Sensitivity Analysis Based on the Fisher Information Matrix Applied to Systems With Random Design Inputs

Abstract Uncertainties in the parameters adopted during the design process make it challenging to design against the reliability of an engineering system. The identification of parameters that are more sensitive to uncertainties is carried out by a sensitivity analysis of the distribution of the output variables. In this context, we have explored the relation between the Fisher information matrix (FIM) and the design entropy, to develop a framework to analyze the degree of change of the probability of failure and entropy as a result of the variation of input parameters. It is found that the changes in the entropy and probability of failure, associated to the variation of the parameters of the distribution of the input variables, are linear combinations of the eigenvalues of the FIM and the projections of the eigenvectors onto the sensitivity vectors, respectively. As an application, the FIM-based sensitivity analysis is performed from Monte Carlo simulations in a physical dynamic structure subjected to random design parameters drawn from Gaussian and Gamma distributions.