Inverse uncertainty quantification for imprecise structure based on evidence theory and similar system analysis

Due to the imprecise structure originated from the limitation of knowledge level or lack of information, the inverse problems for identifying the unknown parameter of system will face the challenges in the solving mechanism and the computational cost. Compared with the traditional inverse problems, this kind of inverse problems not only need to identify the unknown parameter, but also need to quantify the uncertainty caused by the imprecise structure. In this paper, a basic solving framework based on evidence theory for this inverse uncertainty quantification is established to inversely estimate the effect of the uncertainties in imprecise structure on the unknown parameters. In order to overcome the computing bottleneck problem caused by the coupling of evidence-based uncertainty propagation and the inverse computation, an efficient similar system analysis method is further proposed. Firstly, the marginal interval analysis method is developed to transform the evidence-based uncertain inverse problem into several deterministic inverse problems at the marginal collocation points. Afterwards, the similar system analysis method is proposed by adequately utilizing the similarity of systems at any two adjacent marginal collocation points to further improve the computational efficiency of several deterministic inverse problems. Because of the coupling effect of the above two strategies, the proposed uncertain inverse method decouples the time-consuming multi-layer nested inverse procedure, and then greatly reduces the computational cost of inverse uncertainty quantification based on evidence theory. Two numerical examples and one engineering application are provided to verify the high efficiency of the proposed uncertain inverse method.