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Abstract
Reliable predictions of the dynamic loads and the lifetime of structures are inﬂuenced by the limited accuracy concerning the level of structural damping. The mechanisms of damping cannot be derived analytically from ﬁrst principles, and in the design of structures the damping is therefore based on experience or estimated from measurements. This thesis consists of an extended summary and three papers which focus on enhanced methods for identiﬁcation of damping from random structural vibrations. The developed methods are validated by stochastic simulations, experimental data and fullscale measurements which are representative of the vibrations in small and largescale structures.
The ﬁrst part of the thesis presents an automated procedure which is suitable for estimation of the natural frequencies and the modal damping ratios from random response of structures. The method can be incorporated within existing time domain Operational Modal Analysis (OMA) techniques to automatically select the most representative time lag in the correlation function and model order of the system, by ﬁtting a cluster of estimated frequencies and damping ratios to the dynamic response data. The procedure is applied to stochastic simulations of the tower accelerations of an 8 MW oﬀshore wind turbine generator during downtime. This is a scenario in which a limited amount of damping is expected to be available. Therefore, it may be signiﬁcant for the next generation of wind turbines for which estimates from ﬁeld measurements may be applied for design optimization. The expected level of error in the estimates of damping computed by stochastic simulations is validated by real vibration measurements of an oﬀshore wind turbine in nonoperating conditions. The best biasvariance error tradeoﬀ in the damping estimates is obtained by the covariance driven stochastic subspace (COVSSI) identiﬁcation technique in combination with the automated method. It has been estimated that the average damping in the fundamental foreaft mode is 42% lower than the damping in the sideside mode and the scatter is within the expected standard deviation. It is notoriously diﬃcult to separate the magnitude of the multiple sources of damping in oﬀshore wind turbine generators. The magnitude of energy dissipation depends on the vibration amplitude and is associated with a spatial location which can be described by the nonclassical viscous damping matrix.
The second part of the thesis demonstrates how the spatial location of damping can be obtained by a derived explicit expression of the nonclassical damping matrix. The modal parameters without a speciﬁc scaling are required in the expression as well as the mass distribution. This expression can be incorporated into an outputonly system identiﬁcation technique as well as in traditional experimental modal analysis techniques. The identiﬁed damping matrix is of high accuracy and yields a realvalued symmetric matrix from simulations. It is furthermore shown, by measurements of a modelscale ﬁvestory shear building, that the estimated complexvalued mode shapes are reproducible and their convergence concerning the measurement duration validates that the nonclassical damping matrix can be reconstructed robustly by estimating the complexvalued modal parameters of dynamic structures.
In the last part of the thesis a method for identiﬁcation of damping in hysteretic systems is presented. The method extends the postprocessing of the estimates obtained by the classical COVSSI technique. Hysteresis is modeled by the BoucWen model which is represented by an equivalent linear relaxation model. The linear relaxation model is related to the BoucWen model by explicit expressions of the relation between the model parameters obtained by harmonic averaging. These expressions are incorporated in the identiﬁcation procedure and they depend on the identiﬁcation of a cluster of nonoscillatory poles, the rootmeansquare of the displacement response and the resonance frequency. Synthetic data provided by a benchmark challenge on identiﬁcation of singledegreeoffreedom (SDOF) systems with hysteresis is used for validation. The displacement response from random excitation of a hysteretic system is contained in the data set, by which it is shown that the model parameters identiﬁed by the method can predict the response at both low and highlevels of excitation amplitudes.
The ﬁrst part of the thesis presents an automated procedure which is suitable for estimation of the natural frequencies and the modal damping ratios from random response of structures. The method can be incorporated within existing time domain Operational Modal Analysis (OMA) techniques to automatically select the most representative time lag in the correlation function and model order of the system, by ﬁtting a cluster of estimated frequencies and damping ratios to the dynamic response data. The procedure is applied to stochastic simulations of the tower accelerations of an 8 MW oﬀshore wind turbine generator during downtime. This is a scenario in which a limited amount of damping is expected to be available. Therefore, it may be signiﬁcant for the next generation of wind turbines for which estimates from ﬁeld measurements may be applied for design optimization. The expected level of error in the estimates of damping computed by stochastic simulations is validated by real vibration measurements of an oﬀshore wind turbine in nonoperating conditions. The best biasvariance error tradeoﬀ in the damping estimates is obtained by the covariance driven stochastic subspace (COVSSI) identiﬁcation technique in combination with the automated method. It has been estimated that the average damping in the fundamental foreaft mode is 42% lower than the damping in the sideside mode and the scatter is within the expected standard deviation. It is notoriously diﬃcult to separate the magnitude of the multiple sources of damping in oﬀshore wind turbine generators. The magnitude of energy dissipation depends on the vibration amplitude and is associated with a spatial location which can be described by the nonclassical viscous damping matrix.
The second part of the thesis demonstrates how the spatial location of damping can be obtained by a derived explicit expression of the nonclassical damping matrix. The modal parameters without a speciﬁc scaling are required in the expression as well as the mass distribution. This expression can be incorporated into an outputonly system identiﬁcation technique as well as in traditional experimental modal analysis techniques. The identiﬁed damping matrix is of high accuracy and yields a realvalued symmetric matrix from simulations. It is furthermore shown, by measurements of a modelscale ﬁvestory shear building, that the estimated complexvalued mode shapes are reproducible and their convergence concerning the measurement duration validates that the nonclassical damping matrix can be reconstructed robustly by estimating the complexvalued modal parameters of dynamic structures.
In the last part of the thesis a method for identiﬁcation of damping in hysteretic systems is presented. The method extends the postprocessing of the estimates obtained by the classical COVSSI technique. Hysteresis is modeled by the BoucWen model which is represented by an equivalent linear relaxation model. The linear relaxation model is related to the BoucWen model by explicit expressions of the relation between the model parameters obtained by harmonic averaging. These expressions are incorporated in the identiﬁcation procedure and they depend on the identiﬁcation of a cluster of nonoscillatory poles, the rootmeansquare of the displacement response and the resonance frequency. Synthetic data provided by a benchmark challenge on identiﬁcation of singledegreeoffreedom (SDOF) systems with hysteresis is used for validation. The displacement response from random excitation of a hysteretic system is contained in the data set, by which it is shown that the model parameters identiﬁed by the method can predict the response at both low and highlevels of excitation amplitudes.
Original language  English 

Publisher  DTU Mechanical Engineering 

Number of pages  124 
Publication status  Published  2017 
Series  DCAMM Special Report 

Volume  S231 
ISSN  09031685 
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Dive into the research topics of 'Identification of Damping from Structural Vibrations'. Together they form a unique fingerprint.Projects
 1 Finished

Enhanced evaluation of structural damping using Operational Modal Analysis
Bajric, A., Høgsberg, J. B., Thomsen, J. J., Chatzi, E. & Peeters, B.
Technical University of Denmark
15/01/2014 → 11/01/2018
Project: PhD