Force identification and response estimation in floating and suspension bridges using measured dynamic response
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The trend of constructing bridges that are longer, more slender, and more flexible increases the importance of the assessment of dynamic behavior. Herein, it is imperative to have a good understanding of the environmental loads on the structure. It is therefore of interest to develop tools that can help in the assessment of possible uncertainties involved in the modeling of environmental loads and the corresponding response effects. This doctoral project discusses estimation of dynamic loads and responses in existing bridges using measured response data, also known as (model-based) inverse force identification. To this end, various Kalman-type algorithms that belong to a stochastic class of methods that have been developed in recent years are applied for estimation of inputs and states. The thesis consists of five papers that are either published or submitted. In these papers, the focus is on modern types of bridges in Norwegian conditions, where wind and wave loads are important. Two case studies of monitored bridges are presented. The first is the Bergsøysund bridge, an 840 m long floating bridge. The second is the Hardanger bridge, a suspension bridge with a main span of 1310 m. Accurate models of bridges are highly important since the inverse force identification is an ill-posed problem that is generally sensitive to errors in the system model and measurement noise. For both bridges under consideration, a system identification by means of operational modal analysis is undertaken. By making use of the obtained modal parameters, a sensitivity-based finite element (FE) model-updating scheme is carried out. For the Bergsøysund bridge, a theoretical framework for the model sensitivity is presented that also takes into account the fluid-structure interaction as frequency-dependent added mass and damping. The challenges here are the large uncertainties related to the system identification, which are complicated by closely spaced complex modes with high damping, nonwhite excitation by the wave forces and the arch shape of the bridge that produces combined bendingtorsion mode shapes. Although the FE model is overall improved, a robust model validation remains difficult for the floating type of bridges. On the other hand, the updating for suspension bridges works well. Even though the Hardanger bridge has over 20 important modes below 1 Hz, these are lightly damped with distinct pure bending or torsion shapes. This results in less difficulties in both the system identification and the modelling from blueprint drawings. If a reduction in the load uncertainties is sought, the force identification methods must be tested with the actual data from the structures during operation. In this thesis, comprehensive testing of the input and state estimation is carried out. There are a few factors for the long-span bridges that dictate some critical limitations. First, the multimode behavior of the bridges leads to a great number of unknown modal forces that have to be identified. As a consequence, this also necessitates a very dense sensor network of accelerometers. Furthermore, the uncertainties in the (FE) models can be critical. For the floating bridges, these model errors are basically still so significant that the inverse force identification is highly affected. The identified wave forces on the Bergsøysund bridge have the correct order of magnitude but have some frequency content that does not agree with first-order wave theory. These errors are also not consistent between the datasets. However, the full-field response estimation seems to be more accurate. This type of application could be used to monitor stresses for fatigue. Concluding from the results from the Hardanger bridge, the study of force identification of wind loads seems feasible. The more “regular” mechanical behavior and lower model uncertainties in suspension bridges lead to better a potential. The main limitation found here is the high number of modes requiring an equally high number of acceleration outputs. Apart from this, both the input and state estimation seem to work well. In investigations on the Hardanger bridge, both the buffeting and self-excited forces can be distinctly observed, although currently, only their combined sum is estimated. The dynamical behavior of suspension bridges and floating bridges is complex due to the uncertainties in the multimode behavior, stochastic excitation and interaction with the air and water. Full-scale input and state estimation therefore remain very complicated for these types of structures, but the current work shows potential in the application of the inverse methodology.