Monitoring bridges has been an important tool for many years to understand the condition of a bridge, and it is important because it can prevent damage and reduce the risk of human losses. In this study, the focus is to develop and investigate three differ ent physical models representing vibration responses of the hanger cables in the Great Belt Bridge in normal operational conditions, because these components are subject to high vibration and loads. An approach for a model updating strategy is developed, a nd a comparative analysis of the three models is made to select the best-suited physical models for developing a Structural Health Monitoring strategy for the hanger cables. An iterative non -linear optimization method with the natural frequencies as the characteristic quantities is used for the model updating of one model, while for the two other models, model updating is conducted by solving for the axial load directly. The comparative analysis is conducted based on a plot illustrating the trend of the thr ee models. It is concluded that the trend of the physical models is approximately the same, making it possible to switch from one model to the other with a deterministic correction. The updated results show good agreement between the physical and the actua l model, and the simplest model, in relation to computational effort, can be chosen as the best -suited physical model and it is concluded that it is a pinned -pinned beam model. ii Table of Contents Abstract ................................ ................................ ................................ ................................ ................. i List of Figures ................................ ................................ ................................ ................................ ..... iii List of Tabl es ................................ ................................ ................................ ................................ ...... iii Nomenclature ................................ ................................ ................................ ................................ ...... iv 1 Introduction ................................ ................................ ................................ ................................ ... 1 1.1 State of the Art ................................ ................................ ................................ ...................... 1 1.1.1 Characteristic quantities for model updating ................................ ................................ . 2 1.1.2 Optimization strategies for model updating ................................ ................................ ... 3 2 Methodology ................................ ................................ ................................ ................................ . 6 2.1 Overview of essential steps in the study ................................ ................................ ............... 6 2.2 Presentation of hanger monitoring data ................................ ................................ ................. 6 2.3 Derivation of shape function and frequency equation for physical models ........................ 10 2.3.1 Transverse vibration of a string under tension ................................ ............................. 10 2.3.1.1 Frequency equation ................................ ................................ ................................ .. 13 2.3.2 Transverse vibration of axially loaded Bernoulli -Euler beam ................................ ..... 14 2.3.2.1 Frequency equation for Fixed -Fixed beam ................................ .............................. 19 2.3.2.2 Frequency equation for pinned -pinned beam ................................ ........................... 20 2.4 Updating of physical models ................................ ................................ ............................... 21 2.4.1 Updating of string model and pinned -pinned beam model ................................ .......... 23 2.4.2 Updating of fixed -fixed beam model ................................ ................................ ........... 23 3 Results and interpretation ................................ ................................ ................................ ........... 25 3.1 Natural frequencies and mode shapes ................................ ................................ ................. 25 3.2 Axial Load ................................ ................................ ................................ ........................... 27 3.3 Comparison of the three physical models ................................ ................................ ........... 29 4 Future work ................................ ................................ ................................ ................................ . 31 5 Conclusion ................................ ................................ ................................ ................................ .. 32 6