Comparisons of Means for Estimating Sea States from an Advancing Large Container Ship

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1 Downloaded from orbt.dtu.dk on: Jan 31, 18 Comparsons of Means for Estmatng Sea States from an Advancng Large Contaner Shp Nelsen, Ulrk Dam; Andersen, Ingrd Mare Vncent; Konng, Jos Publshed n: Proceedngs of the PRADS 13 Publcaton date: 13 Lnk back to DTU Orbt Ctaton (APA): Nelsen, U. D., Andersen, I. M. V., & Konng, J. (13). Comparsons of Means for Estmatng Sea States from an Advancng Large Contaner Shp. In Proceedngs of the PRADS 13 General rghts Copyrght and moral rghts for the publcatons made accessble n the publc portal are retaned by the authors and/or other copyrght owners and t s a condton of accessng publcatons that users recognse and abde by the legal requrements assocated wth these rghts. Users may download and prnt one copy of any publcaton from the publc portal for the purpose of prvate study or research. You may not further dstrbute the materal or use t for any proft-makng actvty or commercal gan You may freely dstrbute the URL dentfyng the publcaton n the publc portal If you beleve that ths document breaches copyrght please contact us provdng detals, and we wll remove access to the work mmedately and nvestgate your clam.

2 Proceedngs of the PRADS13 - October, 13 CECO, Changwon Cty, Korea Comparsons of Means for Estmatng Sea States from an Advancng Large Contaner Shp Ulrk D. Nelsen 1), Ingrd Mare V. Andersen 1) and Jos Konng ) 1) Techncal Unversty of Denmark, DK-8 Kgs. Lyngby, Denmark ) MARIN, 67 AA Wagenngen, The Netherlands Abstract The paper deals wth sea state estmaton from a contaner carrer (9, TEU) en-route. Knowledge of the on-ste sea state s fundamental nput to any knd of nservce decson support system that evaluates performance of, e.g., acceleratons, fuel effcency, and hull grder strength, related to shp-wave nteractons n a seaway. In the paper, sea state estmates are produced by three means: the wave buoy analogy, relyng on shpboard response measurements, a wave radar system, and a system provdng the nstantaneous wave heght. The presented results show that for the gven data, recorded on fve dfferent days of contnuous operaton, the agreement between the estmatng means s reasonable; n terms of both absolute (mean) values and hourly trends of ntegrated sea state parameters. Keywords Sea state estmaton; decson support system; wave buoy analogy; wave radar system; nstantaneous wave heght. Introducton Knowledge of the sea state n whch a shp s operatng s of outmost mportance as nput parameter for most on-board decson support systems as well as for proper shp performance montorng wth regards to fuel effcency. The sea state data,.e. the wave perod, the sgnfcant wave heght and the mean relatve wave drecton, can be estmated by several means. Ths ncludes wave radar systems, analyss of shp response measurements or by forecast and hndcast of meteorologcal data. For decson support and shp performance systems, accuracy as well as relablty of the sea state estmate s mportant and hence the method must be robust. Moreover, nformaton about the sea state should be avalable at actual shp poston and at actual tme of operaton n the seaway. The latter requrement on-ste and on-tme avalablty of the sea state estmate excludes use of hndcast data when decson support and performance systems are consdered. Ths paper presents results related to sea state estmates obtaned from an n-servce (large) contaner vessel, where the consdered means for sea state estmaton are based on three dfferent procedures: 1) the wave buoy analogy, ) a wave radar system, and 3) drect measurement of the nstantaneous wave heght at shp bow. The frst and second authors have worked extensvely on the wave buoy analogy durng recent years. Fundamentals of the analogy s gven n a subsequent secton but, drectly reflected by the name, the estmaton prncple follows that of a tradtonal wave rder buoy, where moton measurements are processed to gve the sea state estmate. The other two means for sea state estmaton, ) and 3), are based on commercally avalable systems, whch are, respectvely, the WaMoS II wave radar system and The WaveGude system by Dutch company Radac. It should be noted that ths paper does not contan verfcaton and/or parameter studes related to the wave buoy analogy, n terms of, e.g., numercally generated data. The focus heren s on analyss of full-scale data from a 9, TEU contaner vessel, where the presentaton of results from the three estmatng means s the central pont. In ths connecton, t s noteworthy that all data have been collected as part of the EU FP7 project TULCS (Tools for Ultra Large Contaner Shps, project no. 316). Sea State Estmaton - The Wave Buoy Analogy Although focus s prmarly on results, the followng secton brefly outlnes key ponts of the wave buoy analogy. Fundamentals of the approach are gven but the secton s by no means comprehensve and for detals the lterature should be consulted, e.g. Isek and Terada (), Tannur et al. (3), Nelsen (6, 8a) and Pascoal et al. (7, 8). If a set of shp responses are assumed statonary and lnear wth the ncdent waves, the complex-valued transfer functons, ( e, ) and j ( e, ) for the th and jth responses, yeld the theoretcal relatonshp between the th and the jth components of the cross spectra S j ( e ) and the drectonal wave spectrum E( e, ) through the followng ntegral equaton

3 j e ) ( e, ) j ( e, ) E( e, ) S ( d (1) where the bar denotes the complex conjugate, and wth beng the headng of the shp (relatve to the waves) and e beng the encounter frequency. It should be noted that the complex-valued transfer functons are wrtten as functons of only the headng and the encounter frequency, snce the mplcaton of changng operatonal parameters s understood. The wave spectrum s advantageously estmated n the wave frequency () doman. Ths means that the speedof-advance or trple-valued functon problem n followng sea needs to be consdered. Ths problem, governed by the Doppler Shft, has been properly ncorporated by Isek and Ohtsu (), for detals see Nelsen (6). In terms of matrx notaton, Eq. (1) can be wrtten b Af (x) () The vector functon f(x) expresses the unknown values of the wave spectrum E(,),.e. the spectral components, whle the vector b contans the elements of S j ( e ), and the coeffcent matrx A has elements accordng to the products of the transfer functons, cf. Eq. (1). In prncple, Eq. () can be solved for x by mnmsng (x) wth ( x) Af ( x) b (3) where represents the L norm. Typcally, Eq. (3) s n ths context dealt wth by parametrc or nonparametrc so-called modellng. Parametrc Modellng In the parametrc approach, Eq. (3) s solved drectly as an optmsaton problem, where the drectonal wave spectrum f(x) E(ω,θ) s ntroduced as a parametersed spectrum. Heren, E(ω,θ) s taken as a -parameter spectrum (Nelsen and Stredulnsky, 1) that allows for mxed sea condtons; exstng n the presence of, e.g., wnd waves and swell: E, E ( ) G (, ) 1 1 E ( ) p, 1, p exp s G (, ) A( s )cos s1 ( s 1) A( s) (s 1) 3 1 H s, 1 ( ) mean, () In Eq. (), E (ω) s a one-dmensonal wave spectrum wth ω p, H s, and λ beng the peak frequency, the sgnfcant wave heght and the shape parameter, respectvely, of the spectrum. G (ω, θ) s the drectonal dstrbuton functon, where θ mean s the mean relatve wave drecton. A(s) s a constant to secure normalsaton and t s evaluated usng the Gamma functon on the spreadng parameter s. Inserton of Eq. () nto Eq. (3) mples a nonlnear optmsaton problem that can be solved usng, e.g., MATLAB by nvokng fmncon, whch s a bult-n functon based on sequental quadratc programmng. Modellng If the equaton system gven by Eq. (3) s solved for the actual spectral components of the drectonal wave spectrum, t mples a hghly underdetermned, or otherwse degenerate, equaton system. However, through modellng (Akake, 198), a stable soluton s facltated by the ntroducton of pror nformaton. Thus, two man assumptons are ntroduced: 1) the drectonal wave spectrum s smoothly changng wth both frequency and drecton, and, ) the wave spectrum s expected to have neglgble values for very low and hgh frequences. Detals of the approach can be found n the lterature, e.g. Nelsen (6, 8a), but t s worth to menton that, as dscussed by Isek and Ohtsu (), the approach ntroduces a stochastc vewpont where the dfference between the left- and the rghthand sde of Eq. () s taken as a whte nose sequence vector w wth zero mean and varance. Secondly, to avod negatve spectral estmates, a non-negatvty constrant s appled to the wave spectrum by use of a coordnate transformaton E(,) = exp(x), e.g. Isek and Ohtsu (). In the approach, the soluton x s obtaned by maxmsaton of the product of the lkelhood functon and the pror dstrbutons. The lkelhood functon s wrtten as P / 1 1 l ( x ) exp Af( x) b () where P s the total number of ntegral equatons derved from Eq. (1). Two pror dstrbutons are consdered, and both dstrbutons seek to mnmse the sum of the second order dfference of the unknown vector x n order to smoothen the changes wth frequency and drecton, respectvely, of the wave spectrum (Nelsen, 6; 8a and Isek and Terada, ). The pror dstrbutons are therefore defned by the mnmsaton of the functonals ε 1mn and ε mn (Press et al., 199) N M 1 mn n1 m1 M N 1 m1 n1 T H x (6) x 1 T H x (7) mn x where N and M are the number of dscrete wave frequences and dscrete headngs. If the functonals ε 1mn and ε mn are assumed to be normal dstrbutons wth zero mean and varance /u and /v, respectvely, the pror dstrbuton s weghted n terms of so-called hyperparameters u and v. Physcally, the hyperparameters control the trade-off between the good-ft of the soluton to the data and the smoothness, or stablty, of

4 the soluton. The posteror dstrbuton p(x u,v, ) s proportonal to the product of the lkelhood functon and the pror dstrbuton (Akake, 198) and can be wrtten, cf. Nelsen (8a), p x u, v, wth det( u H 1 c 1 v H ) PMN 1/ 1 exp x 1 S( x) (8) T S( ) Af ( x) b x u H v H x (9) where c n Eq. (8) s a normalsng factor, ndependent of x and the hyperparameters u and v. The optmum values of the hyperparameters are determned by mnmsng the control crteron ABIC, cf. Akake (198), ABIC ln p ( x u, v, ) dx (1) Wth knowledge of the values of the optmum hyperparameters, the best estmate of x = x * s - schematcally - obtaned from (Press et al., 199), * 1 T 1 x A A A b A A H1 H (11) T u v Hence, the spectral components of the wave spectrum are determned. In practce, the soluton s acheved through an teratve process and, although many detals on algebra and numerc are left out, ths fnalses the approach. Response Combnatons Smlar to the data processng of classcal wave rder buoys, the wave buoy analogy consders a set of three responses smultaneously, snce ths has shown to gve the most accurate and, at the same tme, computatonal effcent sea state estmate (Nelsen, 6). Today, most shps are nstalled wth montorng systems and, typcally, numerous sensors provde nformaton about a (large) number of responses. Ths means that a set of three responses should be selected to acheve the best sea state estmate, and the optmum choce of responses s lkely to depend on gven operatonal condtons at the tme of estmaton. Intal studes towards a dynamc and automatc response selecton have been carred out by Andersen and Storhaug (1). In the referred paper, a conceptual dea s outlned but t s also stated that the dea s not yet ready for practcal use. Consequently, the selecton of responses s based on a manual choce that should reflect both the flterng ssue (a shp acts nherently as a wave flter) and the need for at least one of the consdered responses to be asymmetrc wth respect to wave headng. Further dscussons are found n the lterature (e.g., Nelsen, 6, 8b; Pascoal et al., 7, 8; Tannur et al., 3), but future work on the wave buoy analogy should focus on a (more) automatc selecton process of the optmum response combnaton. Vessel and Full-scale Measurements Man dmensons of the consdered vessel are gven n Table 1 and a photo of the contaner vessel s seen n Fgure 1. The locaton of the Radac system can be seen from the photo and the WaMos wave radar was nstalled on top of the compass deck (portsde). Addtonally, several sensors for moton and acceleraton measurements were mounted at specfc (but dfferent) locatons. In ths paper, consderaton s gven to sway, heave, roll, and ptch measurements that are gven as nput to the wave buoy analogy. It s worth to note that stress measurements were also carred out as part of the measurement campagn. Thus, related studes are presented by Andersen et al. (13a, b), although the focus theren s not on sea state estmaton. Table 1: Man dmensons of shp. Parameter Dmenson L OA 39. m Beam.8 m Draught. m DWT 113, ton Fg. 1: Consdered vessel and locaton of nstantaneous wave heght meters (Radac system). It should be noted that the analyses of sea state estmates have been made as a post-voyage process, although both the WaMos radar and the Radac systems were part of an ntegrated system runnng real-tme on the consdered vessel. A sketch of the ntegrated system s seen n Fgure, where t s noted that overall system desgn and control was done by MARIN whle the wave sensors were nstalled by SIREHNA. Fg. : The WaMos wave radar system and the Radac system (pcture by SIREHNA).

5 Based on the four responses consdered for the wave buoy analogy, two combnatons, or sets, consstng of three responses are formed: a) {sway, heave, roll} b) {sway, heave, ptch} Although studes have been ntated towards an automatc selecton of the optmum set of responses (Andersen and Storhaug, 1), the two sets, a) and b), have been selected by brute-force manner based on experence and prevous fndngs by the frst author n hs studes of the wave buoy analogy. In partcular, the followng results for the wave buoy analogy are, conceptually, based on fndngs by Nelsen and Stredulnsky (1). Thus, n the referred paper, relable and accurate sea state estmatons were made for full-scale data recorded durng sea trals (Stredulnsky, 1). In the analyss of data, Nelsen and Stredulnsky (1) found that the best sea state estmates by the wave buoy analogy were obtaned when results were based on average values consderng eght dfferent response combnatons. Ths approach s also consdered n the present paper. For ths reason, the results of the wave buoy analogy consderng both parametrc and modellng are based on average values obtaned from the combnaton of sets a) and b). Further, smlar studes n ths respect are n progress (Nelsen, 13a; 13b). The analyss of data heren s carred out for fve days of operaton, and for each day hours of contnuous data are avalable. The dates, ncludng approxmate geographcal postons of the vessel and vsual sea state observatons, are as follow; 1 th August 11: Gulf of Aden (gong West, moderate sea state); th August 11: Medterranean Sea (gong West, mld sea state); 16 th September 11: Gulf of Aden (gong East, mld to moderate sea state); th September 11: South of Inda (gong East, mld sea state); and nd October 11: Off Hong Kong (gong North West, severe sea state). Table summarses the operatonal data of the vessel on the consdered dates, ncludng the vsual observaton of the sea state. Table : Operatonal parameters on the specfc dates. Dates Draft Speed [knots] Sea state (vsual obs.) 1 th Aug Moderate th Aug Mld 16 th Sep Mld/moderate th Sep Mld nd Oct Severe Results and Dscussons relatve headng s defned so that = 18 deg. s head sea and = deg. s followng sea; values n between are ether postve, ndcatng waves approachng on starboard, or negatve, correspondng to waves approachng on portsde. Results of the sea state estmatons are presented n Fgures 3,,, 6, and 7. It s noted that the fve fgures are ncluded n separate subsectons, representng the outcome on the ndvdual dates lsted n Table. Each fgure s composed of four plots correspondng to the four sea state parameters (H s, T z, T p, χ) consdered. In the plots, the x-axs spans the -hours perod on the gven day, and sets of the sea state parameters have been estmated for each hour. The nput to the wave buoy analogy, n terms of tme seres data, s taken as the mddle -mnutes perod wthn each hour, and the same perod s consdered for extractng (mean value) estmates of the WaMos and the Radac systems. It s noteworthy that the Radac system,.e. the nstantaneous wave heght meter, does not facltate nformaton about (relatve) wave headng. Moreover, the nstantaneous wave heght s measured n the encounter doman. Thus, n order to compare the characterstc wave perods (T z and T p ) estmated by Radac wth the other estmatng procedures, t s necessary to transform nto the true doman. Ths transformaton s not possble wthout the combned knowledge of the speed and the wave headng of the vessel. In general, nformaton about the wave headng s not avalable f the sea state, ncludng all relevant parameters, has not been estmated by some other means. In ths study, the wave headng s known as a result of WaMos and/or the wave buoy analogy. Heren, the headng of WaMos s used to transform the encountered characterstc perods of the Radac system nto the true doman. Another general remark s related to the flterng effect of a shp consderng assocated wave nduced responses. Inherently, ths phenomenon can have an nfluence on the results by the wave buoy analogy, snce the phenomenon bascally means that wave energy may not be properly recognsed at relatvely short wave perods (Nelsen, 8b). Smlarly, the estmates of wave perod(s) by WaMos can be compromsed due to lmtatons n antenna revoluton speed and mage resoluton. In theory, the Radac system s the only system capable to recognse the entre range of wave perods but, on the other hand, sprays from wave mpacts and local wavehull dsturbances may affect estmates negatvely. Obvously, the relatve (or absolute) wave measure as obtaned by the Radac system can tself be used as nput to the wave buoy analogy; see, e.g. Nelsen (8b). In the followng subsectons, the man fndngs and comments related to the sea state estmates for the specfc dates are addressed n bullet lsts mmedately followng the correspondng fgures. Comparsons of the dfferent means for sea state estmatons are made for four (ntegrated) sea state parameters: Sgnfcant wave heght H s, zero-upcrossng perod T z, peak perod T p, and relatve mean wave headng. The

6 Sea State Parameters on 1 th August 11 Sea State Parameters on th August 11 6 Sgnfcant wave heght H s (1Aug) Pararametrc WaMos II Radac 6 Sgnfcant wave heght H s (Aug) Pararametrc WaMos II Radac : 6: 1: 18: Zero upcrossng perod T z (1Aug) 1 : 6: 1: 18: Peak perod T p (1Aug) 1 : 6: 1: 18: Zero upcrossng perod T z (Aug) 1 : 6: 1: 18: Peak perod T p (Aug) 1 : 6: 1: 18: : 6: 1: 18: 18 Relatve mean wave headng χ (1Aug) 18 Relatve mean wave headng χ (Aug) 9 9 [deg.] [deg.] : 6: 1: 18: Fg. 3: The legend s dentcal n all plots. NB. the Radac system cannot not estmate wave headng. Man fndngs and comments: In agreement wth vsual observatons, all estmatng means fnd sgnfcant wave heghts, H s, representng a moderate sea state, reducng to mld at the end of the day. Both approaches of the wave buoy analogy estmate less energy, reflected by H s, than the other two means for most of the consdered perod. Specfcally, lttle dfference s seen between the parametrc and the approach. In general, estmates of the zero-upcrossng perod, T z, agree well. The pcture s not completely the same wth the peak perod, T p, and, somewhat pecularly, the Radac system s consstently on the low sde wth T z but on the hgh sde wth T p. The agreement between estmates of the relatve mean wave headng, χ, s good; the three estmatng means ndcatng bow-quarterng waves approachng on portsde. 18 : 6: 1: 18: Fg. : The legend s dentcal n all plots. Man fndngs and comments: A mld sea state s estmated by all the estmatng means (n agreement wth vsual observatons). However, the approach fnds very lttle energy n the encountered sea states durng all day. Ths observaton could be a result of wave flterng, nherently beng a problem wth the wave buoy analogy (Nelsen, 8b), although t s not seen for the parametrc method. Except for estmates from the Radac system, there s a far agreement between wave perods; both T z and T p. The Radac system estmates unrealstc hgh values of T p far out of scale; most lkely explaned because of low-frequency nose of a consderable amount, relatvely speakng. The agreement between estmates of χ s mxed; better and worse durng some perods wth no consstency. The explanaton for the observaton could be that low sea states may have complex drectonal and frequency dstrbutons whch, n general, nfluences results of both WaMos and the wave buoy analogy.

7 Sea State Parameters on 16 th September 11 Sea State Parameters on th September 11 6 Sgnfcant wave heght H s (16Sep) Pararametrc WaMos II Radac 6 Sgnfcant wave heght H s (Sep) Pararametrc WaMos II Radac : 6: 1: 18: Zero upcrossng perod T z (16Sep) 1 : 6: 1: 18: Peak perod T p (16Sep) 1 : 6: 1: 18: Zero upcrossng perod T z (Sep) 1 : 6: 1: 18: Peak perod T p (Sep) 1 : 6: 1: 18: : 6: 1: 18: 18 Relatve mean wave headng χ (16Sep) 18 Relatve mean wave headng χ (Sep) 9 9 [deg.] [deg.] : 6: 1: 18: Fg. : The legend s dentcal n all plots. NB. the Radac system cannot not estmate wave headng. 18 : 6: 1: 18: Fg. 6: The legend s dentcal n all plots. NB. the Radac system cannot not estmate wave headng. Man fndngs and comments: The sgnfcant wave heght ncreases durng the day, and the trend s reflected by all estmatng means. The actual values of H s represent a mld to moderate sea state whch s n agreement wth the vsual observatons, and generally the estmates of the four means devate only lttle from each other. Relatvely small varatons n the estmated wave perods (T z and T p ) are observed between WaMos and both approaches of the wave buoy analogy. Results of the Radac system agree, on the other hand, poorly and show rather unrealstc values n some cases. The relatve mean wave headng s rangng between bow-quarterng (approachng on starboard) and head sea, whch s found for all three means, although the method has two off-values. Man fndngs and comments: As seen from the plot of H s, estmates of the energy contaned n the sea state are rather low. The observaton apples to all four means and s n lne wth vsual observatons. The result of the Radac system s, however, sghtly off compared to the three other estmatng means, beng consstently to the hgher sde. A far agreement s seen between the estmated wave perod(s), although the Radac results are standng out the most, smlarly to estmatons at the other dates. Small varatons are observed between the parametrc and the approach when the relatve mean wave headng s consdered but both methods estmate waves approachng on starboard as bow-quarterng to head sea. Estmates by WaMos ndcate, on the other hand, a beam sea durng the entre day.

8 Sea State Parameters on nd October 11 [deg.] 1 Sgnfcant wave heght H s (Oct NB. Dfferent scale) : 6: 1: 18: 1 Zero upcrossng perod T z (Oct) : 6: 1: 18: 1 : 6: 1: 18: Peak perod T p (Oct) Relatve mean wave headng χ (Oct) 18 : 6: 1: 18: Pararametrc WaMos II Radac Fg. 7: The legend s dentcal n all plots. NB. the Radac system cannot not estmate wave headng. Man fndngs and comments: All the four estmatng means show the same trend: The sea state ncreases durng the frst half of the day and reaches a relatvely severe condton from around noon. Some varatons are seen n the values of H s wth results of the wave buoy analogy beng a lower bound (6-1 m) whereas Radac results are an upper bound (1-13 m). Note the dfference n scale on the y-axs compared to the plots for the other dates. Consderng the zero-upcrossng perod, the WaMos estmates yeld an upper bound whereas the Radac estmates yeld a lower bound; an observaton almost applcable to the whole day. The same observaton cannot be made wth respect to the peak perod, where the Radac system fnds the hghest values consstently. Reasonable agreement s seen for the relatve mean wave headng (wth a few exceptons) consderng estmates by the parametrc approach and by WaMos. However, results of the method are n most cases devatng sgnfcantly. Wave Spectra by the Wave Buoy Analogy The wave buoy analogy provdes the complete (frequency-drectonal) dstrbuton of energy as ts soluton. In addton to the ntegrated sea state parameters, examples of wave spectra can therefore be studed. Below, a few results are shown for both the approach and the parametrc approach. It s noteworthy that, n the ndvdual case, the wave spectrum s, as mentoned prevously, based on one -mnutes perod of tme seres data consderng set(s) of responses. Fgure 8 shows an example of the wave spectrum obtaned on 1 th August at 17:3. In the specfc 1-D plot, t s observed that the parametrc method produces a spectrum wth slghtly less energy than the method. Despte a small dfference between the energy n the spectra t s nterestng to note how close the two spectra are shape-wse; keepng n mnd that the method solves for the ndvdual spectral components n the complete drectonal wave spectrum. In the lower plots of Fgure 8, the drectonal wave spectrum s seen as polar dagrams mapped as contour plots. In the plots, the absolute vessel headng s degrees and, thus, the plots are used to nfer that the relatve mean wave headng s about -11 deg. Obvously(!), both observatons less energy n the parametrc spectrum and that of the relatve mean wave headng can be seen from the upper and lower plots, respectvely, n Fgure 3. [m s] 7 6 Wave spectra by WBA at 17:3 Parametrc Wave freq. [Hz] Fg. 8: Typcal wave spectra on 1 th Aug. n the late afternoon by wave buoy analogy; ntegrated frequency spectrum (top) and drectonal spectrum (bottom). Another example of wave spectra produced by the wave buoy analogy can be seen n Fgure 9. In the fgure, the wave spectrum on nd October at 1:3 s llustrated. Based on the ntegrated frequency spectrum (upper plot) t s evdent that, n ths case, the parametrc and the approaches yeld wave spectra whch are slghtly dfferent shape-wse. The total amount of energy n the ndvdual spectra s almost the same, but the method estmates a spectrum wth a sharper Parametrc

9 peak compared to the parametrc method. In terms of practcal applcatons, t s lkely that ths dfference, by tself, wll have lttle nfluence. However, a more fundamental problem s vsble from the polar plots at the bottom of Fgure 9. It s seen that both methods estmate two local peaks but the method has the two peaks separated at two very dstnct headngs whch s not the case for the parametrc method. The reason for the dscrepancy between the two methods s not known but, because of the agreement between the relatve mean wave headng of WaMos and the parametrc method, t s lkely that the result of the method s nconsstent. It s noteworthy that ths type of problem has been observed n only a few cases. [m s] Wave freq. [Hz] Wave spectra by WBA at 1: Fg. 9: Typcal wave spectra on nd Oct. around noon by wave buoy analogy; frequency spectrum (top) and drectonal spectrum (bottom). Summary and Conclusons Parametrc Overall, the man conclusons are the followng: o In the study, three fundamentally dfferent wave estmatng procedures were used to obtan ntegrated sea state parameters from an nservce operatng contaner vessel. The estmatng means were the wave buoy analogy, the WaMos II wave radar system, and the Radac system. o In general, there s a reasonable agreement between results of the wave buoy analogy, consderng both the parametrc and the approach, and the WaMos wave radar. In ths study, the Radac estmatons were, on average, the most off compared to the (two) other estmatng means. o The two ndvdual approaches of the wave buoy analogy are about equally computatonal effcent and produced qute smlar estmates for most of the studed data. As n prevous Parametrc o studes, t s therefore dffcult to recommend the one method n favour of the other. In the future, t would be of nterest to develop a procedure used wth the wave buoy analogy to automatcally select an optmum set of responses. Acknowledgement The authors sncerely thank ther colleague Prof. Jørgen Juncher Jensen for many useful dscussons. The full scale data used has been obtaned through the EU project TULCS (Tools for Ultra Large Contaner Shps), project no Frutful dscussons wth the project partners are acknowledged and, n partcular, thanks are gven to Dr. Quentn Derbanne, Bureau Vertas, for provdng transfer functons and valuable comments n ths respect. References Akake, H. (198). Lkelhood and Bayes Procedure, n Statstcs, Unversty Press. Andersen, I.M.V. and Storhaug, G. (1). Dynamc Selecton of Shp Responses for Estmaton of Onste Drectonal Wave Spectra, Proceedngs of OMAE1 (Ro de Janero, Brazl). Andersen, I.M.V. and Jensen, J.J. (13a). Hull Grder Fatgue Damage Estmatons of a Large Contaner Vessel by Spectral Analyss, Proceedngs of PRADS13 (Changwon Cty, Korea). Andersen, I.M.V., Jensen, J.J. and Nelsen, U.D. (13b). Evaluaton of Response Predcton Procedures usng Full Scale Measurements for a Contaner Shp, Proceedngs of PRADS13 (Changwon Cty, Korea). Isek, T. and Ohtsu, K. (). estmaton of drectonal wave spectra based on shp motons, Control Engneerng Practce, Vol. 1, pp. -3. Isek, T. and Terada, D. (). Estmaton of Drectonal Wave Spectra for Shp Gudance Systems, Internatonal Journal of Offshore and Polar Engneerng, Vol. 1, pp. -3. Nelsen, U.D. (6). Estmatons of on-ste drectonal wave spectra from measured shp responses, Marne Structures, Vol. 19, pp Nelsen, U.D. (7). Response-based estmaton of sea state parameters nfluence of flterng, Ocean Engneerng, Vol. 3, pp Nelsen, U.D. (8a). Introducng two hyperparameters n estmaton of wave spectra, Probablstc Engneerng Mechancs, Vol. 3, pp Nelsen, U.D. (8b). The wave buoy analogy - Estmatng hgh-frequency wave exctatons, Appled Ocean Research, Vol. 3, pp Nelsen, U.D. (13a). Integratng external data nto the wave buoy analogy, work n progress. Nelsen, U.D. (13b). The stochastc varablty of a sea state as measured by shpboard estmaton technques, work n progress. Nelsen, U.D. and Stredulnsky D.C. (1). Sea state estmaton from an advancng shp A comparatve

10 study usng sea tral data, Appled Ocean Research, Vol. 3, pp Pascoal, R., Guedes Soares, C. and Sørensen, A.J. (7). Ocean wave spectral estmaton usng vessel wave frequency motons, Journal of Offshore Mechancs and Arctc Engneerng, Vol. 19, pp Pascoal, R. and Guedes Soares, C. (8). Nonparametrc wave spectral estmaton usng vessel motons, Appled Ocean Research, Vol. 3, pp Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterlng, W.T., (199). Numercal Recpes n FORTRAN, Cambrdge Unversty Press. Stredulnsky, D.C. (1). Quest Q319 Sea Tral Summary and Wave Fuson Analyss, DRDC Atlantc TM 1-1, Defence R&D Canada Atlantc. Tannur, E.A., Sparano, J.V., Smos, A.N. and Da Cruz, J.J. (3). Estmatng drectonal wave spectrum based on statonary shp moton measurements, Appled Ocean Research, Vol., pp

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