odelig of Ship Propulsio Performace Bejami Pjedsted Pederse (FORCE Techology, Techical Uiversity of Demark) Ja Larse (Departmet of Iformatics ad athematical odelig, Techical Uiversity of Demark) Full scale measuremets of the propulsio power, ship speed, wid speed ad directio, sea ad air temperature, from four differet loadig coditios has bee used to trai a eural etwork for predictio of propulsio power. The etwork was able to predict the propulsio power with accuracy betwee 0.8-.8%, which is about the same accuracy as for the measuremets. The methods developed are iteded to support the performace moitorig system SeaTred developed by FORCE Techology (FORCE (008)). WTC 009 Pederse
KEY WORDS Propulsio; performace; moitorig; o-liear eural etwork regressio; eural etworks; fuel cosumptio Egie Efficiecy Propeller Efficiecy Hull Efficiecy Wid ITRODUCTIO As part of the Idustrial PhD project ''Ship Performace oitorig'' automatic data samplig equipmet was istalled o the taker ''Torm arie'' i Jauary 008 ad so far data from four differet loadig coditios are available. odelig of these loadig coditios are fudametal to achievig a good solutio. I the future, the variatio i draught ad trim will be added as variables. Ship propulsio performace (referred to as the performace) is a measure of the eergy cosumptio at a certai state, i.e. speed, loadig coditio, weather coditio ad other factors. Durig the lifetime of the ship the performace will decrease e.g. the fuel cosumptio will icrease at a certai state or the speed will decrease at a certai power settig. This is maily due to foulig of the hull ad propeller. A typical tred of the speed reductio is illustrated i Figure. Hece, performace evaluatio is about comparig the fuel efficiecy or propeller power at oe time to aother time, i other words to compare the ship at oe state with aother state. Sice a ship is subjected to exteral factors such as wid, waves, shallow water, chage i sea water temperature, etc. as illustrated i Figure, it is ulikely that the ship will ever be i the exact same situatio more tha oce. Furthermore these exteral factors ca be difficult to measure accurately ad thus a similar situatio will ot be detected. This deterioratio is oly a few percet ad is therefore difficult to detect with traditioal performace moitorig methods. Figure : Icrease of the fuel cosumptio as a effect the foulig Traditioally, the problem has bee solved by calculatig a theoretical propulsio power for the actual coditio usig stadard empirical resistace ad propulsio methods, for example Harvald, S. A. (983) or Holtrop, J. (984) methods. For the estimatio of the wid resistace a method proposed by Isherwood, R. (97) ca be used if o wid resistace coefficiets are available for the ship. Fuel Poor aiteace Power Propeller Foulig Thrust Figure : Performace variables Waves Shallow Water Resistace Draught Water & Trim Temp/ Desity Hull Foulig These empirical methods are derived from model tests ad sea trials, ad sice most model test are carried out i a desig coditio (eve keel) ad speed, this is the regio where it should be applied. I operatio the ship will travel i may other coditios i.e. ballast draught ad trimmed coditios. Cosequetly these methods give a rough estimate of the propulsio power rather tha a accurate referece poit. If some measured values from model tests or sea trials are available, they ca be used to adjust the empirical data ad thus give a more accurate result. Aother part of the problem is to have sufficiet iput data for the aalysis i order to capture the dyamics of the propulsio power. This is relevat for the traditioal method ad ay other method that ca be used. A short descriptio of the iput is give below: Draught ad trim - usually these fudametal variables for the power estimatio are foud from visual observatio or from the loadig computer before departure; sometimes the arrival coditio is determied by observatios, but usually oly from the loadig computer. Some ships are equipped with dyamic draught measurig devices, but these are very sesitive devices which deliver a sigal with a sigificat variace. Draught ad trim have approximately a accuracy of 0.m, as that is the usual scale for draughts marks. Power measuremet - the power ca be measured i differet ways. easurig the propeller shaft torque with a torsiometer, ad the rate of revolutio with a tachometer will give the direct power delivered to the propeller ad is thus the preferable method. The mai egie fuel cosumptio is also a fairly good measuremet, but it is ecessary to have sufficiet iformatio of the fuel quality. A chage i the mai egie performace will also show a chage i the fuel cosumptio, so it ca be difficult to determie the propeller ad hull performace from the fuel performace aloe. Speed through the water - is measured by the speed log that is based upo the Doppler priciple. Experiece shows that the sigal from the speed logs has a tedecy to drift ad hece may ship officers do ot trust the speed logs. It is also possible to estimate the speed through the water from the sea curret determied by a meteorological progosis ad from the speed WTC 009 Pederse
over groud give by the GPS avigator. Although the speed log ca drift it is expected to give more reliable results tha the oe estimated from the sea curret ad GPS speed. Relative wid speed ad directio - is measured by a doppler aemometer Airmar Weatherstatio T PB00 mouted o top of the superstructure. At this positio the wid speed ad directio is altered from the free stream wid due to the presece of the ship. Traditioal methods for estimatig the wid resistace is based o wid tuel tests ad hece assumes that the wid speed ad directio is udisturbed. Sice the udisturbed wid speed ad directio is ukow from measuremets, the measured (disturbed) values are used directly i the empirical model, although this is ot correct. Furthermore, the wid resistace coefficiets are i this case determied empirically, which iduce additioal ucertaity. Air temperature - is also measured by the Airmar Weatherstatio T PB00 uit. The air temperature ca vary sigificatly withi a few hours, which has a direct effect o the air desity ad cosequetly o the ship resistace, e.g. for the ship travelig with a speed of 5 kots i 0 m/s ad 0 C headwid the air resistace will be 5k ad total resistace 953+5 68 k, for the ship ad wid speed, but with a air temperature of 0 C the wid resistace is 99k ad the total resistace 953+99 5 k. The differece i air desity has a relative ifluece o total resistace of (68-5) / 68.4%. For the preset measuremet the air temperature varies betwee 4.5-8.8 C ad has a variace of ~0.47. Sea water temperature - is usually measured oce daily by the egie crew. The seawater temperature has a sigificat impact o the sea water desity ad viscosity, ad cosequetly o the resistace. The differece betwee sailig i 0 C ad 30 C seawater results i a frictioal resistace aroud 7%, ad for the preset type of ship the frictioal resistace accouts for 90% of the total resistace. Traditioal Performace Evaluatio Traditioally the performace has bee evaluated by rather simple procedures, where the daily fuel cosumptio has bee reported i the ''oo Report'' together with distace traveled over the last 4 hours, the correspodig average observed speed ad a sigle weather observatio. This method gives a limited umber of observatios sice there is a maximum of 365 observatios per year. The the days i port are deducted, together with observatios icludig maeuverig, shallow water ad sigificat chages i speed or headig. This might leaves 00 observatios per year, each with oly oe weather observatio which itroduces a sigificat ucertaity, sice the weather ca chage cosiderably durig 4 hours. SHIP PROPULSIO THEORY Classical ship propulsio procedures ca be used as a referece poit for the model. I these models the effects of ocea waves have bee eglected due to the ucertaity of both the estimate, the added resistace from the waves ad measurig the actual wave height ad period. The total resistace thus cosists of the still water resistace R SW ad the wid resistace R wid. Resistace First, the still water resistace is foud usig the followig equatio: R C ρ SU () SW tot SW The coefficiet C tot is defied as: C tot C v + C R + C A + C AA () C v, Viscous resistace coefficiet: Defied as C v C f (+k) where the frictioal part C f, is determied from the formula: 0.075 C f ( log ( ) ) (3) 0 Re LwlU R e (4) R e is the Reyolds ν k is the form factor that accouts for 3D flow effects aroud the hull, usually i the regio 0-0.5. C R, Residual resistace coefficiet is maily accoutig for the eergy radiated by waves made by the ship. C R ca be estimated empirically by e.g. Harvald, S. A. (983) or Holtrop, J. (984), but the discrepacies ca be up to 50% possibly makig C R the most difficult variable to determie i ship resistace. C A, Icremetal resistace coefficiet, accouts for differeces i the hull roughess of the model ad the ship. It is usually costat ad i the regio of 0.5-0.55 0-3 C AA, Allowace icludes air ad steerig resistace. Wid Resistace I almost all coditios the hull ad superstructure of the ship will result i a resistace compoet from the relative wid (the resistace ca be egative, i case of strog followig wids!). The wid resistace is calculated by Rwid CX ρair AT VR (5) Where the wid resistace coefficiet C x, is determied empirically, by e.g. Isherwood, R. (97), or by model tests, ad vary with the relative wid directio, γ R. A T is the trasverse projected area above the waterlie ad V R is the relative wid speed. The wid coefficiet C x assumes that the wid speed ad directio is udisturbed by the ship, which aturally is impossible for the o-board measuremets. WTC 009 Pederse 3
Propulsio The efficiecy of the propeller η D behid the ship is foud by combiig the results from model tests of the propeller aloe, the so called ope water test ad model tests of the ship, with ad without the propeller. If model tests are ot available the values, wake fractio, w, thrust deductio, t, ad relative rotative efficiecy ca be estimated by e.g. Harvald, S. A. (983) or Holtrop, J. (984). This results i the overall propulsio efficiecy η D. Usig the above described methods with the empirical method by Harvald, S. A. (983) the propulsio power has bee calculated for the measured coditios. This is illustrated i Figure 3. d () z j g w x i ji i 0 x are the measured iput data. y are is the output, i this case the propulsio power The etwork beig used for this problem is a so called oe hidde layer (z -z ). Figure 4 illustrates a equivalet etwork with multiple output variables, whereas the preset method oly uses oe output (y ). (8) Assumig that the ship is sailig i calm ad deep water (depth/draught>8), the propulsio power ca thus be writte as: D D ( RSW Rwid P η U + ) (6) A o-liear method has bee developed based o the relatio i (5), but did oly show slightly better results tha a similar liear method. Both the liear ad o-liear method resulted i a relative above 5% ad was quickly discarded. Figure 4: A sigle hidde layer artificial eural etwork, with multiple outputs. The etwork is a o-liear regressio model with additive Gaussia oise ad traied with a Bayesia learig scheme. Figure 3: Propulsio calculatio by empirical calculatios, for data set # (Table ), where Tm is the mea draught ad Tr is the trim. ARTIFICIAL EURAL ETWORK A artificial eural etwork (A) is a advaced form of oliear regressio that ca be used to model complex relatioships betwee iput ad output variables. A ca be described as liear combiatios of oliear regressio models, with oliear basis fuctios, z j. y ( x) j 0 w () z kj kj (7) After differet attempts of modelig the propulsio power by usig the physical ad empirical relatio, a eural etwork was tested ad immediately showed surprisigly good results. Usig a eural etwork efficietly thus requires sufficiet iput variables, hidde uits, as well as a sufficiet amout of data to trai with. From the physical relatios of the ship propulsio theory the most importat variables for the propulsio power, P, ca be deducted to: ship speed, U, wid speed, V R ad directio, γ R, air temperature, T air ad seawater temperature, T SW. Cosequetly the iput ad output variables are defied as: x y P [ U V γ T T ] R R The relatioship betwee the differet variables ad the propulsio power is also kow to a certai extet, e.g. the power is expected to be proportioal to the ship speed cubed. air SW WTC 009 Pederse 4
TEST DATA SET The data has bee collected oboard the 0,000 dwt taker Torm arie where a umber of measuremet were cotiuesly logged, from where oly the relevat data for this problem has bee take. The samplig was split ito itervals of 0 miute time series with 0 miutes itervals. The samplig frequecy of the times series was secod, but may of the measuremets had icosistet sigals, i.e. sometime more tha 0 secod itervals. Power ad speed were more or less cosistetly updated every 3 secods. aturally the recorded data icluded samples from ostatioary situatios as well as situatios with zero forward speed. Oe sigificat variable to the variatios i the samples was the chage of headig. Eve small chages (less tha ) of the headig, had sigificat ifluece o the measured propulsio power. Samples with excessive variace i the headig have thus bee excluded. The sea state has a sigificat ifluece o the ship resistace ad hece the propulsio power. o direct measuremets of the sea state have bee made, but the wid drive waves ca be represeted by the true wid speed to a certai extet. akig this assumptio the swell is ot icluded. I Table the key figures for each dataset are outlied. It is oted that the ship speed itervals are approximately i the same regio for each sample. The distributios of the ship ad true wid speed are illustrated i Figure 5-Figure 8. It should be oted that the Beaufort wid force (BF) 5 starts at approximately 6 kots wid speed. I this coditio the wid drive waves are aroud m high, which is whe the sea state starts to ifluece the added resistace. From Figure 5 ad Figure 6 it is oted that oly a few occurreces are above this level ad thus data sets # ad # ca be regarded as calm water coditios. Data set #3 ad #4 o the other had has a more sigificat cotributio of measuremets above BF 5 ad the added resistace must be regarded as a extra cotributio. Table : Traied data sets, where represets the umber of 0 miute recordig widows Data umber ea Trim U mi - P mi -P max set of Samples draught, T m Ta- Tf U max [m] [m] [kots] [kw] 38.4 0.0 3.6-5. 839-36 7.4.4 4.3-7574- 83 3 4 7.85.7 4 63.5 0.0 6. 3.6-5. 3.4-6. 7750-948.5 9764-6 aalyzed, for the ship speed, U, propulsio power, P ad apparet wid speed, V R. The air temperature has bee eglected sice it is very stable. For every 0 miute period the relative stadard deviatio, (,/μ ) has bee foud ad for every dataset the average of the relative stadard deviatio, has bee determied: (9) μ is the stadard deviatio for the th time series μ is the mea value for the th time series x idicate the iput iput/output variable (U, P, V R, γ R ) Similarly the average of the relative stadard deviatio μ,, ca be foud. μ μx, μ (0) The average of the relative stadard deviatio average of the relative stadard deviatio μ ad the are show for every dataset i Table ad Table 3. It is oted that both the measured power ad ship speed are all less tha, but for the wid speed there are sigificat variatios. Table : The average of the relative stadard deviatio μ U μ P μ V R 38 0.6% 0.8% 0.0% 36 0.6% 0.7% 8.0% 3 4 0.6% 0.6%.4% 4 63 0.6%.0% 7.9% Table 3: The stadard deviatio of the relative stadard deviatio U P V R 38 0.% 0.4% 5.9% 36 0.3% 0.% 3.7% 3 4 0.% 0.% 7.% 4 63 0.3% 0.5% 4.8% The iput data are the mea values of the 0 miutes time series. I order to justify this, spreadig of the sigal has bee WTC 009 Pederse 5
Figure 7: Ship speed ad true wid speed distributio of sample #3 Figure 5: Ship speed ad true wid speed distributio of sample # Figure 8: Ship speed ad true wid speed distributio of sample #4 TRAIIG The traiig ad test has bee performed by a eural etwork (DTU toolbox (00) Larse, J. (993), ackay, D. J. C. (99), Pederse,. (997), Svarer, C.; Hase, L. & Larse, J. (993)) The traiig procedure has bee restarted 0 times i order to esure that the etwork foud the best possible solutio for that particular case. Figure 6: Ship speed ad true wid speed distributio of sample # I order to validate, each data test set (-4 i Table ) has bee divided ito 5 traiig ad test subsets, where 0% of the data set has bee left oly for testig ad the remaiig part for traiig. Before the subdivisio the data set was permutated radomly. I order to fid the best umber of hidde uits the etwork has bee traied with respectively 5, 0, 5 ad 0 hidde uits. RESULTS Due to the ature of the iput data which is the mea values of the time series of 0 miutes, the resultig etwork is able to predict the mea propulsio power for a period of 0 miutes. The results of each etwork have bee evaluated by the relative sum of the s squared, : ( Pˆ P ) test, ~ () P test, test, WTC 009 Pederse 6
The mea of the relative has also bee foud i order to give more Pˆ P test, test, P test, ω () ˆ P test, P test, are the predicted values of the test data are the test samples from the set is umber of test set Every dataset set has bee traied with a etwork 5, 0, 5 ad 0 hidde uits. Each of these etworks has bee traied five times i order to alterately use 0% of the data set for testig. I order to validate the results the ω ad the squared ~ : 5 K K k K 5 K k ω ω (3) ~ ~ (4) Where K is the total umber traiig/test set (5). I Table 4 these two quatities are show for each of the data sets. It is oted that data set #3 ad #4 are much better results tha # ad #, this is most likely because the limited dataset (4 ad 63), are sampled aroud the same time, ad thus have very little variatio i the iput variables. This is particularly proouced i Figure 7 where the ship speed has bee 4.5-5 kots about 90% of the time. Takig this ito accout oe should be careful usig this etwork for ship speeds out of this rage! Table 4: Best results ad related s. ea draught Trim Ta- Tf o Hidde Uits squared [m] [m] ~ ω 38.4 0.0 0 0.3%.56% 36 7.4.4 5 0.5%.69% 3 4 7.85.7 0 0.03% 0.8% 4 63.5 0.0 0 0.04%.4% Furthermore the ω ad the squared ~ has bee calculated for the two empirical performace evaluatio methods, Harvald, S. A. (983) ad Holtrop, J. (984). The results are show i Table 5 ad as expected these methods gives rather poor results compared with the data drive methods. Table 5: Cross s for the empirical methods. Harvald, Harvald, Holtrop, J. S. A. S. A. (984) (983) (983) squared squared Holtrop, J. (984) ~ ω ~ ω 38 3.63% 7.9% 6.3% 3.74% 36 7.47% 6.48% 8.8% 7.78% 3 4 5.68%.35% 7.93% 7.4% 4 63 0.75% 3.4% 9.70% 8.4% I the plots of the best solutios, show i Figure 9-Figure, the majority of the predictios are withi a of 500 kw. The predictio distributio is illustrated i Figure 3- Figure 6, i the same plot a Gaussia distributio (show as a blue lie) has bee geerated usig the mea value ad the variace of the predicted s. For # ad # the ormal distributio fits the histograms very well. For #3 the distributio is skewed due to a few outliers ad for #4 the data set is most likely too small to be used, for this purpose, both #3 ad #4 have a small spread, thereby justifyig their use. Figure 9: Predictio s for sample # WTC 009 Pederse 7
Figure 0: Predictio s for sample # Figure 3: Relative distributio of the predicted s for sample # Figure : Predictio s for sample #3 Figure 4: Relative distributio of the predicted s for sample # Figure : Predictio s for sample #4 WTC 009 Pederse 8
helpful moitorig the oboard system ad sedig data home. The work preseted i this paper has bee carried out durig Pederse s PhD study at FORCE Techology ad the Techical Uiversity of Demark, which is sposored by The Daish Idustrial PhD programme ad Daish Cetre of aritime Techology (DCT)/The Daish aritime Fud. REFERECES FORCE (008), SeaTred ifo sheet is available at: http://www.force.dk/e/eu/products+ad+cocepts/produc ts/0800_seatred.htm Harvald, S. A. (983), Resistace ad Propulsio of Ships, Joh Wiley & Sos. Figure 5: Relative distributio of the predicted s for sample #3 Holtrop, J. (984), 'A Statistical re-aalysis of resistace ad propulsio data', Iteratioal Shipbuildig Progress 3, 7-76. Isherwood, R. (97), 'Wid resistace of merchat ships', Royal Istitute of aval Architecture. ITTC (978), 'ITTC RecommededProcedures - Performace, Propulsio978 ITTC Performace Predictio ethod', ITTC, 7.5-003-0.4. DTU toolbox (00), DTU toolbox: eural regressor with quadratic cost fuctio, http://isp.imm.dtu.dk/toolbox Larse, J. (993), 'Desig of eural etwork Filters', PhD thesis, Electroics Istitute, Techical Uiversity of Demark. ackay, D. J. C. (99), 'A practical Bayesia framework for backpropagatio etworks', eural Computatio 4, 448-47. Figure 6: Relative distributio of the predicted s for sample #4 COCLUSIOS It is possible to predict the propulsio power with a relative of less tha.7%, usig a sigle hidde layer eural etwork while classical methods have a relative of more tha 5%. The predictio was carried out for four differet states with the followig iput variables: ship speed, relative wid speed ad directio, air temperature ad sea water temperature. It is emphasized that the predictio should oly be used with variables that lie withi the traiig variable boudaries. As more data is collected oboard the vessel the model will gradually be exteded. Pederse,. (997), 'Optimizatio of Recurret eural etworks for Time Series odelig', PhD thesis, Istitute of athematical odelig, Techical Uiversity of Demark. Svarer, C.; Hase, L. & Larse, J. (993), O Desig ad Evaluatio of Tapped-Delay eural etwork Architectures, i 'Proceedigs of the 993 IEEE Iteratioal Coferece o eural etworks', pp. 46-5. ACKOWLEDGEETS ay thaks to the ship ower Torm ad the crew oboard Torm arie for lettig me istall the equipmet ad providig oo report data. I particular Chief Egieer Rasmus Hoffma, who has showed great iterest i the project ad bee very WTC 009 Pederse 9