Directional importance sampling for ill-proportioned spaces

Directional importance sampling is considered in the original space of loads when the loads are highly correlated and/or highly out of proportion. Under these conditions, the joint probability density function contours are elongated and the application of unbiased directional sampling may result in poor and unstable results. It is shown that a major improvement can be achieved by applying importance sampling to the directional sampling technique. In this way better and quite stable results can be obtained. Also, it is shown that uncertainties in structural strength may affect directional sampling in load space. Some illustrative examples are given.