Advanced line sampling with adaptive important direction for structural failure probability

Illustrations are used to analyze the limitation of line sampling(LS) firstly. For linear limit state, the efficiency of LS is affected by the dispersion of the actual important direction from the optimal one, the bigger the dispersion is, the lower the efficiency is. For non-linear limit state, in case that the actual important direction deviates from the optimal one greatly, the efficiency and the precision of LS decrease seriously, even wrong results are obtained. For these problems of LS, an advanced LS is presented with adaptive important direction. In standard normal space, the presented LS adapts direction from coordinate original point to the available failure point as an initialized important direction. By sampling exploringly and modifying gradually, the initialized important direction approaches the optimal one, then the advantages in precision and efficiency of LS is exerted completely. Numerical and engineering examples are used to verify the advantages of the presented method.