The importance sampling is merged with directional simulation in this paper. A sampling
function is defined on the unit hyper sphere which samples random directions. The
directions are sampled around a direction that aims to the design point. The sampling
function uses spherical coordinates to generate random directions. The method is made
adaptive by a closed form updating rule to renew the sampling parameters. To reduce the
number of calls on the limit state function, a root finding procedure is put forward. The …

In this paper, an adaptive directional importance sampling (ADIS) method is presented. The
algorithm is based on a directional simulation scheme in which the most important directions
are sampled exact and the others by means of a response surface approach. These most
important directions are determined by a β-sphere enclosing the most important part (s) of
the limit state. The β-sphere and response surface are constantly updated during sampling
with information that becomes available from the exact evaluations making the scheme …