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IOMAC'13
5th International Operational Modal Analysis Conference
2013 May 13-15 Guimarães - Portugal
DAMPING ESTIMATION OF A PROTOTYPE
BUCKET FOUNDATION FOR OFFSHORE WIND
TURBINES IDENTIFIED BY FULL SCALE TESTING
Mads Damgaard1, Lars Bo Ibsen
2, Lars V. Andersen
3, Palle Andersen
4, Jacob K. F. Andersen
5
ABSTRACT
Wave loading misaligned with wind turbulence often introduces large fatigue loads on offshore wind
turbine structures. In this particular case, the structure is sensitive to resonant excitation acting out of
the wind direction due to a small aerodynamic damping contribution in the cross-wind direction.
Therefore, in order to assess the fatigue damage accumulation during the lifetime of the offshore wind
turbine structure, a correct estimation of the cross-wind modal damping is necessary. This paper
describes the cross-wind modal damping of the lowest eigenmode of a fully operational Vestas V90-
3.0 MW offshore wind turbine installed on a prototype bucket foundation. The foundation and the
turbine tower are equipped with a monitoring system with 15 Kinemetrics force balance
accelerometers and a Digitexx acquisition system. Using free vibration decays from “rotor-stop” tests
and operational modal techniques, the cross-wind modal damping is estimated on a regular basis.
Analyses show maximum cross-wind damping at rated wind speed. For higher wind speeds decreasing
damping is observed, mainly due to blade pitch activation. In addition, a high structural acceleration
level is needed to activate the soil damping.
Keywords: Free vibration decay, Frequency Domain Decomposition, offshore wind turbines,
Operational Modal Analysis, Stochastic Subspace Identification, system identification.
1. INTRODUCTION
Wind energy is expected to be a dominating energy source in the coming years. The increased size of
the offshore wind turbines and the demand for cost-effective turbines mean that the turbine system has
become more flexible and thus more dynamically active – even at low frequencies. Therefore, the
excitation frequencies related to waves and turbine blades passing the tower are close to the structural
resonance frequency. In order to obtain a reliable estimate of the fatigue life of the wind turbine
structure, the structural dynamic properties must be analysed. Contrary to civil engineering structures
1 Industrial PhD Fellow, Vestas Turbines R&D, mdamg@vestas.com
2 Professor, Department of Civil Engineering, Aalborg University, lbi@civil.aau.dk
3 Associate Professor, Department of Civil Engineering, Aalborg University, la@civil.aau.dk
4 Managing Director, Structural Vibration Solutions, pa@svibs.com
5 Manager, Vestas Turbines R&D, jakfa@vestas.com
M. Damgaard, L. Bo Ibsen, L. V. Andersen, P. Andersen, Jacob K. F. Andersen
2
like high-rise buildings, dams and cable-stayed or suspension bridges, wind turbine structures are
exposed to periodic loading from the rotor blades, and in the presence of emergency stop or too high
wind velocity the rotor blades pitch out of the wind. The blades thus have to be able to turn around
their longitudinal axis. The variable and cyclic loads on the rotor, the tower and the foundation call for
a full appreciation of the dynamic behaviour of the wind turbine structure during its service life, i.e. an
accurate numerical model that identifies the dynamic properties of the wind turbine structure is
favourable. However, limited physical knowledge about the dynamic wind turbine system makes it
difficult to establish a mathematical model based on pure physics and fundamental laws. This in turn
justifies experimental modal analysis capable of validating and improving the numerical model [1].
An operational wind turbine is subjected to harmonic excitation from the rotor. The first excitation
frequency to consider is the rotor rotational frequency 1P. The second excitation frequency is the blade
passing frequency. For a three-bladed wind turbine, this frequency is three times the 1P frequency and
is denoted the 3P frequency. Without sufficient system damping, the resonant behaviour of the turbine
can cause severe loads inducing fatigue damage. Large fatigue loads are often observed at wind parks
characterised by a large degree of wind-wave misalignment due to a small amount of aerodynamic
damping in the cross-wind direction. However, contradictory estimates of the damping are obtained by
different authors [2], which illustrates the importance of this paper.
This chapter outlines the motivation for investigating the dynamic properties of offshore wind
turbines. Turbine characterisation and site conditions for the considered wind turbine structure are
included in the chapter. A brief introduction to different damping techniques is given in Chapter 2
with focus on the theoretical background and the practical aspects in the literature. Chapter 3 deals
with the monitoring system followed by documentation of results in Chapter 4. Finally, in Chapter 5 a
brief summary of the main findings of the present work is given with a description of what the
findings can be used for in further applications.
1.1. Wind Turbine Structure and Site Conditions
The aim of this paper is to determine the cross-wind modal damping δ1 of the lowest eigenmode
of an offshore wind turbine installed on a prototype bucket foundation in Frederikshavn, Denmark.
The wind turbine structure is a part of an offshore research test field with a total of four wind turbine
structures and has been created as a joint research and development program between the Department
of Civil Engineering at Aalborg University and Universal Foundation A/S. The following subsections
are based on [3].
1.1.1. Foundation
The bucket foundation is a welded steel structure consisting of a tubular centre column connected to a
steel bucket through flange-reinforced stiffeners. A vertical steel skirt extending down from a
horizontal base resting on the soil surface ensures the overall stabilisation by a combination of earth
pressures at the skirt and the vertical bearing capacity of the bucket. The prototype bucket foundation
is designed with a diameter of 12 m and a skirt length of 6 m. Figure 1a shows the geometry of the
bucket foundation. During the installation process, the bucket foundation penetrates the seabed due to
a combination of self-weight and applied suction. Lowering the pressure in the cavity between the
bucket and the soil surface generates a water flow, which causes the effective stresses to be reduced
around the tip of the skirt. Hence, the penetration resistance is reduced. Figure 1b shows the bucket
foundation in Frederikshavn after installation in late 2002.
1.1.2. Wind Turbine
The bucket foundation is placed below a fully operational Vestas V90-3.0 MW offshore wind turbine
with a fixed gear ratio. The turbine has a cut-in wind speed of 3.5 m/s, a rated wind speed of 15 m/s
and a cut-out wind speed of 25 m/s. The hub height is approximately 80 m, and the diameter at the
tower bottom is 4.2 m. Figure 2a and Figure 2b show the wind turbine.
5th International Operational Modal Analysis Conference, Guimarães 13-15 May 2013
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1.1.3. Test Field
The offshore research field in Frederikshavn consists of four 2.0-3.0 MW wind turbines located next
to the harbour. Three of the turbines are located in the sea, while the investigated offshore wind
turbine structure in this paper is located in a basin with a water depth of 4 m. Geotechnical
investigations in the basin show that the soil profile primarily consists of cohesionless soils. From
seabed at level -4.1 m to -11.4 m, well graded to graded fine sand is found based on the classification
method proposed by [4]. Below this, ungraded deposit of sand and silt with varying small organic
content is identified, and below level -15 m, sand without organic content is found. The sand layer has
a unit weight γm of 19.5 kN/m3
and a relative density ID of 90%. The permeability of the sand is so
large that no pore pressure build-up appears during cyclic loading.
Figure 2 The Vestas V90-3.0 MW offshore turbine in Frederikshavn: (a) Geometry of the turbine, (b) Normal
production state. All dimensions are in millimetres.
2. EXPERIMENTAL DAMPING TECHNIQUES
In the traditional experimental modal technology, a set of frequency response functions at several
points along the structure are estimated from the measured response and excitation [5], [6]. These
functions contain all the information to determine the resonance frequencies fk, damping ratios ζk and
Figure 1 The prototype bucket foundation in Frederikshavn: (a) Geometry of the foundation concept, (b) After
installation in late 2002. All dimensions are in millimetres.
M. Damgaard, L. Bo Ibsen, L. V. Andersen, P. Andersen, Jacob K. F. Andersen
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mode shapes of the structure. A few attempts to excite parked onshore wind turbines by
measurable excitation have been done, see [7], [8], [9]. However, for offshore wind turbines the input
excitation is difficult to measure, and the modal properties are almost impossible to estimate. In
addition, accurate modal identi-fication under actual operating conditions is difficult to extract by
traditional experimental technologies. In the following two major procedures of estimating cross-wind
modal properties of offshore wind turbines are introduced.
2.1. Free Vibration Tests
In general, the inherent modal damping in a freely vibrating system can be estimated in two ways;
either by measuring the free structural response after application of a sinusoidal load with a frequency
equal to the eigenfrequency of the structure [10] or by measuring the free structural response after the
application of an impulse. The application of an impulsive load has been reported in [2], [11], [12],
[13]. In these publications, the modal damping of offshore wind turbines has been determined by
“rotor-stop” tests. The wind turbine is effectively left to freely vibrate after the generator shuts down
and the blades pitch out of the wind. As an example, Figure 3a shows the raw output acceleration
signal for a “rotor-stop” test. As indicated in Figure 3a, the wind turbine structure behaves almost as a
single-degree-of-freedom (SDOF) system with linear viscous damping, and the corresponding
damping coefficient cv is so low that the system is undercritically damped. Wind turbine structures are
characterised by closely spaced modes occurring at nearly identical frequencies. Therefore, it is
important that the measured free decay only contains modal vibrations from one single mode as shown
in Figure 3b. The modal damping δ1 is found by least-squares fitting of a linear function to the natural
logarithm of the rate of decay of the transient response. However, modal damping estimation from free
vibration tests of wind turbines is only related to the structure. The aerodynamic effects that influence
the mode shapes are simply ignored. Therefore, a much more efficient and economical method of
estimating modal parameters of wind turbine structures is by ambient vibration tests, where the
stochastic wind excitation is used as the excitation source.
Figure 3 Raw output signal during a “rotor-stop” (a) Fore-aft tower acceleration ay as a function of time t, (b)
Fore-aft tower acceleration ay as a function of side-side acceleration ax.
2.2. Ambient Vibration Tests
Ambient modal analysis, also denoted operational modal identification, allows determination of the
inherent dynamic properties and aerodynamic effects of a structure by measuring only the structural
response and using the ambient or natural operating forces as unmeasured input. Originally,
operational modal analysis was developed for modal estimation of civil engineering structures like
buildings and bridges, where the application of the theory has been written in many excellent papers.
5th International Operational Modal Analysis Conference, Guimarães 13-15 May 2013
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However, application of operational modal identification to operational wind turbines is not a
straightforward task. The method relies on the assumption that the system is time invariant, which is
violated for a wind turbine. The nacelle rotates about the tower, the rotor rotates around its axis and
the pitch of the blades may change. A way to handle this problem is to find a suitable period, where
blade pitch angle θb, wind speed vwind and rotor speed vrotor remain unchanged. Moreover, steady state
broadband random excitation is assumed in operational modal identification. Wind excitation fulfils
this requirement, but deterministic signals introduced by the harmonic frequencies 1P and 3P will take
place. For non-parametric methods in the frequency domain, these harmonics must be identified and
separated from the structural modes. For time-domain methods, where the modal parameters are
extracted directly by fitting parameters to the raw time histories, the harmonics are just estimated as
very highly damped modes and do not need to be filtered out. Several robust operational modal
identification methods have been developed in the past, see [14], [15] for a detailed literature review.
In this paper, two techniques are considered in order to evaluate the cross-wind modal damping δ1 of
the wind turbine in Frederikshavn; the Enhanced Frequency Domain Decomposition technique and the
Stochastic Subspace Identification technique. A short introduction to the two techniques is given
below.
2.2.1. Enhanced Frequency Domain Decomposition
The Enhanced Frequency Domain Decomposition (EFDD) technique is a non-parametric frequency
domain method and is an extension of the Basic Frequency Domain (BFD) technique [16]. As the
input excitation is assumed stationary, zero mean Gaussian white noise, the response is also Gaussian
distributed. Hence, the system response is completely described by its covariance function or auto and
cross spectra. From the linear dynamic theory [17], the system response is a linear combination of the
mode shape multiplied by the modal coordinate
(1)
Inserting Eq. (1) into the expression of the covariance function provides
(2)
where the superscript H denotes the complex conjugate transpose and the superscript T is the non-
conjugated transpose. The spectral density function for each known discrete circular frequency can
be obtained by Fast Fourier Transformation (FFT) of Eq. (2):
(3)
The spectral density function is often estimated using the Welch method [18], where the
time records are divided into nd contiguous data segments. It is beneficial to use a window function to
reduce the leakage introduced by the FFT with an overlap between segments to compensate for the
loss of information due to tapering of the data segments when the segments are multiplied by the
window function. The objective is now to decouple the Hermitian spectral density function
and describe it by superposition of single-degree-of-freedom (SDOF) systems, each corresponding to
an individual mode. The decomposition is done by taking the Singular Value Decomposition (SVD) of
each output spectral density matrix ,
(4)
where is the singular value diagonal matrix of the scalar singular values , and
is a unitary matrix of the singular vectors . It should be noticed that Eq. (4)
has the same form as Eq. (3). Assuming a white noise excitation, i.e. a diagonal spectral input matrix,
a lightly damped structure and geometrically orthogonal mode shapes for closely spaced modes, it is
shown in [16] that, near a peak in the frequency spectrum, the first singular vector is an estimate of
the mode shape , and the corresponding singular value is the auto power spectral density function
of the corresponding SDOF system. The SDOF auto power spectral density function around the peak
M. Damgaard, L. Bo Ibsen, L. V. Andersen, P. Andersen, Jacob K. F. Andersen
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is identified by comparing the estimated mode shape with the singular vectors for the
frequencies around the mode. Using a MAC criterion [19], an auto spectral bell function can be found.
The modal damping δk is then easily obtained by transforming the auto spectral bell function to time
domain by inverse FFT. Finally, to improve the estimated mode shape , the singular vectors that
correspond to the singular values in the SDOF spectral bell function are averaged jointly. The average
is weighted by multiplying the singular vectors with their corresponding singular value, i.e. singular
vectors close to the peak of the SDOF spectral bell have a large influence on the mode shape estimate.
2.2.2. Stochastic Subspace Identification
The Stochastic Subspace Identification (SSI) techniques are all formulated and solved using linear
state space formulations [20] given by
(5)
(6)
where Eq. (5) is called the state equation that models the dynamic behaviour (position and velocity) of
the physical system, and Eq. (6) is denoted as the observation equation. The physical system is
modelled by an n×n state matrix , where n is the model order, i.e. the number of considered
eigenvalues μ that completely characterise . By introducing a stochastic Gaussian white noise
process of dimension n×1 that represents the input driving the system dynamics, the state matrix
transforms the state of the system to a new state . The system output that can be observed is
defined by and is determined from the summation of a stochastic Gaussian white noise process
related to the measurement noise and the product of the state vector and the s×n observation matrix
. s is the number of sensor positions. The overall aim is now to determine an estimate of the system
matrix and the observation matrix for different model orders n. Based on traditional eigenvalue
analysis of linear dynamic systems [17], the modal damping δk is found from the pole λk of , and the
observable eigenvector is found from the product of the observation matrix and the eigenvector
. The estimation of and can either be performed from the measured time signals (data-driven
stochastic subspace identification) or from the correlations of the time signals (covariance-driven
subspace identification). The last-mentioned is due to the fact that it is required that the system
response is a realisation of a Gaussian distributed process with zero mean. Thus, a state space model
having the correct covariance function will be able to completely describe the statistical properties of
the system response.
In order to predict the state vector and system response in Eq. (5) and Eq. (6) optimally, an
innovation form of a Kalman Filter is used [20]
(7)
(8)
where is the Kalman gain and the vectors are called innovations. Assuming that measurements
are given for some initial time to and collected in a matrix
, the optimal predictors and are chosen defined as the mean value
of the state vector and the system response for all the measurements , respectively. This is
given by the conditional means
, (9)
(10)
where it is assumed that and are uncorrelated. The conditional mean on both sides of Eq. (5) and
Eq. (6) then reads
(11)
(12)
5th International Operational Modal Analysis Conference, Guimarães 13-15 May 2013
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By inserting Eq. (9) recursively into itself i times for each time step q and using this result in Eq. (10),
the estimated states for several values q can be written as [21]
(13)
where is denoted the extended observability matrix. This matrix can be determined by a Singular
Value Decomposition of the matrix that only includes the information of
the system response from the measurements. However, before using the SVD, is pre and
postmultiplied with weight matrices and ,
(14)
The values of and depend on the stochastic subspace identification algorithm. Both the
Unweighted Principal and Weighted Principal algorithms [20] are used in this paper. As indicated in
Eq. (14), the number of block rows in determines the size of the extended observability matrix
and thereby the maximum state space dimension as the product of block rows and the dimension of the
measured system response vector . In conclusion, the procedure of the Stochastic Subspace
Identification is as follows; firstly, establish the matrices and for a given number of block
rows based on the measurements, secondly, determine the extended observability matrices and
from Eq. (14) and finally, determine the states and using the same procedure as used for
establishing Eq. (13). Thus, assuming that it has been possible to estimate the states for n instance in
time, the dynamic system matrix and observation matrix can be found from a least regression
problem by minimising the residual .
Figure 4 Kinemetrics force balance accelero-meters: (a) Sensor positions in tower and foundation, (b) Sensor
mounting by use of magnets
3. MONITORING SYSTEM
In order to measure the modal space of the wind turbine in Frederikshavn, the tower and foundation
are equipped with a monitoring system consisting of 15 Kinemetrics force balance accelerometers,
model FBA-ES-U. A portable data acquisition system PDAQ-8 from DigiTexx Data Systems Inc. is
placed inside the turbine, and based on the Data Streamer Remote Monitoring and Acquisition
Software from Digitexx Systems Inc., real time data is collected and processed. The accelerometers
are mounted on consoles attached to the structure by magnets at four different levels. Figure 4a and
Figure 4b show the sensor position and the sensor mounting, respectively. It should be noticed that
generator speed vgen, blade pitch angle θb and wind speed vwind are gathered during the acceleration
measurements.
M. Damgaard, L. Bo Ibsen, L. V. Andersen, P. Andersen, Jacob K. F. Andersen
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4. INTERPRETATION OF MEASURED TIME SIGNALS
Results from the ambient and free vibrations tests on the wind turbine structure in Frederikshavn are
presented in the following.
Figure 5 Data presentation of test number 7: (a) Singular values for each channel as a function of the frequency,
(b) Spectogram of a channel placed in the top of the tower. The rotational rotor frequency 1P, the lowest
eigenmode and the blade passing frequencies 3P and 6P are clearly represented in the plots.
4.1. Ambient Vibration Tests
In the period primo October 2012 - ultimo November 2012, a total of 100 ambient vibration tests were
investigated for the Vestas V90-3.0 MW wind turbine. A sampling frequency of 200 Hz has been
used. However, since only the properties for the lowest eigenmode are of interest, the signals are
low–pass filtered followed by a decimation of order 160. Figure 5a and Figure 5b show the singular
values and the short-time Fourier transformation of test number 7, respectively. As indicated the
energy related to the rotational rotor frequency 1P, the lowest eigenmode and the blade passing
frequency 3P are almost independent of time during the test. As a starting point for modal parameter
estimation, the EFDD technique has been applied. As earlier mentioned, the method operates in the
frequency domain, which means that leakage will always be introduced when applying the Fourier
transformation and assuming periodicity. To reduce the leakage, long recording times of 2 hours have
been used [22], [23]. Contrary to the SSI technique, the harmonic component from the rotational rotor
frequency 1P must be separated from the structural mode in the EFFD technique. Therefore, it has
been utilised that a random response is approximately Gaussian distributed in case of multiple random
inputs, whereas a harmonic response follows a sinusoidal probability density function [18].
5th International Operational Modal Analysis Conference, Guimarães 13-15 May 2013
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Hence, at each frequency the measurements are bandpass filtered, and a statistical test derived from a
Kurtosis calculation [24] is performed to identify the harmonic components.
In order to substantiate the cross-wind modal damping δ1 of the lowest eigenmode , the SSI
technique has been applied. Figure 6 shows the cross-wind modal damping δ1 using the EFDD
technique and SSI technique with Unweighted Principal Component (UPC) and Weighted Principal
Component (PC). As indicated, the three methods agree very well. This is supported by the MAC
values that indicate excellent agreement between the eigenmodes from the EFFD technique and the
SSI techniques with values higher than 0.95 for the main part of the measurements. As an example, the
eigenmode for test number 41 is shown in Figure 7a, which follows an elliptical trace. To verify
how well the modelled system from the SSI technique approximates the measured system, Figure 7b
shows the modelled and measured auto-spectra for test number 41. According to Figure 6, the
estimated cross-wind damping δ1 seems to reach an extreme value of approximately 0.05 at rated wind
speed. Afterwards the damping slightly decreases for higher wind speeds. By investigating the blade
pitch angle θb as function of mean wind speed vwind for each measurement, cf. Figure 8, it is clearly
observed that after rated wind speed the blade pitch angle θb increases drastically. This may in turn
reduce the fore-aft modal damping and thereby also the side-side damping due to coupling effects
Figure 6 Cross-wind modal damping δ1 of the lowest eigenmode for ambient vibration tests by use of the
Enhanced Frequency Domain Decomposition technique and the Stochastic Subspace Identification technique
with Unweighted Principal Component (UPC) and Weighted Principal Component (PC) algorithms.
Figure 7 Model outputs from the SSI-UPC technique for test number 41: (a) Side-side eigenmode , (b)
Measured and modelled auto-spectra.
M. Damgaard, L. Bo Ibsen, L. V. Andersen, P. Andersen, Jacob K. F. Andersen
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between the two closely spaced mode shapes that occur at nearly identical frequencies.
Figure 8 Blade pitch angle θb as a function of mean
wind speed vwind.
4.2. Free Vibration Tests
A total of 67 “rotor-stop” tests from the years 2004-2008 have been analysed. In general, during a
“rotor-stop”, the oscillatory deformation of the wind turbine structure is attenuated. This may be due
to a combination of geometrical damping, i.e. radiation of energy into the subsoil, sea, air and material
damping due to conversion of mechanical energy into heat. Since the water depth is approximately 4
m at the test site in Frederikshavn, the hydrodynamic damping δwater has negligible impact on the
measured system damping δ1 [2]. In addition, the aerodynamic damping δaero on the tower is
insignificant and hence, the measured system damping δ1 from the “rotor-stop” tests is mainly driven
by steel hysteretic damping δsteel and soil damping δsoil. The last-mentioned is a combination of
geometric damping and material damping due to slippage of grains with respect to each other. The
system damping δ1 as a function of the acceleration level ay during the “rotor-stop” test are shown in
Figure 9 with an R-square value of 0.95, meaning that the fit of the amplitude peaks explains 95% of
the total variation in the data about the average. With a steel hysteretic damping δsteel value of 0.01 in
terms of the logarithmic decrement [2], it can be stated that the soil damping δsoil is in the range of
0.004-0.04 logarithmic decrement for an acceleration level between 0.8 m/s2
and 2.1 m/s2. Assuming
normal distributed accelerations in the cross-wind direction during power production, the ambient
vibration tests show that the 95% quantile of the acceleration level for a mean wind speed vwind
between 5 m/s and 20 m/s is in the range of 0.02 m/s2-0.6 m/s
2. This may in turn indicate a maximum
soil damping δsoil of approximately 0.01 logarithmic decrement during power production as indicated
in Figure 9.
5th International Operational Modal Analysis Conference, Guimarães 13-15 May 2013
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Figure 9 System damping δ1 as a function of
acceleration level for the lowest bending mode
based on “rotor-stop” tests. The accelerometer placed
in the top of the turbine is used.
5. CONCLUSIONS
Experimental analysis of the cross-wind modal damping δ1 of the lowest eigenmode of an
offshore wind turbine installed on a bucket foundation has been presented. Inherent dynamic
properties and aerodynamic effects are evaluated with free and ambient vibration tests, where
frequency domain and time domain modal identification algorithms are utilized. Several interesting
conclusions can be drawn:
■ Non-parametric and parametric operational modal techniques show good agreement for the cross-
wind modal damping δ1 of an offshore wind turbine.
■ The cross-wind modal damping δ1 tends to de-crease for wind speeds vwind higher than rated wind
speed. Blade pitch regulation and the presence of coupled eigenmodes are believed to explain the
observation.
■ “Rotor-stop” tests indicate that notable soil damping δsoil in the cross-wind direction is introduced
for a significantly higher acceleration level than observed during power production.
Future work will concern comparison of the experimental modal findings with an aerodynamic model
of the turbine coupled with a lumped-parameter model of the soil and bucket foundation.
ACKNOWLEDGEMENTS
The authors are grateful for the financial support from the research project Cost Effective Monopile
Design funded by the Danish Energy-technological Development and Demonstration Program.
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