Model Updating with Closed-Loop Strain Mode Shapes

Abstract

M ODEL updating is a method of correcting analytical models, such as the finite element model, by improving the correlation between the measured data and the analytical model. The correlation can be determined by a penalty function that involves modal data such as natural frequencies and mode shapes [1,2]. However, a modal sensitivity matrix that is ill conditioned due to a lack of modal data can incur inaccurate model updating. For more efficient model updating, we need to increase the amount of modal data. Recently, some researchers have used closed-loop schemes to capture additional modal data [3,4]. Strain mode shapes have also been used instead of displacement mode shapes because of their perceived advantages [5,6]. For example, the difference in the strain mode shapes of an intact case and a damaged case is greater than the corresponding difference in the displacement mode shapes. This phenomenon explains why strain mode shapes are generally considered more sensitive than displacement mode shapes with respect to the local change of a structure. However, this property is valid when the local change of a structure can change the displacement mode shapes because strain mode shapes are spatial derivatives of displacement mode shapes. If we simultaneously use strain mode shapes and the closed-loop scheme, we can enhance the performance of model updating. We, therefore, propose a novel method of combining strain mode shapes and the closed-loop scheme for effective model updating. In addition, to demonstrate the feasibility of the proposed method, we provide a numerical simulation of model updating based on the closed-loop strain mode shapes.