Network Reliability Assessment Research Articles

Bayesian improved cross entropy method with categorical mixture models for network reliability assessment

We employ the Bayesian improved cross entropy (BiCE) method for rare event estimation in static networks and choose the categorical mixture (CM) as the parametric family to capture the dependence among network components. The proposed method is termed BiCE-CM. At each iteration of BiCE-CM, the mixture parameters are updated through the weighted maximum a posteriori (MAP) estimate, which mitigates the overfitting issue of the standard improved cross entropy (iCE) method through a novel balanced prior, and we propose a generalized version of the expectation–maximization (EM) algorithm to approximate this weighted MAP estimate. The resulting importance sampling distribution is proved to be unbiased. For choosing a proper number of components K in the mixture, we compute the Bayesian information criterion (BIC) of each candidate K as a by-product of the generalized EM algorithm. The performance of the proposed method is investigated through a simple illustration, a benchmark study, and a practical application. In all these numerical examples, the BiCE-CM method results in an efficient and accurate estimator that significantly outperforms the standard iCE method and the BiCE method with the independent categorical distribution.

Research on Reliability Prediction Methods for Dynamic Networks Based On Deep Neural Networks

In reality many networks, such as information storage networks, can be modelled as a multi-state stochastic flow network. The reliability of an information storage network is the probability that the network is able to deliver the required amount of information data to the specified server, and its an important metric to assess the performance of an information storage network. Most existing multi-state network reliability assessment algorithms are calculated using very small capacity vectors. However, calculating the reliability of such a network requires reuse of algorithms and is inefficient when the network size, demand, etc., changes rapidly, resulting in managers not making timely decisions accordingly. In order to obtain reliability metrics quickly, this paper proposes a dynamic network reliability prediction model based on deep neural networks (DNNs), which allows the corresponding reliability to be obtained quickly even when the network is changing rapidly. Finally, a local information storage network is used as an example for validation to illustrate the feasibility of the prediction model.

A Validation of the Phenomenon of Linearly Many Faults on Burnt Pancake Graphs with Its Applications

“Linearly many faults” is a phenomenon observed by Cheng and Lipták in which a specific structure emerges when a graph is disconnected and often occurs in various interconnection networks. This phenomenon means that if a certain number of vertices or edges are deleted from a graph, the remaining part either stays connected or breaks into one large component along with smaller components with just a few vertices. This phenomenon can be observed in many types of graphs and has important implications for network analysis and optimization. In this paper, we first validate the phenomenon of linearly many faults for surviving graph of a burnt pancake graph BPn when removing any edge subset with a size of approximately six times λ(BPn). For graph G, the ℓ-component edge connectivity denoted as λℓ(G) (resp., the ℓ-extra edge connectivity denoted as λ(ℓ)(G)) is the cardinality of a minimum edge subset S such that G−S is disconnected and has at least ℓ components (resp., each component of G−S has at least ℓ+1 vertices). Both λℓ(G) and eλ(ℓ)(G) are essential metrics for network reliability assessment. Specifically, from the property of “linearly many faults”, we may further prove that λ5(BPn)=λ(3)(BPn)+3=4n−3 for n⩾5; λ6(BPn)=λ(4)(BPn)+4=5n−4 and λ7(BPn)=λ(5)(BPn)+5=6n−5 for n⩾6.

Network reliability analysis through survival signature and machine learning techniques

As complex networks become ubiquitous in modern society, ensuring their reliability is crucial due to the potential consequences of network failures. However, the analysis and assessment of network reliability become computationally challenging as networks grow in size and complexity. This research proposes a novel graph-based neural network framework for accurately and efficiently estimating the survival signature and network reliability. The method incorporates a novel strategy to aggregate feature information from neighboring nodes, effectively capturing the response flow characteristics of networks. Additionally, the framework utilizes the higher-order graph neural networks to further aggregate feature information from neighboring nodes and the node itself, enhancing the understanding of network topology structure. An adaptive framework along with several efficient algorithms is further proposed to improve prediction accuracy. Compared to traditional machine learning-based approaches, the proposed graph-based neural network framework integrates response flow characteristics and network topology structure information, resulting in highly accurate network reliability estimates. Moreover, once the graph-based neural network is properly constructed based on the original network, it can be directly used to estimate network reliability of different network variants, i.e., sub-networks, which is not feasible with traditional non-machine learning methods. Several applications demonstrate the effectiveness of the proposed method in addressing network reliability analysis problems.

A new method for multi-state flow networks reliability estimation based on a Monte Carlo simulation and intersections of sets

The problem of the assessment of a multi-state flow network reliability can be very time-consuming, especially for large networks. Simulation approaches alleviate this problem by generating random capacity vectors and comparing them with d-MPs or d-MCs, for estimation of network reliability. In this study, a new approach to compare randomly generated vectors with a given list of vectors is developed. The presented method is based on intersections of some sets of indices of a given list of vectors. The computational complexity of the presented approach is examined and compared with existing approaches. Two comprehensive examples are provided to estimate the network reliability and compare the effectiveness of the presented method with existing ones. Numerical experiments show that the presented method is usually more efficient than existing ones especially if the network unreliability is estimated using d-MCs.

Study of the Telecommunication Networks Performance and Reliability Indicators

It is currently urgent to improve the technical characteristics and increase the efficiency of telecommunication networks because of the global problem of ensuring the reliable transmission, processing and protection of commercial information in telecommunication networks. The aim of this study is to assess the reliability indicators of telecommunication networks and analyse the level of their development. The aim was achieved through the methods that were used to assess the reliability of the entire network: the generalized method of analytical assessment of the telecommunication network reliability; connection-based metrics; scaling of telecommunication networks, and application of unified reliability indicators to routine control, operation and maintenance. As a result of the research, the indicators of telecommunication networks were studied with and without using connection-based metrics. As a result, the network metrics were also divided into distribution and generation/transmission reliability and telecommunication network metrics – into connection-, performance-, and condition-based metrics, which showed improvements in network performance and reliability. As a prospect for further research, studying and improving the telecommunication network reliability indicators is suggested.

Bayesian improved cross entropy method for network reliability assessment

We identify the zero count problem (or overfitting) of cross-entropy-based methods in the context of network reliability assessment, and propose a consistent Bayesian estimator that mitigates this issue. Thereby, we derive the posterior predictive distribution of importance sampling distribution parameters that replaces the weighted maximum likelihood estimation employed in the standard cross entropy optimization. For rare event estimation, we embed the Bayesian estimator into the improved cross entropy (iCE) method and provide theoretical insights into the adaptive selection of intermediate target distributions in the iCE. The modified version of the iCE, termed the Bayesian iCE (BiCE), is proved to be unbiased. By contrast, even with higher computational cost, the standard iCE method is often significantly biased when solving network reliability problems. Our numerical investigations indicate that a uniform prior in the proposed BiCE method performs suboptimally, and an informative symmetric Dirichlet prior is suggested.

Analysis of data transmission network construction technologies with high requirements for information security, reliability, and latency

The scientific article is dedicated to the analysis of contemporary approaches and technologies in the construction of data transmission networks aimed at ensuring information security, reliability, and minimal latency. The necessity of comprehensively considering factors influencing network efficiency with a focus on reliability and security is substantiated. Network analysis enables the creation of an infrastructure that meets the demands of the modern information environment, comprehensively weighing the advantages and disadvantages of each network technology during construction. For the mathematical evaluation of data transmission network reliability, a Markov model is proposed, which is based on Markov processes theory. Developed using the Python programming language and relevant libraries, the model allows for a quantitative assessment of data transmission network reliability, considering various failure factors, state transitions, and recovery. The model facilitates forecasting network states and planning preventive organizational and technical measures to ensure reliability and security, in light of the constantly increasing demands for service quality and confidential information protection. An analysis of transmission delay methods has revealed a correlation between the transmission speed and volume of information with various factors, such as bandwidth, network load, connection type and speed, and data processing by network nodes. The research underscores the need to choose specific methods based on the network’s characteristics and its intended tasks. Based on the analysis results, to construct efficient networks that meet information security, reliability, and transmission delay requirements, there is a recognized need for comprehensive development of evaluation systems and the creation of a unified evaluation model.

Reliability assessment of water distribution network using specific forms of state space models

ABSTRACT This article introduces methods used for the assessment and prediction of water distribution network (WDN) reliability. A failure rate expressed as the number of failures per operating day is considered to be the basic measure of the achieved WDN reliability level. The proposed method is based on the assumption that information about WDN failures is available in the form of long-term time series. The authors propose a mathematical model using specific forms of state space models which takes into account a seasonal effect and an intervention variable. The proposed model enables us to identify and assess both long-term trends in WDN reliability evolution and short-term reliability changes related to seasonal effects and also to predict the future development of WDN reliability. The practical applicability of the proposed method is demonstrated by assessing the information set based on long-term observations of the selected WDN failures.

Pareto-based grouping meta-heuristic algorithm for humanitarian relief logistics with multistate network reliability

This article considers a biobjective location-routing problem to deliver relief resources to the victims affected by a disaster under uncertainty in demand, transportation infrastructure, and travel time. Since transportation networks are exposed to a considerable level of uncertainty, choosing the reliable path for relief goods to be transmitted to the affected areas ensures the arrival of these supplies. For the first time, route reliability is calculated based on the multistate theory, and the universal generating function technique is used for network reliability assessment. The problem is formulated as a multiperiod robust biobjective mixed-integer programming model. Two objective functions are considered: (a) decreasing the sum of arrival times of relief vehicles at the demand nodes for delivering aids to the affected areas, and (b) increasing the minimum route reliability for all the serving vehicles. A novel multiobjective grouping algorithm is proposed to obtain the Pareto-optimal solutions of the problem. Then, its performance is compared with two other multiobjective grouping algorithms. To evaluate the solution method, the algorithms are implemented on various test problems and compared statistically. A case study is presented to illustrate the potential applicability of our model. Additionally, to determine the effect of the changes in the main parameters of the problem on the value of objective functions, the sensitivity analyses are performed and the managerial insights are given.

Multi‐scale seismic reliability assessment of networks by centrality‐based selective recursive decomposition algorithm

AbstractAs lifeline networks such as transportation or electricity networks in modern societies are intricately interlocked, a small number of components damaged by natural or man‐made disasters can have a great impact on network performance. For this reason, it is essential to assure the capability of rapid assessment of network reliability to make prompt follow‐up measures. Despite the rapid development of various algorithms and computing power, the capability is still limited due to computational cost for analyzing the connectivity of a single origin and destination (O/D) node pair in large‐scale networks. Therefore, this paper introduces a new algorithm utilizing network centrality, termed “centrality‐based selective recursive decomposition algorithm” (CS‐RDA). By preferentially decomposing the node which is most likely to belong to the min‐cut identified based on the betweenness centrality, the convergence of the bounds on the O/D connectivity can be expedited significantly. This paper also introduces a new multi‐scale analysis approach termed “edge‐betweenness algorithm.” The algorithm groups components such that its modularity is maximized, by sequentially removing edges that have the highest level of betweenness centrality. As a result, the reliability of large‐scale networks can be accurately evaluated in a short time owing to the reduced complexity of the simplified network. The proposed methods are successfully demonstrated by a hypothetical network example, the highway bridge networks in San Jose and San Diego in California, USA.

Analysis and design of energy storage capacity of AC-DC hybrid power distribution unit with energy storage to improve the reliability of power grid

Based on the development of AC-DC distribution network, a new AC-DC distribution device with energy storage structure is designed in this paper. This paper first analyzes the existing AC-DC power distribution equipment and network reliability assessment methods. On this basis, the design is put forward, the energy storage link is placed at the DC high voltage side. The constraints of energy storage as an critical load backup power supply are defined and the mathematical model is established. In this paper the timing Monte Carlo method is used to calculate the reliability of the device and the power grid. The model in this paper can be applied to a variety of distribution network structure and energy storage scenarios, with high accuracy. It is concluded that the AC-DC distribution unit has remarkable effect in improving reliability.

ЗАСТОСУВАННЯ В МУЛЬТИАГЕНТНІЙ СИСТЕМІ УПРАВЛІННЯ МОДЕЛІ ФУНКЦІОНУВАННЯ ФРАГМЕНТУ ТЕЛЕКОМУНІКАЦІЙНОЇ МЕРЕЖІ CИСТЕМИ ЗВ’ЯЗКУ ЗБРОЙНИХ СИЛ УКРАЇНИ

Today, there are many standards that describe the architecture and mechanisms for monitoring and controlling elements of the Carrier Ethernet network, but there is no single methodology and requirements for the control system of such a communication network are not formed. This article proposes a solution to this problem by modeling the process of functioning of a telecommunication network based on this technology to manage its configuration. To create this model, the AnyLogic simulator was selected. The aim of the work is to identify the relationship between the reliability indicators of a telecommunication network based on Carrier Ethernet technology and the process of functioning of the telecommunication network management and recovery subsystems. As well as obtaining the dependence of the availability factor on the duration of the time between failures, the time of failure and on the quantitative characteristics of the configuration of the simulated network fragment. The multi-agent system, which is part of the control system, is in interaction with it. The use of a distributed telecommunications network control facility based on Carrier Ethernet technology at MASU will provide a demonstration of the dynamics of changes in the state of a fragment of a telecommunications network and obtain an estimate of network reliability. The solution to the problem of building the MASU model is based on the use of agent-based modeling, which belongs to the class of agent-based models. The paper uses the provisions of probability theory, control theory and system theory. The novelty of the presented model lies in the selection of a new Carrier Ethernet control object, the selection of an original set of control and management mechanisms for their inclusion in the model, and the use of the mathematical apparatus of agent modeling. Using the presented model to study the functioning of a telecommunication network allows you to track the behavior of each node and each route with its own failure and recovery rates for a network structure of any complexity, and allows you to solve problems associated with determining the length of time to lose connectivity in the route and the duration of the time between failures all routes simultaneously, allows you to form an assessment of network reliability and fault tolerance.

Reliability‐oriented optimal planning of charging stations in electricity–transportation coupled networks

To coordinate the increasing application of electric vehicles (EVs), the deployment of charging stations becomes vital for supporting the charging and navigation for EVs, which also affects the reliability of the corresponding electricity network. To achieve the balanced reliability in both the electricity network and EV trip, an optimal planning method for charging stations in the electricity-transportation coupled networks is proposed. Firstly, an integrated management strategy of EVs is demonstrated to model the reliability enhancement of the two networks. Thereafter, a coupled network reliability assessment method based on the quasi-sequential Monte Carlo simulation is presented. This study proposes a novel reliability-oriented multi-objective optimal planning model for charging stations planning problem, which is resolved by implementing the optimal planning scheme from the candidate nodes. Additionally, correlation analysis is performed to ensure that the proposed model can be solved quickly for large-scale electricity network with complex transportation flow input data. A test case is presented and simulated to validate the feasibility and effectiveness of the proposed method.

A literature review on network reliability analysis and its engineering applications

The applications of networks can be observed in numerous engineering realms mainly computers and communication, transportation, electric transmission and oil and gas distribution. Estimating the reliability of such networks is a critical task for the well-being of society as well as a nation. The paradigm of network reliability has evolved considerably over the past few decades. The purpose of this article is to present the developments in network reliability domain in a laconic manner. This paper discusses the various metrics used to evaluate network connectivity along with their mathematical backgrounds. The various algorithms namely State Enumeration, Sum of disjoint product, Minimal Cut Set, Factoring theorem, Cellular Automata, Subset Simulation, Percolation theory, Binary Decision Diagrams, and Universal Generating Functions are enumerated in this review study. The application part of algorithms with their advantages, limitations and scope are presented. Finally, the methodologies used for assessment of network reliability are discussed. This article aims at providing a holistic view of the network reliability practices, which may prove to be helpful for researchers across the globe.

Water Distribution Network Reliability Assessment and Isolation Valve System

Mechanical reliability analysis of water distribution networks (WDNs) refers to the assessment to provide correct service to customers under abnormal functioning conditions due to system component failures. Mechanical reliability depends on the isolation valve system (IVS) effectiveness in isolating a network segment and on the failure probability. The main aim of this work was the formal development of reliability indicators considering pressure-driven analysis (PDA) for customer demand and topological changes. Three factors influencing reliability were identified: (1) the hydraulic behavior of the still-connected network; (2) the topological performance of the IVS; and (3) the topological performance of the IVS with respect to unintended isolation. The reliability performance assessment of the network over time depends on the hydraulic capacity of the WDN under abnormal functioning conditions and on two IVS performance topological indicators of the risk of disconnection and unintended isolations. The hydraulic capacity was computed using PDA, whereas the topological risks were computed considering the unsupplied demand in the isolated segment and the normalized failure probability, i.e., the probability of a segment disconnection for an assumed failure occurrence in the network. The development of a modularity index for an IVS was achieved in a consistent framework and the integrated design of an IVS and district metering areas was introduced. The framework allows the analysis of the isolation valve failure. A real Apulian WDN was used to discuss and demonstrate the theoretical findings.

Evaluating component importance and reliability of power transmission networks subject to windstorms: methodology and application to the nordic grid

We present a procedure for the efficient assessment of component importance and network reliability in power transmission grids subject to wind hazards. A stochastic wind load model is learned from windstorm data. Component fragility models are established by combining information on the design wind loads prescribed by the relevant structural codes and the observed failure rate in the network as a whole. Network performance is assessed by a DC power flow model, which accounts for cascading failures and potential islanding due to load redistribution after initial failure events caused by the windstorms. Besides evaluating the network reliability, selected importance measures are defined to rank single components according to their influence on the overall system reliability. We thereby distinguish component importance related to initial failures triggered by the windstorms and component importance related to potential subsequent cascading failures. The procedure is demonstrated by application to the Nordic Grid model of the electrical power transmission network in Denmark, Norway, Sweden, and Finland. We find that the procedure can provide an efficient basis for planning network improvements in terms of (1) strengthening vulnerable line segments against wind loads and (2) increasing line capacities to limit cascading failures.

An Efficient Algorithm for Enumerating all Minimal Paths of a Graph

The enumeration of all minimal paths between a terminal pair of a given graph is widely used in a lot of applications such as network reliability assessment. In this paper, we present a new and efficient algorithm to generate all minimal paths in a graph G(V, E). The algorithm proposed builds the set of minimal paths gradually, starting from the source nodes. We present two versions of our algorithm; the first version determines all feasible paths between a pair of terminals in a directed graph without cycle, and this version runs in linear time O(|V| + |E|). The second version determines all minimal paths in a general graph (directed and undirected graph). In order to show the process and the effectiveness of our method, an illustrative example is presented for each case.

Information-dependent seismic reliability assessment of bridge networks based on a correlation model

The focus of this study is the seismic reliability assessment of bridge networks, which is normally recognised with temporal and spatial variations similar to other engineered systems. The essence of such variation is that the assessment actually changes with available information. The relevant ‘information’ is clarified here and simply divided into two categories, i.e. the basic properties of the network together with the hazards and the real performance of part of the network. Correspondingly, approaches to an assessment with different categories of information are identified, and the framework for an information-dependent seismic reliability assessment is formulated. The basis for such information-dependent assessment is the description of the dependence structure of the seismic performance of bridges. Here, a correlation model that covers different aspects relevant to bridge performance is derived to play such role and is combined with the fragility analysis of individual bridges to realise the network reliability assessment and the importance measure of components in the priority of information collection. The proposed framework, together with the correlation model, is demonstrated in an example of a traffic network that connects 8 cities by highways with 12 standard reinforced-concrete overpass bridges in California.

Quantum-inspired Boolean states for bounding engineering network reliability assessment

Significant methodological progress has taken place to quantify the reliability of networked systems over the past decades. Both numerical and analytical methods have enjoyed improvements via a host of advanced Monte Carlo simulation strategies, state space partition methods, statistical learning, and Boolean functions among others. The latter approach exploits logic to approximate network reliability assessments efficiently while offering theoretical error guarantees. In parallel, physicists have made progress modeling complex systems via tensor networks (TNs), particularly quantum many-body systems. Inspired by the representation power of quantum TNs, this paper offers a new approach to efficiently bound all-terminal network reliability (ATR). It does so by exactly solving a related network Boolean satisfiability counting problem (or #SATNET), represented as a TN, by counting configurations in which all network nodes are connected to at least a neighbor. Our #SATNET counting outperforms state-of-the-art approximate and exact counters for the same problem as shown for challenging two-dimensional lattice networks of increasing size. While the over-counting from #SATNET increases exponentially relative to the number of configurations that satisfy ATR problems (or #RELAT), the bias is predictable for ideal networks, such as lattices, and our upper bound is guaranteed with 100% confidence. This bound also cuts through the upper bound from other analytical methods for the ATR problem, such as recursive decomposition algorithms (RDA)—a desirable feature when exact or approximate methods with error guarantees fail to scale. Clearly, our goal is not to solve the general stochastic network reliability problem, which remains a #P problem in the computational complexity hierarchy (i.e., a counting version of non-deterministic polynomial time [NP] problems for which there is no known polynomial time algorithms to find their solutions). Instead, we present a novel bounding technique for network reliability, which relies on exactly counting configurations for our network satisfiability problem by using quantum computing principles. We offer a proof for the counting bound to hold in a connectivity ATR sense, and illustrate trends with cubic and lattice networks. Overall, the proposed method provides an alternative to available system reliability assessment approaches, and opens directions for future research, especially as discoveries in logic, algebraic projections, and quantum computation continue to accrue.