Investigation on a novel reliability analysis approach integrating adaptive space division and direction sampling

Multitudes of algorithms have been proposed to evaluate the failure probability of components and systems. Among all these algorithms, direction sampling is a promising one. However, a major computational effort involved in direction sampling is that for each direction sample a root-searching process needs to be conducted to obtain the distance between the origin and the failure surface, which can be computationally expensive. In addition, the failure probability along a direction is hard to obtain when the direction vector intersects the failure surface multiple times. This paper proposes a novel approach to obtain densely populated points locating on the failure surface and utilizing these points to conduct reliability analysis with direction sampling. The process of obtaining the population consists in dividing the initial hypercube space into multiple lattice grids, identifying the grids crossing the failure surface, and dividing these grids into smaller ones. The iterative division process stops when the grids cut across by the failure surface are small enough so that the centers of these grids can be considered located on the failure surface. Several numerical tests are performed to validate the applicability of the proposed approach. Through these tests, it can be concluded that for the situation where the intersection between the direction vector and the failure surface is unique, the proposed approach will lead, with high accuracy, to a failure probability. For the situation where the intersection is not unique, satisfactory estimation of failure probabilities can also be achieved using approximation methods. For high-dimensional reliability problems, clustering techniques can be utilized to reduce the computational cost.