Uncertainty Propagation Using a Stochastic Finite Element Approach

The present study focuses on the development of a general framework for propagating the effects of parametric uncertainty, modeled as random fields, from input to output for complex engineering systems via Stochastic Finite Element techniques. These techniques are similar in concept to deterministic finite element approaches in that they approximate both input and output quantities in terms of finite dimensional series expansions and exploit orthogonality relationships to arrive at equations for associated system unknowns. In the stochastic case, the input quantities are random fields with probabilistic or statistical descriptions that are assumed to be obtainable. The inner products are mathematical expectations. A major advantage of the approach is its ability to be implemented as an external loop around deterministic analytical codes. Thus, the approach is a reasonable extension to current traditional deterministic simulations.