Iman Behmanesh

Effects of prediction error bias on model calibration and response prediction of a 10-story building

This paper investigates the application of Hierarchical Bayesian model updating to be used for probabilistic model calibration and response prediction of civil structures. In this updating framework the misfit between the identified modal parameters and the corresponding parameters of the finite element (FE) model is considered as a Gaussian distribution with unknown parameters. For response prediction, both the structural parameters of the FE model and the parameters of the misfit error functions are considered. The focus of this paper is to (1) evaluate the performance of the proposed framework in predicting the structural modal parameters at a state that the FE model is not calibrated (extrapolation from the model), and (2) study the effects of prediction error bias on the accuracy of the predicted values. The test structure considered here is a ten-story concrete building located in Utica, NY. The modal parameters of the building at its reference state were identified from ambient vibration data using the NExT-ERA system identification method. The identified modal parameters are used to calibrate parameters of the initial FE model as well as the misfit error functions. Before demolishing the building, six of its exterior walls were removed and ambient vibration measurements were also collected from the structure after wall removal. These data are not used to calibrate the model; they are only used to validate the predicted results. The model updating framework of this paper is applied to estimate the modal parameters of the building after removal of the six walls. Good agreement is observed between the model-predicted modal parameters and those identified from vibration tests.

Bayesian FE Model Updating in the Presence of Modeling Errors

A new likelihood function is proposed for probabilistic damage identification of civil structures that are usually modeled with many simplifying assumptions and idealizations. Data from undamaged and damaged states of the structure are used in the likelihood function and damage is identified through a Bayesian finite element (FE) model updating process. The new likelihood function does not require calibration of an initial FE model to a baseline/reference model and is based on the difference between damaged and healthy state data. It is shown that the proposed likelihood function can identify structural damage as accurately as two other types of likelihood functions frequently used in the literature. The proposed likelihood is reasonably accurate in the presence of modeling error, measurement noise and data incompleteness (number of modes and number of sensors). The performance of FE model updating for damage identification using the proposed likelihood is evaluated numerically at multiple levels of modeling errors and structural damage. The effects of modeling errors are simulated by generating identified modal parameters from a model that is different from the FE model used in the updating process. It is observed that the accuracy of damage identifications can be improved by using the identified modes that are less affected by modeling errors and by assigning optimum weights between the eigen-frequency and mode shape errors.

Probabilistic Damage Identification of the Dowling Hall Footbridge Using Bayesian FE Model Updating

This paper presents a probabilistic damage identification study on a full-scale structure, the Dowling Hall Footbridge, through Bayesian finite element (FE) model updating. The footbridge is located at Tufts University campus and is equipped with a continuous monitoring system that measures the ambient acceleration response of the bridge. A set of data is recorded once an hour or when triggered by large vibrations. The modal parameters of the footbridge are extracted based on each set of measured ambient vibration data and are used for model updating. In this study, effects of physical damage are simulated by loading a small segment of footbridge’s deck with concrete blocks. The footbridge deck is divided into five segments and the added mass on each segment is considered as an updating parameter. Overall, 72 sets of data are collected during the loading period (i.e., damaged state of the bridge) and different subsets of these data are used to find the location and extent of the damage (added mass). Adaptive Metropolis Hasting algorithm with adaption on the proposal probability density function is successfully used to generate Markov Chains for sampling the posterior probability distributions of the five updating parameters. Effect of the number of data sets used in the identification process is investigated on the posterior probability distributions of the updating parameters.

Hierarchical Bayesian Model Updating for Probabilistic Damage Identification

This paper presents the newly developed Hierarchical Bayesian model updating method for identification of civil structures. The proposed updating method is suitable for uncertainty quantification of model updating parameters, and probabilistic damage identification of the structural systems under changing environmental conditions. The Bayesian model updating frameworks in the literature have been successfully used for predicting the “parameter estimation uncertainty” of model parameters with the assumption that there is no underlying inherent variability in the updating parameters. However, different sources of uncertainty such as changing ambient temperature or wind speed, and loading conditions will introduce variability in structural mass and stiffness of civil structures. The Hierarchical Bayesian model updating is capable of predicting the underlying variability of updating parameters in addition to their estimation uncertainty. This approach is applied for uncertainty quantification and damage identification of a three-story shear building model. The proposed updating framework is finally implemented for uncertainty quantification of model updating results based on experimentally measured data of a footbridge which is exposed to severe environmental conditions. In this application, the stiffness parameter of the model is estimated as a function of measured temperature through the Hierarchical framework.

Probabilistic damage identification of the Dowling Hall footbridge through Hierarchical Bayesian model updating

In this paper, a Hierarchical Bayesian finite element model updating framework is applied for probabilistic identification of simulated damage on the Dowling Hall Footbridge. The footbridge is located at Tufts campus and is equipped with a continuous monitoring system, including 12 accelerometers. Structural damage is simulated by the addition of mass on a small segment of the footbridge, and the Hierarchical framework is used to identify the location and extent of the damage (added mass), and to quantify the prediction uncertainties. This framework is well suited for applications to civil structures, where the structural properties (stiffness, mass) can be considered timevariant due to changing environmental conditions such as temperature, wind speed, or traffic.

Hierarchical Bayesian Calibration and Response Prediction of a 10-Story Building Model

This paper presents Hierarchical Bayesian model updating of a 10-story building model based on the identified modal parameters. The identified modal parameters are numerically simulated using a frame model (exact model) of the considered 10-story building and then polluted with Gaussian white noise. Stiffness parameters of a simplified shear model~- representing modeling errors - are considered as the updating parameters. In the Hierarchical Bayesian framework, the stiffness parameters are assumed to follow a probability distribution (e.g., normal) and the parameters of this distribution are updated as hyperparameters. The error functions are defined as the difference between model-predicted and identified modal parameters of the first few modes and are also assumed to follow a predefined distribution (e.g., normal) with unknown parameters (mean and covariance) which will also be estimated as hyperparameters. The Metropolis-Hastings within Gibbs sampler is employed to estimate the updating parameters and hyperparameters. The uncertainties of structural parameters as well as error functions are propagated in predicting the modal parameters and response time histories of the building.

Bayesian FE Model Updating of the Dowling Hall Footbridge

The Dowling Hall Footbridge is located on the Medford campus of Tufts University. The bridge consists of two 22 m spans and it is 3.9 m wide. The footbridge is composed of a steel frame with a reinforced concrete deck. Figure 28.1 shows the south view of the footbridge.