An efficient inverse method for structural identification considering modeling and response uncertainties

Abstract

The inverse problem analysis method provides an effective way for the structural parameter identification. Due to the coupling of multi-source uncertainties in the measured responses and the modeling parameters, the inverse of unknown structural parameter will face the challenges in the solving mechanism and the computational cost. In this paper, an uncertain inverse method based on convex model and dimension reduction decomposition is proposed to realize the interval identification of unknown structural parameter according to the uncertain measured responses and modeling parameters. Firstly, the polygonal convex set model is established to quantify the uncertainties of modeling parameters. Afterwards, a space collocation method based on dimension reduction decomposition is proposed to transform the inverse problem considering multi-source uncertainties into a few interval inverse problems considering response uncertainty. The transformed interval inverse problem involves the two-layer solving process including interval propagation and optimization updating. In order to solve the interval inverse problems considering response uncertainty, an efficient interval inverse method based on the high dimensional model representation and affine algorithm is further developed. Through the coupling of the above two methods, the proposed uncertain inverse method avoids the time-consuming multi-layer nested calculation procedure, and then effectively realize the inverse uncertainty quantification of unknown structural parameters. Finally, two engineering examples are provided to verify the effectiveness of the proposed uncertain inverse method.