Nonlinear Combination of Load Processes

An important problem in structural reliability is the combination of time-variant stochastic loadings. The failure probability in the case of nonlinear combinations of stochastic processes can be approximated by the mean crossing rates of time-variant loadings out of the safe domain of structural states. Except for linearly bounded safe domains, these rates are difficult to compute; therefore, the quality of veirious linearization points is investigated. Comparisons are made of some examples showing that for time-variant problems the Hasofer-Lind point is often suboptimal. A linearization at the point of maximum local outcrossing density might generally produce non-degenerate, sufficiently accurate results.