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An adaptive solution to semiactive control of cable vibration is formulated by extending the linear quadratic Gaussian (LQG) control from time domain to frequency domain. Frequency shaping is introduced via the frequency dependent weights in the cost function to address the control effectiveness and robustness. The Hilbert-Huang transform (HHT) technique is further synthesized for online tuning of the controller gain adaptively to track the cable vibration evolution, which also obviates the iterative optimal gain selection for the trade-off between control performance and energy in the conventional time domain LQG (T-LQG) control. The developed adaptive frequency-shaped LQG (AF-LQG) control is realized by collocated self-sensing magnetorheological (MR) dampers considering the nonlinear damper dynamics for force tracking control. Performance of the AF-LQG control is numerically validated on a bridge cable transversely attached with a self-sensing MR damper. The results demonstrate the adaptivity in gain tuning of the AF-LQG control to target for the dominant cable mode for vibration energy dissipation, as well as its enhanced control efficacy over the optimal passive MR damping control and the T-LQG control for different excitation modes and damper locations. [ABSTRACT FROM AUTHOR]

Vibration measurement is one of the most widely used methods for tension evaluation and condition assessment of stay cables in cable-stayed bridges. In the existing practice, the tension force of a cable is identified from the measured modal frequencies with the use of the taut string theory or empirical formulae, by assuming pre-determined structural parameters (geometric and material parameters) and boundary conditions of the cable. As a result, an inaccurate estimation of the cable tension may be obtained when there is an error in the pre-determined structural parameters and boundary conditions. Moreover, the commonly used empirical formulae are not applicable in the case when the cable is intermediately attached with dampers. In the present study, a method enabling simultaneous identification of cable tension and other structural parameters from the measured modal frequencies is developed. A precise finite element model (FEM) accounting for cable flexural rigidity, sag-extensibility, spatial variability of dynamic tension, boundary conditions, lumped masses and intermediate supports and/or dampers is first formulated as the reference model in parameter identification so that the modeling error is minimized. Then the measured multiple modal frequencies are used together with the FEM to figure out a nonlinear least-square optimization scheme which helps eliminate measurement error and allows for simultaneous identification of the cable tension and other structural parameters. Application of the proposed method to the Dongting Lake Bridge cables from in-situ ambient vibration measurements illustrates high identification accuracy and fidelity of the proposed method. [ABSTRACT FROM AUTHOR]

For the purpose of developing a vibration-based tension force evaluation procedure for bridge cables using measured multimode frequencies, an investigation on accurate finite element modelling of large-diameter sagged cables taking into account flexural rigidity and sag extensibility is carried out in this paper. A three-node curved isoparametric finite element is formulated for dynamic analysis of bridge stay cables by regarding the cable as a combination of an “ideal cable element” and a fictitious curved beam element in the variational sense. With the developed finite element formulation, parametric studies are conducted to evaluate the relationship between the modal properties and cable parameters lying in a wide range covering most of the cables in existing cable-supported bridges, and the effect of cable bending stiffness and sag on the natural frequencies. A case study is eventually provided to compare the measured natural frequencies of main cables of the Tsing Ma Bridge and the computed frequencies with and without considering cable bending stiffness. The results show that ignoring bending stiffness gives rise to unacceptable errors in predicting higher order natural frequencies of the cables, and the proposed finite element formulation provides an accurate baseline model for cable tension identification from measured multimode frequencies. [Copyright &y& Elsevier]