Interval-Based Approach for Uncertainty Propagation in Inverse Problems

A new class of interval-based computational algorithms for parameter identification under uncertainty in structural engineering problems is presented. The iterative method allows passing directly from uncertain raw measurements to sharp (tight) bound estimates of the unknown parameters by exploiting interval FEMs and adjoint-based optimization techniques. Overestimation in interval width is handled successfully using the inclusion isotonicity property of interval arithmetic. First, an update of the iterative solution proceeds in a degenerated interval form until it becomes insignificant, and then the update is switched to full interval form, allowing uncertainty propagation and sensitivity analysis. A new containment-stopping criterion, which is intrinsic to intervals, is used. Example problems are then presented and discussed to show the effectiveness of the proposed inverse method in estimating the range of Young's moduli from given ranges in displacements.