Reliability analysis of mechanical systems using directional simulation

Reliability analysis of mechanical systems, in some special circumstances, may suffer technical difficulties which need desirable solutions. One such a case may exist when working in a space of highly correlated random variables and/or the space of random variables with extremely different variances. If in these spaces; which are so-called "extremely non-proportional spaces"; the relevant limit state function is also highly nonlinear, simulation methods are normally preferred for reliability analysis. Directional simulation is one of these methods which is fully well-known. This method, however, may be not efficient if it is crudely applied in these spaces. In such conditions, directional simulation often needs a massive computational effort in order to achieve good and reasonable results. In this paper reliability analysis of a blade of a hydro-kinetic turbine (as an important mechanical system) is performed whose random variable's variances are extremely different and thus create a non-proportional space for directional simulation. To make the analysis more efficient, use of an importance sampling technique with a set of novel relationships is proposed in this paper. These relationships make the required calculations not only possible, they facilitate the computations to be very fast and efficient compared to those normally used in conjunction with traditional importance sampling methods.