The Science of Making Torque from Wind (TORQUE 2016)
Journal of Physics: Conference Series 753 (2016) 072034

IOP Publishingdoi:10.1088/1742-6596/753/7/072034

A new motion compensation algorithm of floating lidar system
for the assessment of turbulence intensity
Atsushi Yamaguchi and Takeshi Ishihara The University of Tokyo, 7-3-1
Hongo Bunkyo, Tokyo, 113-8656, JAPANatsushi@bridge.t.u-tokyo.ac.jp

Abstract. In this study, a new motion compensation algorithm was proposed and verified byusing numerical simulation. Compensated horizontal mean wind speed by using conventional
method shows good agreement with reference wind speed regardless of the motion of thefloater. However, turbulence intensity is always overestimated. The overestimation is moresignificant when the maximum pitch angle of the floater motion is larger. When proposed
method is used, the overestimation of the turbulent intensity is improved and estimatedturbulent intensity shows better agreement with reference value. There still remains
underestimation of the turbulence intensity with the bias of -1.1%. This is probably caused by
the low sampling frequency in LIDAR measurement and further research is needed to model
the high frequency component of the wind speed for LIDAR measurement.

1. Introduction
For the efficient assessment of offshore wind climate, floating LIDAR has been used. The floating
LIDAR experiences the motion induced mainly by wave and compensation is needed. There are two
approaches to compensate the floater motion, mechanical compensation [1] and software-based
compensation [2][3][4]. Tiana-Alsia et al.[1] proposed a mechanical compensation system andmeasured mean wind speed better than non-compensated case. The other approach, software based
compensation has an advantage that it does not require any additional hardware to compensate thefloater motion except for the floater motion measurement system. Schlipf et al.[2] proposed a newwind field reconstruction algorithm from LIDAR and applied the algorithm to floating LIDAR andestimate the mean wind speed and turbulence intensity and showed that estimated mean wind speed
and turbulence intensity by using proposed method showed good agreement with the fixe LIDAR
measurement results. Wolken-Möhlmann and Lange [3] apply a compensation algorithm to asimulated synthetic three dimensional wind field and showed that the algorithm works to measuremean wind speed. Yamaguchi and Ishihara [4] also proposed a motion compensation algorithm andverified the algorithm for different floater motion. However, they did not verify the estimation
accuracy of turbulence intensity. As the sampling frequency of the LIDAR is typically much lower
than sonic anemometer, large uncertainty on the measurement of turbulence intensity is expected. In
this study, first, the estimation accuracy of turbulence intensity by using conventional motion
compensation method was investigated, and the effect of turbulence intensity and the floater motion
on the estimation error is investigated. Then, a new motion compensation algorithm is proposed forthe assessment of turbulent intensity and verified by using numerical simulation.
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The Science of Making Torque from Wind (TORQUE 2016)
Journal of Physics: Conference Series 753 (2016) 072034

IOP Publishingdoi:10.1088/1742-6596/753/7/072034

2. Generation of three dimensional synthetic wind field and calculation of LoS-speed underfloater motion
In this study, first, three dimensional synthetic turbulent wind fields were generated by using themethod described in [5]. In this method, first, time-varying three dimensional turbulent windcomponents are generated in 𝑦- 𝑧 plane (i.e., the plane perpendicular to the mean wind direction) byconsidering turbulence spectrum and spatial correlations of turbulent wind component. The turbulence
spectrum are assumed to follow standard Kaimal spectrum and the spatial correlations to follow
exponential decay model as specified in IEC61400-1 [6]. The ratios of turbulence intensity between
wind direction, cross wind direction and vertical direction are also assumed to follow the valuẽ ′ (𝑦, 𝑧, 𝑡) =specified in IEC61400-1[6]. Note that generated three dimensional turbulent wind field 𝐮
′ (𝑦,
′ (𝑦,
′ (𝑦,
′
̅̅̅̅̅̅̅̅̅̅̅̅̃ (𝑦, 𝑧, 𝑡) is 0 and the𝑧, 𝑡), 𝑣̃𝑧, 𝑡), 𝑤̃𝑧, 𝑡)) is normalized so that the mean wind speed 𝐮(𝑢̃standard deviation of the wind speed in longitudinal direction (𝜎𝑢̃ ) is 1. Then, considering the mean̂ (𝑦, 𝑧, 𝑡), is
wind speed and turbulence intensity, the dimensional turbulent wind field in 𝑦- 𝑧 plane 𝐮̃ ′ (𝑦, 𝑧, 𝑡) by equation (1)calculated from non-dimensional turbulent wind field 𝐮̂ (𝑦, 𝑧, 𝑡) = 𝜎𝑢 × 𝐮
̃ ′ (𝑦, 𝑧, 𝑡) + 𝑢̅(𝑧)𝐮(1)Here, 𝜎𝑢 is the actual turbulence intensity in longitudinal direction and 𝑢̅(𝑧) is the mean wind speed asa function of height. In this study, a power law with the exponent of 0.1 is assumed for the verticalprofile of wind speed. The turbulence intensities were varied from 8% to 15%. Lastly, this time
̂ (𝑦, 𝑧, 𝑡) is extended to the wind field in 𝑥- 𝑦- 𝑧 space 𝐮(𝑥, 𝑦, 𝑧, 𝑡) =varying wind field in 𝑦- 𝑧 plane 𝐮𝐮(𝐱, 𝑡) by assuming Taylor’s frozen turbulent hypothesis as shown in equation (2).
̂ (𝑦, 𝑧, 𝑡 −𝐮(𝐱, 𝑡) = 𝐮𝑥)̅̅̅̅̅̅𝑢(𝑧)(2)A pulsed LIDAR is chosen as an example in this study. A pulsed LIDAR emits the laser beam in four
directions (in recent models, five directions including vertical), and measures the wind speed
component in line of sight (LoS), which is called LoS speed. This process takes about one second.
Then, horizontal and vertical wind speed is estimated assuming that wind field does not change during
one cycle (four to five seconds) and horizontally uniform.
In this study, the LoS speed of the pulsed LIDAR was calculated in the three dimensional wind fieldmentioned above considering the motion of the LIDAR. The LoS speed of the LIDAR at 𝑖th level attime 𝑡 can be calculated by using equation (3).
𝑉𝐿𝑂𝑆 (𝑖, 𝑡) = (𝐮[𝐥𝑖 (𝑡), 𝑡] −d𝐥𝑖 (𝑡)
𝛏̂[𝐥𝑖 (𝑡), 𝑡]) ⋅|𝐥𝑖 (𝑡)|dt(3)Here, 𝐥𝑖 (𝑡) is the position vector at which the LoS is measured at level 𝑖 and time 𝑡, and 𝛏̂[𝐥𝑖 (𝑡), 𝑡] isthe displacement of the LoS measurement point due to the floater motion and can be calculated inequation (4).
𝜉𝑥̂𝛏[𝐥𝑖 (𝑡), 𝑡] = (𝜉𝑦 ) + 𝐑(𝜃𝑥 , 𝜃𝑦 , 𝜃𝑧 )(𝐥𝑖 (𝑡) − 𝐠)𝜉𝑧(4)Here, 𝜉𝑥 , 𝜉𝑦 , 𝜉𝑧 , 𝜃𝑥 , 𝜃𝑦 and 𝜃𝑧 are the surge, sway, heave, roll, pitch and yaw component of the floater
motion, respectively. 𝐑(𝜃𝑥 , 𝜃𝑦 , 𝜃𝑧 ) is the rotation matrix and 𝐠 is the position vector of the centre ofgravity of the floater.
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The Science of Making Torque from Wind (TORQUE 2016)
Journal of Physics: Conference Series 753 (2016) 072034

IOP Publishingdoi:10.1088/1742-6596/753/7/072034

The floater motion is derived from the motion of the Fukushima offshore substation floater [7].
Because the floater motion is mainly excited by wave force, the frequency of the floater motion has apeak around peak wave period (5s to 8s). With same phase information, four different amplitudes were
tested by setting the maximum pitch angle as 5 degree, 10 degree, 15 degree and 20 degree. Figure 1
shows the example of the floater motion used in this study.

pitch angle (degree)

25
20
15
10
5
0
-5
-10
-15
0

100

200

300

400

500

time (s)Figure 1 example of the pitch motion of the floater used in this study
3. Estimation accuracy of turbulence intensity by using conventional motion compensation
algorithm
The points where LoS speed is measured in a typical pulsed LIDAR system are shown in figure 2. The
LoS speed is measured along four LoSs (i.e., east, north, west and south) with the constant angle
𝑊𝑆𝜃0 between LoS and vertical (𝐥𝐸𝑖 , 𝐥𝑁𝑖 , 𝐥𝑖 and 𝐥𝑖 in Figure 2). In latest model, the LoS speed is alsomeasured along vertical axis (𝐥𝐶𝑖 in Figure 2). It takes about one second to measure one LoS speed.
Table 1 shows an example of LoS measurement. When LoS speed at 𝐥𝐸𝑖 is measured at 𝑡 = 1, LoS at 𝐥𝑁𝑖
is measured at 𝑡 = 2, etc.

LIDAR

Figure 2 Typical pulsed LIDAR with its laser emission direction
Table 1 Example of LoS measurement (+: measured; -: not measured)
𝑡
1
2
3
4
5
6

𝐥𝑁
𝑖
+
+

𝐥𝑊
𝑖
+
-

𝐥𝑖𝑆
+
-

𝐥𝐸𝑖
+
-

𝐥𝐶𝑖
+
-

The wind velocity can be estimated assuming that wind field is horizontally uniform and temporary
steady for five seconds, thus the horizontal wind speed at ℎ𝑖 and 𝑡 = 3 can be calculated by solving
following equations.
3

The Science of Making Torque from Wind (TORQUE 2016)
Journal of Physics: Conference Series 753 (2016) 072034

IOP Publishingdoi:10.1088/1742-6596/753/7/072034(3)(𝑉𝐿𝑂𝑆 (𝑖, 2) − 𝑉𝐿𝑂𝑆 (𝑖, 4))2sinθ0(3)(𝑖,(𝑉𝐿𝑂𝑆 1) − 𝑉𝐿𝑂𝑆 (𝑖, 3))
𝑣𝑖 |𝑡=3 =2sinθ0Here, 𝑢𝑖 |𝑡=3 and 𝑣𝑖 |𝑡=3 are the east-west component and the north-south component of the horizontal
wind velocity at ℎ𝑖 and 𝑡 = 3, respectively, and 𝑉𝐿𝑂𝑆 (𝑖, 𝑡) is the measured LoS speed at ℎ𝑖 and 𝑡.
𝑢𝑖 |𝑡=3 =When the LIDAR is on a floater and in motion, these equations has to be modified. Yamaguchi and
Ishihara (2015)[3] proposed an algorithm to compensate the floater motion. This method consists offollowing four steps.
1) Interpolation of measured LoS speed to the target height.
𝐸
When the floater experience pitch motion (i.e., rotation along 𝑦 axis), 𝐥𝐸𝑖 and 𝐥𝑊
𝑖 moves to 𝐥′𝑖 and𝑊𝐸𝐥′𝑊
𝑖 , respectively as shown in figure 3. The height of 𝐥′𝑖 and 𝐥′𝑖 are not ℎ𝑖 any more. To estimate𝐸the horizontal wind speed at ℎ𝑖 , the LoS are interpolated at 𝛌𝑖 and 𝛌𝑊
𝑖 where the height is ℎ𝑖 . In
𝐸
𝐸𝐸
the case of Figure 3, 𝛌𝑖 is interpolated from 𝐥𝑖 and 𝐥𝑖+1 .

LIDARFigure 3 Interpolation of measured LoS wind speed to the target height𝑁𝑆2) Estimation of horizontal wind speed in 𝐨 − 𝛌𝐸𝑖 − 𝛌𝑊
𝑖 plane and 𝐨 − 𝛌𝑖 − 𝛌𝑖 plane.
𝐸
𝑊
Once, the LoS wind speed at 𝛌𝐸𝑖 and 𝛌𝑊
𝑖 are obtained, the horizontal wind speed in 𝐨 − 𝛌𝑖 − 𝛌𝑖plane can be calculated easily. It is noted that in this algorithm, when horizontal wind speed in𝐨 − 𝛌𝐸𝑖 − 𝛌𝑊
𝑖 plane is estimated, as shown in Figure 4, the whole the LIDAR measurement
system is “frozen” and the pitch angle 𝜃𝑦 at 𝑡 = 3 is used together with the measured LoS speed at
𝛌𝐸𝑖 at 𝑡 = 4 (𝑉𝐿𝑜𝑆 (𝑖, 4)) and at 𝛌𝑊
𝑖 at 𝑡 = 2 (𝑉𝐿𝑜𝑆 (𝑖, 2)). In other world, the horizontal wind speed in𝐸𝑊𝐨 − 𝛌𝑖 − 𝛌𝑖 at 𝑡 = 3 is estimated.

LIDAR

Figure 4 Estimation of horizontal wind speed in 𝐨 − 𝛌𝐸𝑖 − 𝛌𝑊
𝑖 plane (conventional algorithm)
3) Estimation of horizontal wind velocity.

4The Science of Making Torque from Wind (TORQUE 2016)
Journal of Physics: Conference Series 753 (2016) 072034

IOP Publishingdoi:10.1088/1742-6596/753/7/072034

𝑁
𝑆
From the horizontal wind speed in 𝐨 − 𝛌𝐸𝑖 − 𝛌𝑊
𝑖 plane and 𝐨 − 𝛌𝑖 − 𝛌𝑖 plane, the horizontal
wind velocity is calculated.
4) Correction of wind speed considering LIDAR speed.
The wind velocity obtained above only includes the effect of the floater inclination but the error
related to the floater movement (floater speed) is not included. The floater speed is added to theobtained wind speed above to estimate the true wind speed.

Table 2 summarises the data used in this algorithm to estimate the wind velocity at conventionalalgorithm at 𝑡 = 3. In this algorithm, LoS-speed measured at 𝑡 = 1, 2, 3 and 4 are used. However,during these four seconds, it is assumed that the LIDAR inclination angle does not change and LIDAR
motion velocity is constant. This assumption has an advantage that the algorithm is simple and thenumerical verification shows that it can estimate the horizontal mean wind speed with the error of lessthan 1% even under large floater motion, where if no correction is applied, the estimation error ofhorizontal wind speed reaches 1.5% [2].
Table 2 Summery of the data used in conventional algorithm at 𝑡 = 3 (x: measured and used, +:measured but not used, -: not measured)
𝑡
1
2
3
4
5
6

𝐥𝑁
𝑖
x
+

𝐥𝑊
𝑖
X
-

𝐥𝑖𝑆
x
-

𝐥𝐸𝑖
x
-

𝐥𝐶𝑖
+
-

LIDAR angle
+
+
x
+
+
+

LIDAR velocity
+
+
x
+
+
+

However, this method includes large errors in the measurement of turbulence intensity. Figure 5 showsthe estimated turbulence intensity for different maximum pitch angle and reference value. It is shownthat the estimation error of the conventional algorithm becomes higher as the maximum pitch angle
increases. Figure 7 shows the estimated and reference time series of wind speed. The estimated windspeed by conventional method shows unrealistically larger amplitude of fluctuation compared to thereference value, which causes the overestimation of the turbulence intensity. This is caused by theassumption that LIDAR angle and LIDAR motion velocity stays constant during four seconds, which
in reality is not correct.
turbulence intensity [-]0.25

conventional [4]0.2reference value

0.15

0.1

0.05

0

0

5

10

15

20

25

30

35

Maximum pitch angle [degree]

Figure 5 The estimated turbulence intensity for different maximum pitch angle [3]4. A new motion compensation method for floating lidar
A new motion compensation algorithm is proposed in this study to solve the problem of theconventional method. Following three steps summarizes the new algorithm.
1) Interpolation of measured LoS to the target height.
5

The Science of Making Torque from Wind (TORQUE 2016)
Journal of Physics: Conference Series 753 (2016) 072034

IOP Publishingdoi:10.1088/1742-6596/753/7/072034

This step is exactly same as the conventional algorithm mentioned in the previous section.
𝑁𝑆2) Estimation of horizontal wind speed in in 𝐨 − 𝛌𝐸𝑖 − 𝛌𝑊
𝑖 plane and 𝐨 − 𝛌𝑖 − 𝛌𝑖 plane considering
the floater motion velocity.
In this algorithm, the pitch angles of the floater at the time of measurement of LoS are used.
Figure 5 shows the estimation of horizontal wins speed in 𝐨 − 𝛌𝐸𝑖 − 𝛌𝑊
𝑖 plane in the proposed𝐸
algorithm. The LoS speed, 𝑉𝐿𝑜𝑆(𝑖,4) at 𝛌𝑖 under pitchangle 𝜃𝑦 at 𝑡 = 4 (Figure 6(a)) and 𝑉𝐿𝑜𝑆(𝑖,2) at
𝛌𝑊
𝑖 under pitchangle 𝜃𝑦 at 𝑡 = 2 (Figure 6(b)) are combined as shown in Figure 6(c) and horizontal𝐸𝑊wind speed in 𝐨 − 𝛌𝐸𝑖 − 𝛌𝑊𝑖 is estimated. When horizontal wind speed in 𝐨 − 𝛌𝑖 − 𝛌𝑖 isestimated, the floater motion speed is considered at each time of the LoS speed measurement.
(a)

(b)

(c)

LIDAR

LIDAR

LIDAR

Figure 6 Estimation of horizontal wind speed in 𝐨 − 𝛌𝐸𝑖 − 𝛌𝑊
𝑖 plane (proposed algorithm)(a) LoS speed at 𝑡 =4, (b) at 𝑡 =2, (c) the plane where horizontal speed is estimated3) Estimation of horizontal velocity.
The estimation of the horizontal velocity is carried out in similar way as the conventional method.
Table 3 summarizes the data used for the proposed algorithm. Compared to the conventional algorithm(Table 2), the LIDAR inclination angle and motion velocity for all the time steps are used, whichmakes the estimation more realistic.
Table 3 Summery of the data used in the proposed algorithm at 𝑡 = 3 (x: measured and used, +:measured but not used, -: not measured)
𝑡
1
2
3
4
5
6

𝐥𝑁
𝑖
x
+

𝐥𝑊
𝑖
x
-

𝐥𝑖𝑆
x
-

𝐥𝐸𝑖
x
-

𝐥𝐶𝑖
+
-

LIDAR angle
x
x
x
x
+
+

LIDAR velocity
x
x
x
x
+
+

5. Results and discussion
By using the conventional and proposed method, horizontal wind speed is estimated for every secondand compared by changing maximum floater inclination angle and turbulence intensity. Figure 7
shows an example of the time history of calculated wind speed and reference wind speed. It is clearthat mean wind speed shows good agreement with the reference value, for both method, but thefluctuating component differs considerably. The conventional method sometimes overestimates theinstantaneous wind speed and sometimes underestimates. This causes overestimation of the turbulence
intensity.

6

The Science of Making Torque from Wind (TORQUE 2016)
Journal of Physics: Conference Series 753 (2016) 072034

conventional
若林(2015)IOP Publishingdoi:10.1088/1742-6596/753/7/072034

reference
真値

proposed
本手法

wind speed (m/s)

30
25
20
15
10

5
298

318

338

358

378

398

time (s)Figure 7 time history of instantaneous wind speed
Figure 8 shows the comparison of mean wind speed and turbulent intensity for conventional andproposed motion compensation method. Little difference can be seen between conventional andproposed methods for the estimation of mean wind speed. However, measured turbulent intensity byusing conventional method and proposed method differs considerably. Especially when the maximum
angle of floater motion is larger, calculated turbulent intensity tend to be larger, which causes large
error in the measurement of turbulent intensity. When proposed method is used, estimated turbulence
intensity shows relatively better agreement with reference value, regardless of the maximum
inclination angle. However, still, there exists a bias of -1.1% on the estimation of the turbulence
intensity.
This bias is probably caused by the limitation in the temporal resolution in LIDAR measurement. As it
takes a few second to estimate the horizontal wind speed, turbulence related to smaller eddy than thistime scale cannot be captured. Further research is needed for the modelling of this high frequency
component of the wind speed for the measurement of turbulence intensity by using Doppler LIDAR.
6. Conclusion
In this study, a new motion compensation algorithm was proposed and verified by using numericalsimulation for mean wind speed and turbulence intensity. Following results were obtained.
1.

2.

Compensated horizontal mean wind speed by using conventional method shows good agreementwith reference wind speed regardless of the motion of the floater. However, turbulence intensity
is always overestimated. The overestimation is more significant when the maximum pitch angleof the floater motion is larger. This is due to overestimation and underestimation of theinstantaneous wind speed.
When proposed method is used, the overestimation of the turbulent intensity is improved andestimated turbulent intensity shows better agreement with reference value. There still remains
underestimation of the turbulence intensity with the bias of -1.1%. This is probably caused by the
low sampling frequency in LIDAR measurement and further research is needed to model the highfrequency component of the wind speed for LIDAR measurement.

7

(a) mean wind speed (conventional)
20(b) mean wind speed (proposed)
20

15

15

10
R2=0.996
5010R2=0.997
5
0

0

5

10
15
reference (m/s)

200conventional

R2=0.0874
5°

10°

15°

20°

20

30%

20%

10%

5
10
15
reference (m/s)(c) turbulent intensity (proposed)(c) turbulent intensity (conventional)
30%

conventional

IOP Publishingdoi:10.1088/1742-6596/753/7/072034

proposed (m/s)

conventional (m/s)

The Science of Making Torque from Wind (TORQUE 2016)
Journal of Physics: Conference Series 753 (2016) 072034

20%
R2=0.802
10%

0%

0%
0%

10%

20%

0%

30%

reference

10%

20%

30%

reference

Figure 8 comparison of mean wind speed and turbulent intensity
7. References
[1]
[2]
[3]
[4]
[5]
[6]
[7]

J.Tiana-Alsina, M. A. Gutiérrez, I, Würth, J. Puigdefábregas and F. Rocadenbosch, Motion
compensation study for a floating Doppler wind lidar, IGARSS, Milan, Italy, 2015.
D. Schlipf, A. Rettenmeier, F. Haizmann, M. Hofsäß, M. Courtney and P. W. Cheng, Model
based wind vector field reconstruction from lidar data, Proceedings of the 11th German Wind
Energy Conference DEWEK 2012.
G. Wolken-Möhlmann, B. Lange. Simulation of motion-induced measurement errors for windmeasurements with LIDAR on floating platforms. Proceedings of ISARS conference, Paris,
2010.
A. Yamaguchi and T. Ishihara, Floating offshore wind measurement system by using LIDAR
and its verification, EWEA2015, 2015.
T. ISHIHARA, P. V. Phuc and A. Yamaguchi, Response analysis of wind turbine support
structures using measured wind speed (in Japanese), Wind Engineering Symposium Japan, 265270, 2008.
IEC61400-1: 2005, Design requirement of wind turbine, 2005.
A. Yamaguchi and T. Ishihara, Current status of research activity on floating offshore windturbine in Japan, OFFSHORE2013, 2013.

Acknowledgement
This study was carried our as a part of Fukushima FORWARD project, funded by ministry of
economy, trade and industry of Japan.
8