Abstract: A computer-based method for determining a probability that no path exists from a starting node to a target node within a network of nodes and directional links between pairs of nodes. The nodes and directional links form paths of a reliability graph and the method is performed using a computer coupled to a database. The method includes selecting a set of paths between the starting node and the target node that have been determined to be reliable, calculating a reliability of the union of the selected path sets, setting an upper bound for unreliability of the set of all paths, selecting a set of minimal cutsets from all cutsets that lie between the starting node and the target node, calculating the probability of the union of the minimal cutsets, and setting a lower bound for the unreliability of the set of all cutsets.

Abstract: A cross-spectral correlation function of a structure may be determined by providing a finite element model of the structure having a plurality of elements each having a centroid. A plurality of composite centroids may be determined wherein each one of the composite centroids is based on at least one of the elements. The cross-spectral correlation function between at least one pair of the elements in the finite element model may be assigned to be the cross-spectral correlation function of the composite centroids that include the centroids of the elements. If the pair of elements is included in the same composite centroid, then the cross-spectral correlation function between the elements is assigned to be the autocorrelation function of the composite centroid that includes the pair of elements.

Abstract: A computer-based method for determining a probability that no path exists from a specified starting node to a specified target node within a network of nodes and directional links between pairs of nodes is described. The nodes and directional links form paths of a reliability graph and the method is performed using a computer coupled to a database that includes data relating to the nodes and the directional links The method includes selecting a set of paths, from the set of all paths, between the starting node and the target node that have been determined to be reliable, calculating a reliability of the union of the selected path sets, setting an upper bound for the unreliability of the set of all paths, based on the calculated reliability, selecting a set of minimal cutsets from all such cutsets that lie between the starting node and the target node, calculating the probability of the union of the minimal cutsets, and setting a lower bound for the unreliability of the set of all cutsets.

Abstract: A cross-spectral correlation function of a structure may be determined by providing a finite element model of the structure having a plurality of elements each having a centroid. A plurality of composite centroids may be determined wherein each one of the composite centroids is based on at least one of the elements. The cross-spectral correlation function between at least one pair of the elements in the finite element model may be assigned to be the cross-spectral correlation function of the composite centroids that include the centroids of the elements. If the pair of elements is included in the same composite centroid, then the cross-spectral correlation function between the elements is assigned to be the autocorrelation function of the composite centroid that includes the pair of elements.

Abstract: A computer-based method for determining a probability that no path exists from a specified starting node to a specified target node within a network of nodes and directional links between pairs of nodes is described. The nodes and directional links form paths of a reliability graph and the method is performed using a computer coupled to a database that includes data relating to the nodes and the directional links. The method includes selecting a set of paths, from the set of all paths, between the starting node and the target node that have been determined to be reliable, calculating a reliability of the union of the selected path sets, setting an upper bound for the unreliability of the set of all paths, based on the calculated reliability, selecting a set of minimal cutsets from all such cutsets that lie between the starting node and the target node, calculating the probability of the union of the minimal cutsets, and setting a lower bound for the unreliability of the set of all cutsets.