Dynamics Of Cascading Failures Research Articles

Robustness analysis of interdependent network accounting for failure probability and coupling patterns.

The robustness of interdependent networks against perturbations is an important problem for network design and operation. This paper focuses on establishing a cascading failure dynamics model and analyzing the robustness for interdependent networks, in which the states of the nodes follow certain failure probability and various connectivity patterns. First, to describe the removal mechanism of an overloaded node, the failure probability associated with the load distribution of components was proposed. Then, we present the node capacity cost and the average capacity cost of the network to investigate the propagation of cascading failures. Finally, to discuss the impact of the configuration parameters on robustness, some numerical examples are conducted, where the robustness was analyzed based on the proposed method and different interdependence types. Our results show that, the larger the overload parameter, the more robust the network is, but this also increases the network cost. Furthermore, we find that allocating more protection resources to the nodes with higher degree can enhance the robustness of the interdependent network. The robustness of multiple-to-multiple interdependent networks outperforms that of one-to-one interdependent networks under the same coupling pattern. In addition, our results unveil that the impact of coupling strategies on the robustness of multiple-to-multiple interdependent networks is smaller than that of one-to-one interdependent networks.

Catastrophic cascade of failures in interdependent hypergraphs.

The failures of individual agents can significantly impact the functionality of associated groups in interconnected systems. To reveal these impacts, we develop a threshold model to investigate cascading failures in double-layer hypergraphs with interlayer interdependence. We hypothesize that a hyperedge disintegrates when the proportion of failed nodes within it exceeds a threshold. Due to the interdependence between a node and its replica in the other layer, the disintegrations of these hyperedges could trigger a cascade of events, leading to an iterative collapse across these two layers. We find that double-layer hypergraphs undergo abrupt, discontinuous first-order phase transitions during systemic collapse regardless of the specific threshold value. Additionally, the connectivity measured by average cardinality and hyperdegree plays a crucial role in shaping system robustness. A higher average hyperdegree always strengthens system robustness. However, the relationship between system robustness and average cardinality exhibits non-monotonic behaviors. Specifically, both excessively small and large average cardinalities undermine system robustness. Furthermore, a higher threshold value can boost the system's robustness. In summary, our study provides valuable insights into cascading failure dynamics in double-layer hypergraphs and has practical implications for enhancing the robustness of complex interdependent systems across domains.

Retracted: Cascading Failure Dynamics against Intentional Attack for Interdependent Industrial Internet of Things

Retracted: Cascading Failure Dynamics against Intentional Attack for Interdependent Industrial Internet of Things

Scaling laws of failure dynamics on complex networks

AbstractThe topology of the network of load transmitting connections plays an essential role in the cascading failure dynamics of complex systems driven by the redistribution of load after local breakdown events. In particular, as the network structure is gradually tuned from regular to completely random a transition occurs from the localized to mean field behavior of failure spreading. Based on finite size scaling in the fiber bundle model of failure phenomena, here we demonstrate that outside the localized regime, the load bearing capacity and damage tolerance on the macro-scale, and the statistics of clusters of failed nodes on the micro-scale obey scaling laws with exponents which depend on the topology of the load transmission network and on the degree of disorder of the strength of nodes. Most notably, we show that the spatial structure of damage governs the emergence of the localized to mean field transition: as the network gets gradually randomized failed clusters formed on locally regular patches merge through long range links generating a percolation like transition which reduces the load concentration on the network. The results may help to design network structures with an improved robustness against cascading failure.

Dynamics of cascades in spatial interdependent networks.

The dynamics of cascading failures in spatial interdependent networks significantly depends on the interaction range of dependency couplings between layers. In particular, for an increasing range of dependency couplings, different types of phase transition accompanied by various cascade kinetics can be observed, including mixed-order transition characterized by critical branching phenomena, first-order transition with nucleation cascades, and continuous second-order transition with weak cascades. We also describe the dynamics of cascades at the mutual mixed-order resistive transition in interdependent superconductors and show its similarity to that of percolation of interdependent abstract networks. Finally, we lay out our perspectives for the experimental observation of these phenomena, their phase diagrams, and the underlying kinetics, in the context of physical interdependent networks. Our studies of interdependent networks shed light on the possible mechanisms of three known types of phase transitions, second order, first order, and mixed order as well as predicting a novel fourth type where a microscopic intervention will yield a macroscopic phase transition.

Effects of collapse probability on cascading failure dynamics for duplex weighted networks

Effects of collapse probability on cascading failure dynamics for duplex weighted networks

Recursive traffic percolation on urban transportation systems.

This paper proposes a recursive traffic percolation framework to capture the dynamics of cascading failures and analyze potential overloaded bottlenecks. In particular, compared to current work, the influence of external flow is considered, providing a new perspective for the study of regional commuting. Finally, we present an empirical study to verify the accuracy and effectiveness of our framework. Further analysis indicates that external flows from different regions affect the network. Our work requires only primary data and verifies the improvement of the functional network.

Data-Integrity Aware Stochastic Model for Cascading Failures in Power Grids

The reliable operation of power grids during cascading failures is heavily dependent on the interdependencies between the power grid components and the supporting communications and control networks. Moreover, the system operators’ expertise in dealing with cascading failures can play a pivotal role during contingencies. In this paper, a dynamical probabilistic model is developed based on Markov-chains, which captures the dynamics of cascading failures in the power grid. Specifically, a previously developed Markov-chain based model is extended to capture the trade-off between the benefits of having a robust communication infrastructure and its vulnerability from data integrity (e.g., cyber-attacks). State-space reduction of the complex interactions between power grids, communication networks and system operators is achieved by judiciously specifying the state variables of the Markov chain. The impact of system operators’ probability of error during a cascade-mitigation action is incorporated into the model as a function of the state variables of the Markov chain. A point of diminishing returns is observed beyond which the effect of information infidelity outweighs the benefits of having more information. For a given level of cyber threat, an optimal size of a communication network is observed that minimizes the expected number of transmission-line failures before the cascade stops.

Vulnerability analysis of the global liner shipping network: from static structure to cascading failure dynamics

Robust maritime transportation networks are essential to the development of world economy. But vulnerability of the global liner shipping network (GLSN) to unexpected interruptions has become apparent since the COVID-19 pandemic began, in that a single port interruption could be sufficient to trigger a cascading failure (i.e., port congestion propagation). To understand the vulnerability of the GLSN under such cascading failures, we propose a novel cascading model, which incorporates the realistic factor of liner shipping service routes’ behavior of port rotation adjustments under port failures. We apply the model to an empirical GLSN, showing that the GLSN under cascading failures is significantly more vulnerable than its static structure. Regarding two common adjustments of service routes’ port rotations (i.e., skipping failed ports and choosing alternative ports), we find that choosing alternative ports increases the GLSN vulnerability to cascading failures. Within the proposed model, we also introduce a metric termed port dynamic criticality to characterize the contribution of each port to the overall network robustness against cascading failures, finding it significantly and positively associated with port’s topological centrality in the initial GLSN. These findings provide managerial insights into preventing or mitigating port congestion propagation in the GLSN.

Greedy control of cascading failures in interdependent networks

Complex systems are challenging to control because the system responds to the controller in a nonlinear fashion, often incorporating feedback mechanisms. Interdependence of systems poses additional difficulties, as cross-system connections enable malicious activity to spread between layers, increasing systemic risk. In this paper we explore the conditions for an optimal control of cascading failures in a system of interdependent networks. Specifically, we study the Bak–Tang–Wiesenfeld sandpile model incorporating a control mechanism, which affects the frequency of cascades occurring in individual layers. This modification allows us to explore sandpile-like dynamics near the critical state, with supercritical region corresponding to infrequent large cascades and subcritical zone being characterized by frequent small avalanches. Topological coupling between networks introduces dependence of control settings adopted in respective layers, causing the control strategy of a given layer to be influenced by choices made in other connected networks. We find that the optimal control strategy for a layer operating in a supercritical regime is to be coupled to a layer operating in a subcritical zone, since such condition corresponds to reduced probability of inflicted avalanches. However this condition describes a parasitic relation, in which only one layer benefits. Second optimal configuration is a mutualistic one, where both layers adopt the same control strategy. Our results provide valuable insights into dynamics of cascading failures and and its control in interdependent complex systems.

Retracted] Cascading Failure Dynamics against Intentional Attack for Interdependent Industrial Internet of Things

The emerging Industrial Internet of Things (IIoT) provides industries with an opportunity to collect, aggregate, and analyze data from sensors, including motion control, machine‐to‐machine communication, predictive maintenance, smart energy grid, big data analysis, and other smart connected medical systems. The physical systems and the cyber systems are organically integrated, forming an interdependent IIoT. This system provides us with enormous advantages, but at the same time, it also introduces the main safety challenges in the design and operation phase. To exploit the security threats of IIoT systems, in this paper, we propose a novel security‐by‐design approach for interdependent IIoT environments across two different levels, namely, theory modeling and runtime simulation. Our method theoretically analyzes the cascading failure dynamics of the intentional attack network. Simultaneously, we verified the theoretical results through simulations and gave the risk factors that affect the system’s security to mitigate potential security attack threats. Besides, we prove its applicability through comparative simulation experiments to study application environments that rely on IIoT, which shows that our method helps identify risk factors and mitigate IIoT attacks’ mechanism.

A Stochastic Model of Cascading Failure Dynamics in Cyber-Physical Power Systems

Uncertain events such as renewable generation and load fluctuation will introduce uncertainties into the grid that might severely affect the system's robustness against cascading failure. A stochastic model for studying the cascading failure dynamics of cyber-physical power systems is proposed, the aim being to examine the impacts of uncertainties on the system's vulnerability to cascading failure. This model retains the structural and operating characteristics of cyber-physical power systems. Topological failure and communication operational failure described by data traffic model are considered as being deterministic, whereas grid operational failure described by probabilistic load flow model is considered as being stochastic. Stochastic methods are used to select the failure-prone components and to determine the time of failure of each selected component. Moreover, the effects of load uncertainty and heavy load demands on the system's vulnerability to cascading failure are studied. Simulation results indicate that the failure propagation of a cyber-physical power system is the result of repeated mutual triggering between the power network and the coupled communication network. In addition, the increased load uncertainty can cause cascading failure, and the higher the load uncertainty the more severe the blackouts. Moreover, higher load demand makes the coupled system more vulnerable to cascading failure.

The Robustness of Interdependent Networks With Traffic Loads and Dependency Groups

Existing researches on cascading failures of interdependent networks are mainly based on the percolation theory and do not consider the influence of dynamic load propagation and dependency groups. In this paper, we develop a novel interdependent system model to capture this phenomenon, also known as the hybrid cascading failure model. A degree-based targeted attack strategy on the cascading failure process of interdependent networks is studied. Combining dependency groups, interdependent relations, and traffic loads, small fraction of initial failed nodes may lead to the complete fragmentation of interdependent networks. The influence of two different dependency groups distributions on the robustness of interdependent networks under three coupling preferences is studied respectively. We provide a thorough analysis of the dynamics of cascading failures in interdependent networks initiated with a targeted attack. The system robustness is quantified as the surviving fraction of nodes in the giant connected component at the end of cascading failures. Our results highlight the need to consider loads, group effects and coupling preferences when designing the robust interdependent networks. And it is necessary to take steps in the early stage to reduce the losses caused by the large-scale cascading failures of infrastructure networks.

Uncovering community structure in networks via hybrid clustering using cascading failure dynamics and topological metric functions

Many networks have community structure — groups of nodes within which connections are dense but between which they are sparser. While there exists a range of algorithms for community detection in networks, most of them try to discover this important mesoscale structure from a topological point of view solely. Here we develop a hybrid clustering approach for uncovering the community structure in a network using a combination of information on local topology of the network and on the dynamics of the cascading failures. The originality of the proposed approach is that we introduce a novel fusion of the dynamic behaviors of the cascading failures and topological metric functions in the [Formula: see text]th-nearest neighbor density scheme, which integrates both the global and local structural information of a given network for community detection. The experimental results on both artificial random and real-world benchmark networks indicate the effectiveness and reliability of our approach.

Robustness of Interdependent Cyber-Physical Systems Against Cascading Failures

Integrated cyber-physical systems, such as the smart-grid, are increasingly becoming the underpinning technology for major industries. A major concern regarding such systems are the seemingly unexpected large scale failures, which are often attributed to a small initial shock getting escalated due to intricate dependencies within and across the individual (e.g., cyber and physical) counterparts of the system. In this paper, we develop a novel interdependent system model to capture this phenomenon, also known as cascading failures. Our framework consists of two networks that have inherently different characteristics governing their intradependence: first, a cyber -network where a node is deemed to be functional as long as it belongs to the largest connected (i.e., giant) component; and, second, a physical network where nodes are given an initial flow and a capacity , and failure of a node results with redistribution of its flow to the remaining nodes, upon which further failures might take place due to overloading (i.e., the flow of a node exceeding its capacity). Furthermore, it is assumed that these two networks are interdependent . For simplicity, we consider a one-to-one interdependence model where every node in the cyber-network is dependent upon and supports a single node in the physical network, and vice versa. We provide a thorough analysis of the dynamics of cascading failures in this interdependent system initiated with a random attack. The system robustness is quantified as the surviving fraction of nodes at the end of cascading failures, and is derived in terms of all network parameters involved (e.g., degree distribution, load/capacity distribution, failure size, etc.). Analytic results are supported through an extensive numerical study. Among other things, these results demonstrate the ability of our model to capture the unexpected nature of large-scale failures, and provide insights on improving system robustness.

Impacts of Operators’ Behavior on Reliability of Power Grids During Cascading Failures

Human operators play a key role in the reliable operation of critical infrastructures. However, human operators may take actions that are far from optimum. This can be due to various factors affecting the operators’ performance in time-sensitive and critical situations such as reacting to contingencies with significant monetary and social impacts. In this paper, an analytic framework is proposed based on Markov chains for modeling the dynamics of cascading failures in power grids. The model captures the effects of operators’ behavior quantified by the probability of human error under various circumstances. In particular, the observations from historical data and information obtained from interviews with power-system operators are utilized to develop the model as well as identify its parameters. In light of the proposed model, the noncritical regions of power-system's operating characteristics with human-factor considerations are characterized under which the probability of large cascading failures is minimized.

Abnormal dynamics of cascading edge failures with congestion effect

Considering congestion effects in realistic network environments, we give a new method to adjust dynamically adjust the weight of the congested edge. We calculate the load on an edge based on the revised betweenness method and propose a novel model with three states of edges to investigate the dynamics of cascading failures in the ring network, the BA scale-free network, and the real traffic networks in London. By two robust metrics, we surprisingly observe the abnormal dynamics of cascading propagation, especially compared with that in the unadjustable weight, the curves of cascading dynamics in the adjustable weight are more irregular, which means that enhancing the capacity of each edge is not always better to avoid the cascading propagation. In addition, our simulation results show that the dynamical change of the edge’s weight makes the heterogeneous BA networks more vulnerable.

A Stochastic Model of Cascading Failure Dynamics in Communication Networks

In this brief, we propose a stochastic model based on state transition theory to investigate the dynamics of cascading failures in communication networks. We describe the failure events of the nodes in the network as node state transitions. Taking a probabilistic perspective, we focus on two uncertain conditions in the failure propagation process: which node in the network will fail next and how long it will last before the next node state transition takes place. The stochastic model gives each overloaded element a probability of failing, and the failure rate is relevant to the degree of overloading. Moreover, the time dimension is considered in the stochastic process, by removing a node after a time delay when its traffic load exceeds its capacity. We employ this proposed model to study the dynamics of cascading failure evolution in a Barabasi–Albert scale-free network and an Internet AS-level network. Simulation results reveal the effects of the initial failure pattern, community structure and network design parameters on the dynamic propagation of cascading failures.

Electrical and topological drivers of the cascading failure dynamics in power transmission networks

To systematically study key factors affecting cascading failures in power systems, this paper advances algorithms for generating synthetic power grids with realistic topological and electrical features, while computationally quantifying how such factors influence system performance probabilistically. Key parameters affecting line outages and power losses during cascading failures include line redundancy, load/generator layout and re-dispatch strategies. Our study combines a synthetic power grid generator with a direct current (DC) cascading failure simulator. The impact of each of the factors and their interactions unravel useful insights for interventions aimed at reducing the probabilities of large blackouts on existing and future power systems. Moreover, conclusions drawn from a spectrum of different power grid topologies and electrical configurations offer more generality than typically attained when studying specific test cases. Line redundancy and distributed generation appear as the most efficacious parameters for reducing the probabilities of large power losses and multiple line overloads, although the effect decays with network density. Also, re-dispatch strategies are critical on the distribution of the cascading failure size in terms of line failures. These and related results provide the basis for probabilistic analyses and future design of evolving power transmission systems under uncertainty.

Modeling the Dynamics of Cascading Failures in Power Systems

In this paper, we use a circuit-based power flow model to study the cascading failure propagation process, and combine it with a stochastic model to describe the uncertain failure time instants, producing a model that gives a complete dynamic profile of the cascading failure propagation beginning from a dysfunctioned component and developing eventually to a large-scale blackout. The sequence of failures is determined by voltage and current stresses of individual elements, which are governed by deterministic circuit equations, while the time durations between failures are described by stochastic processes. The use of stochastic processes here addresses the uncertainties in individual components’ physical failure mechanisms, which may depend on manufacturing quality and environmental factors. The element failure rate is related to the extent of overloading. A network-based stochastic model is developed to study the failure propagation dynamics of the entire power network. Simulation results show that our model generates dynamic profiles of cascading failures that contain all salient features displayed in historical blackout data. The proposed model thus offers predictive information about occurrences of large-scale blackouts. We further plot cumulative distribution of the blackout size to assess the overall system’s robustness. We show that heavier loads increase the likelihood of large blackouts and that small-world network structure would make cascading failure propagate more widely and rapidly than a regular network structure.