Long-term Response of Offshore Structures: Some Practical Aspects

Transcription

1 Long-term Response of Offshore Structures: Some Practcal Aspects A. Papaleo, F.J.M. Sousa, E.C.P. Lma and L.V.S. Sagrlo COPPE Federal Unversty of Ro de Janero Workshop: Statstcal models of the metocean envronment for engneerng uses 30/September/2013 Brest-France

2 INTRODUCTION Presentaton Scope: Present two topcs of a research work on response-based desgn of offshore structures; Jont probablty dstrbuton model for metocean data; Response-based methodology to defne the desgn metocean condtons;

3 MOTIVATION Desgn of rsers and moorng lnes for turret- and spread-moored floatng systems: dynamc response depends on the ntensty and drectonalty of the envronmental actons consstency of usng the tradtonal 100-yr envronmental condtons n the desgn?? long-term response analyss s the best desgn methodology

4 RESPONSE-BASED ANALYSIS Long-term dstrbuton of the response peaks F R r Nd 1 s s,d d F R Ss,d (r s,d )f S sd s pd F R S=s,d (r s,d ) short-term dstrbuton of the response peaks (r s,d) mean short-term frequency of response peaks p(d ) dscrete probablty dstrbuton of the vessel draft along tme (full,ballast,half-loaded, etc.) f S (s) jont probablty dstrbuton functon (pdf) of metocean data related to wave, wnd and current Our reasearch: obtan an f s (s) for a large number of metocean parameters solve and make practcal use of F R (r)

5 METOCEAN JOINT PDF MODEL Avalablty of smultaneous data of waves, wnd and current Condtonal Modellng Approach (CMA) dffcult to be used for more than two metocean parameters Model based on the Nataf s Transformaton margnal dstrbutons of metocean parameters and ther correlaton coeffcents matrx unlmted number of metocean parameters

6 ENVIRONMENTAL PARAMETERS The model developed deals wth 10 metocean parameters: Hs ws = S 1 wnd sea sgnfcant wave heght, Tp ws = S 2 wnd sea wave spectral peak perod ws = S 3 wnd sea drecton Hs ss = S 4 swell sgnfcant wave heght Tp ss = S 5 swell spectral peak perod ws = S 6 swell drecton V w = S 7 mean wnd velocty w = S 8 wnd drecton V c = S 9 superfcal current velocty and = S 10 superfcal current drecton c

7 NATAF-BASED PDF MODEL Nataf-based jont pdf model (Der Kureghan and Lu, 1986): 10 f s 1 F s, F s S 1 1 fss FS s S1 1 S f S (s ) margnal PDF of the th varable F S (s ) margnal CPF of the th varable -1 (.) nverse of the standard Gaussan CPF (.) PDF of the standard Gaussan dstrbuton 10 (.) jont PDF of ten correlated standard Gaussan varables Nataf correlaton coeffcents matrx, ρ

8 NATAF-BASED MODEL Nataf correlaton coeffcents l, j F 1 S 1 y F y 1 S S S j 2 S j S j 2 N y1, y2,, jdy1dy2 N,j Nataf correlaton coeffcent l,j lnear correlaton coeffcent between S and S j S, Sj mean values of S and S j S, Sj standard devatons of S and S j Nataf model s a standard procedure for LINEAR varables! How to deal wth the angular varables??? for an angular varable 0 = 360!!

9 CIRCULAR STATISTICS Crcular varable sample (Fsher,1993) : θ, 1 2, sample mean: N arcsn S R arccos C R sample standard devaton: s 2log R N 0.5 where C, S and R are gven by C cos sn N 1 S 2 2 N 1 R C S

10 MARGINAL DISTRIBUTION OF A CIRCULAR VARIABLE Wrapped Normal dstrbuton (unmodal) f c p 1 2 s cosp p1 crcular s s crcular mean standard devaton Equvalent Normal on the real lne f l 1 exp 2 2 lnear Crcle 2log Real s mod2 lnear mean standard devaton

11 MARGINAL DISTRIBUTION OF A CIRCULAR VARIABLE Wrapped Normal dstrbuton (multmodal) f Nm p 1 2 s cosp 1 p1 Nm Nm number of modes Multmodal Normal on the real lne f Nm 1 1 exp 2 2

12 CORRELATION INVOLVING CIRCULAR VARIABLES Sample crcular correlaton between = ( 1, 2,..., N ) and = ( 1, 2,..., N ) [Fsher and Lee, 1983]: 4 AB CD N E F N G H c, c 1 1, A to G: functons of and j A measure of sample lnear-crcular correlaton between = ( 1, 2,..., N ) and X = (x 1, x 2,..., x N ) [Marda, 1976]: 2 2 cl 2 r r 2r12r13r ,X 2 1 r r 12, r 13, r 23 : functons of and x j 23

13 CORRELATION INVOLVING CIRCULAR VARIABLES Correlaton coeffcents when crcular varables are represented on the real lne few theoretcal solutons avalable numercal algorthms to solve the problem (Sagrlo et al., 2011) Practcal results: metocean database for a locaton n Campos Basn offshore Brazl metocean database of 4000 measurements at each 3-h measurements made by PETROBRAS Research Center

14 Probablty Densty Functon Probablty Densty Functon FITTED MARGINAL DISTRIBUTIONS FOR LINEAR VARIABLES Wnd Sea Wnd Sea - Sg. Wave Heght 0.4 Wnd Sea - Peak Perod Data Lognormal Data Webull (3P) Normalzed Value - Hs/ Hs Normalzed value - Tp/ Tp Sgnfcant wave heght - Lognormal Spectral peak perod Webull 3P

15 Probablty Densty Functon Probablty Densty Functon FITTED MARGINAL DISTRIBUTIONS FOR LINEAR VARIABLES Swell Sea Swell Sea - Sg. Wave Heght Data Webull (2P) 0.16 Swell Sea - Peak Perod Data Webull (3P) Normalzed Value - Hs/ Hs Normalzed value - Tp/ Tp Sgnfcant wave heght Webull 2P Spectral peak perod Webull 3P

16 Probablty Densty Functon Probablty Densty Functon FITTED MARGINAL DISTRIBUTIONS FOR LINEAR VARIABLES Wnd velocty 0.16 Superfcal current velocty Wnd Velocty Data Truncated Webull (3P) 1.6 Current Velocty Data Webull (2P) Normalzed Value - Vw/ Vw Normalzed Value - Vc/ Vc Truncated Webull 3P Webull 2P

17 Probablty Densty Functon Probablty Densty Functon FITTED MARGINAL DISTRIBUTIONS FOR ANGULAR VARIABLES Wnd sea drecton 0.6 Wnd drecton 0.6 Wnd Sea Drecton Wnd Drecton 0.4 Data 3 Wrapped Normals 0.4 Data 3 Wrapped Normals Drecton (rad) Mxture of Wrapped Normals (3 modes) Drecton (rad) Mxture of Wrapped Normals (3 modes)

18 Probablty Densty Functon Probablty Densty Functon FITTED MARGINAL DISTRIBUTIONS FOR ANGULAR VARIABLES Swell drecton 0.6 Current drecton Swell Sea Drecton Data 2 Wrapped Normals 0.8 Current Drecton Data 2 Wrapped Normals Drecton (rad) Mxture of Wrapped Normals (3 modes) Drecton (rad) Mxture of Wrapped Normals (2 modes)

19 CORRELATIONS Data correlaton coeffcents - lnear varables Parameter Hs ws Tp ws Hs ss Tp ss V w V c Hs ws Tp ws Hs ss Tp ss V w V c

20 CORRELATIONS Data correlaton coeffcents crcular varables Parameter ws ss w c ws ss w c Data on the crcle Parameter ws ss w c ws ss w c Data on the real lne

21 CORRELATIONS Data correlaton coeffcents lnear vs. crcular varables Parameter Hs ws Tp ws Hs ss Tp ss V w V c ws ss w c Angular data on the crcle Parameter Hs ws Tp ws Hs ss Tp ss V w V c ws ss w c All data on the real lne

22 SOME BI-DIMENSIONAL JOINT DISTRIBUTIOS Measured data Ftted jont pdf model Hs x Tp wnd sea Hs wnd sea x Wnd velocty

23 Probablty densty functon A PRACTICAL APPLICATION USING THE JOINT PROBABILITY MODEL Long-term headng angle dstrbuton of a half-loaded turret-moored FPSO (320 kdwt tanker) FPSO headng dstrbuton Orgnal measured data ( 4000 sea states) Data smulated JPM ( set ponts) Headng angle (degres)

24 Advantages NATAF-BASED JOINT PDF MODEL SUMMARY a smple model that can represent a large number of metocean parameters; once the margnal dstrbutons and correlaton matrx are stablshed, any low order jont pdf (nn) s easly obtaned taylor-made model for relablty analyss and Monte Carlobased numercal smulatons Cautons an approxmate model based on a weak measure of statstcal dependency the correlaton coeffcent sometmes the correlaton matrx may become numercally sngular On gong work: mprove the treatment of correlatons nvolvng angular varables

25 LONG-TERM RESPONSE-BASED ANALYSIS Proposal: how to use response-based analyss to defne shortterm metocean data to be employed n the desgn of rsers and moorng lnes (storm wave desgn methodology) defne desgn metocean data assocated to extreme responses of the structure nstead of those related to extreme envronmental events (e.g., 100-yr events)

26 LONG-TERM RESPONSE-BASED ANALYSIS Some remarks on long-term analyss: full long-term response analyses of rsers and moorng lnes usng FEM-based tme-doman codes are very tme-consumng ; hardly used n the desgn practce; an alternatve s to perform long-term analyses usng analytcal and frequency-doman methods;

27 LONG-TERM RESPONSE EVALUATION Long-term ntegral evaluaton For more than two metocean data n S : Monte Carlo Smulaton F R r Nd 1 s,d F (r s,d R,d )f s S s S d Solved by Monte CarloSmulaton sd s pd s s,d d F R Ss,d (r s,d )f S s ds Ns k1 sk,d d F R Ss,d Ns (r s k,d ) Ns number of Monte Carlo samples s k k th generated metocean data sample generated from f S (s)

28 LONG-TERM RESPONSE EVALUATION Response parameter: lne top tenson (Sousa et. all, OMAE 2012) De-coupled analyss for each MCS generated set of metocean data (S = s k ) Frst step: Statc analyss of the system by program APROA Second step: short-term analyss by program FX_TENSION aproxmate frequency doman stochastc analyss short-term dstrbuton F R S=s,d (r s,d ): Hermte/Wntersten or Raylegh Long-term extreme response evaluaton: program FX_LTERM

29 LONG-TERM RESPONSE ANALYSIS Turret-FPSO n 1300m water depth: 8 ol producton flexble rser samples of metocean data for each Monte Carlo Smulaton 5-6 dstnct MC smulatons (or samples /3-4h PC) 100-yr response: mean + 2 x standard devatons

30 EQUIVALENT DESIGN CONDITIONS Short-term desgn condtons (desgn metocean data set) taken from MC smulatons as the set of metocean parameters whose short-term extreme response (3-h return perod) s numercally VERY CLOSE to the long-term N-yr response ths equvalent metocean condton S= s s used to perform more refned dynamc smulatons for desgn check verfcatons

31 EQUIVALENT DESIGN CONDITIONS Short-term desgn wave approach desgn metocean data : response-based nstead extreme envromental events (e.g.,100-yr metocean desgn condtons) developed case by case,.e., n the beggnng of the desgn process a smplfed long-term response analyss s performed to establsh a Response-based Metocean Techncal Specfcaton Plataform RR 45 Desgn Metocean Data Structure Lmt State Wnd sea Swell Current Wnd Flex Rser 8 Ol Top tenson Hs, Tp, ws Hs, Tp, ss Vc, Vv, Curvature Radus TDP Flex Rser 6 Gas Top tenson Curvature Radus TDP Lne # 1 Top Tenson

32 REMARKS ON THE DESIGN METOCEAN DATA BASED ON LONG-TERM ANALYSIS Advantages response-based methodology; less desgn condtons than those analysed today; Dfcultes metocean people and structural desgners have to work togheter t depends on the avalablty of smplfed models for long-term analyss floatng system changes: update metocean data for desgn On gong work analytcal/smplfed tme-doman models for representng bendng moment behavour along a rser ther desgn lmt states such as bendng radus, secton utlzaton factors for SCRs, etc.

33 Merc beaucoup! Thank you! Obrgado!

34 Tz (s) Condtonal Modellng Approach Example - jont model for Hs and Tz f f f Hs,Tz Hs hs, tz f hsf tzhs hs fhs hs tzhs f Tz Hs Tz Tz hs, hs Tz Hs Tz hs a bhs hs cexp dhs Tz Hs Tz a,b,c,d constants obtaned from data Hs (m)

35 Closed-form soluton for dynamc tenson FX_TENSION: Short-term analytcal lne dynamc tenson analyss Offset from statc analyss Moton RAOs are transfered to lne top Aproxmate tenson RAO usng a closed-form soluton for the lne dynamc tenson by Aranha et al. (2001) Short-term dstrbuton: Raylegh (neglectng LF second order effects) or Hermte (LF+WF) Results benchmarked wth ANFLEX

36 Statc equlbrum analyss APROA - Numercal Nonlnear Code K( X) X F F external forces on the hull and lnes: Sea and swell wave drft forces; Statc wnd forces Current loadng K(X)X - Restorng forces (analytcal catenary equatons) rsers moorng lnes X - Equlbrum poston vessel headng statc offset

37 Long-term analyss summary FX_LTERM : Long-term Monte Carlo Smulaton