An improved recursive decomposition algorithm for reliability evaluation of lifeline networks

                                                              Liu Wei^1,2 and Li Jie^1,2

1. Department of Building Engineering, Tongji University, Shanghai 200092, China
2. State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China

Abstract: The seismic reliability evaluation of lifeline networks has received considerable attention and been widely
studied. In this paper, on the basis of an original recursive decomposition algorithm, an improved analytical approach to
evaluate the seismic reliability of large lifeline systems is presented. The proposed algorithm takes the shortest path from
the source to the sink of a network as decomposition policy. Using the Boolean laws of set operation and the probabilistic
operation principal, a recursive decomposition process is constructed in which the disjoint minimal path set and the disjoint
minimal cut set are simultaneously enumerated. As the result, a probabilistic inequality can be used to provide results that
satisfy a prescribed error bound. During the decomposition process, different from the original recursive decomposition
algorithm which only removes edges to simplify the network, the proposed algorithm simplifies the network by merging
nodes into sources and removing edges. As a result, the proposed algorithm can obtain simpler networks. Moreover, for
a network owning s-independent components in its component set, two network reduction techniques are introduced to
speed up the proposed algorithm. A series of case studies, including an actual water distribution network and a large urban
gas system, are calculated using the proposed algorithm. The results indicate that the proposed algorithm provides a useful
probabilistic analysis method for the seismic reliability evaluation of lifeline networks.

Keywords: lifeline system; network reliability; path-based recursive decomposition algorithm; disjoint minimal path;
disjoint minimal cut; network reduction; reliability bound
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