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Network reliability analysis remains a challenge due to the increasing size and complexity of networks. This paper presents a novel sampling method and an active learning method for efficient and accurate network reliability estimation under node failure and edge failure scenarios. The proposed sampling method adopts Monte Carlo technique to sample component lifetimes and the K-terminal spanning tree algorithm to accelerate structure function computation. Unlike existing methods that compute only one structure function value per sample, our method generates multiple component state vectors and corresponding structure function values from each sample. Network reliability is estimated based on survival signatures derived from these values. A transformation technique extends this method to handle both node failure and edge failure. To enhance efficiency of proposed sampling method and achieve adaptability to network topology changes, we introduce an active learning method utilizing a random forest (RF) classifier. This classifier directly predicts structure function values, integrates network behaviors across diverse topologies, and undergoes iterative refinement to enhance predictive accuracy. Importantly, the trained RF classifier can directly predict reliability for variant networks, a capability beyond the sampling method alone. Through investigating several network examples and two practical applications, the effectiveness of both proposed methods is demonstrated.

Many dynamical systems are subjected to stochastic influences, such as random excitations, noise, and unmodeled behavior. Tracking the system's state and parameters based on a physical model is a common task for which filtering algorithms, such as Kalman filters and their non-linear extensions, are typically used. However, many of these filters use assumptions on the transition probabilities or the covariance model, which can lead to inaccuracies in non-linear systems. We will show the application of a stochastic coupling filter that can approximate arbitrary transition densities under non-Gaussian noise. The filter is based on transport maps, which couple the approximation densities to a user-chosen reference density, allowing for straightforward sampling and evaluation of probabilities., Comment: Published in Advances in Reliability, Safety and Security ESREL 2024 Contributions, https://esrel2024.com/wp-content/uploads/articles/part9/transport-map-coupling-filter-for-state-parameter-estimation.pdf

First-passage probability estimation of high-dimensional nonlinear stochastic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel approach, termed 'fractional moments-based mixture distribution', to address such challenge. This approach is implemented by capturing the extreme value distribution (EVD) of the system response with the concepts of fractional moments and mixture distribution. In our context, the fractional moment itself is by definition a high-dimensional integral with a complicated integrand. To efficiently compute the fractional moments, a parallel adaptive sampling scheme that allows for sample size extension is developed using the refined Latinized stratified sampling (RLSS). In this manner, both variance reduction and parallel computing are possible for evaluating the fractional moments. From the knowledge of low-order fractional moments, the EVD of interest is then expected to be reconstructed. Based on introducing an extended inverse Gaussian distribution and a log extended skew-normal distribution, one flexible mixture distribution model is proposed, where its fractional moments are derived in analytic form. By fitting a set of fractional moments, the EVD can be recovered via the proposed mixture model. Accordingly, the first-passage probabilities under different thresholds can be obtained from the recovered EVD straightforwardly. The performance of the proposed method is verified by three examples consisting of two test examples and one engineering problem.