  Performing reliability analysis on complex systems is often computationally
expensive. In particular, when dealing with systems having high input
dimensionality, reliability estimation becomes a daunting task. A popular
approach to overcome the problem associated with time-consuming and expensive
evaluations is building a surrogate model. However, these computationally
efficient models often suffer from the curse of dimensionality. Hence, training
a surrogate model for high-dimensional problems is not straightforward.
Henceforth, this paper presents a framework for solving high-dimensional
reliability analysis problems. The basic premise is to train the surrogate
model on a low-dimensional manifold, discovered using the active subspace
algorithm. However, learning the low-dimensional manifold using active subspace
is non-trivial as it requires information on the gradient of the response
variable. To address this issue, we propose using sparse learning algorithms in
conjunction with the active subspace algorithm; the resulting algorithm is
referred to as the sparse active subspace (SAS) algorithm. We project the
high-dimensional inputs onto the identified low-dimensional manifold identified
using SAS. A high-fidelity surrogate model is used to map the inputs on the
low-dimensional manifolds to the output response. We illustrate the efficacy of
the proposed framework by using three benchmark reliability analysis problems
from the literature. The results obtained indicate the accuracy and efficiency
of the proposed approach compared to already established reliability analysis
methods in the literature.
