A modified variance-based importance measure and its solution by state dependent parameter

To overcome the disadvantage of traditional variance-based importance measures, i.e. the effects of different realizations of input variables on output response may mutually counteract each other, a modified variance-based importance measure is presented for importance analysis of the input variables. The proposed measure analyses the importance of the input variables comprehensively in terms of the expectation and variance of the output response. Compared with the traditional variance-based importance analysis method, the modified importance measure indices not only reflect the old one, but also provide a very useful supplement for it. Furthermore, combined with the advantages of the state dependent parameter model, a solution to the proposed measure indices is provided. Several examples are introduced to show that the modified importance measure is more comprehensive and reasonable, and the solution based on the state dependent parameter method can improve computational efficiency considerably with acceptable precision.