THE APPLICATION OF PROBABILISTIC METHODS IN FINITE ELEMENT ANALYSISThe ability to quantify the uncertainty simulation results of complex large scale mining simulations is becoming increasingly important. The inherent randomness in material properties and geological parameters plays a cruital role for the interpretation of the obtained simulation results. The integration of probabilistic methods into the finite element analysis framework provides the possibility to quantify the reliability of the structural mechanical response of a mine. The point estimation methodOne alternative to the classical Monte-Carlo simulations to estimate moments of a performance function is the point estimate method. Point estimate methods (PEM) refer to the category of probabilistic methods where probability distributions for continuous random variables are modelled by discrete “equivalent” distributions having two or more values. Most PEM approaches are based on two-point estimates (i.e., two values for each xi), but references to third- and higher-order point estimates can be found in the literature (Harr, 1987). Later, Harr (1989) presented a modified procedure derived from the correlation matrix of the random variables. The estimate points were defined based on a diagonalized form of the correlation matrix, which was obtained based on the eigenvalues and eigenvectors of the correlation matrix. One of the significant improvements is that the number of required evaluations of the performance function from 2n to 2n. Examples
 Fig. 1: Comparison between shaft deflection measurement and experimental results with lower and upper bounds assuming probabilistic distributions of a selected set of material properties References
|
