Optimal, risk-based operation and maintenance planning for offshore wind turbines

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1 Optmal, rsk-based operaton and mantenance plannng for offshore wnd turbnes John Dalsgaard Sørensen Aalborg Unversty # & Rsø DTU, Denmark # Sohngaardsholmsvej 57, DK-9 Aalborg, Denmark e-mal: jds@cvl.aau.dk Summary or offshore wnd turbnes costs to operaton and mantenance are substantal. Ths paper descrbes a rsk-based lfe-cycle approach for optmal plannng of operaton and mantenance. The approach s based on pre-posteror Bayesan decson theory. Deteroraton mechansms such as fatgu corroson, wear and eroson are assocated wth sgnfcant uncertanty. Observatons of the degree of damage can ncrease the relablty of predctons, especally n connecton wth condton-based mantenance. The approach can be used for gearboxes, generators, cracks, corroson, etc. The paper also descrbes how probablstc ndcators can be used to quantfy ndrect nformaton about the damage state for crtcal components, e.g. gearboxes.. Introducton Costs to operaton and mantenance for offshore wnd turbnes can be very large compared to other costs, and can be expected to ncrease when wnd farms are placed at deeper water depths and n more harsh envronments. Ths paper descrbes a rsk-based lfe-cycle approach for optmal plannng and desgn of offshore wnd turbnes. or other offshore nstallatons such as ol & gas nstallatons, cost-effectve procedures for rsk-based nspecton plannng have been developed durng the last -5 years and are used at several locatons world wd see e.g. Moan [], aber et al. [2] and Sørensen et al. [3]. These procedures are based on preposteror Bayesan decson theory. Ths paper descrbes how procedures based on a smlar theoretcal bass can be appled for wnd turbnes, especally offshore wnd farms. or wnd turbnes the man aspects related to operaton and mantenance are avalablty, relablty and cost reductons. Mantenance actvtes can be dvded n correctve and preventve (tme-tabled or condtone mantenance. Condtoned mantenance usng observatons from e.g. condton montorng and nspectons should optmally be based on rsk and pre-posteror Bayesan decson theory. In secton 2 the basc prncples are descrbed. In secton 3 applcaton to optmal mantenance plannng s consdered. Secton 4 gves an example applcaton related to gearboxes n wnd turbnes. 2. Optmal plannng of nspecton and mantenance gure shows a decson tree related to the lfe cycle of an engneerng structure such as a wnd turbne or wnd farm. The decsons taken by the decson maker (desgner / owner / ) and observatons of uncertan parameters (unknown at the tme of the decson) are: At the desgn stage a decson on the optmal desgn parameters z = ( z,..., z N ) s made whch n prncple should mze the total expected benefts mnus costs durng the whole lfetme such that safety requrements are fulflled at any tme. In practce requrements from standards and actual costs of materals are used to determne the optmal desgn. Durng the lfetme contnuous montorng of the wnd turbnes and nspectons of crtcal components / detals are performed. These are ndcated n the box repeated nspecton/mantenance n fgure. Each box conssts of: o a decson on tmes and types of nspecton / montorng for the rest of the lfetme o observatons from nspecton / montorng

2 o decson on eventual mantenance / repar based on the nspecton / montorng results Realsaton of uncertan parameters such as wnd and wave clmat strengths, degradaton, model uncertantes wll take place durng the lfetme. It s noted that these uncertantes can be dvded n aleatory and epstemc uncertantes. Aleatory uncertanty s nherent varaton assocated wth the physcal system or the envronment t can be characterzed as rreducble uncertanty or random uncertanty. Epstemc uncertanty s uncertanty due to lack of knowledge of the system or the envronment t can be characterzed as subjectve uncertanty, reducble uncertanty. The total cost s the sum of all costs n the remanng part of the lfetme after the decson tme. gure. Decson tree for optmal mantenance plannng. The approach can be used for operaton and mantenance plannng related to dferent falure & error types n Gearbox, Generator, Rotor blades, Blade ptch mechansm, Yaw mechansm, Man shaft, Tower / support structure (fatgue cracks, corroson), urther, decsons related to operaton and mantenance are related to dfferent tme scales: short (mnutes) for decson related to e.g. parkng the wnd turbn medum (days) for e.g. decsons on when to start offshore mantenance / repar actons dependng on e.g. weather forecasts, or long (months / years) for e.g. preventve mantenance and nspecton / montorng plannng for gear boxes. An mportant step n rsk-based nspecton & mantenance plannng s collecton of data / nformaton and probablstc modellng of ths nformaton. Informaton can come from Condton Montorng Systems (CMS), nspectons or ndcators. Indcators that contan ndrect nformaton on e.g. falure rates can be formulated and updated based on Bayesan statstcs, see aber & Sørensen [4]. The sze of wnd turbnes for electrcty producton has ncreased sgnfcantly durng the last decades both n producton capablty and n sze. Compared to onshore turbnes and buldng structures, humans spent lttle tme n the vcnty of offshore turbnes one could argue that the relablty of offshore structures can be lower than for onshore turbnes. The concept of partal safety factors and characterstc values has been adopted from cvl engneerng. However, due to the domnance of the wnd loads the level of relablty of wnd turbnes s somewhat lower than the average structural relablty. The current relablty level of cvl engneerng standards has emerged over many years of evolutonary development through whch a level of relablty acceptable to the publc has been reached. Ths level ensures that a low rsk of human njury s obtaned at reasonable costs. Thus the cost of avodng human njury s mplct n current wnd

3 turbne standards. or offshore turbnes the probablty of human njury durng storm condtons s small. One could therefore argue that neglectng the prce of preventng human njury, whch s hgh n ndustralzed countres, would open a possblty for assessng a lower level of structural relablty of offshore turbnes by cost-optmzaton, and further that optmal plannng of operaton and mantenance can be based on cost-beneft analyses. In the followng frst general formulatons to asses the optmal relablty level are brefly descrbed, and next these are extended to the stuaton of optmal plannng of nspecton and mantenance durng operaton. 2. ormulaton of relablty-based optmsaton problems for wnd turbnes rst, t s assumed that the wnd turbnes are systematcally rebuld n case of falure. The man z = z,...,, e.g. dameter and thckness of tower and man desgn varables are denoted ( z N ) dmenson of wngs. The ntal (buldng) costs s denoted ( z) C I, the drect falure costs are the benefts per year are b and the real rate of nterest s r. alure events are modeled by a Posson process wth rate λ. The probablty of falure s P ( z). The optmal desgn s determned from the followng optmzaton problem, see e.g. Rackwtz [5]: C, z s.t. W ( z) = z z l P ( z) P b r C u z CI C ( z) CI ( z) C λp ( z) + C C r + λp () z, =,..., N () where l z and u z are lower and upper bounds on the desgn varables. C s the reference ntal cost of correspondng to a reference desgn z. P s the mum acceptable probablty of falure e.g. wth a reference tme of one year. Ths type of constrant s typcally requred by regulators. The optmal desgn z * s determned by soluton of (). If the constrant on the * mum acceptable probablty of falure s omtted, then the correspondng value P ( z ) can be consdered as the optmal probablty of falure related to the falure event and the actual cost-beneft ratos used. The falure rate λ and probablty of falure can be estmated for the consdered falure event, f g X,..., X, z and a stochastc model for the stochastc varables, a lmt state equaton, ( n ) ( X,..., ) X n are establshed. If more than one falure event s crtcal, then a seres-parallel system model of the relevant falure modes can be used. Next, the stuaton s consdered where the assumptons are the same as above except that the wnd turbne s assumed not to be rebuld n case of falure. The desgn lfetme s T L and the probablty of falure of a component or the structure n the tme nterval [,T ] s denoted P ( T,z). The annual probablty of falure s ΔP ( T, z ) = P ( T, z) P ( T, z) The optmal desgn z s.t. l ΔP T L W ( z) = t = z z z u b C wth T n [years]. * z s determned from the followng optmzaton problem: CI ( ( )) ( z) P t, z ( ) ( t, z) ΔP, t TL + r, =,..., N t C TL C ΔP t = C ( t, z) ( ) t + r (2)

4 where Δ P s the mum acceptable annual probablty of falure. 2.2 Inspecton / Mantenance Included gure 2. Deteroraton mechansms such as fatgu corroson, wear and eroson are assocated wth sgnfcant uncertanty. Observatons of the degree of damage D(t) can ncrease the relablty of predctons usng Bayesan statstcal technques as llustrated n fgure 2. Generally an nspecton at tme T and assocated mantenance/repar wll decrease the uncertanty and the expected mean damage level at tme T 2 wll be smaller snce most realzatons wth large damage level at tme T can be expected to be mantaned/repared. The model n secton 2. s now extended to nclude tme-varyng degradaton and damage accumulaton (e.g. wear, fatgue and corroson). It s assumed that the wnd turbne s not rebuld n case of falure. gure 3. Inspecton plannng decson tree. The performance of wnd turbnes s subject to a number of uncertantes. These nclude operatonal condtons, materal characterstcs and envronmental exposure. The uncertantes are due to nherent physcal randomness and uncertantes assocated wth the models used to assess the performance of the systems. If, furthermor the statstcal bass for the assessment of the uncertantes s lmted then also statstcal uncertantes may be mportant.

5 When nspecton plannng for wnd turbnes s consdered, t s mportant to take all these uncertantes nto consderaton, as they wll strongly nfluence the future performance of the systems. It s also mportant to realze that the degree of control of the engneerng systems acheved by the nspectons s strongly nfluenced by the relablty of the nspectons,.e. ther ablty to detect and sze degradaton. The relablty of nspectons themselves may be subject to sgnfcant uncertanty and ths must be taken nto account n the plannng of nspectons. The decson problem of dentfyng the cost optmal nspecton plan may be solved wthn the framework of pre-posteror analyss from the classcal decson theory see e.g. Raffa and Schlafer [6] and Benjamn and Cornell [7]. Here a short summary s gven, see e.g. Sørensen et al. [8], Madsen & Sørensen [9], aber et al. [2] and Sørensen et al. [3]. The nspecton decson problem may be represented as shown n fgure 3 whch s extracted from the general decson tree n fgure. In the general case the parameters defnng a nspecton plan are the possble repar / mantenance actons whch are modeled by the decson rule d, the number of nspectons N n the servce lfe T L, the tme ntervals between nspectons and possble repar/mantenance t = t, t,..., t ) and the nspecton qualtes q = q, q,..., q ). ( 2 N ( 2 N These nspecton parameters are wrtten as e = ( N, t, q). The outcome of nspectons (typcally a damage level, e.g. a crack sz the extent of corroson or wear) s modeled by a random varable S snce t s unknown at the tme of decson makng. A decson rule d (S) s then appled to the outcome of the nspecton to decde whether or not repar / mantenance should be performed. The dfferent uncertan parameters (stochastc varables) modelng the state of nature such as load varables and materal characterstcs are collected n X = X, X,..., X ). ( 2 n If the total expected costs are dvded nto fabrcaton, nspecton, repar, mantenanc strengthenng and falure costs and a constrant related to a mum annual (or accumulate falure probablty Δ P s added then the optmzaton problem can be wrtten z, d s.t. W( z, = B( z, C ( z, C l z z z t u ΔP ( t, z, ΔP I IN, =,..., N, t =,2,..., T ( z, C L REP ( z, C ( z, (3) W ( z, e, s the total expected benefts mnus costs n the servce lfe tme T L, B s the expected benefts, C I s the ntal costs, C IN s the expected nspecton costs, C REP s the expected costs of repar and C s the expected falure costs. The annual probablty of falure n year t s Δ. The N nspectons are assumed performed at tmes T T2... T N TL. P, t The total captalzed benefts are wrtten N B( z, = B ( P ( T )) (4) T = ( + r) where the th term represents the captalzed benefts n year gven that falure has not occurred earler, B s the benefts n year, P ( T ) s the probablty of falure n the tme nterval, T ] and r s the real rate of nterest. [ The total captalzed expected nspecton costs are

6 C IN N ( e, = CIN, ( q) ( P ( T )) (5) T = ( + r) where the th term represents the captalzed nspecton costs at the th nspecton when falure has not occurred earler, C ( q ) s the nspecton cost of the th nspecton. IN, The total captalzed expected repar costs are C REP N ( e, = CR, PR T = ( + r) (6) where C R, s the cost of a repar at the th nspecton and P R s the probablty that a repar s performed after the th nspecton when falure has not occurred earler. The total captalzed expected costs due to falure are estmated from TL C ( e, = C ( t) ΔP, t P (7) COL AT t t= ( + r) where C (t) s the cost of falure at the tme t. P s the condtonal probablty of collapse COL AT of the wnd turbne gven fatgue falure of the consdered component and models the mportance / consequence of fatgue falure. The probabltes of falure at year t and the probablty of repar can be determned as descrbed n e.g. Madsen et al. (99). It s noted that f the nspecton / mantenance opton s removed then the optmzaton problem (3) s smplfed to (2). The above model s n prncple related to a sngle wnd turbne and a sngle component. or wnd turbne placed n a wnd farm wth many crtcal components the same basc formulaton can be used, but the ntal costs, nspecton, repar and falure costs should be formulated as a basc cost plus margnal costs for each extra wnd turbne n the park. 3. Mantenance plannng gure 4. Bath-tub model for lfetme falure rate. or many components subject to degradaton / damage accumulaton the model n fgure 4 can be used to llustrate the development of the falure rate durng the lfetme. Intally a hgh falure

7 rate can be expected due to fabrcaton / burn-n defects. Next, a perod wth a normal constant falure / defect rate wll take place. Correctve mantenance s performed n ths perod. At the end of the lfetme of the component the falure / defect rate can be expected to ncrease. If the falure rate ncreases strongly (tme to falure s known ) then preventve mantenance should be performed. If the falure rate s moderately ncreasng deteroraton / damage can be observed before falur and condton control / condton & rsk based mantenance should be performed and planned usng the prncples descrbed above for rsk-based nspecton & mantenance/repar plannng. The rsk-based methods descrbed n secton 2 can thus be used to optmal plannng of decsons on future nspectons / condton montorng (tme and type), and mantenance / repar actons based on (unknown) observatons from future nspectons / montorng takng nto account uncertanty and costs. The next secton shows n more detal how ths can be used for typcal components n wnd turbnes. 4. Example mechancal component n wnd turbne: gearbox gure 5. Repeated nspecton/mantenance. In ths example the theoretcal models outlned n secton 2 and 3 are llustrated consderng gearboxes n wnd turbnes. Only the process of plannng repeated nspecton and mantenance / repar s consdered, see fgure 5. Examples of nspecton methods and nspecton results for gearboxes are: Vsual nspecton: though nspecton covers: ndcaton of extent of wear Ol analyss: wth tme ntervals a sample s taken ndcatng extent of wear Magnet: wth tme ntervals a representatve sample s taken ndcatng extent of wear materal Investgaton of ol flters: wth tme ntervals a representatve sample s taken ndcatng extent of wear materal Partcle countng onlne: contnuously representatve samples are taken ndcatng extent of wear materal Condton montorng: contnuously the vbraton response s montored and used to ndcate mechancal changes

8 All these assessment methods gve ndrect nformaton on the damage/deteroraton state of the gearbox, snce the damage/deteroraton state s not measured drectly. The ndcators wll have dfferent relabltes wth respect to nformaton about the real damage state and they wll have dfferent costs. These aspects can be modelled usng the rsk-based nspecton & mantenance plannng approach descrbed n secton 2. In order to use the pre-posteror Bayesan decson models optmal, rsk-based nspecton & mantenance plannng t s further necessary to formulate decson rules for mantenance / repar actons gven nspecton/montorng results,.e. t s beforehand decded whch future mantenance / repar to perform when future nspecton results become avalable. The models to be establshed are: A determnstc model for damage / deteroraton accumulaton as functon of tme: D (t) A stochastc model for uncertan parameters n the damage accumulaton model such that a probablstc model for the damage accumulaton can be obtaned,.e. the probablty of certan damage levels can be calculated A stochastc model for the uncertanty / relablty of each nspecton type A decson model d (S) for repar / mantenance (acton) gven future result of nspecton / condton montorng, A model for costs related to nspectons, mantenanc repar and possble falure (ncludng loss of ncome) It s noted that nformaton from contnuous qualty control and montorng systems can be used to establsh the stochastc models. gure 6. Examples of damage accumulaton.

9 gure 6 shows examples of realsatons of damage accumulaton as functon of tme. If tme and damage are dscretzed n damage states T, T2, T3,... and D, D2, D3,... then the probablstc nformaton needed s: Condtonal probabltes related to damage accumulaton process: P ( D( T ) = d D( t) = d j ),.e. the probablty that the damage at tme T s d gven that the damage at tme t s d j. P D T = d I T = where ( ) Condtonal probabltes related to nspecton method: ( ) ( ) I obs I ( T ) s the uncertan (unknown) nspecton result at tme T gvng ndrect nformaton about the damage state D ( T ) at tme T. I obs s the actual nspecton result. Usng these probabltes the probablty of falure at tme T gven an nspecton result I obs at tme T can be estmated by: ( D( T ) D D( T ) = x) P D( T ) = x I( T ) ( I ) P ( T I ) = P = dx (8) obs where D s the damage level correspondng to falure where e.g. a complete exchange s necessary. It s noted that the model for the relablty of the nspecton methods modelled though P ( D( T ) = d I( T ) = I obs ) can be formulated n dfferent ways dependent on the type of nformaton avalable usng Bayes rule. An example decson model d (S) could be: where If D M D( T ) < DR If D R D( T ) < D D M and R then mantenance then repar D are damage levels correspondng to mantenance and repar. The probablty of repar at tme T gven an nspecton result I obs at tme T s estmated by: ( D D( T ) < D D( T ) = x) P D( T ) = x I( T ) obs ( I ) P ( T I = P = dx (9) R obs ) R The probabltes n (8) and (9) are used n equatons (5) - (7) to estmate the total expected costs and next n equaton (3) to obtan the optmal nspecton tmes. The model can easly be extended wth: Informaton from: More nspecton methods Montorng systems Inspecton / montorng from other (correlate components Decsons on Whch of several nspecton methods to use (ncl. smultaneous use of several nspecton methods) Whch of several mantenance methods to use Overall plannng for: Many components Wnd farms Detaled plannng for offshore operatons (e.g. n case of falure) takng nto account Uncertantes n weather forecasts Cost: materel, loss of ncom obs

10 5. Conclusons A rsk-based lfe-cycle approach for optmal plannng of operaton and mantenance s descrbed. The approach s theoretcally based on pre-posteror Bayesan decson theory and can be used when deteroraton mechansms such as fatgu corroson, wear and eroson are present and can be observed by nspecton and/or montorng before falure of the component consdered. The rsk based approach can ratonally take nto account the uncertanty related to the deteroraton and the future costs related to nspecton/montorng, mantenanc repar and falure (loss of ncome). Observatons of the degree of deteroraton damage can ncrease the relablty of predctons, especally n connecton wth condton-based mantenance usng Bayesan updatng. The approach can be used for gearboxes, generators, cracks, corroson, etc. urther, t s descrbed how probablstc ndcators can be used to quantfy ndrect nformaton about the damage state for crtcal components. The approach s llustrated for applcaton to gear-boxes n stuatons where deteroraton can be observed before falure. Acknowledgements The work presented n ths paper s part of the projects Probablstc desgn of wnd turbnes, grant no and Bottlenecks, grant no supported by the Dansh Research Agency. The fnancal support s greatly apprecated. References. Moan, T.: Relablty-based management of nspecton, mantenance and repar of offshore structures. Structure and Infrastructure Engneerng, Vol., No., 25, pp aber, M.H., Engelund, S., Sørensen, J.D. & A. Bloch (2). Smplfed and generc rsk based nspecton plannng. Proc. OMAE 2, S&R paper Sørensen, J.D. & M.H. aber (2), Generc nspecton plannng for steel structures, Proc. ICOSSAR, USA. 4. aber, M.H. & J.D. Sørensen: Indcators for nspecton and mantenance plannng of concrete structures. Structural Safety, Vol. 24, 22, pp Rackwtz, R. (2), Rsk control and optmzaton for structural facltes, Proc. 2th IIP TC7 Conf. On System modelng and optmzaton, Trer, Germany. 6. Raffa, H. & Schlafer, R. (96), Appled Statstcal Decson Theory. Harward Unversty Press, Cambrdge Unversty Press, Mass. 7. Benjamn, J.R. and Cornell, C.A. (97), Probablty, statstcs and decson for cvl engneers, McGraw-Hll, NY. 8. Sørensen, J.D., aber, M.H., Rackwtz, R. and Thoft-Chrstensen, P.T. (99), Modelng n optmal nspecton and repar, Proc. OMAE9, Stavanger, Norway, pp Madsen, H.O. & J.D. Sørensen (99), Probablty-Based Optmzaton of atgue Desgn Inspecton and Mantenance. Proc. Int. Symp. on Offshore Structures, Glasgow.