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. 2018 Apr 12;13(4):e0195727.
doi: 10.1371/journal.pone.0195727. eCollection 2018.

Modeling Joint Restoration Strategies for Interdependent Infrastructure Systems

Free PMC article

Modeling Joint Restoration Strategies for Interdependent Infrastructure Systems

Chao Zhang et al. PLoS One. .
Free PMC article


Life in the modern world depends on multiple critical services provided by infrastructure systems which are interdependent at multiple levels. To effectively respond to infrastructure failures, this paper proposes a model for developing optimal joint restoration strategy for interdependent infrastructure systems following a disruptive event. First, models for (i) describing structure of interdependent infrastructure system and (ii) their interaction process, are presented. Both models are considering the failure types, infrastructure operating rules and interdependencies among systems. Second, an optimization model for determining an optimal joint restoration strategy at infrastructure component level by minimizing the economic loss from the infrastructure failures, is proposed. The utility of the model is illustrated using a case study of electric-water systems. Results show that a small number of failed infrastructure components can trigger high level failures in interdependent systems; the optimal joint restoration strategy varies with failure occurrence time. The proposed models can help decision makers to understand the mechanisms of infrastructure interactions and search for optimal joint restoration strategy, which can significantly enhance safety of infrastructure systems.

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.


Fig 1
Fig 1. Diagram of interdependent infrastructure networks.
Fig 2
Fig 2. Analysis flowchart for interaction process.
Fig 3
Fig 3. An illustrative example of the interaction process.
Substation node P6 physically fails at t = 1, and it is restored at t = 3.
Fig 4
Fig 4. Average hourly service consumption of Guilin in China.
(a) electric power; (b) water.
Fig 5
Fig 5. The electric power network and the water supply network.
The red squares nodes (P1-P10) are the power plant nodes, while the blue squares nodes (W1-W6) are the water plant nodes. The red lines are electric transmission lines, and the blue lines are water pipelines.
Fig 6
Fig 6. Numbers of functional nodes in two networks at each time step.
(a) Initial node failures occur in the power network; (b) initial node failures occur in the water network.
Fig 7
Fig 7. The fitness value during different generations.
(a) failures happening at 1 AM; (b) failures happening at 1 PM.
Fig 8
Fig 8. Time duration of the optimal strategy with change of θ/φ.

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Grant support

The work is supported by National Science Foundation of China, grant number 71301095 to CZ and 71704111 to JK; the URL of the funder is "". The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.