Efficient Integration of Sampling-Based Spatial Conditional Failure Joint Probability Densities

Joint probability density functions (JPDFs) can be used to describe the likelihood of spatial position or events that are dependent on spatial position. Event-based JPDFs are often based on computational outcomes at specific locations, where the number of potential locations may be unlimited. The efficiency and accuracy associated with the estimation of the conditional failure JPDF is dependent on the number of spatial locations and the number of limit state evaluations at each spatial location. An approach is presented for the estimation of a fracture mechanics-based conditional failure JPDF within a finite domain. An approximate JPDF is constructed using probability of fracture values associated with anomalies placed at discrete points along the perimeter of the component and at selected locations within the interior of the component. The discrete points are connected to form a mesh of elements, and anomaly occurrence rates are assigned to elements based on their relative volumes. The final JPDF is obtained from an adaptive refinement of the element mesh where elements are subdivided based on contribution to component risk. The results can be applied to the risk assessment of components that are susceptible to fracture failure.