Probabilistic importance analysis of the input variables in structural systems

• Two new probabilistic importance measures (PIMs) are defined.
• The properties of PIMs are illuminated and proved in detail.
• Solution based on probability density function evolution method is proposed.
• PIMs of correlated input variables are solved based on Copula transformation.

To measure the effects of input variables’ realization on variance of the output performance function and on the failure probability of structural system, two new probabilistic importance measures (PIMs) are defined. As an input variable takes its realization according to its probability distribution, the two PIMs can quantify the possibility of reducing the variance of the output performance function and the possibility of improving the structural system reliability, respectively. After the properties of the PIMs are illuminated and proved in detail, a solution based on the probability density function evolution method (PDEM) is constructed to evaluate the PIMs. The solution is used to solve the PIMs with correlated input variables based on the Copula transformation. Examples demonstrate that the proposed solution on the PDEM can improve the computational efficiency greatly with acceptable precision, and the solution based on the conjunction of the PDEM and the Copula transformation can effectively solve the PIMs with correlated input variables.