Chapter 1 Introduction
1.1.1 Resilience
From the engineering perspective, resilience is the speed of returning to the steady state after a disruption (Batabyal et al., 2007), which is an index to assess the performance of an infrastructure system. Unlike the conventional risk analysis that pursues fail-safe, resilience represents a “safe-to-fail” position to contain and minimize the failure that may result from unpredictable disturbance and impact (Ahern, 2011; Fang and Zio, 2019).
When an infrastructure system is affected by a disaster, it is first disrupted, suffering a loss of performance; then, it may adapt to the disruption with the available components in the infrastructure system, such as the previously redundant facilities and capacities;
last, the external effort intervenes to restore the affected component, assisting the system to recover to its original functionality. Hence, the performance status’ transition of the infrastructure system influenced by disruption can be divided into three phases as in Figure 1.1: normal (T < te), deterioration (T = te ~ ts) and recovery (T = ts ~ tf).
Figure 1.1 System performance transition under the disruption (adapted from Henry and Emmanuel Ramirez-Marquez (2012)) 1.1.2 Interdependent infrastructure systems
Interdependency is generally illustrated as two infrastructure systems dependent on each other (Rinaldi et al., 2001). That is, it describes the complex interrelation among different infrastructure systems, which can cause the cascading effect during the disruption and constrain the restoration schedule. The infrastructure systems may be interdependent from the perspective of either physical connection or functional association. Due to such interdependency, the failure of a component in a network may cause cascading effects within the network or even across interdependent networks. For instance, the disconnection of electric power transmission can result in the malfunction of the telecommunication system, but such malfunction can block the transmission of the system status of the electric power system, and thus the telecommunication system influences the electric power system reversely.
In this study, four kinds of interdependency are introduced and considered following the categorizing method by Rinaldi et al. (2001), which are physical, cyber, geographic,
Performance
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and logical, and the relative method will be reviewed and discussed in Section 2.2. Herein, the considered interdependencies covers the interrelations among the roadway, electric power, and telecommunication systems. In summary, the considered interdependencies are presented in Figure 1.2.
Figure 1.2 Summary of the considered interdependencies
1.1.3 Restoring interdependent infrastructure systems
Of three phases in the transition of system performance as Figure 1.1, this study focuses on the phase regarding the external efforts, the restoration in the phase of system recovery. As the restoration is to recover the functionality of the infrastructure system, optimizing the schedule of the restoration can reduce the loss of resilience, which is to boost the recovery of the infrastructure system through the external effort. That is, through optimizing the sequence of the disrupted components to be restored, the resilience loss can be minimized, and the grey area in Figure 1.1 is thus lessened.
However, the interrelation among different infrastructure systems complicates the optimization of the restoration. In order to restore some parts of the telecommunication facilities, some specific electric power components should first be recovered, but with the limited amount of the restoration resource, this consideration may contradict the goal to
recover the electric power network as restoring such electric power components could not benefit the recovery of the electric power network.
Research goal
In light of the growing needs of emergency response for natural disasters and the research gap in the restoration of the interdependent infrastructure networks, this study proposes a problem for infrastructure resilience optimization, which focuses on the recovery phase of system performance after a given disruption. In contrast to the studies regarding restoring the interdependent infrastructure networks in the existing literature, this study further considers two types of interdependency which are still rarely modeled and accordingly optimizes the restoration of three infrastructure networks in one objective function: (i) incomplete information of the amount of demand as the cyber interdependency (ii) the restoration interdependency over multi-layer networks.
(i) Cyber interdependency: the transmission of the demand information in the roadway network relies on the telecommunication services. If the telecommunication services are failed, it can cause the difficulty to the optimization of the restoration schedule due to the incomplete information of the amount of demand.
(ii) Restoration interdependency: the roadway network provides the restoration crews of all the infrastructure networks with the connection between their depots and the disrupted components. If the disrupted components in any infrastructure systems are not accessible to the depot through the roadway network, the restoration on those components is not feasible.
Additionally, the cross-network interdependency further increases problem complexity and collectively presents the methodologically challenging perspectives. A
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network flow approach is applied to capture network dynamics and interactive effects between multi-layer networks explicitly. Numerical experiments are conducted for the restoration of the roadway, electric power supply, and telecommunication systems (three-layer networks) under the impact of flood-related disruption.
Thesis organization
The organization of this thesis is demonstrated in Figure 1.3. Chapter 2 covers the concept and the assessment method for resilience, and the interdependency is categorized and studied. In the same chapter, the relevant studies of the restoration of the interdependent infrastructure systems are reviewed, where the research gap in the existing literature is discussed. Next, in Chapter 3, the characteristic of the restoration of the interdependent infrastructure networks and the interdependent network restoration problem, are stated and analyzed. Then, a mathematical model is developed to solve the problem. In Chapter 4, the test multi-layer interdependent infrastructure networks are implemented to manifest the implementation of the stated problem and the capability of the developed model. Last, the conclusion is presented in Chapter 5 to summarize the findings of this research and provide some recommendation for future studies.
Figure 1.3 Thesis organization
CHAPTER 2 LITERATURE REVIEW
From the perspective of disaster management, recovering the functionality of the community through the restoration after severe disasters is an essential task, and resilience is a concept and an index to measure the process of the restoration of the infrastructure systems. In this chapter, the assessment approaches for resilience, several types of classification for the interdependency, and the methods to model optimize the restoration schedule of the interdependent infrastructure systems are summarized; last, the research gap in the existing literature is outlined.
Resilience assessment
Following the introduction of the resilience in Section 1.1.1, resilience is an index to analyze the capability of the infrastructure systems. Conceptually, a system is considered as being resilient for its capabilities in three aspects (Fiksel, 2003; Nan and Sansavini, 2017; Vugrin et al., 2010):
(i) Absorptive capability is to reduce the initial impact of a disaster.
(ii) Adaptive capability is to adjust the system to balance disaster impact and maintain a certain level of system performance.
(iii) Restorative capability is to repair the failed system components.
These capabilities are highly related to system structure and the strengths of system components against disaster impact. For instance, a structure designed with higher redundancy is more likely to improve the adaptive capability, as redundant components may share the workload of the damaged ones and continue the functionality of the system.
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Woods (2015) also sorted the resilience into four concepts:
(i) Resilience as rebound: it refers to how a system rebounds from disruption and returns to previous or normal states.
(ii) Resilience as robustness: some researches label resilience as robustness, which is the ability to absorb perturbations.
(iii) Resilience as graceful extensibility: this concept views resilience as how to extend adaptive capacity in the face of surprise.
(iv) Resilience as sustained adaptability: it indicates the ability to manage the adaptive capacities of systems.
From the description of those four concepts, they can all be categorized into the three capabilities mentioned above: robustness as the absorptive capability, graceful extensibility, and sustained adaptability as the adaptive capability, and rebound as the restorative capability.
Vugrin et al. (2010) concluded the distinguishing characteristic for the abovementioned capabilities: the absorptive capability and the adaptive capability are the internal measurements for the system impact, while the restorative capability is the exogenous measurement through total recovery effort which often requires external effort.
This study aims at studying the external effort that can fortify the resilience of the infrastructure systems, which is the restorative capability through optimizing the restoration process. In order to analyze the restorative capability, an assessment approach is needed, and thus, the assessment approaches are reviewed as followed.
2.1.1 Resilience assessment approaches
The resilience assessment approaches can be classified into two categories from the
review paper (Hosseini et al., 2016): qualitative and quantitative. The qualitative category includes methods according to conceptual frameworks, which provide some guiding principles or offering the semi-quantitative indices from the questions for experts’
assessment. The quantitative assessment approaches contain two sub-categories: general measures and structural-based models, while the quantitative approaches are more suitable for this thesis because they can quantify the performance of the optimization of the infrastructure restoration schedule.
General measures are one type of quantitative assessment approaches for resilience;
they quantify the performance of a system regardless of the system structure (Hosseini et al., 2016). Herein, based on the concept of service stability, several studies (Ghosn et al., 2016) also converge on a formula for the quantification of resilience (RES) defined as Equation (1), which is the integral of the performance of a system over time:
𝑅𝑅𝑅𝑅𝑅𝑅 = ∫𝑡𝑡𝑡𝑡00+𝑡𝑡ℎ𝑄𝑄(𝑡𝑡)𝑑𝑑𝑡𝑡 𝑡𝑡ℎ
(1)
Bruneau et al. (2003) proposed a deterministic static metric corresponding to the grey area in Figure 1.1 for measuring the resilience loss R as defined in Equation (2), where Q(t) measures the functionality level of the integrated system.
𝑅𝑅 = � [100 − 𝑄𝑄(𝑡𝑡)]𝑡𝑡𝑓𝑓
𝑡𝑡0
𝑑𝑑𝑡𝑡 (2)
2.1.2 Performance indicators for infrastructure networks
From Equations (1) and (2), the definition of the performance indicators (𝑄𝑄(𝑡𝑡)) for the infrastructure networks is required to evaluate the resilience of the infrastructure system. The network-performance indicators are suggested to be considered either the
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topology or the functionality of networks (Ghosn et al., 2016). The topology-based performance metrics study the performance from the perspectives of connectivity and efficiency; herein, the connectivity is considered as the number of the connecting paths from the supply node to the consumption nodes; the efficiency is measured as to how efficient the transmission of the utility between different nodes. However, the topology-based metrics cannot capture the functional aspect of the infrastructure networks.
The flow-based functional performance metrics combine network topology with flow patterns, which are considered as the amount of flow that a damaged network can deliver to the demand nodes comparing to what it delivers before the disruption. Such metrics consider the flow capacity and the supply and demand constraints in an optimization framework (Ghosn et al., 2016).
Interdependency categorization
With the preface to the interdependency in Section 1.1.2, interdependency illustrates the interrelations among the infrastructure systems, and it can be presented in many different aspects. Rinaldi et al. (2001) categorized interdependencies into four types:
physical, cyber, geographic, and logical interdependencies.
(i) Physical interdependency means that the state of one infrastructure system is dependent on the material output(s) of another.
(ii) Cyber interdependency implies the relationships between infrastructure systems based on information transmitted through the relevant infrastructure.
(iii) Geographic interdependency means that a local environmental event can cause state changes in all infrastructure systems.
(iv) Logical interdependency includes other state dependencies between different
infrastructure systems, which is not via the physical, cyber, or geographic connection.
It is recognized that such classification can well sort out the interdependency related issues in several practical cases.
Lee et al. (2007) identified five types of interrelationship between infrastructure systems, where these authors denoted those types of dependence as the interdependency in their studies.
(i) Input dependence indicates the infrastructure components requires the services from another infrastructure component as the input.
(ii) Mutual dependence implies that a group of infrastructure components are dependent on the activities of each other.
(iii) Shared dependence means that some infrastructure systems share the same physical components or activities.
(iv) EXCLUSIVE OR dependence illustrates the activities that some specific infrastructures are the exclusive providers.
(v) Collocated dependence specifies that the components of two or more infrastructure systems are located in a similar geographical region.
P. Zhang and Peeta (2011) also proposed a way to categorize interdependencies.
(i) Functional interdependency indicates that the functioning of one system requires inputs from or can be substituted by another system.
(ii) Physical interdependency means some infrastructure systems are coupled through shared physical attributes.
(iii) Budgetary interdependency implies that several infrastructure systems share the same resource allocation budget, especially during disaster recovery.
(iv) Market interdependency means that all of the infrastructure systems are interacting
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in the same economic system.
Ouyang (2014) reviewed the abovementioned and other types of interdependencies through studying some extreme events, such as extreme natural disaster and large-scale terrorist attack. However, the classification by Lee et al. and Zhang and Peeta does not cover some scenarios. For instance, the classification by Lee et al. cannot sort the scenario that the electric power systems and the telecommunication services are prioritized during the restoration process, and the categorization by Zhang and Peeta cannot sort the event that the debris-covered streets could block the emergency response personnel. Herein, Ouyang (2014) recognized that the classification proposed by Rinaldi et al. could well sort out the interdependency related issues in several practical cases.
Modeling interdependent infrastructure systems
In the review paper of modeling interdependent critical infrastructure systems (Ouyang, 2014), five major types of approaches have been adopted for analyzing interdependency across infrastructure systems:
(i) Empirical approaches analyze the interdependencies of the infrastructure systems through historical data and expert experience.
(ii) Agent-based approaches implement a bottom-up method that contains autonomous agents and their interactions to analyze the decision-making processes in the infrastructure systems. Herein, the reaction of the agents is based on their objectives, the pricing strategies, learning, and adaptation to the simulation environment, and the capacity expansion decisions (P. Zhang et al., 2011). However, the result of the simulation highly depends on the assumptions about the behaviors of the agent.
(iii) System-dynamics-based approaches model the dynamic behavior of the
interdependent infrastructure systems by capturing important causes, effects, and factors under the scenarios of disruption.
(iv) Economic-theory-based approaches view the operation of the infrastructure systems as the intermediate goods in the market of the economy, where the interdependencies are analyzed through economic interdependencies.
(v) Network-based approaches exploit the network structure, a common characteristic of infrastructure systems, and they are useful for analyzing physical interdependencies and the cascading disruptions (P. Zhang et al., 2011).
Herein, network-based approaches model each single infrastructure system by a respective network and describe the interdependencies between them by inter-links.
Depending on whether particle flows in the networks are de facto modeled, network-based approaches can be further categorized into two groups: topology-network-based methods and flow-based methods.
To explicitly describe the interdependencies in the infrastructure systems, this research adopts the network flow method to capture the dynamics of system evolution in terms of how restoration units and relevant resources move across systems. Accordingly, infrastructure systems are represented as the combination of networks, and the interdependencies are modeled using logical constraints in the formulation.
Restoring interdependent infrastructure networks
The relevant literature of modeling the interdependent infrastructure networks can be generally grouped according to research goals: performance evaluation, design, mitigation, and recovery models. For recovery models, most studies focus on analyzing the changing functional states of systems upon the restoration of failed components
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(Ouyang, 2014). To optimize restoration can be viewed as a network design problem to add (restore) links to the disrupted network, while the scheduling of restoration also needs to be addressed. Lee et al. (2007) modeled the restoration of services in interdependent infrastructure systems by explicitly identifying interdependencies using network flow approaches. Nurre et al. (2012) proposed an integrated network design and scheduling problem to optimize the restoration of a single infrastructure network to maximize weighted total arrived demand. Cavdaroglu et al. (2013) optimized integrating restoration and scheduling decisions with the objective function of the performance over the horizon of the restoration plan and implemented logical constraints to describe the interdependencies. González et al. (2016) optimized the restoration strategy of selecting the components to be restored through minimizing the cost of preparation, reconstruction, surplus or deficit supply, and commodity flow, and they also developed the iterative use of the interdependent network design problem to account for the order of the reconstruction. Almoghathawi et al. (2019) proposed a resilience-driven restoration model with multiple objectives, including maximizing the resilience and minimizing the restoration cost. In their study, they used ε-constraint method to generate Pareto-optimal solutions and demonstrated the tradeoff between the resilience and the restoration cost.
Karakoc et al. (2019) integrated a resilience-driven mixed integer programming model to schedule the restoration process of the disrupted interdependent infrastructure networks with the index of geographically distributed social vulnerability. Herein, this study incorporated the concept of community resilience to the restoration process.
These studies mostly model and discuss the complication of disruption patterns over interdependent infrastructure systems at a conceptual level and focusing on the perspective of system functionality. Other than functional interdependency, however, restoration interdependency which can be manifested as the accessibility/feasibility of
components in the different system required for the deployment of restoration is rarely considered in the existing literature. That is, the disruption to the roadway network which enables the restoration crews to access the disrupted components in other infrastructure networks is rarely included in the existing literature.
Restoration with incomplete information
In Section 2.2, the cyber interdependency regards the interaction between infrastructure systems through the information. That is, if the infrastructure system transmitting the information, such as the telecommunication systems, fails after the disruption, some information in other infrastructure systems can be incomplete, influencing the decision process for the restoration. However, the relevant literature is emerging but still rare, and few studies consider the factor of incomplete information involving in the restoration process.
There is some literature analyzed the incomplete information during the restoration from different perspectives. Çelik et al. (2015) addressed incomplete information about the debris amounts along the roads in the debris clearance problem using a partially observable Markov decision model. X. Zhang et al. (2018) optimized the resilience-based network design under uncertainty and developed a nonlinear function to consider the non-deterministic case about the disrupted capacity, the restoration speed, and the degree to which the component can recover of the system component. Fang and Sansavini (2019) formulated a two-stage stochastic programming model to minimize the expected system resilience loss, considering the uncertainty of the repair time and the total amount of repair resource units.
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Restoration interdependency
Sharkey et al. (2016) identified restoration interdependencies by analyzing several news reports/articles about the restoration efforts after Hurricane Sandy. This study provides a classification scheme including five distinct classes of restoration interdependency: traditional precedence, effectiveness, options precedence, time-sensitive options, and competition for resources. Herein, the most frequently observed restoration interdependency is traditional precedence. It means that the restoration task in an infrastructure system cannot be started until the restoration task in another one is complete. That is, the feasibility of restoring the specific component requires the
Sharkey et al. (2016) identified restoration interdependencies by analyzing several news reports/articles about the restoration efforts after Hurricane Sandy. This study provides a classification scheme including five distinct classes of restoration interdependency: traditional precedence, effectiveness, options precedence, time-sensitive options, and competition for resources. Herein, the most frequently observed restoration interdependency is traditional precedence. It means that the restoration task in an infrastructure system cannot be started until the restoration task in another one is complete. That is, the feasibility of restoring the specific component requires the