Application of Operational Modal Analysis and Blind Source Separation / Independent Component Analysis Techniques to Wind Turbines

Transcription

1 Applcaton of Operatonal Modal Analyss and Blnd Source Separaton / Independent Component Analyss Technques to Wnd Turbnes S. Chauhan +, M. H. Hansen *, D.Tchernak + + Brüel & Kjær Sound & Vbraton Measurement A/S, Skodsborgvej 307, DK-2850 Nærum, Denmark * Wnd Energy Dvson, Rsø Natonal Laboratory for Sustanable Energy, Techncal Unversty of Denmark, Frederksborgvej 399, DK-4000, Rosklde, Denmark Emal: schauhan@bksv.com, dtchernak@bksv.com, morten.hansen@rsoe.dk Nomenclature t Tme ω Frequency x(t) Vector of output observatons H Frequency Response Functon F Input Force [] H Hermtan of a matrx G XX, G FF Response and Force Power Spectra R pqk, S pqk Mathematcal Resdue Terms A Mxng system or mxng matrx s(t) Source sgnals Φ r Modal vector assocated wth r th mode η r Ψ Modal coordnates assocated wth r th mode Modal flter matrx Abstract Wnd turbnes are complex structures and ther dynamcs vary sgnfcantly n operaton, n comparson to that under stand stll (parked) condtons. Presence of rotatonal loads and consderable aeroelastc effects makes t dffcult to apply conventonal system dentfcaton technques to wnd turbnes. Operatonal Modal Analyss (OMA) s a technque of determnng dynamc characterstcs of a structure based on the output responses only (Input exctaton s assumed to be stochastc and ts nformaton s not requred). Recently t was shown by means of analytcal and expermental studes that Blnd Source Separaton and Independent Component Analyss (BSS/ICA) technques, whch are more common n bo-magng, wreless communcatons etc, can also be utlzed for system dentfcaton purposes n typcal output only scenaros. Ths paper explores the possblty of applyng these technques (OMA and BSS/ICA) to wnd turbnes. These technques lend themselves very well to ths stuaton as wnd turbne s a huge structure and also, stochastc exctaton of turbne from the wnd can be used as nput. However, tme varant nature of operatng wnd turbnes and presence of harmonc components n exctaton, stll pose several challenge to applcaton of OMA and BSS. To tackle these ssues one at a tme, ths paper focuses n understandng only the aeroelastc effects, thus avodng effect of rotatonal loads (and hence presence of harmonc components n exctaton force). Aeroelastc effects are sgnfcant even n case of parked wnd turbnes, thus studes are conducted on smulated data obtaned for a parked turbne. Ablty of OMA and BSS/ICA technques n determnng dampng, whch s a

2 combnaton of both structural and aeroelastc dampng, s assessed by means of these studes. An OMA algorthm SSI-DATA (Data based Stochastc Subspace Identfcaton) and a BSS technque called Second Order Blnd Identfcaton (SOBI) are used for ths purpose. It s shown that these technques work satsfactorly on parked turbne data, pavng way to conduct further studes on more complex case of operatonal wnd turbne. 1. Introducton Utlzaton of only output response data for system dentfcaton purposes started way back n 1970s [1-4], however t was not tll early 1990s that researchers started takng note of these technques. Durng early 1990s, James et al. [5] proposed the NExT framework for utlzng output response tme hstores for modal parameter estmaton purposes, thus layng foundaton of Operatonal Modal Analyss. Ths research was a result of work performed at Wnd Energy Research Organzaton at Sanda labs for testng wnd turbnes. NExT nvolved a four stage process; data acquston, calculaton of correlaton functons, use of tradtonal parameter estmaton algorthms for fndng system parameters and fnally extracton of mode shapes. NExT was ntally appled to a parked Vertcal Axs Wnd Turbne (VAWT). However, wnd turbnes behave very dfferently n operaton, n whch case aeroelastc effects are domnant and aeroelastc dampng s sgnfcant n comparson to structural dampng. Thus, NExT was subsequently appled to rotatng VAWTs [5] Horzontal Axs Wnd Turbne (HAWT) [6] and other structures lke a rocket durng launch [7]. It was noted n [5] that mode shape nformaton s mportant to explan changes n dampng wth ncrease n turbne rotaton rate and that better technques are requred for estmatng low ampltude modes and removal of harmonc peaks. Surprsngly, though OMA subsequently got popular n varous cvl engneerng applcatons (Brdges, buldngs, stadums etc) there wasn t much follow up wth respect to wnd turbnes. One of the possble reasons for ths could be that applcaton of OMA to wnd turbnes s not a straght forward task due to the presence of consderable aeroelastc effects along wth presence of rotatonal components. In case of a parked wnd turbne, all OMA assumptons and also those pertanng to Modal Analyss (System beng lnear, statonary and tme nvarant) are vald n general, except that aeroelastc effects are stll consderable even n case of a parked wnd turbne. The case of operatonal wnd turbnes s dfferent though, as n addton to aeroelastc effects, rotatonal loads come nto effect. Perodc nature of aerodynamc forcng, turbne system and the fact that system s now tme-varant poses varous challenges as these stuatons do not lend themselves naturally to OMA algorthms. However, possblty of estmatng actual modal parameters whch can ad n better understandng of dynamcs of operatng wnd turbnes are major ncentves to be ganed. As mentoned earler, aerodynamcs plays an mportant role whle desgnng wnd turbnes and t was durng 1980s that the aeroelastc vbratons n wnd turbnes were frst notced. These problems were stall-nduced edgewse blade vbratons, whch later led to the development of a method for determnng dampng for edgewse blade modes [8]. Ths method utlzed an excter mechansm through whch a partcular mode s excted by means of a harmonc force and decayng response at the end of the exctaton s used to estmate the dampng. In [11], the excter mechansm method along wth an Operatonal Modal Analyss algorthm, Stochastc Subspace Identfcaton (SSI) [9, 10] were used for estmatng aeroelastc dampng of operatonal wnd turbne modes. In ths work, t was shown that blade ptch and generator torque varatons can be used as excter mechansms for exctng partcular modes of nterest. However, ths method suffers from lmtatons on account of the fact that excted turbne vbratons are not pure modal vbratons and therefore the estmated dampng s not actual dampng. Yet another lmtaton of ths method was that t was not possble to acheve requred ptch ampltudes to excte suffcently modes other than the tower modes. SSI method performed better n comparson to the prevous method, though longer tme hstores and averagng technques were requred. It was also able to estmate the closely spaced modes whch caused problems for excter method. Thus SSI showed promse n determnng characterstcs of an operatonal wnd turbne. Ths frst use of SSI for OMA of wnd turbnes showed two lmtatons. Frst, the user was requred to have some pre-knowledge of modal dynamcs of the nvestgated turbne to be able to dentfy aeroelastc modes. Second, the aerodynamc exctaton of rotor blades contan harmoncs of nteger multples of the rotor speed due to the rotatonal samplng of the turbulence of wnd, whch are dentfed as modes n a standard SSI method. The focus and motvaton of ths paper s to carry on these nvestgatons further, to explore the possblty of usng OMA technques for estmatng modal parameters, especally the effect of aerodynamc dampng, ncludng ther varaton wth rotatonal speed, for an operatonal wnd turbne. Addtonally, use of an emergng technque called Blnd Source Separaton / Independent Component Analyss for ths purpose s also llustrated n the paper. As t was prevously mentoned, the presence of perodc aeroelastc forces does not ft very well wth the OMA assumptons; t s decded to tackle one problem at a tme and hence current study focuses only on effect of aeroelastc dampng n case of parked wnd turbnes and therefore, effects of perodc forces s avoded.

3 To avod the uncertantes unavodable for real measured data, the OMA and BSS methods are appled to smulated data generated by HAWC2 Wnd Turbne smulator [35]. The smulated data are acceleraton tme hstores generated for a number of ponts located on the tower and rotor blades. The output of OMA and BSS algorthms (namely, wnd turbne modal parameters ncludng aerodynamc dampng) are compared wth modal parameter obtaned from the egenvalue solver embedded nto HAWC2 code. Snce aerodynamc forces are excluded n the Egen value solver of HAWC2, t only provdes the structural modal parameters, and the aerodynamc dampng s not accounted for. Ths makes nvald the drect comparson of modal parameters from the two expermental methods and the egenvalue solver. However, from prevous studes t s known, whch and how the modes are affected by aerodynamc effects and ths provdes useful means of assessng the performance of OMA and BSS technques to parked wnd turbnes. Followng secton dscusses the modal dynamcs of wnd turbnes and theoretcal background of OMA and BSS/ICA technques. Secton 3 ncludes detals of smulated data and results of applcaton of OMA and BSS/ICA studes conducted on ths data. Conclusons and scope of future work are presented n secton Theoretcal Background 2.1 Modal Dynamcs of Wnd Turbnes The modal dynamcs of wnd turbnes s governed by the flexbltes of the three man substructures: tower bendng, drve tran torson, and blade bendng (and torson). All commercal MW-szed wnd turbnes have almost the same sequence of lower order modes at standstll (Refer Fgure 1). The frst two modes are the longtudnal and lateral (relatve to the wnd) tower bendng modes, followed by the frst drve tran torson mode and three rotor modes domnated by the frst bendng mode of the three blades, whch s called the flapwse bendng mode. The order of the drve tran torson mode relatve to the rotor modes may dffer from turbne to turbne, however, the mutual order of the rotor modes are the frst yaw and tlt modes followed by the symmetrcal flapwse rotor mode. Modes no. 7 and 8 are asymmetrcal rotor modes that are domnated by the second bendng mode of the blades, whch s called the edgewse bendng mode. The next modes are often the rotor modes domnated by the thrd blade bendng mode, but for turbnes wth hgh towers they may be the second tower bendng modes. Fgure 1: Modes of a Standstll Wnd Turbne The frequences of tower bendng modes, drve tran torson modes, and symmetrcal rotor modes are almost ndependent of rotor speed (except for centrfugal stffenng effects on the blade bendng modes). The asymmetrcal rotor modes couple n pars of forward and backward whrlng modes for each blade bendng (or torson) modes. If a par of whrlng modes belongng to a blade mode s pure, then ther modal frequences n the

4 nertal frame wll be gven by the partcular blade mode frequency plus and mnus the rotor speed (see [12] for more detals on modal dynamcs of turbnes). The dampng ratos of all turbne nvolvng out of rotor plane veloctes or rotaton of the blades about ther lengthaxs (the ptch axs) wll be hghly affected by the aerodynamc dampng due to the drect aeroelastc couplng from angles of attack and thereby the aerodynamc forces along the blades. The frst longtudnal tower bendng mode s therefore hghly damped wth common dampng ratos around 20% for ptch-regulated turbnes. However, for stall-regulated turbnes ths aeroelastc tower dampng depends on the stall characterstcs of ts blade arfols whch n some cases can lead to negatve aerodynamc dampng of tower bendng modes. Rotor modes nvolvng flapwse blade bendng modes are also hghly damped wth common dampng ratos above 20% for ptchregulated turbnes, but may also be low or negatvely damped as the tower modes for stall-regulated turbnes. The total aeroelastc dampng of the frst lateral tower bendng mode and the rotor modes nvolvng edgewse blade bendng modes are much less affected by the aerodynamc dampng because the blade moton occur mostly n the rotor plane. Ther dampng ratos therefore do not depend hghly on the operatonal condtons of the turbne (wnd speed, blade ptch settng, and rotor speed); however these modes are low damped, and n some cases of stall-regulated turbnes even slghtly negatvely damped by the aeroelastc nteracton of aerodynamc forces and turbne moton. 2.2 Operatonal Modal Analyss (OMA) and Blnd Source Separaton / Independent Component Analyss (BSS/ICA) Technques Ths secton descrbes brefly man theoretcal concepts and mportant assumptons behnd Operatonal Modal Analyss and utlzaton of BSS/ICA for OMA purposes. For more detaled understandng of OMA and assocated algorthms one can refer [13]. Operatonal Modal Analyss As stated n prevous secton, OMA s a system dentfcaton technque based only on measured output responses. OMA does not requre nput force nformaton but t makes certan assumptons about the nature of the nput exctaton forces. These nclude, 1) Power spectrum of the nput force s assumed to be broadband and smooth. Ths means that the nput power spectra s constant and has no poles or zeroes n the frequency range of nterest. 2) Input forcng s further assumed to be unformly dstrbuted spatally. Both these assumptons mply that exctaton s consdered stochastc n tme and space. Mathematcally, f {X(ω)} s the measured response and {F(ω)} s the nput force, the relatonshp between them n terms of frequency response functon (FRF) [H(ω)] s gven as follows [14]: Now multplyng Eq. (14) and Eq. (15) or wth averagng, { ( ω) } [ H ( ω) ]{ F( ω) } X = (01) { X ( )} H { F( ω) } H [ H ( ω) ] H ω = (02) { X ( )}{ X ( ω) } H [ H ( ω) ]{ F( ω) }{ F( ω) } H [ H ( ω) ] H ω = (03) [ G ( )] [ H ( ω) ] [ G ( ω) ] [ H ( ω) ] H XX ω = (04) where [G XX (ω)] s the output response power spectra and [G FF (ω)] s the nput force power spectra. Gong back to the assumpton that nput force spectrum s constant, t s easy to note that output response power spectra [G XX (ω)] s proportonal to the product [H(ω)][H(ω)] H and order of output response power spectrum s twce that of frequency response functons. Snce [G FF (ω)] s constant, [G XX (ω)] can be expressed n terms of frequency response functons as [ G ( ω )] [ H ( ω) ][ I ][ H ( ω) ] H XX FF (05)

5 Partal fracton form of G XX for partcular locatons p and q s gven as G pq ( ) = R R N pqk pqk pqk pqk k = 1 jω λk jω λk jω k λk S ω (06) S ( λ ) jω ( ) whch ndcates that power spectrum data not only contans nformaton about postve poles (λ k ) of the system but also negatve poles (-λ k ), or n other words, the same nformaton twce. R pqk and S pqk are k th mathematcal resdue terms and are not to be confused wth resdue terms obtaned usng FRF based model as these term do not contan modal scalng nformaton (snce nput force s not measured). It s mportant to note that ths equaton shows that power spectra contans all nformaton needed to defne the dynamc characterstcs of a system (except for modal scalng factor), provded the OMA assumptons are true. Blnd Source Separaton (BSS) or Independent Component Analyss (ICA) BSS/ICA can be seen as an extenson to Prncpal Component Analyss (PCA) whch ams at recoverng the source sgnals from a set of observed nstantaneous lnear mxtures wthout any a pror knowledge of the mxng system. Mathematcally, ICA problem can be formulated as x ( t) = A s( t) (07) where x(t) s a column vector of m output observatons representng an nstantaneous lnear mxture of source sgnals s(t) whch s a column vector of n sources at tme nstant t. A s an m X n matrx referred to as mxng system or more commonly as mxng matrx. A detaled dscusson of the subject of BSS/ICA can be found n [15-21] whch provdes general ntroducton and detals of varous aspects of BSS/ICA. BSS technques am at recoverng both the source sgnals s(t) and system mxng matrx A and n that sense they bear basc smlarty wth OMA. In recent tmes there have been attempts at utlzng these technques for OMA purposes [22-27]. These papers, llustrate the use of BSS/ICA technques to analytcal and expermental data. BSS/ICA technques are less tme consumng and avod the need of tradtonal stablty/consstency dagram whch are sometmes dffcult to nterpret. From theoretcal pont of vew, lnk between BSS/ICA and modal analyss can be establshed through the concept of expanson theorem [28] and modal flters [29-31]. Accordng to the expanson theorem response of a dstrbuted parameter structure can be expressed as x( t ) = r = 1 φ η ( t ) (08) where Φ r are the modal vectors weghted by the modal coordnates η r. For real systems, however, response of the system can be represented as a fnte sum of modal vectors weghted by the modal coordnates. To obtan a partcular modal coordnate η from response vector x, a modal flter vector ψ s requred such that and so that or r r T ψ = 0, for j (09) φ T ψ 0, for = j (10) φ N T T ψ x( t) = ψ φ η ( t) (11) r= 1 ψ φ η T r r = (12) Thus modal flter performs a coordnate transformaton from physcal to modal coordnates. Multplyng the system response x wth modal flter matrx Ψ T results n uncouplng of the system response nto sngle degree of freedom (SDOF) modal coordnate responses η. In order for ψ to exst, the assocated modal vector Φ must be lnearly ndependent wth respect to all other modal vectors [29]. Ths s also the reason why ICA / BSS based technques can be utlzed for the purpose of decomposng the output system response nto a product of modal vectors and correspondng modal coordnate responses. A modal flter vector s unque f and only f the number of sensors used for the modal flter

6 mplementaton s equal to the number of lnearly ndependent modal vectors contrbutng to the system response. In ths work, Second Order Blnd Identfcaton (SOBI) algorthm s used for OMA purposes. SOBI algorthm utlzes jont dagonalzaton procedure [15, 32, 33] to estmate an orthogonal matrx that dagonalzes a set of covarance matrces [25]. One mportant aspect of BSS/ICA algorthms, n relaton wth OMA, s that one can at most extract as many modes as number of sensors used to collect the output response. 3. Smulatons on a Vrtual Turbne: Results and Dscussons The vrtual turbne used n present analyss s the 5MW machne desgned by Jonkman [34] as a numercal reference turbne. The modelng and smulatons are performed usng the nonlnear aeroelastc mult-body code called HAWC2 [35]. Smulaton s done for a standstll case, where the blades are at fne ptch and the drve tran s locked by an assumed mechancal brake on the generator sde of the gearbox. The wnd speed s 18 m/s n hub heght wth a logarthmc wnd shear. Stochastc forcng of the turbne s acheved by smulated atmospherc turbulence wth a low ntensty of 5% obtaned usng Mann s turbulence model of correlated turbulence wth a Kamal spectrum. The length of turbulence box s km (18 m/s tmes s, where frst 100 s are reserved for unsaved transents leavng a tme seres of s), and there are sheets of 32 by 32 ponts. The longtudnal resoluton of turbulence box s therefore m, whch s sgnfcantly longer than n turbulence boxes used for normal 10 mn smulatons for aeroelastc turbne analyss. The coarse resoluton leads to artfcal exctaton at the updatng frequency of Hz (18 m/s dvded by m), whch must be neglected n the followng analyss. Response tme hstores n terms of acceleratons are recorded n all three drectons at 25 locatons on the turbne; 10 on the tower and 5 each on the three blades. Tower measurements are done at a heght of 10, 20, 30, 40, 50, 60, 70, 80, 90 and 99.5 m from the base. Blade measurements are at a radal dstance of 1.0, 8.33, 28.15, and 63.0 m. 200 mnutes of data s collected at a samplng rate of 50 Hz gvng a total of 6,00,000 sample pont. 3.1 Operatonal Modal Analyss Smulated data s processed usng Stochastc Subspace Identfcaton (SSI) algorthm. Vertcal acceleratons for the tower and radal acceleratons for one of the blade algned wth the tower (Blade 1 n Fgure 2), are neglected for ths analyss. Thus only 60 channels of response data are analyzed. The measurement drectons at varous locatons on the turbne are ndcated n Fgure 2. Orgnal tme hstores are downsampled by a factor of 10 so as to obtan a useful frequency range of Hz. Addtonally, projecton channels are used to enhance the performance of the algorthm [36]. Fgure 3 shows the stablzaton dagram obtaned usng SSI. Note that n the stablzaton dagram only stable modes are ndcated.

7 Blade 3 Blade 2 Blade 1 Tower Fgure 2: Measurement Locatons and Degrees of Freedom Fgure 3: Stablzaton Dagram for SSI Algorthm SSI s able to fnd all eght modes n the frequency range of 0-1 Hz. However, the stablty wth regards to modes at 0.60 and 0.62 Hz s not as good as other modes. A total of 11 modes are obtaned between 0-2 Hz frequency range as lsted n Table 1.

8 3.2 Blnd Source Separaton / Independent Component Analyss In case of BSS/ICA the smulated response s downsampled by a factor of 5 to get a useful frequency range of 0-5 Hz. In ths case as well, the same 60 channels are used for analyss as n case of OMA. Fgure 4 show the plot of auto-power spectra of modal coordnate responses η, obtaned usng SOBI algorthm and modal frequences and dampng values are lsted n Table 1. As stated n secton 2, SOBI decouples the system response to correspondng SDOF modal coordnate responses. Here the algorthm s set to dentfy 36 modes n frequency range of 0-5 Hz. It s antcpated that the frst 8 modes, whch are the focus of ths study, wll be obtanable amongst the 36 modes dentfed by SOBI. It s mportant to note that, from algorthmc pont of vew, one can estmate at most 60 modes from ths dataset, as the total number of sensors consdered s 60. Obvously, not all the modal coordnate responses resultng from SOBI correspond to actual modes. It can be clearly seen from Fgure 4 that n some cases the resultant modal coordnate response s not due to an underlyng SDOF system (or that the output response has not been decoupled nto SDOF modal coordnate responses). However, all the modes n frequency range of nterest are well dentfed. The process of fndng out modal frequency and dampng correspondng to each mode nvolves calculatng correlaton functons for modal coordnate responses representng the underlyng SDOF system and usng zero crossng and logarthmc decrement method for estmatng frequency and dampng. Fgure 4: Auto-power Spectra of SOBI Modal Coordnate Responses

9 3.3 Result Comparson and Dscusson Table 1 shows the comparson of OMA and BSS/ICA results wth modes obtaned from Egen value solver. It also ncludes three modes between 1-2 Hz frequency range, n order to further compare the performance of SSI and SOBI. It s very nterestng to note that, though modal frequences obtaned from Egen value solver match well wth those obtaned from SSI and SOBI, same sn t the case wth dampng estmates. However, ths s on expected lnes as Egen value solver doesn t take nto consderaton aerodynamc forces. Modes nvolvng out of rotor plane moton (Modes 2, 4, 5, 6, 9, 10, 11) are damped by the aerodynamc forces, even at standstll. Ths s due to the larger blade surface that nteracts wth surroundng ar when the blades vbrate due to flapwse bendng or tower longtudnal bendng, thus, showng an ncrease n dampng due to aerodynamc effects. Decrease of dampng of other modes s also realstc due to negatve aerodynamc dampng of nplane vbratons when the flow around the blades s separated/stalled. Ths s seen n case of frst lateral tower bendng mode. The edgewse bendng modes and drve tran torsonal mode are not much affected by the aerodynamc forces and hence the dampng s comparable to structural dampng obtaned through theoretcal calculatons. The second yaw mode at 1.53 Hz (Plot 3,3 n Fgure 4) s not very well dentfed.e. the modal coordnate response s not entrely due to ths mode. Ths results n nconsstent dampng estmate and hence t s not ncluded n compled results (Table 1). The Cross MAC plot n Fgure 5 ndcates that mode shapes from SSI and SOBI match well for most modes, although not for all the modes (Drve tran torsonal and edgewse bendng modes). Table 1: Mode Comparson Mode Egen value Solver OMA (SSI) BSS/ICA (SOBI) Mode name number Freq Damp Freq Damp Freq Damp 1 Frst lateral Tower Bendng Frst longtudnal Tower Bendng Frst drve tran torson Frst yaw Frst tlt Frst symmetrc flapwse bendng Frst edgewse vertcal bendng Frst edgewse horzontal bendng Second yaw Second tlt Second symmetrc flapwse bendng

10 Fgure 5: Cross-MAC between SSI and SOBI modes 4. Conclusons and Scope of Future Work Man motvaton for conductng these studes was to assess performance of OMA and BSS/ICA technques when appled to wnd turbnes. Snce wnd turbnes are complex structures, t was decded to focus on one ssue at a tme and thus studes were conducted on parked turbnes. In case of a parked turbne, the rotatonal forces don t come nto play, although aeroelastc effects are stll sgnfcant. An OMA algorthm, SSI-DATA and a BSS technque, SOBI, are appled to smulated data obtaned for a parked wnd turbne. Results show that both technques perform satsfactorly. It s notced that dampng values obtaned usng two technques are qute smlar, but they dffer consderably from the dampng values obtaned from Egen value solver. Ths s due to the fact that dampng obtaned from SSI-DATA and SOBI are a combnaton of structural and aeroelastc dampng where as Egen value solver provdes only structural dampng. Where as aeroelastctty results n ncreasng dampng of certan modes and decreasng dampng of others, dependng on how the surface nteracts wth surroundng ar; there are some modes lke edgewse bendng and drve tran torsonal modes n whose case dampng s not affected as aeroelastc effects are not sgnfcant. These results are on expected lnes and hence very encouragng. As mentoned before, the real challenge n case of wnd turbnes les n establshng ther dynamc characterstcs whle n operaton when the system becomes tme varant and rotatonal loads come nto play along wth the aeroelastc effects. Based on the encouragng results of ths work, the future course of acton nvolves carryng out studes on smulated data for operatng wnd turbnes. Dependng on the success of studes conducted on smulated dataset, these studes wll be substantated wth studes on data obtaned from real operatonal wnd turbne. From a broader perspectve, benefts to be ganed out of ths study are n terms of better understandng of dynamcs of operatonal wnd turbne and makng tools lke OMA sutable and robust for applcaton to wnd turbnes.

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