Important sampling in high dimensions

This paper draws attention to a fundamental problem that occurs in applying importance sampling to 'high-dimensional' reliability problems, i.e., those with a large number of uncertain parameters. This question of applicability carries an important bearing on the potential use of importance sampling for solving dynamic first-excursion problems and static reliability problems for structures with a large number of uncertain structural model parameters. The conditions under which importance sampling is applicable in high dimensions are investigated, where the focus is put on the common case of standard Gaussian uncertain parameters. It is found that importance sampling densities using design points are applicable if the covariance matrix associated with each design point does not deviate significantly from the identity matrix. The study also suggests that importance sampling densities using random pre-samples are generally not applicable in high dimensions.