Uncertainty Updating of Finite Element Models Using Interval Analysis

Uncertainties in structural parameters and measurements can be accounted for by incorporating interval analysis into the updating scheme of finite element models using a response-surface function. To facilitate the interval arithmetic operation, two different strategies are proposed in this paper to transform the response-surface function into a corresponding interval response-surface function. These strategies minimize the inherent interval overestimation that can arise from the variable dependency of the surrogate model. In the first strategy, the natural extension and centered-form extension methods are used to mitigate the interval overestimation of the surrogate model, which may or may not contain interaction terms. In the second strategy, the natural extensión method is also adopted to realize the interval transformation of the surrogate model containing interaction terms but an affine arithmetic is further introduced to minimize the interval overestimation. To demonstrate the efficacy of the proposed method, model parameters are determined from an instrumented model of a cable-stayed bridge tested on a shaking table. Results show that the proposed updating method is feasible and effective for applications to finite element models of complex bridge structures.