A recursive decomposition algorithm for network seismic reliability evaluation

Li, Jie; He, Jun

doi:10.1002/eqe.174

Cited by 77 publications

(59 citation statements)

References 14 publications

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“…1 is, the less is its contribution to the connectivity of the system. It is illustrated in functions (5) and (8). The recursive decomposition algorithm prioritizes solving for the shortest road and the shortest cut set.…”

Section: The Algorithm Structure Of the Complex Network Connectivitymentioning

confidence: 99%

Optimal distribution of reliability for a large network based on connectivity

Ling-li

2008

Appl. Math. Mech.-Engl. Ed.

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It is a non-polynomial complexity problem to calculate connectivity of the complex network. When the system reliability cannot be expressed as a function of element reliability, we have to apply some heuristic methods for optimization based on connectivity of the network. The calculation structure of connectivity of complex network is analyzed in the paper. The coefficient matrixes of Taylor second order expansion of the system connectivity is generated based on the calculation structure of connectivity of complex network. An optimal schedule is achieved based on genetic algorithms (GA). Fitness of seeds is calculated using the Taylor expansion function of system connectivity. Precise connectivity of the optimal schedule and the Taylor expansion function of system connectivity can be achieved by the approved Minty method or the recursive decomposition algorithm. When error between approximate connectivity and the precise value exceeds the assigned value, the optimization process is continued using GA, and the Taylor function of system connectivity needs to be renewed. The optimization process is called iterative GA. Iterative GA can be used in the large network for optimal reliability attribution. One temporary optimal result will be generated every time in the iteration process. These temporary optimal results approach the real optimal results. They can be regarded as a group of approximate optimal results useful in the real project.

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Section: The Algorithm Structure Of the Complex Network Connectivitymentioning

confidence: 99%

Optimal distribution of reliability for a large network based on connectivity

Ling-li

2008

Appl. Math. Mech.-Engl. Ed.

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“…However, for the node weighted network and general weighted network, the proposed algorithm can also be used after some small changes are made. A detailed process was illustrated by Li and He (2002).…”

Section: Structure Function and Related Theoremsmentioning

confidence: 99%

“…Also, Yoo and Deo (1988) compared four current algorithms and concluded that Dotson's algorithm was the most effi cient. Introducing the concept of "system structure function" and combining Dotson's algorithm with computer storage, Li and He (2002) presented a recursive decomposition algorithm, in which the probabilistic inequality is used to control the computation time and ensure the error bound remained within the predefi ned scope. This algorithm provides an effi cient approach for large network reliability evaluation.…”

Section: Introductionmentioning

confidence: 99%

An improved recursive decomposition algorithm for reliability evaluation of lifeline networks

Liu

2009

Earthq. Eng. Eng. Vib.

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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 simplifi es 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.

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“…where j = 1− j means the complement of j, which is viewed as a Boolean variable in the RDA [5]. It is clear from the above definition that the larger I prob, ji means a larger influence of edge j on node i.…”

Section: Introductionmentioning

confidence: 98%

“…where P Si is the seismic reliability of node i, M is the number of all disjoint minimal paths between the source and node i, L il is a disjoint minimal path between the source and node i, which can be obtained using the RDA [5]; *P{L il }/* p j can be expressed as…”

Section: Introductionmentioning

confidence: 99%

Genetic algorithm for seismic topology optimization of lifeline network systems

Liu

Bao

2008

Earthq Engng Struct Dyn

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SUMMARYLifeline systems, such as water distribution and gas supply networks, usually cover large areas. For these systems, seismic design is always a difficult problem because of the complexity of large-scale networks. In this paper, a topology optimization technology for lifeline networks is established. Firstly, in order to speed up the convergence of optimization process, an element investment importance analysis is carried out to evaluate the importance of components to the lifeline network. Then a topology optimization model is established. The aim of the model is to find the least-cost network topology while the seismic reliability between the sources and each terminal satisfies prescribed reliability constraints. For this optimization problem, a genetic algorithm, which takes network topologies as the individuals of its population, is used to search for the optimal solutions by suitable operators, including selection, crossover and mutation operators. The capacity of the proposed algorithm is illustrated by its applications to a simple example network consisting of 10 nodes and an actual network with 391 nodes located in a large city of China.

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A recursive decomposition algorithm for network seismic reliability evaluation

Cited by 77 publications

References 14 publications

Optimal distribution of reliability for a large network based on connectivity

Optimal distribution of reliability for a large network based on connectivity

An improved recursive decomposition algorithm for reliability evaluation of lifeline networks

Genetic algorithm for seismic topology optimization of lifeline network systems

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