High-dimensional multivariate normal integrals for a discrete approximation of the first-passage density

As the density of the first-passage event of a stochastic structural system under random dynamic loading may be approximately expressed in terms of an intersection of elementary failure events at a sufficiently large number of time instants, the application of algorithms for the computation of high-dimensional multivariate normal integrals is desirable if a first-order approach is to be followed. In this paper several existing methods that seem suitable for this purpose are compared and a modification of the algorithm proposed by Pandey in 1998 is presented. The results suggest that, using these multivariate normal integration methods, a fast and sufficiently accurate computation of the first-passage density is possible.