In the Thesis a new method is developed for optimising the shape of mechanical elements by considering the interaction of these elements with a multiphase uncertainty environment whose approximation model achieves a significant number of degrees of freedom (DOF). The Thesis analyses the process of dust formation during the handling of granular material. Different experimental designs are used to derive metamodels and to analyse the segregation of granular material in the silo discharge depending on the oscillation frequency, amplitude, and geometrical characteristics of the silo.