Parametric sensitivity analysis of the importance measure

To overcome the difficulties in computing the parametric sensitivity of the importance measure, a new moment-independent importance measure based on the cumulative distribution function is proposed to represent the effects of model inputs on the uncertainty of the output. Based on that, definitions of the parametric sensitivities of the importance measure are given, and their computational formulae are derived. The parametric sensitivities illustrate the influences of varying some variables distribution parameters to the input variables importance measures, which provide an important reference to improve or change the performance properties. The probability density function evolution method, an efficient tool due to its high efficiency and precision, is applied into computing the proposed importance measure and its parametric sensitivities. Finally, three examples including the Ishigami test function, a structure model and a mechanism model are adopted to illustrate the feasibility and correctness of the proposed indices and solution.