Uncertainty and Sensitivity Analysis of Damage Identification Results Obtained Using Finite Element Model Updating

A full-scale seven-story reinforced concrete shear wall building structure was tested on the UCSD-NEES shake table in the period October 2005-January 2006. The shake table tests were designed so as to damage the building progressively through several historical seismic motions reproduced on the shake table. A sensitivity-based finite element (FE) model updating method was used to identify damage in the building. The estimation uncertainty in the damage identification results was observed to be significant, which motivated the authors to perform, through numerical simulation, an uncertainty analysis on a set of damage identification results. This study investigates systematically the performance of FE model updating for damage identification. The damaged structure is simulated numerically through a change in stiffness in selected regions of a FE model of the shear wall test structure. The uncertainty of the identified damage (location and extent) due to variability of five input factors is quantified through analysis-of-variance (ANOVA) and meta-modeling. These five input factors are: (1-3) level of uncertainty in the (identified) modal parameters of each of the first three longitudinal modes, (4) spatial density of measurements (number of sensors), and (5) mesh size in the FE model used in the FE model updating procedure (a type of modeling error). A full factorial design of experiments is considered for these five input factors. In addition to ANOVA and meta-modeling, this study investigates the one-at-a-time sensitivity analysis of the identified damage to the level of uncertainty in the identified modal parameters of the first three longitudinal modes. The results of this investigation demonstrate that the level of confidence in the damage identification results obtained through FE model updating, is a function of not only the level of uncertainty in the identified modal parameters, but also choices made in the design of experiments (e.g., spatial density of measurements) and modeling errors (e.g., mesh size). Therefore, the experiments can be designed so that the more influential input factors (to the total uncertainty/variability of the damage identification results) are set at optimum levels so as to yield more accurate damage identification results.