  Flow network models can capture the underlying physics and operational
constraints of many networked systems including the power grid and
transportation and water networks. However, analyzing reliability of systems
using computationally expensive flow-based models faces substantial challenges,
especially for rare events. Existing actively trained meta-models, which
present a new promising direction in reliability analysis, are not applicable
to networks due to the inability of these methods to handle high-dimensional
problems as well as discrete or mixed variable inputs. This study presents the
first adaptive surrogate-based Network Reliability Analysis using Bayesian
Additive Regression Trees (ANR-BART). This approach integrates BART and Monte
Carlo simulation (MCS) via an active learning method that identifies the most
valuable training samples based on the credible intervals derived by BART over
the space of predictor variables as well as the proximity of the points to the
estimated limit state. Benchmark power grids including IEEE 30, 57, 118, and
300-bus systems and their power flow models for cascading failure analysis are
considered to investigate ANR-BART, MCS, subset simulation, and
passively-trained optimal deep neural networks and BART. Results indicate that
ANR-BART is robust and yields accurate estimates of network failure
probability, while significantly reducing the computational cost of reliability
analysis.
