  Rare event probability estimation is an important topic in reliability
analysis. Stochastic methods, such as importance sampling, have been developed
to estimate such probabilities but they often fail in high dimension. In this
paper, we propose a new cross-entropy-based importance sampling algorithm to
improve rare event probability estimation in high dimension. We focus on the
cross-entropy method with Gaussian auxiliary distributions and we suggest to
update the Gaussian covariance matrix only in a one-dimensional subspace. For
that purpose, the main idea is to consider the projection in the
one-dimensional subspace spanned by the sample mean vector, which gives an
influential direction for the variance estimation. This approach does not
require any additional simulation budget compared to the basic cross-entropy
algorithm and we show on different numerical test cases that it greatly
improves its performance in high dimension.
