Importance measure of correlated normal variables and its sensitivity analysis

In order to explore the contributions by correlated input variables to the variance of the polynomial output in general engineering problems, the correlated and uncorrelated contributions by correlated inputs to the variance of model output are derived analytically by taking the quadratic polynomial output without cross term as an illustration. The analytical sensitivities of the variance contributions with respect to the distribution parameters of input variables are derived, which can explicitly expose the basic factors affecting the variance contributions. Numeric examples are employed and their results demonstrate that the derived analytical expressions are correct, and then they are applied to two engineering examples. The derived analytical expressions can be used directly in recognition of the contributions by input variables and their influencing factors in quadratic or linear polynomial output without cross term. Additionally, the analytical method can be extended to the case of higher order polynomial output, and the results obtained by the proposed method can provide the reference for other new methods.