Critical location identification and vulnerability analysis of interdependent infrastructure systems under spatially localized attacks
Introduction
Infrastructure systems, such as electric power, water supply, telecommunication and emergence service systems, form the backbone for functioning of a community or nation and provide essential services to support the well-being of its citizens. However, these systems are currently subject to many types of hazards, such as unavoidable natural hazards, component aging, sharp demand increase and climate change, which increase their failure probabilities and vulnerability. Also, infrastructure systems are not isolated but highly interconnected and mutually interdependent [31], [33]. Interdependencies can improve infrastructure operational efficiency, but they may also increase system vulnerability, i.e., small failures in one system can result in cascading failures within it and across to other systems, causing large economic loss and affecting people’s life in the disaster area. Hence, to better protect interdependent infrastructures, for each type of hazards, it requires modeling their direct impact on infrastructure components and then analyzing their system-level vulnerability for identifying mitigation strategies, where the term “vulnerability” in this paper is interpreted to associate with a disruptive event and is quantified as the performance drop of a system under an event [44].
To model and analyze the vulnerability of interdependent infrastructure systems, there exist many approaches in the literature, such as empirical approaches, agent based approaches, system dynamics based approaches, economic theory based approaches, network based approaches and others. A detailed review of these approaches is provided by the author in the reference [24]. This paper addresses the problem of identifying critical locations in infrastructure systems, which needs their topological and geographical information, so a network-based approach is used in this paper for their vulnerability modeling. This paper next will only review some recent network-based vulnerability studies on interdependent infrastructure systems. This type of approaches models each system by a network and describes their interdependencies by inter-links, which enable to capture system topological features and flow characteristics for identifying critical system components [10], [16], [5].
Depending on the failure modes, network-based vulnerability studies on interdependent systems can be grouped into three types. The first is vulnerability studies under random failures, which are usually modeled by randomly removing a certain fraction or number of infrastructure components [15], [29], [3], [34], [36], [37], [38], [6]. The second is vulnerability studies under natural hazards, such as earthquakes, hurricanes and lightening, and their impacts on infrastructure components are usually modeled according to fragility curves, which provide the probability of exceeding a certain damage state threshold conditional to a selected hazard intensity measure, such as peak ground acceleration or peak ground velocity or permanent ground deformation for seismic hazards [1], [11], [14], [32], [8], 3 second gust wind speed for hurricane hazards [13], [22], [26]. The third is vulnerability studies under intentional attacks, which can be further grouped into two types, depending on whether component geographical proximity is considered by the attack strategies.
The first type of intentional attacks is non-proximity-based attacks, where a set of important components (nodes or edges) is selected as the attack objective without considering their geographical proximity. This type of attacks has been studied in two ways in the literature. One is random networks based studies where only node degree distributions of networks of concern are used for analysis and the largest component size is taken as the performance metric to quantify system vulnerability under the removal of a fraction of critical nodes selected according to their degree. This type of studies can be analytically solved by generating function method when the network size tends to infinity, and results show that interdependencies increase system vulnerability in contrast to independent scenarios, while interdependent networks are difficult to defend by strategies such as protecting the high degree nodes that are found useful to significantly reduce the vulnerability of single networks [18]. The other is specific networks based studies, where system topological information and sometimes component physical properties and flow-related parameters are used for analysis. This type of studies is usually analyzed by Monte-Carlo simulation technique or advanced algorithms, and usually takes more practical system operation models and performance metrics to quantify system vulnerability. In this case, the critical components can be selected not only by initial degree and recalculated degree [12], [42], but also by component load levels [38], or by some optimization techniques or advanced algorithms to select components whose failures can cause the largest vulnerability [27], [39], [40], [43].
The second type of intentional attacks is proximity-based attacks that a set of components (nodes or edges or both) distributed in close proximity to each other in a localized area is selected as the attack objective. This type of attacks can simulate bomb attacks and military weapons with mass destruction. For interdependent randomly diluted square lattices with average node degree between 2.5 and 4.0, and the dependencies between nodes with and across networks are constrained less than a certain distance, Berezin et al. [4] modeled localized attacks by removing all nodes within a certain distance from a random attack center, and found that localized attacks can be more harmful than random attacks with the same intensities. Note that this purely topology-based study only takes the largest component size as the performance metric to quantify system vulnerability, which has weak correlations to those results obtained when the infrastructure system flow properties are considered [17], [23], [25], [9]. Also, this study only considers node failures within the attack influence area and the failures of edges that cross the area are not taken into account, but a recent work from the author shows that considering edge failures in the attack area will affect the position of critical locations [28]. For specific infrastructure networks, some scholars have considered their vulnerability by removing both nodes and edges co-located in the same attack influence area, which enables to identify the critical area so that the failures of components inside such an area lead to the largest vulnerability. Patterson and Apostolakis [30] made such a vulnerability analysis on interdependent systems in a university campus area by dividing the infrastructure map into a generic hexagonal grid with a small radius 7 m and each failure or attack influence area is modeled by a hexagon. Johansson and Hassel [19] have made a similar analysis to identify critical locations in interdependent systems by considering square attack influence areas with two different sizes 5×5 km2 and 2.5×2.5 km2. Note that the results from these studies depend on the shape of attack influence area (square, hexagon, etc.) and the attack influence area size as well as how the infrastructure map is partitioned into small attack influence areas.
This paper studies a type of spatially localized attacks that a set of infrastructure components located within or crossing a circle shaped spatially localized area is subject to damage while other components outside the area do not directly fail, which belongs to the second type of intentional attacks. For this type of attacks, this paper proposes an algorithm to identify critical locations in interdependent systems, where node and edge failures are both considered in the attack areas and infrastructure flow properties are also included for analysis. Note that different with previous research on identifying critical components or locations in infrastructure networks, which do not consider the spatial proximity of components in the critical component set [2], [20], [35], this paper identifies the critical components constrained to be all located within a limited circle shaped localized area. Also, different with the works from Patterson and Apostolakis [30] and Johansson and Hassel [19], which identify the critical components or locations based on the partition of infrastructure map, this paper does not partition the map and uses a proposed algorithm to exactly find out the critical locations. The rest of the paper is organized as follows: Section 2 provides a network-based vulnerability model of interdependent infrastructure systems. Section 3 introduces the model of spatially localized attacks and the approach to identify critical locations. Section 4 takes interdependent power and gas systems in Harris County, USA as an example to identify critical locations and make pertinent vulnerability analysis. Section 5 discusses the findings and extensions and Section 6 provides conclusions and future research.
Section snippets
Modeling vulnerability of interdependent infrastructure systems
This paper defines vulnerability of an infrastructure system under a specific disruptive event as its performance drop, then the critical location is an area that failures of components located within and crossing this area can make the largest vulnerability. Hence, to identify critical locations, it first needs a vulnerability model of interdependent systems, which can simulate the cascading failures within and between multiple systems and enable to compute system vulnerability under a
Modeling spatially localized attacks and identifying critical locations
To model spatially localized attacks, it needs to first define spatially localized areas and then describe how components within an area would fail. As a starting point, this paper considers circle shaped spatially localized areas, where a localized area has a circle shape determined by a center and a radius r, and assume all components located within or crossing the area are all failed. These assumptions can be relaxed and will be further discussed in the Section 5. Some other types of
Applications and results
This section will take interdependent power and gas systems in Harris County, Texas, USA as an example to identify critical locations in these systems and make pertinent vulnerability analysis from four aspects: effects of attack radius on critical locations and their associated vulnerability, comparison of vulnerability under spatially localized attacks and equivalent random failures, comparison of vulnerability by considering purely node failures and by considering both node and edge failures
Discussions
The results in Section 4 show that (1) Infrastructure interdependencies and attack radius largely affect the position of critical locations; (2) Spatially localized attacks on interdependent systems are less harmful than equivalent random failures; (3) In most values of attack radius, critical locations by considering only node failures do not change when considering both node and edge failures in the attack area; (d) for many values of attack radius critical locations identified by
Conclusions
This paper proposes an approach to identify critical locations in interdependent infrastructure systems, and the critical location is characterized by critical location center determined by a series of inequalities, which describe the shortest spherical distance between the center and each component in the optimum maximal component set is less than or equal to the attack radius. To better protect infrastructure systems, increasing the security inspection in the critical location center area or
Acknowledgments
This material is based upon work supported in part by the National Natural Science Foundation of China under Grant 51208223, 61572212 and the Fundamental Research Funds for the Central Universities under Grant 2014QN166. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the sponsors. The author also acknowledges the data shared by Dr. Dueñas-Osorio through his Structural and Infrastructure
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