A Computational Framework for Efficient Reliability Analysis of Complex Networks

With the growing scale and complexity of modern infrastructure networks comes the challenge of developing efficient and dependable methods for analysing their reliability. Special attention must be given to potential network interdependencies as disregarding these can lead to catastrophic failures. Furthermore, it is of paramount importance to properly treat all uncertainties. The survival signature is a recent development built to effectively analyse complex networks that far exceeds standard techniques in several important areas. Its most distinguishing feature is the complete separation of system structure from probabilistic information. Because of this, it is possible to take into account a variety of component failure phenomena such as dependencies, common causes of failure, and imprecise probabilities without reevaluating the network structure. This cumulative dissertation presents several key improvements to the survival signature ecosystem focused on the structural evaluation of the system as well as the modelling of component failures. A new method is presented in which (inter)-dependencies between components and networks are modelled using vine copulas. Furthermore, aleatory and epistemic uncertainties are included by applying probability boxes and imprecise copulas. By leveraging the large number of available copula families it is possible to account for varying dependent effects. The graph-based design of vine copulas synergizes well with the typical descriptions of network topologies. The proposed method is tested on a challenging scenario using the IEEE reliability test system, demonstrating its usefulness and emphasizing the ability to represent complicated scenarios with a range of dependent failure modes. The numerical effort required to analytically compute the survival signature is prohibitive for large complex systems. This work presents two methods for the approximation of the survival signature. In the first approach system configurations of low interest are excluded using percolation theory, while the remaining parts of the signature are estimated by Monte Carlo simulation. The method is able to accurately approximate the survival signature with very small errors while drastically reducing computational demand. Several simple test systems, as well as two real-world situations, are used to show the accuracy and performance. However, with increasing network size and complexity this technique also reaches its limits. A second method is presented where the numerical demand is further reduced. Here, instead of approximating the whole survival signature only a few strategically selected values are computed using Monte Carlo simulation and used to build a surrogate model based on normalized radial basis functions. The uncertainty resulting from the approximation of the data points is then propagated through an interval predictor model which estimates bounds for the remaining survival signature values. This imprecise model provides bounds on the survival signature and therefore the network reliability. Because a few data points are sufficient to build the interval predictor model it allows for even larger systems to be analysed. With the rising complexity of not just the system but also the individual components themselves comes the need for the components to be modelled as subsystems in a system-of-systems approach. A study is presented, where a previously developed framework for resilience decision-making is adapted to multidimensional scenarios in which the subsystems are represented as survival signatures. The survival signature of the subsystems can be computed ahead of the resilience analysis due to the inherent separation of structural information. This enables efficient analysis in which the failure rates of subsystems for various resilience-enhancing endowments are calculated directly from the survival function without reevaluating the system structure. In addition to the advancements in the field of survival signature, this work also presents a new framework for uncertainty quantification developed as a package in the Julia programming language called UncertaintyQuantification.jl. Julia is a modern high-level dynamic programming language that is ideal for applications such as data analysis and scientific computing. UncertaintyQuantification.jl was built from the ground up to be generalised and versatile while remaining simple to use. The framework is in constant development and its goal is to become a toolbox encompassing state-of-the-art algorithms from all fields of uncertainty quantification and to serve as a valuable tool for both research and industry. UncertaintyQuantification.jl currently includes simulation-based reliability analysis utilising a wide range of sampling schemes, local and global sensitivity analysis, and surrogate modelling methodologies

Reliability Analysis of Networks Interconnected With Copulas

Abstract With the increasing size and complexity of modern infrastructure networks rises the challenge of devising efficient and accurate methods for the reliability analysis of these systems. Special care must be taken in order to include any possible interdependencies between networks and to properly treat all uncertainties. This work presents a new approach for the reliability analysis of complex interconnected networks through Monte Carlo simulation and survival signature. Application of the survival signature is key in overcoming limitations imposed by classical analysis techniques and facilitating the inclusion of competing failure modes. The (inter)dependencies are modeled using vine copulas while the uncertainties are handled by applying probability boxes and imprecise copulas. The proposed method is tested on a complex scenario based on the IEEE reliability test system, proving its effectiveness and highlighting the ability to model complicated scenarios subject to a variety of dependent failure mechanisms.</jats:p

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

Reliability analysis of a complex system with hybrid structures and multi-level dependent life metrics

In practical engineering, the presence of dependent evidence is not rare due to various imperfections. Misuse of such information in reliability analysis will lead to conflicting or even erroneous results. In this paper, we propose a Bayesian reliability approach for complex systems with dependent life metrics. Notions such as explicit evidence and implicit evidence are established based on an identification of different roles of multiple dependent evidence in the likelihood construction. A likelihood decomposition method is developed to convert the overall likelihood into a product of Explicit Evidence-based Likelihood (EEL) function and Implicit Evidence-based Likelihood (IEL) function. An inferential diagram is developed to intuitively generate the required implicit evidence taking both outer-source information and the system configuration into consideration. An algorithm is then presented for implementation. The contribution of our work is a systematic investigation of the role of dependent evidence in system reliability evaluation and a full Bayesian approach that is applied to various system reliability models. Extensive numerical cases and a practical engineering case are demonstrated for validation and to illustrate the benefits of our approach