Outcrossings from Convex Polyhedrons for Nonstationary Gaussian Processes

This technical note concerns the estimation of the outcrossing rate of nonstationary Gaussian vector processes from a convex polyhedral limit-state surface enclosing the origin. The theoretically most attractive approach for this type of problem in time-dependent structural reliability analysis is to employ the concept of first-passage probability in stochastic-process theory. Because the use of the generalized Rice formula poses some difficulty, the outcrossing problem is formulated in another way; i.e., using the original Rice formula directly. This situation allows the multidimensional integral to be reduced to a one-dimensional integral. This then allows the formulation (which applies also to smooth nonstationary processes) to be extended to time-dependent domain boundaries. An example is given to illustrate the method.