(c) 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.This works presents a simplified Vertical Azimuth Display (VAD) motion simulator for off-shore wind lidars. The simulator is rooted to the case of a conically-scanning lidar (e.g., the Zephyr lidar), where the wind speed vector is retrieved from the Line-of-Sight velocities over one scan period. The methodological part addresses the geometrical foundations of the simulator and how the lidar attitude is assimilated in matrix form. The discussion part considers the case of time-invariant, horizontally-homogeneous wind under two motional cases of the lidar, static and dynamic. Cases examples are parameterized by Horizontal Wind Speed, Wind Direction and tilt amplitude.Postprint (author's final draft

Gutiérrez Antuñano, Miguel Ángel

Rocadenbosch Burillo, Francisco

Tiana Alsina, Jordi

English

J. Tiana-Alsina

F. Rocadenbosch

M. A. Gutierrez-Antunano

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Vertical Azimuth Display simulator for wind-Doppler lidar error assessment

UPCommons. Portal del coneixement obert de la UPC

UPCommons Portal del coneixement obert de la UPC http://upcommons.upc.edu/e-prints Tiana, J.; Rocadenbosch, F.; Gutiérrez, M.A. (2017) Vertical Azimuth Display simulator for wind-Doppler lidar error assessment. IGARSS 2017: International Geoscience and Remote Sensing Symposium: Texas, Estats Units: July 23-28, 2017: proceedings book. IEEE. Pp. 1614-1617. Doi: http://dx.doi.org/10.1109/IGARSS.2017.8127282. © 2017 IEEE. Es permet l'ús personal d'aquest material. S’ha de demanar permís a l’IEEE per a qualsevol altre ús, incloent la reimpressió/reedició amb fins publicitaris o promocionals, la creació de noves obres col·lectives per a la revenda o redistribució en servidors o llistes o la reutilització de parts d’aquest treball amb drets d'autor en altres treballs. Tiana, J.; Rocadenbosch, F.; Gutiérrez, M.A. (2017) Vertical Azimuth Display simulator for wind-Doppler lidar error assessment. IGARSS 2017: International Geoscience and Remote Sensing Symposium: Texas, Estats Units: July 23-28, 2017: proceedings book. IEEE. Pp. 1614-1617. Doi: http://dx.doi.org/10.1109/IGARSS.2017.8127282. (c) 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. VERTICAL AZIMUTH DISPLAY SIMULATOR FORWIND-DOPPLER LIDAR ERRORASSESSMENT.J. Tiana-Alsina1,2,∗, F. Rocadenbosch1,3, IEEE senior member, M. A. Gutie´rrez-Antun˜ano11Remote Sensing Laboratory (RSLab), Department of Signal Theory and Communications (TSC), Universitat Polite`cnica de Catalunya (UPC)2Nonlinear Dynamics, Nonlinear Optics and Lasers (DONLL), Department of Physics (DFIS), Universitat Polite`cnica de Catalunya (UPC)3Institute for Space Studies of Catalonia (IEEC)∗Corresponding author: jordi.tiana@upc.eduABSTRACTThis works presents a simplified Vertical Azimuth Display (VAD)motion simulator for off-shore wind lidars. The simulator is rootedto the case of a conically-scanning lidar (e.g., the Zephyr lidar),where the wind speed vector is retrieved from the Line-of-Sight ve-locities over one scan period. The methodological part addressesthe geometrical foundations of the simulator and how the lidar atti-tude is assimilated in matrix form. The discussion part considers thecase of time-invariant, horizontally- homogeneous wind under twomotional cases of the lidar, static and dynamic. Cases examples areparameterized by Horizontal Wind Speed, Wind Direction and tiltamplitude.Index Terms— Wind, remote sensing, doppler lidar, verticalazimuth display algorithm, Euler angles, resource assessment1. INTRODUCTIONOffshore wind power production has been proposed to take bene-fit from the energy of strong and homogeneous wind fields that arefound over the oceans. During the last few decades Europe is lead-ing offshore wind power industry by installing and operating windfarms connected-to-grid, both in shallow and deep waters sites [1][2]. However, the related costs are significantly greater than landbased wind farms. Consequently, one of the main difficulties tobe overcome, associated with this technology is cost optimization.Remote sensing technologies such as wind lidars, provide a cost-effective solution, specially now that its use is expect to be acceptedin the next IEC Standard for Power Performance verification [3], byusing nacelle lidar or floating systems. Besides, wind-lidar couldalso be a great tool for other applications such as detection of yawmisalignment (i.e., the angular offset between Wind Direction (WD)and wind turbine orientation), and monitoring general atmosphericconditions with a view to evaluate or manage on-site operations [4].Remote sensing on floating offshore platforms like buoys per-mits to estimate wind speeds without the need of using expensiveequipment such as wind-monitoring towers [5][6]. Additionally, re-mote sensing devices as floating wind Doppler lidars enable to eval-uate the wind resource in a larger area since they are more versatileand can be easily re-deployed [7]. On the other hand, and due to themotion of the sea, floating lidar devices can degrade the measure-ment of the wind vector [8][9][10][11].This work has been funded by the Spanish Ministry of Economy andCompetitiveness (MEC) - European Regional Development (FEDER) fundsunder TEC2015-63832-P project.Floating lidar buoys suffer from translational and rotationalmotion which has to be understood in order to find an appropiatemethodology to compensate the errors induced on wind measure-ments. On one hand, translational motion (sway, surge and heave,along the X, Y and Z axes, respectively) can be easily compensatedby subtracting the motion vector from the measured wind vector,which justifies that translation motion in the horizontal plane isnot studied in this work. On the other hand, rotational motion isstudied elsewhere (roll, pitch and yaw, around the X, Y and Z axes,respectively) is more difficult to be canceled out. Thus, buoy tiltinghas a strong impact on the line of sight (LoS) measurements of thelidar, which can induce a non-negligible bias on the measured windvector [10][11] and which justifies the need for further insight. Inthe present work, and with the aim of analysing and deconvolvingthe effect of lidar motion on the radial velocity measured along eachLoS a VAD simulator is developed. Towards this end, the simulatoruses given attitude data (pitch and roll information). The simulatoris capable to reproduce different motion conditions and compute thecorresponding Line-of-Sight (LoS) velocity measurements.This paper is structured as follows: Sect. 2 presents the concep-tual and analytical foundations of the simulator. Sect. 3 discussessimulation results under simplified conditions of static and dynamictilting over the pitch axis. Sect. 4 gives conclusion remarks and fu-ture improvements.2. METHODOLOGYHere we consider the case of a vertically aimed lidar system witha scanning cone containing multiple LoS (Fig.1). For example, inthe case of the ZephIR 300 lidar, the LoS are scanned in a cone of30 deg width from the vertical. The Vertical Azimuth Display (VAD)algorithm enables to retrive the wind-vector components (u, v, w)by combining the wind-speed projections along each LoS (i.e. theradial speed on each LoS) over a conical scan [12][13]. In the case ofthe ZephIR, 50 LoS are combined in each conical scan at a frequencyof 1 scan/s.According to Euler’s rotation theorem, any rotation can be de-scribed by three angles. There are several conventions for Euler an-gles, depending on the axes where the rotations are carried out. Herewe use roll-pitch-yaw angle (x-y-z convention), where ψ is roll, θis pitch and φ is yaw.. The rotation matrix defining the compositerotation or rotated coordinate system can be written as:R = RψRθRφ, (1)whereRψ ,Rθ , andRφ are the component rotation matrices describ-Fig. 1. Schematic of the geometry of the VAD conically-scanningtechnique [12][13] and lidar rotational motion (Euler angles).ing rotation about x-axis (roll), y-axis (pitch), and z-axis (yaw), re-spectively.Rψ =1 0 00 cos(ψ) sin(ψ)0 − sin(ψ) cos(ψ) ,Rθ =cos(θ) 0 − sin(θ)0 1 0sin(θ) 0 cos(θ) ,Rφ = cos(φ) sin(φ) 0− sin(φ) cos(φ) 00 0 1 . (2)By using roll-pitch-yaw angles, obtained from time-series from theinertial measurement units (IMUs) of the lidar buoy, the geometryof the problem or lidar attitude (Fig. 2) can be known at each suc-cesive scanning LoS. As a result the problem is invertible (i.e., hasan inverse function). Finally, each LoS and the corresponding LoSvelocity in the rotated coordinate system can be written asrˆrotLoS = R · rˆLoS ,~vrotLoS = ~vLoS · rˆrotLoS , (3)where rˆLoS is a unit vector along the LoS, ~vLoS is the LoS veloc-ity vector, R is the rotation matrix of Eq. 1. rˆrotLoS and ~vrotLoS arethe counterparts of rˆLoS and ~vLoS in the rotated coordinate system.Superindex “rot” is a reminder of “rotated coordinate system”.Simulation approach.- A motion simulator with the constitutiveEqs. 1-3 above has been implemented. A time-static and spatially-uniform wind vector is used, thus being the main oversimplification.Thus, a constant wind field exclusive of wind-field random fluctua-tions is used. The simulated motional behavior can either be staticor periodic (sinusoidal like, in the present case). System parametersare the intensity [m/s] and direction [deg] of the simulated wind-field, the amplitude and frequency of the rotational motion. In theFig. 2. Example of a single conical scan for a fixed (red) and moving(black) lidar buoy. Blue lines represent the LoS velocity vector inthe rotated coordinate system, ~vrotLoS . Red lines show the scanningtrajectory in the fixed reference coordinate system. Ts stands for thetotal scanning time.following and for the sake of comparison, the angular frequency isftilt = 0.3 Hz, the reference velocity is ~vref =(10,0,0) and the mea-surement height is h = 100 m.3. RESULTSStatic tilt.- The first simulation case studies the effect of static tiltabout the pitch axis. Motion angles range from 0 to 15 deg, windspeeds from 0 to 20 m/s and wind directions from 0 to 360 deg. Thehorizontal wind speed (HWS) error is a signed quantity obtained asthe diference between the HWS velocity input (fixed reference coor-dinate system) and the VAD-estimated HWS velocity in the rotatedreference coordinate system. Figure 3a does the parameter studyby varying the wind direction (WD) and the pitch amplitude in theranges above while keeping the wind speed constant (10 m/s overx-axis). In response, Fig. 3a shows a systematic underestimation ofthe HWS which monotollicaly grows as the tilt amplitude increases.Here, it is worth noting that the HWS error goes to zero when theWD is aligned with the rotation axis (y-axis for the pitch angle). Thisis an expected result since the projected wind vector on the tiltedscanned cone gives a ymmetric number of LoSs with over/under-estimated radial speeds. On the other hand Fig. 3b does now theparametric study by varying the HWS pitch amplitude while keep-ing a constant WD (0 deg). Figure 3b shows that the error increaseswhen the wind-speed intensity also increases. In spite of the specificset of values used to vary the HWS, it is worth noting that the rel-ative error on the HWS (i.e., the ratio between the HWS error andthe input HWS, figure not shown) remains constant for a given tiltangle. Analogous results (though 90 deg shifted) are reencounteredwhen the simulation is performed for the roll angle.Dynamic tilt.- Next, error performance on the retrieved HWS forthe case of sinusoidal pitch tilt is studied. The simulation frequencychoosen is 0.3 Hz because is a typical figure measured in similar li-dar buoys in the nearshore mediterranean sea [14]. The initial phaseFig. 3. Error behavior of the retrieved HWS in response to statictilt and (a) different wind directions relative to lidar (WD [deg]), (b)wind speed intensities (HWS [m/s]).is 0 deg, corresponding to the lidar scanning cone pointing in thevertical direction (i.e. no initial tilt). Figure 4 shows the error per-formance for the same parameter space as in Figure 3. The resultsobtained differ from the ones shown with a static tilt because bothnegative and positive biases are retrieved while swepping the WD.The two points marked white and black are choosen as representativeof such positive and negative biases.Figure 5 gives a more in-depth discussion for the two selectedpoints. Thus, Fig. 5 shows the projections of the reference windvector (~vref = (u, v, w), w = 0 for horizontal wind) over the ro-tated coordinate system during one scan period of the lidar as well asthe retrieved VAD velocity vector (~vrot = (ur, vr, wr)) for the twostudy points in (black and white) in Fig. 4. Important is to mentionthat these projections are shown in Fig. 5 over the reference (i.e.,fixed) coordinate system XYZ and more specifically, on the XZ, YZand XY planes. Left and right panels correspond to the black andwhite points of Fig. 4 respectively.On one hand, for the black-point case (angular amplitude,12.5 deg; WD, 35 deg; Fig. 5 a,b,c) retrieved velocity componentsur and vr are slightly underestimated (Fig. 5 c, blue arrow belowthe red arrow). Besides, as a consequence of the assymetric amountof tilt of the scanning cone over one scanning period, the VAD algo-Fig. 4. Error behavior of the retrieved HWS in response to sinu-soidal pitch tilting (ftilt = 0.3 Hz) for (a) different wind directions(WD [deg]) relative to lidar, and (b) wind speed intensities (HWS[m/s]). White and black dots refer to the two case examples analisedin Fig. 5 (pitch motion amplitude of 12.5 deg and wind directions of35 and 125 deg, respectively).rithm retrieves a net upside vertical component, wr (Fig. 5 a,b). Thesame figure panels show the underestimation over x- and y- axes.On the other hand, for the white-point case (angular amplitude,12.5 deg; WD, 35 deg; Fig. 5 d,e,f, i.e. 90-deg rotated with respectto the previous case) the opposite behavior occurs. This is character-ized by an overestimation of the retrieved wind component, ur andvr (Fig. 5 f), and by a net downside vertical component, wr (Fig. 5d,e). Here, it is worth noting the unbalanced behaviour of the ab-solute error (-1.2 to +0.4 m/s in Fig. 4a; -1.3 to 0 m/s in Fig. 4b)resulting from asymetries on the LoS velocity projections for differ-ent WDs.4. CONCLUSIONSA VAD motion simulation for off-shore wind lidars has been pre-sented for the case of a conically-scanning lidar (50 LoS, 1 scan/s)and VAD velocity-vector retrieval over one scan period (these fig-ures not being a limitation). The simulator uses pitch-roll-yaw Eu-lers angle formulation to relate the LoS-velocity projections of theFig. 5. Scanning trajectory (black line) and LoS-projected velocities(blue line) during one scanning period of the moving lidar repre-sented over the fixed coordinate system (XZ, YZ, and XY planes).(a, b, c) Black-dot case in Fig. 4 corresponding to an angular ampli-tude of 12.5 deg and wind direction of 35 deg. (d, e, f) White-dotcase corresponding to an angular amplitude of 12.5 deg and winddirection of 125 deg. Insets represent the reference wind velocityvector (red arrow) and the retrieved one (blue arrow) in the fixedcoordinate system.wind vector and lidar attitude in the fixed coordinate system (ref-erence observation system) to the rotated coordinate system, wherethe velocity vector is VAD retrieved. Two main motional lidar caseshave been considered to study the HWS retrieval error: static and dy-namic (sinusoidal) pitch tilt [angular amplitudes range, 0 − 15 deg;wind speed, 0 − 20 m/s; and WD, 0 − 180 deg, normalised windvelocity (when not parameterized), 10 m/s]. Results are summarisedin Figs. 3-4. The static case has shown that the HWS error is nilwhen the WD is aligned with the rotation axis (Y axis for pitch tilt).For WD between 60 to 120 deg (normalised wind velocity 10 m/s),HWS errors lie between 0 to −0.075 m/s (i.e., −0.75%) while forWD between 0 to 45deg and 135 to 180 deg display HWS errorsbetween −0.1 to −0.25 m/s (i.e., −1% to −2.5%). The dynamiccase has yieded non-symmetric HWS errors that are roughly be-tween +0.5 m/s and −1.2 m/s (Fig. 4) when the WD is varied inthe margin above (normalised wind velocity 10 m/s). Future stud-ies are to include all 6 degrees of freedom in order to better un-derstand the effects of second-order motion error sources on the re-trieved HWS. As a further step, the simulator is also to assimilatenon-homogeneous wind fields to study the impact of turbulence onwind velocity retrievals.5. REFERENCES[1] A. Arapogianni, I. Pineda, and J. Moccia, “The European off-shore wind industry - Key trends and statistics 2012,” Tech.Rep., The European Wind Energy Association, Jan. 2013.[2] Global Wind Energy Council, “Global wind report annual mar-ket update 2015,” Tech. Rep., Global Wind Energy Council,April 2016.[3] International Electrotechnical Commission, “IEC 61400-12wind turbine power performance testing,” Tech. Rep., Inter-national Electrotechnical Commission, February 1998.[4] A. Scholbrock, P. Fleming, D. Schlipf, A. Wright, K. Johnson,and N. Wang, “Lidar-enhanced wind turbine control: Past,present, and future,” in 2016 American Control Conference(ACC). American Control Conference, July 2016, pp. 1399–1406.[5] Carbon Trust, “Carbon Trust Offshore Wind Acceleratorroadmap for the commercial acceptance of floating lidar tech-nology,” Tech. Rep., Carbon Trust, Nov. 2013.[6] J. P. Mathisen, “Measurement of wind profile with a buoymounted lidar,” Energy Procedia, vol. 00, no. 00, pp. 12, 2013.[7] Y. L. Pichugina, R. M. Banta, W. A. Brewer, S. P. Sandberg,and R. M. Hardesty, “Doppler lidar–based wind-profile mea-surement system for offshore wind-energy and other marineboundary layer applications,” Journal of Applied Meteorologyand Climatology, vol. 51, pp. 327–349, February 2011.[8] G. Wolken-Mo¨hlmann, H. Lilov, and B. Lange, “Simula-tion of motion induced measurement errors for wind measure-ments using lidar on floating platforms,” Fraunhofer IWES,Am Seedeich, vol. 45, pp. 27572, 2011.[9] J. Gottschall, G. Wolken-Mo¨hlmann, T. Viergutz, andB. Lange, “Results and conclusions of a floating-lidar offshoretest,” Energy Procedia, vol. 53, pp. 156 – 161, 2014.[10] J. Gottschall, H. Lilov, G. Wolken-Mo¨hlmann, and B. Lange,“Lidars on floating offshore platforms; about the correctionof motion-induced lidar measurement errors,” in EWEA 2012Proc., EWEA 2012, Ed., 2012.[11] E. Burin des Roziers M. Pitter, J. Medley, M. Mangat,C. Slinger, and M. Harris, “Performance stability of ZephIRin high motion enviroments: floating and turbine mounted,”Tech. Rep., Zephir, 2014.[12] V. A. Banakh, I. N. Smalikho, F. Ko¨pp, and C. Werner, “Rep-resentativeness of wind measurements with a cw doppler lidarinthe atmospheric boundary layer,” Appl. Opt., vol. 34, no. 12,pp. 2055–2067, 1995.[13] S. W. Henderson, P. Gatt, D. Rees, and M. Huffaker, LaserRemote Sensing, Chapter 7: Wind LIDAR, Optical Scienceand Engineering. CRC Press, 2005.[14] M. Grifoll, J. Navarro, E. Pallares, L. Ra`fols, M. Espino, andA. Palomares, “Ocean–atmosphere–wave characterisation ofa wind jet (ebro shelf, nw mediterranean sea),” Nonlin. Pro-cesses Geophys., vol. 23, pp. 143–158, 2016.

(c) 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.This works presents a simplified Vertical Azimuth Display (VAD) motion simulator for off-shore wind lidars. The simulator is rooted to the case of a conically-scanning lidar (e.g., the Zephyr lidar), where the wind speed vector is retrieved from the Line-of-Sight velocities over one scan period. The methodological part addresses the geometrical foundations of the simulator and how the lidar attitude is assimilated in matrix form. The discussion part considers the case of time-invariant, horizontally-homogeneous wind under two motional cases of the lidar, static and dynamic. Cases examples are parameterized by Horizontal Wind Speed, Wind Direction and tilt amplitude

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Vertical Azimuth Display simulator for wind-Doppler lidar error assessment

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