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

Interval Predictor Model for the Survival Signature Using Monotone Radial Basis Functions

This research describes a novel method for approximating the survival signature for very large systems. In recent years, the survival signature has emerged as a capable tool for the reliability analysis of critical infrastructure systems. In comparison with traditional approaches, it allows for complex modeling of dependencies, common causes of failures, as well as imprecision. However, while it enables the consideration of these effects, as an inherently combinatorial method, the survival signature suffers greatly from the curse of dimensionality. Critical infrastructures typically involve upward of hundreds of nodes. At this scale analytical computation of the survival signature is impossible using current computing capabilities. Instead of performing the full analytical computation of the survival signature, some studies have focused on approximating it using Monte Carlo simulation. While this reduces the numerical demand and allows for larger systems to be analyzed, these approaches will also quickly reach their limits with growing network size and complexity. Here, instead of approximating the full survival signature, we build a surrogate model based on normalized radial basis functions where the data points required to fit the model are approximated by Monte Carlo simulation. The resulting uncertainty from the simulation is then used to build an interval predictor model (IPM) that estimates intervals where the remaining survival signature values are expected to fall. By applying this imprecise survival signature, we can obtain bounds on the reliability. Because a low number of data points is sufficient to build the IPM, this presents a significant reduction in numerical demand and allows for very large systems to be considered

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

Multidimensional resilience decision-making for complex and substructured systems

Complex systems, such as infrastructure networks, industrial plants and jet engines, are of paramount importance to modern societies. However, these systems are subject to a variety of different threats. Novel research focuses not only on monitoring and improving the robustness and reliability of systems, but also on their recoverability from adverse events. The concept of resilience encompasses precisely these aspects. However, efficient resilience analysis for the modern systems of our societies is becoming more and more challenging. Due to their increasing complexity, system components frequently exhibit significant complexity of their own, requiring them to be modeled as systems, i.e., subsystems. Therefore, efficient resilience analysis approaches are needed to address this emerging challenge. This work presents an efficient resilience decision-making procedure for complex and substructured systems. A novel methodology is derived by bringing together two methods from the fields of reliability analysis and modern resilience assessment. A resilience decision-making framework and the concept of survival signature are extended and merged, providing an efficient approach for quantifying the resilience of complex, large and substructured systems subject to monetary restrictions. The new approach combines both of the advantageous characteristics of its two original components: A direct comparison between various resilience-enhancing options from a multidimensional search space, leading to an optimal trade-off with respect to the system resilience and a significant reduction of the computational effort due to the separation property of the survival signature, once a subsystem structure has been computed, any possible characterization of the probabilistic part can be validated with no need to recompute the structure. The developed methods are applied to the functional model of a multistage high-speed axial compressor and two substructured systems of increasing complexity, providing accurate results and demonstrating efficiency and general applicability

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

AnderGray/BivariateCopulas.jl: 0.1.5

&lt;p&gt;Adds frank copula, tests, and code coverage&lt;/p&gt; &lt;h2&gt;What's Changed&lt;/h2&gt; &lt;ul&gt; &lt;li&gt;Add Frank copula by @FriesischScott in https://github.com/AnderGray/BivariateCopulas.jl/pull/16&lt;/li&gt; &lt;/ul&gt; &lt;p&gt;&lt;strong&gt;Full Changelog&lt;/strong&gt;: https://github.com/AnderGray/BivariateCopulas.jl/compare/v0.1.4...v0.1.5&lt;/p&gt

FriesischScott/UncertaintyQuantification.jl: v0.8.1

&lt;h2&gt;UncertaintyQuantification v0.8.1&lt;/h2&gt; &lt;p&gt;&lt;a href="https://github.com/FriesischScott/UncertaintyQuantification.jl/compare/v0.8.0...v0.8.1"&gt;Diff since v0.8.0&lt;/a&gt;&lt;/p&gt; &lt;p&gt;&lt;strong&gt;Merged pull requests:&lt;/strong&gt;&lt;/p&gt; &lt;ul&gt; &lt;li&gt;Add importance sampling (#124) (@Cr0gan)&lt;/li&gt; &lt;li&gt;CompatHelper: bump compat for StatsBase to 0.34, (keep existing compat) (#137) (@github-actions[bot])&lt;/li&gt; &lt;li&gt;Fix bug in subset infinity (#141) (@FriesischScott)&lt;/li&gt; &lt;/ul&gt

FriesischScott/UncertaintyQuantification.jl: v0.8.2

&lt;h2&gt;UncertaintyQuantification v0.8.2&lt;/h2&gt; &lt;p&gt;&lt;a href="https://github.com/FriesischScott/UncertaintyQuantification.jl/compare/v0.8.1...v0.8.2"&gt;Diff since v0.8.1&lt;/a&gt;&lt;/p&gt; &lt;p&gt;&lt;strong&gt;Merged pull requests:&lt;/strong&gt;&lt;/p&gt; &lt;ul&gt; &lt;li&gt;Fix cov estimation with less samples in subsets &gt;= 2 (#142) (@FriesischScott)&lt;/li&gt; &lt;/ul&gt; &lt;p&gt;&lt;strong&gt;Closed issues:&lt;/strong&gt;&lt;/p&gt; &lt;ul&gt; &lt;li&gt;estimate_cov for subset and subset infinity sometimes returns complex number (#138)&lt;/li&gt; &lt;/ul&gt