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Evaluation of Network Redundancy Using Recursive Decomposition Algorithm
Abstract
A method to evaluate the network redundancy based on a recursive decomposition algorithm (RDA) introduced by Li and He in 2002 was employed to calculate the reliability of lifeline networks. A redundancy index proposed by Hoshiya and Yamamoto in 2002 was used to represent the redundancy of networks. RDA is shown to be much more effective, as compared with results of Monte-Carlo simulation. In addition, a limitation of the redundancy index is revealed by case studies.
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Basic consideration is made on how comprehensively we can evaluate potential seismic risk of lifeline systems and gain an insight into the safety by way of information entropy, which transmits information of various kinds under uncertainties. It is clarified that a redundancy index RE defined via Shannon's information entropy can be an index to represent redundancy of a system and whose value plays a role in choosing the best alternative for designing a system or for finding the best damage mitigation measure against earthquake hazard. First, numerical analyses are carried out for a parallel cable system and a water supply network system to justify the validity of RE to represent a redundancy measure. Second, an example is demonstrated on how to elucidate system defect of a water supply network and to find an optimal solution for mitigation.
This article presents an attempt towards a probabilistic event oriented system analysis in engineering. Engineering systems are represented as either complete or incomplete systems of events and as compounds of various subsystems of events. The event oriented system analysis investigates important subsystems in engineering systems, such as operational modes and failure modes and their interrelations. The analysis is also applicable to engineering systems with various relations among the sets of events, such as mutually exclusive and inclusive sets. Further, the systems and subsystems are subjected to probability and uncertainty analysis. The system uncertainty analysis is based on entropy. General relations among the probability, uncertainty of the system and uncertainties of the subsystems are derived by using information theory. Specific mathematical aspects and available methods in the uncertainty modelling of systems and subsystems are summarized. Numerical examples confirm the relevance of the event oriented system analysis and indicate potential improvements in system design. (C) 2000 Elsevier Science Ltd. All rights reserved.
A new probabilistic analytical approach to evaluate seismic system reliability of large lifeline systems is presented in this paper. The algorithm takes the shortest path from the source to the terminal of a node weight or edge weight network as decomposition policy, using the Boolean laws of set operation and probabilistic operation principal, a recursive decomposition process then could be constructed. For a general weight network, the modified Torrieri method (NTR/T method) is introduced to combine with the suggested algorithm. Therefore, the recursive decomposition algorithm may be applied to evaluate the seismic reliability of general lifeline systems. A series of case studies, including a practical district electric power network system and a large urban water supply system, show that the suggested algorithm supplies a useful probabilistic analysis means for the seismic reliability evaluation of large lifeline systems. Copyright © 2002 John Wiley & Sons, Ltd.