Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
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Simulation of Ship Maneuvers Using Recursive Neural Networks
Simulation of Ship Maneuvers Using Recursive Neural Networks
Pages 223-242
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From page 223... ...
ABSTRACT An improved Recursiw Neural Netw rk (RNN) m meuvenng simulation tool for smfa e ships is described inputs to the simulation, ca t in file to m of forces md moments, a e redefined md emended in a mmner that more a cun Italy cultures the physics of ship motion; file new model is used to extend initia effo ts toward RNN so fat e ship simulations These extensions include improved to mutations of propeller thrust, lifl trom deflected rudder, md the explicit inclusion of roll md pitch righting moments Tw m meuvers are simulated: to tick cu cles md honzonta overshoots Simulation emus for file circles averaged over al mrleusrs for such variables a speed, tmjecto y components md heading were 5% or less The bon onto overshoot simulation emus were aso 5% or less for file same va iables with the exception of the t msve~e hajecto y component The emlmation for the latter deficiency is believed to be file result of the exclusion of wind forces a ting on the vehicle, which will be the subject of later w dk INTRODUCTION The Neural Netw rk Development Laborato y wa e tablished at the Nawvl Su fat e Wafae Center NSWC)
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Full-scale data describing a series of maneuvers with varying rudder deflection angles and approach speeds have been acquired for each of two ships, and these data have been used to train and validate three neural networks, one for each ship and type of maneuver. Upon completion of training, data from maneuvers not included in the set of training maneuvers are input into the simulation, and predictions of the motion of the vehicle are obtained.
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The neural network simulations were trained and validated using these maneuvers; a
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, and for recursive neural networks to (Falter, et al., 1997~. A recursive neural network has feedback; the output vector is used as additional inputs to the network at the next time step.
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From page 227... ...
= P(t +6t ) L, q' md r'similar These velocity predictions are then used to compute at each time step the remaming kinematic variables described in Table 1: h secto y components, Euler mgles md accelerations The 56 conhibutions that to m the input vector are described as follow Sewn basic force md moment te ms describe the influence of the conhol inputs md of time-dependent flow held effects: thrust from two propeller., F.,, md 7;,,,, lit fiom two deflected rudder, L,, md Lid,, tw restoring moments resultmg fiom disturbances in pitch md roll, K, md M,, md a Munk moment acting on the hull, NAOMI These temms are developed fiom knowledge of the controls: propeller rotation speeds md rudder deflection mgles, geomet y of the vehicle, md from output variables which are recursed md made available to the inputs A detailed description of these sew n inputs is reserved for the next section Additional inputs are obtamed by retaining past values of the sewn basic inputs This gives the netw rk memo y of the force md moment hi to y acting on the vehicle md pe mits the netw rk to learn of my delay that cm occur between the mplication of the force or moment md the re ponse of the vehicle One past value hom each of fLe tw propeller thmst tffms is retained to provide tw additional inputs For each of the remainmg 5 basic mputs, 7 past values are retained as additional mputs The number of past values to keep is chosen empirically md mpea~ to be a f nction of the fi equency response of fLe vehicle in this case the netw rk is given infommation about past events for a penod of time requu ed for the flow about the vehicle to h avel a dist mce of 0 63L Recursed ouqputs fiom the prior time step are used as six additional contributions to fLe input wctm Fu the more, the ouqput vectorhom one previous time step is retamed md made available as six additional inputs Knowledge of fLe output velocities for tw successive time teps pemmits fLe netw rk to implicitly lean about the accele~tions of fLe vehicle A summary of the w~rious contributions that make up the input vector is provided below m Table 2, md attention is next duected to a detailed ~pl mation of fLe seven basic force md moment inputs Input Des~ription T b puts [,,,(t')
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9 may be determined, and the resultant thrust generated by the propellers may be computed from T - T - T prop rud (10) This final expression was used to approximate the thrust imparted to the vehicle from the starboard and port propellers and represents the first two inputs to the neural network.
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From page 229... ...
(17) Summaizmg, a a given time step, fLe mgle of atak is computed from Eq 14 requaing rudd~s mgle, recmsed vaues of h msve~e velocity, yaw mgula velocity md ship speed, md a vaue for Cr computed dming fLe thrust caculaions The ii t on the mdder is fLen computed from fLe sum of Eqs 15&17, md fLese caculaions a~e pe fo med for fLe ta~boa d md po t mdders md fo m fLe next tw inputs to fLe netw rk b addition to fLe propulsion a d steermg mputs tw nghting moment inputs ae provided to a count for di turb mces m roll md pitch A st dy of meta entac stability reveas fha fLe nghting am m ea h ca e is propo tiona to the dist mce fi om the center of g~vity to a point know a the trmsverse or longitudina meta enter; fLis meta entric height is denoted OMr or OM~ The product of the moment am md fLe weight of the whicle creaes a couple which a ts to restore fLe vehicle to its undist rbed onenta ion These moments may be mproxima ed by K, = pgva sin~ M, = pg VOM~sin9 where V is volumetric displa ement amd ~ md 9 a~e mgles of roll md pitch, respectively The meta enh ic height is commonly decomposed into a differ:me between fLe distmce hom the center of buoymcy to fLe meta ente' BMr or BM~, md fLe di t mce from fLe c:~ter of buoymcy to the center of g avity, BO Fu the more, B md B may be mproximaed for mal roll mdpitch motions by Ir/V ad l~/V, where Ir md 1~ a e moments of me tia of the wetted po tion of the vehicle about the h mswrse or long itu din a c enterl me , re p e ct iw Iy U pp er b omm ds on fLese moments formost ships saisfy Ir < yl2B3L md 1~ < Ih2BL3, where B is the beam md L is the ov~sal length of the vehicle Repla ing fLe f~ction wifh a const mt, the restoring moments may fLen be w itten a (Ig)
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From page 230... ...
As discussed in m earlier section, mfo mation presented to file inputs of a neural network is modified as it flow through file network by the presence of file weights md by file nonlinear outputs of each of file various nodes until it aTives at the output layers of file netw rk Thus, at each time step, m input vector produces a predicted output Actor, this is Glen compared to file actual (target) ouqput vector dete mined fiom the data The difference between file target md predicted ouqput Vectors is a measure of the enor of the prediction The process by which file netw rk is iteratively presented with m input vector m o der to produce outputs that are Glen compared wish a desired output vector is know as traming The pumose of traming is to gradually modify the weights between the nodes in o der to reduce the enor on subsequent itontiuns in other w rd., the neural netw rk learns how to reproduce the conect mswex When the emu has been minimi ed, haming is halted, md the result mt colle tion of weights that have been e tablished among file mmy co reckons m file netw rk represent the knowledge stored m file trained neural net Therefore, a haming algorithm is required to detemmine the eno5 between the predicted ouqputs md file desired target values md to act on this mfo mation to modify file weights until file or is reduced to a minimum The mo t commonly used haming algonthm, Ed the one employed here, is called backpropagation which is a gradient descent algorithm The collection of input md conespondmg target output vectors comprise a training set, md these data are requu ed to prepare the netw rk for f this use Data hles containmg time hi tories of tactical cacle md bon ontal over hoot m reuse.
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These validation data files then demonstrate the predictive capabilities of the network. Three neural networks were trained in this manner to predict Ship 1 tactical circles, Ship 2 tactical circles and Ship 2 overshoots.
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The stopping epoch for 6 is net wok wa selected a epoch 81,760 The network wa restated md Glen hated at this epoch The absolute enor wa 45 1, the average mgle measure wa 0 953 md the conflation coefficient wa 0 963 At this epoch the as curie mgle mea ure rem bed its ma imum, md the absolute en or md file conflation coefficient were ve y close to flair minimum md ma imum, re pectively Figure 7 show that fter the flu t 20,000 epochs most of file points on en h plot are clustered in a relative Iy thin b md This mdicates fhat file solution is relatively moodh wish smal charges to the 6608 weights md bin es at en h epoch c msmg only minor fluctuations m enors This wa t e for bodh Ship I md Ship 2 to tica cu cle simulations with the optimum solution typicaly mpeamg Stiff 60,000 to 80,000 epochs of homing For the Ship 2 overshoot simulation, file optimum solution required a somewhat longer 100,000 to 150,000 epochs of Paining The emu plots were simile to Fig 7 except fhat the pomts clustered in a thicker b md This w uld indicate fhat the evolution town d file optimum solution for the overshoots wa more difficult with smal charges to the weights casing lags fluctuations in solution emu s This topic will be revisited in a la ff section Summai ing, three neura netw rks were twined to predict Ship I to tica circles, Ship 2 to tica circles md Ship 2 overshoots using the procedure described in d is section The results of these simulations proved to be quite encouraging md are detailed next RESULTS Beginnmg wish Ship 1, the netw rk wa twined using 12 to tica circles wish three set a ide for vaidation Figure 8 depicts Ship I circle hajectones predicted by file homed netw rk superimposed upon the a tug trajectories followed by the vehicle in en h ca e the only info motion provided to the twined netw dk was fom time hi tories for po t md staboa d propeller rotation peed md mdder deflection mgles md the initia conditions of file vehicle Compasing the top row of the figure are four of the 12 m meuvers used for homing, md the bottom row contams al 3 vaidation runs The fom homing mns fhat me how represent a mint re of four different rudder mgles md thee different mproach speeds Similarly, the vaidation m meuvers contam three different rudder mgles md two different apron h peed Notice fhat tw of the traming cu cles fhat a e show are led t nets with the of her tw right tub s Solid lines represent the predictions, md dashed Imes are used for file acted path in each cane the steady state pats of file m Feuded =.- Comex md before Execute were reduced to a length dete mined by t'= I, md only a po tion of this sh aight path is show The predictions for file twining cacles are excellent This is the Bust te t that file netw rk must pa s if a relation hip bemused file force md moment inputs md the velocity ouqputs exists, file netw rk must dete mine this connection if the experiments data is poor, or the network is improperly to mutated, Glen file netw rk's pe to m mce on file tminmg data will be conespondmgly poor Neither is the cage here; file homed netw rk ha leamed how Ship I pe to ms a to tica cu cle m meuver That d is is tme is evinced by file pe to mmce of the netw rk on file vaidation cacles Recall that file Rand r on runs were ne s er used to modify file weights during tl Ming, md m this sense, hwe never before hew seen by the netw rk The recursive nema netw rk ha been successfully able to g:~eraize: to make predictions for m meuwrs different fiom, but simile to, those represented m the tminmg set in tw out of the three ca es, file most difficult md nonlinea po tion of the mmeuve' file initia pat of file t na a represented by the adv mce md h msfer, ha hew capt red precisely Predictions for the steady t numg diametffs a e excellent in a I three ca es To qumtify these statements, averaged enm5 for Ship I to tica circles have been tailed in Table 4 for file ti -e critical Or abler a, x, y, ~ md ~ The but number in en h cell is m en or averaged over a I 15 m meuvers, wherea the second number is the emu averaged over file 3 vaidation circles only To give some percentage emus, file absolute enors were no maized by the following scares: average steady peed m the tum of 5 2 m s (17fl/s) , a~emtie tunumg diameter of 651 m (2135O, average peak-to-peak roll vaiaion of 2 8° md m average total headmg vaiaion Table 4 Ship I to tica circle en or mea res avenged over ail m meuvers / avenged over w~lida ion h ICY only
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Fig. 8 Ship 1 tactical circles.
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Fig. 10 Ship 2 tactical circle.
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, average peak-to-peak roll variation of 2.3° and an average heading variation of 560°. Figure 10 displays Ship 2 speed, roll, pitch, heading and the direct neural network outputs: linear and angular velocity components.
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Fig. 12 Ship 2 horizontal overshoot.
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or 10%, the peak-to-peak distmce tlnclllred by 15 m (50fl) or 10%, file peak-topeak roll clla ged by 0 3-0 5° or 30-50% md the peakto-peak heading differed by 1-3° or 2-7/o CONCLUSIONS Reckon e neural netw dks homed on to tick cycle mmeuvffss for tw separate ships were able to predict speed, tmje to y components md heading wish enors averaged over al file data of 5% or less When considering only file vaidaion mmeuwrs, rlm5 for these variables raged fiom 1-7/o Emus in roll e timaes were tom 0 2-0 5° for m avenge roll vaiaion of 2-3° For the more complex overshoot m meuver the emus were only a little higher Speed, longit ding haje to y component, x, md headmg e hibited enors averaged over al file data of 5% or less, wherea considera ion of ju t file va ida ion mmeuve5 increased the enors to 10% or less Roll enors were O 1-0 3° for m average roll vaiaion of 12° The mo t difficult predictions for file overshoots were clearly the trmwerse hajecto y component, y, m integ a qu mtity resultmg prima ily fiom the t msver-e velocity component, x, md to a lesser extent, the heading This is a so file likely red on for file flicker bmd of generali Lion rlr5 a file solution evolved dating Gaining The effects of wind on the or hoot mmeuwrs will be felt shongly m these tw variables a the mmeuwrs are Sways conducted paalel or mti-paalel to the wind duection in file case of the cycles, for which environmental effects could be removed, the networks pe to med well for these tw va iables Clea Iy glen, substmtia improvement is likely to result trom file addition of wind force md moment inputs to the lle r al netw rk models, md f ture w dk will be directed to Allis end Rerlhnv neural netw rks have demon trued m ability a a robust md acurae mmeuvermg simulation tool With the f ther addition of environmental etle ts, the simulation could serve a a plmt model within m admtive conhol system New control cmahildies under investigation include
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md Gae, M "Effcient Techniques m Time-Domain Motion Simulaion Ba cd on A ti ~cia Neural Netw rk," Inten~aiona Symposmm on Ship Motions amd Mmoeuwability, RNA, London, UK, Feb. 1998 pp 1-23 Faler, W
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From page 239... ...
Fu themmore, She accmacy Nat is ultimately achievable is conshamed by the precision enor i herent m She experimental dote used to train the simulation A alternative method for estimating ~esultmg lorces Ed moments from specified control variables is to employ CFD using pote tisl or FANS codes This may prove to be s sup rior method Ed has She added benefit that th geomeby of th vehicle is explicitly defined during this process Coupling CFD computttiorr to the front end of s INN simulation offers th potential for s ye mete to-motion simulsti m capability The mfhors have already commenced efforts m His direction as part of mother effo t Ed work is proceeding DISCUSSION T Ji mg Versuchs mstalt fur Bi memchfffl m e \, Germ my In your presentation, you apply partly ve y complete lorce formulations, for mst me, for prop Her Ed rudder forces, Ed partly ve y simple fommuls, for in tance for Mu k's moment My question is what is impo t mt in mod hng She hyd odynamics by using the neural network technique?
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Obviously each set of data needs to be tagged separately by c m meric representi g She ship Ember But, is His generalisation possible et all? AUTHOR'S REPLY Question I Th moti m of She vehicle is not duectly related to c rudder deflection Ogle or c propeller rotation peed but Instead to She lif force produced by that deflected rudder or to the f u t produced by the propulsor Therefore, She i termedicte step trmsfommmg easily specified Input co trol variables i to She forces Ed moments Nat duect fihe motion of the vehicle is requited How ver, the question is wh ther fihe neural network c m team this t msformstion or wh ther it must be explicitly defined The mthors did not tug the suggested approach in this work
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From page 241... ...
tl so in experimental fluid dynamics The mfhors succeeded again in presenting then work m s clear md unpretentious way Nat serves as s good imtt oduction to She neu ml network technology I hope the pap r will umpire more colleagues to study md incorporate neural networks in ship hyd odynsmics I would lik to add s few references for nemal network applications in ship hyd odynsmics Various applications mcludmg the trimar m ship moti m prediction c m be found in [2] which should be more widely available th m the 1993 reference [3]
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From page 242... ...
COMPIT'2000, Potsdsm, 2000, pp 292-301 5 5 hmeekdubh, H md Bertmm, V "Shiu Desien for Efficiencv md E onomv", Butterworfh & Hememarm, O ford, ISBN 0750641339, 199S 6Koushm, K "Prediction of Propeller h~duced Pressme Pulses Usmg Adffiical Neural Networks", ", I Intemstiorul Co fe~ence on Computer Aunlicstions md I formstion Techmolo~v m fhe Marine Indushies. COMPIT'2000, Potsdsm, 2000, pp 24g-254 AUTHOR'S REPLY Comment I Nemal networks are I kely to bee me more widely used withm fhe maritime commmmity if fhey c m be show to be successf I md if they c m demonstmte fnat they p~esent s istle slterrutiv to e istmg techmiques A large f~action of ext mt neural network ~esearch ~eported in fhe literst re has beff~ concem d with ~demic questions regarding textbook problems ss opposed to explormg spplied problems See fhe literst re ~eview by Psller, 1996 Inmessed spplicstion of neural networks to spplied problems is likely to slleviste bodh concems Comment 2 The mthors sgree thst the inclusion of relevmt physical i formstion to ~educe fhe level of brute force sy tem identfficstion fnat must be performed by fhe neural network is desimble How v r, efforts to better estimste those coefficients fnat me~ely scale th amplitud of th input me not r quned ss descobed m the ~eply to J
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