An efficient method for reliability global sensitivity index by space-partition

The reliability sensitivity index well analyzes how the failure probability of a model is affected by the different sources of uncertainty in the model inputs. In order to improve the efficiency of digital simulation in estimating this index, a method was proposed based on the weighted density, the law of total variance in the successive intervals without overlapping and the space partition. To accelerate the speed of convergence, the law of total variance in the successive intervals without overlapping was proved and used subsequently. The weighted density method generates uniform samples in the possible interval of model inputs, and it can ensure the equivalence of estimation by the weighted density indices. The proposed method can avoid searching the design point; therefore, for the highly nonlinear problem which is difficult to find the design point and the problem of multiple design points, the proposed method can well deal with. In addition, by the idea of space-partition, the dependence of the computational cost on the input dimensionality is removed, and the proposed method only requires one set of input-output samples to obtain all the sensitivity indices, which greatly improves the utilization of samples and computational efficiency. Examples illustrate that the proposed method has higher efficiency, accuracy, convergence and robustness than the existing methods for the problems of high nonlinearity and multiple design points.