very urgent task in practice. Two approaches-recursive decomposition algorithm (RDA) and ordered binary decision diagrams (OBDD) algorithm, which were regarded as the most effective method of evaluating systems' terminal-pair reliability, are described and comparied in this paper. It is known that enumerating all simple paths or minimal cutset would lead to the NP-hard problem, i.e., the number of simple paths or cuts must be non-polynomial in the size of the network. To avoid enumerating all simple paths or minimal cutset, RDA was put forward by assumption of s-independent. By the method, disjoint simple paths or cuts of a network can be obtained directly one by one, and the reliability or the failure probability of a network can be evaluated through accumulating probability of these obtained disjoint paths or cuts. When a large lifeline system is considered, RDA can get a narrow reliability bound of the lifeline system within satisfying computer run time. OBDD is a graph-based data structure for representing Boolean functions. By network traversing with edge expansion diagram, the success-path function of a given network can be constructed based on OBDD. Then the network reliability is obtained by directly evaluating on this OBDD recursively. Although a function requires, in a worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. A dramatic improvement, as demonstrated by the experimental results for a 2-by-n lattice network,is that the number of OBDD nodes is only proportional to the number of the stages.This article consists of three parts. First, the two algorithms' basic principles and realizing process is presented in detail, and the program of evaluating terminal-pair reliability using OBDD algorithm is written with c language. Then, 20 benchmark networks collected in published articles and two large practical networks-Henan power electric system and Shanghai water supply pipeline system, are analyzed using the two methods and Monte Carlo method. Finally, according to the comparison of the examples' results using different methods, empirical conclusions are gained for practical application. Experimental results show that both RDA and OBDD algorithm have better performance than other techniques for large lifeline systems, and especially RDA is very applicable for large networks because of its' ability of supplying approximation of lifeline systems' reliability.