A new directional simulation method for system reliability. Part I: application of deterministic point sets

To assess structural system reliability accurately, simulation is often the only feasible method because of dimensionality, highly nonlinear limit states, small failure probability and other factors. However, simulations can be computationally inefficient when the reliability assessment involves finite element analysis and the cost of structural analysis is large. Efficient directional simulation, as well as other simulation techniques, often can be improved in terms of accuracy and efficiency if the sample points are identified by deterministic point sets rather than generated randomly. This article introduces and investigates various deterministic point sets theoretically and experimentally in conjunction with directional simulation, and identifies one particular point set (Fekete point set) as being especially useful in this regard. New test measures are proposed to evaluate the quality and uniformity of point sets, which are essential in preserving the underlying probability distribution. A companion paper presents a point set refinement scheme using neural networks, which is a technique parallel to importance sampling.