Interval assessments of identified parameters for uncertain structures

This paper investigates a kind of inverse problem for assessing the uncertainties of identified parameters with uncertainties in structural parameters and limited experimental data. The uncertainty is described by the interval model in which only the bounds of uncertain parameters are required. Directly solving this kind of inverse problem involves a double-loop problem where the outer-loop is interval analysis and the inner-loop is deterministic optimization, which requires a large number of calculations. To efficiently evaluate the effect of interval parameters on the identified parameters, a novel method based on the dimension-reduction method and adaptive collocation strategy is proposed. First, the interval inverse problem is transformed into an inverse-propagation problem, and the dimension-reduction interval method is adopted to transform the interval inverse-propagation problem into several one-dimensional interval inverse-propagation problems. Then, an adaptive collocation strategy is proposed to efficiently estimate the lower and upper bounds of identified parameters. Therefore, the double-loop problem can be transformed into several deterministic inverse problems, and the efficiency of solving the uncertain inverse problem is dramatically improved. Two numerical examples and an engineering application are applied to demonstrate the feasibility and efficiency of the proposed method.