Reliability sensitivity analysis involving correlated random variables by directional sampling

Directional sampling based reliability sensitivity analysis for independent normal variables problem is extended for the reliability sensitivity analysis involving correlated random variables. For the reliability and reliability sensitivity problem involving correlated random variables, independent normal transformation techniques, including Nataf transformation or Copula functions, are firstly employed before the implementation of directional sampling. And then the reliability and sensitivity are estimated by the directional sampling in the independent standard normal space. Employing the equivalently transformation techniques between correlated random variables and independent normal ones, the reliability sensitivity of failure probability with respect to the distribution parameters of correlated random variables can be estimated by the chain rule of derivative finally. After simple numerical example is used to demonstrate the validity and feasibility of the presented extended method, it is employed to analyze the reliability and reliability sensitivity for the aeroengine turbine blade with correlated random variables. From the results of examples, it is determined the important parameters with large influence on the reliability, and the presented method can significantly reduce the computational cost than that of classical Monte Carlo simulation. The Nataf transformation can give the equivalently transformation when the random variables are correlated normal distributed, and the Nataf transformation is a way to model the dependence structure of a random vector by a normal copula, parameterized by its correlation matrix.