  The paper presents a new efficient and robust method for rare event
probability estimation for computational models of an engineering product or a
process returning categorical information only, for example, either success or
failure. For such models, most of the methods designed for the estimation of
failure probability, which use the numerical value of the outcome to compute
gradients or to estimate the proximity to the failure surface, cannot be
applied. Even if the performance function provides more than just binary
output, the state of the system may be a non-smooth or even a discontinuous
function defined in the domain of continuous input variables. In these cases,
the classical gradient-based methods usually fail. We propose a simple yet
efficient algorithm, which performs a sequential adaptive selection of points
from the input domain of random variables to extend and refine a simple
distance-based surrogate model. Two different tasks can be accomplished at any
stage of sequential sampling: (i) estimation of the failure probability, and
(ii) selection of the best possible candidate for the subsequent model
evaluation if further improvement is necessary. The proposed criterion for
selecting the next point for model evaluation maximizes the expected
probability classified by using the candidate. Therefore, the perfect balance
between global exploration and local exploitation is maintained automatically.
The method can estimate the probabilities of multiple failure types. Moreover,
when the numerical value of model evaluation can be used to build a smooth
surrogate, the algorithm can accommodate this information to increase the
accuracy of the estimated probabilities. Lastly, we define a new simple yet
general geometrical measure of the global sensitivity of the rare-event
probability to individual variables, which is obtained as a by-product of the
proposed algorithm.
