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.

本文研究了一种用于评估已识别参数的不确定性的反问题，其中结构参数存在不确定性，且实验数据有限。不确定性由区间模型描述，其中仅需要不确定参数的边界。直接求解这类逆问题涉及一个双循环问题，外循环为区间分析，内循环为确定性优化，需要大量的计算。为了有效地评估区间参数对识别参数的影响，提出了一种基于降维方法和自适应搭配策略的新方法。首先，区间逆问题转化为逆传播问题，采用降维区间法将区间逆传播问题转化为若干个一维区间逆传播问题。然后，提出了一种自适应搭配策略来有效地估计已识别参数的下限和上限。因此，可以将双环问题转化为多个确定性逆问题，显着提高求解不确定性逆问题的效率。两个数值例子和一个工程应用被用来证明所提出方法的可行性和效率。因此，可以将双环问题转化为多个确定性逆问题，显着提高求解不确定性逆问题的效率。两个数值例子和一个工程应用被用来证明所提出方法的可行性和效率。因此，可以将双环问题转化为多个确定性逆问题，显着提高求解不确定性逆问题的效率。两个数值例子和一个工程应用被用来证明所提出方法的可行性和效率。