A new algorithm for variance-based importance measures and importance kernel sensitivity

Variance-based importance measure has proven itself as an effective tool to reflect the effects of input variables on the output. Owing to the desirable properties, researchers have paid lots of attention to improving efficiency in computing a variance-based importance measure. Based on the theory of point estimate, this article proposes a new algorithm, decomposing the importance measure into inner and outer parts, and computing each part with a point estimate method. In order to discuss the impacts on the variance-based importance measure from distribution parameters of input variables, a new concept of kernel sensitivity of the variance-based importance measure is put forward, with solving algorithms respectively, based on numerical simulation and point estimate established as well. For cases where the performance function with independent and normally distributed input variables is expressed by a linear or quadratic polynomial without cross-terms, analytical results of the variance-based importance measure and the kernel sensitivity are derived. Numerical and engineering examples have been employed to illustrate the applicability of the proposed concept and algorithm.