Modifications to the ‘directional simulation in the load space’ approach to structural reliability analysis

‘Directional simulation in the load space (DS-LS)’ is a simulation-based technique used to perform reliability analysis of structures subjected to time-invariant or time-variant random loads. To perform DS-LS a location must first be chosen for an ‘origin of simulation’. The origin may be positioned in either the safe or failure region of the load space, and its precise location (with respect to these regions) influences the DS-LS formulation needed to evaluate reliability correctly. The current formulation requires the origin to be positioned in the safe region. However, even for simple structures, the ‘exact’ location of the safe and failure region is not always known explicitly ‘a priori’. Modifications to allow for the possibility of positioning the origin not only in the ‘safe’ region but in the ‘failure’ region are proposed in this paper. Some numerical examples involving one or more stationary continuous Gaussian loads and the simulation of directions by ‘Monte Carlo’ and ‘the hyperspace division method’ are presented to demonstrate the validity of the proposed formulations. Some comments on convergence are made.