Radial Importance Sampling for Structural Reliability

In Cartesian coordinates importance sampling has been remarkably effective in improving the efficiency of Monte Carlo simulation techniques for reliability calculations in structural engineering. The approach is extended in this paper to the (hyper‐) polar coordinate system, firstly using an importance sampling function that has its mean at the radial distance, from the mean vector, where the limit‐state functions are expected to lie. This approach is then refined by using interpolation to estimate the location of the crucial limit state along any radial direction and to censor sampling not in the failure domain. The third development is to approximate, in a radial direction, the "tail" of the original probability density function by an appropriate Gaussian probability density function, and then to apply the established theory for directional simulation. Example applications for a linear limit‐state function and for a circular limit‐state function are given.