Improved methods for fast system reliability analysis through machine-learning-based surrogate models

In the aftermath of a natural disaster, knowledge of the connectivity of different regions of infrastructure networks is crucial to post-event decision making. The specific problem of determining the probability that two nodes in an infrastructure network are disconnected given the edge failure probabilities is known as the two-terminal connectivity problem, a special case of the k-terminal reliability problem. Both problems are known to be computationally intractable for general infrastructure graphs as the network size grows large, which motivates the use of Monte Carlo techniques to estimate the failure probability. However, Monte Carlo techniques are slow to converge due to the large number of realizations of the infrastructure graph required, each of which requires a connectivity evaluation. To improve the computation efficiency of the Monte Carlo approach, this work develops a new framework where the connectivity evaluation is itself estimated with a machine-learning-based surrogate model. The framework is applied to networks with both uncorrelated uniform edge failure probability and correlated edge failure probability, and an extension to node clusters is also proposed. The method first uses spectral clustering to partition the network, and estimates the connectivity of these clusters using both a logistic regression and an AdaBoost classifier. Numerical experiments on a California gas distribution network demonstrate that using the surrogate model to determine cluster connectivity introduces less than five percent error and is two orders of magnitude faster than methods using an exact connectivity evaluation to estimate the probability of network failure through Monte Carlo simulations