Substructure Model Updating Through Iterative Convex Optimization

In order to obtain a more accurate finite element (FE) model for a built structure, experimental data collected from the actual structure can be used to update the FE model. This process is known as FE model updating. Numerous FE model updating algorithms have been developed in the past few decades. However, most existing algorithms suffer computational challenges, particularly when applied to a large structure with dense measurements. The reason is these approaches usually operate on a relatively complicated model for the entire structure. To address this issue, a substructure updating approach is presented in this paper. The Craig-Bampton theory is adopted to condense the entire structural model into a substructure (currently being analyzed) and a residual structure. Dynamic response of the residual structure is approximated using only a limited number of dominant mode shapes. To improve the convergence of this substructure approach for model updating, an iterative convex optimization procedure is developed and validated through numerical simulation with a 200 degrees-of-freedom spring-mass model. The proposed substructure model updating is shown to successfully detect the locations and severities of simulated damage.