Improved point estimation method for analyzing reliability and reliability sensitivity

For low-dimensional and high-nonlinear performance function, an improved point estimation method is proposed for analyzing reliability and reliability sensitivity. In the proposed method, input space is firstly separated into some subspaces to reduce the nonlinearity of performance function in these subspaces. Secondly, low-level sparse grid integration method is used to estimate probabilistic response character in the subspaces. Finally, the probabilistic response characters in every subspace are combined to obtain the reliability and reliability sensitivity. The obvious advantage of the proposed method is its applicability for the reliability and reliability sensitivity of low-dimensional and high-nonlinear model, and it is also adaptive to complex implicit function because it is gradient free. Moreover, input space is partitioned according to the most probable point estimated by uniformly sampling few samples, which helps to improve the estimation efficiency of the reliability and reliability sensitivity. Several test examples demonstrate that for low-dimensional and high-nonlinear model the proposed method is more precise and efficient than existing point estimation methods, i.e., the three-point estimation and the direct sparse grid integral method.