Model updating of a full-scale FE model with nonlinear constraint equations and sensitivity-based cluster analysis for updating parameters

The objective of structural model updating is to reduce inherent modeling errors in Finite Element (FE) models due to simplifications, idealized connections, and uncertainties of material properties. Updated FE models, which have less discrepancies with real structures, give more precise predictions of dynamic behaviors for future analyses. However, model updating becomes more difficult when applied to civil structures with a large number of structural components and complicated connections. In this paper, a full-scale FE model of a major long-span bridge has been updated for improved consistency with real measured data. Two methods are applied to improve the model updating process. The first method focuses on improving the agreement of the updated mode shapes with the measured data. A nonlinear inequality constraint equation is used to an optimization procedure, providing the capability to regulate updated mode shapes to remain within reasonable agreements with those observed. An interior point algorithm deals with nonlinearity in the objective function and constraints. The second method finds very efficient updating parameters in a more systematic way. The selection of updating parameters in FE models is essential to have a successful updating result because the parameters are directly related to the modal properties of dynamic systems. An in-depth sensitivity analysis is carried out in an effort to precisely understand the effects of physical parameters in the FE model on natural frequencies. Based on the sensitivity analysis, cluster analysis is conducted to find a very efficient set of updating parameters.