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Probabilistic Finite Element Model Updating and Damage Detection of Structures by Using Bayesian Statistics
(01. Izmir Institute of Technology, 2022) Ceylan, Hasan; Turan, Gürsoy
Finite element (FE) model updating is extensively employed in many applications of various engineering branches for damage detection purposes. An FE model is expected to reflect the properties of actual structures. However, it is almost impossible for an FE model to carry the properties of the real-life structure. As a result, differences exist between analytical models and actual structures. The aim of model updating is to minimize these differences as much as possible. In model updating procedures, there are inevitable uncertainties due to inevitable measurement noise and modelling errors. Therefore, model updating and damage detection process should be performed in a probabilistic way instead of a deterministic one. To this end, Bayesian model updating methods have gained much attention in the literature to account for the uncertainties of the parameters to be updated. Among these methods, those that use the concept of system modes have gained much more attention since it enables researchers to account for modelling error uncertainties and to avoid mode matching problem. For those methods, discrepancies between system modes and measured modes are considered and system modes are updated to obtain those that best fit the measured modes. Further, system modes are connected to the FE model via eigenvalue equations. In this study, a two-stage Bayesian model updating method which utilizes the concept of system modes has been firstly reformulated to compare three different assumptions on the modelling error variance of eigenvalue equations. Results reveal that the Bayesian model updating formulations that use the system modes concept give unreasonably too small posterior uncertainties for the updated parameters. This makes the probabilistic approach questionable since getting such small uncertainties may almost be equivalent to a deterministic approach. To increase the posterior uncertainty levels to more reasonable levels, a two-stage sensitivity-based Bayesian model updating methodology is proposed in this study. The results show that the proposed method successfully improves the updating results and increases the posterior uncertainties to more realistic levels.
Enhancing Earthquake Performance of Civil Structures Via Structural Control
(Izmir Institute of Technology, 2021) Şenol, Vedat; Turan, Gürsoy
In this study, two different benchmark buildings (3 and 20-story) are employed to attenuate structural responses under seismic disturbances. As control devices, active (actuators), semi-active (Magneto-rheological dampers), passive (Tuned mass dampers and Friction Pendulum Bearings), and hybrid controllers are utilized. The 3-story structure is modeled linearly and employed to apply to different control strategies. Some control algorithms: LQR, PDD-state-feedback, pole-placement, $H_{\infty}$, $ H_2 $, are used with active and semi-active control devices. As passive devices, TMDs and FPBSs are utilized on the nominal-linear model. Thereafter, hybrid controllers are employed: one composed of a TMD and actuator/MRD and one composed of an FPBS and actuator/MRD. A robust controller, $\mu$-synthesis, is employed to control the same linear structure having uncertainties in mass, stiffness, and damping matrices within reasonable ranges. A nonlinearly-modeled 20-story benchmark structure is employed to implement passive and hybrid control strategies. As passive devices, STMD and MTMD setups are employed. Further, a robust control algorithm is used through an actuator serially connected to the STMD. Subsequently, variations caused by nonlinearities are determined. These variations are regarded as uncertainties, and the $\mu$-synthesis is utilized in the design of a robust controller on a truncated linear model. Then, the designed robust control is employed to control the 20-story benchmark structure modeled nonlinearly. The structural responses in both frequency and time domains are discussed. Matlab, Python, and OpenSees framework (Tcl/Tk) were employed to realize all linear and nonlinear simulations throughout the study.

Phd Degree / Doktora

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