On Safe Navigation Support System using GPS Compass

Transcription

1 Proceedings o he 6 h Inernaional Ship Sabiliy Workshop, 5-7 June 27, Belgrade, Serbia On Sae Navigaion Suppor Sysem using GPS Compass Daisuke erada, Naional Deense Academy, derada@nda.ac.jp asahiro amashima, FLUID ECHNO Co., Ld., mamashima@luidechno.com Ikuo Nakao, FLUID ECHNO Co., Ld., inakao@luidechno.com Akihiko asuda, Japan Fisheries Research and Educaion Agency, amasuda@arc.go.jp ABSRAC For making he onboard use o operaional guidance in he IO second generaion inac sabiliy crieria easible, i is proposed o use a GPS compass or esimaing a direcional wave specrum onboard based on Wave Buoy Analogy. As a discussing in 98s, i he direcional wave specrum can be esimaed onboard, hen ship moions, a bending sress and so on can be esimaed and prediced wihou direc measuremen o hem based on he linear superposiion heory. Since as he basic heory a Bayesian saisics, namely a general sae space modeling procedure, is used, he proposed mehod can even use under navigaion in he ollowing seas. In order o veriy he eeciveness o he proposed mehod, model experimens and onboard experimens are carried ou. As he resuls, i is conirmed he eeciveness o he proposed mehod, alhough several uure asks exiss. Keywords: General sae space modelling procedure, Ensemble Kalman Filer, Nonlinear observaion.. INRODUCION I goes wihou saying ha i is mos imporan ask or a capain, oicers and sailors o remain a sae navigaion in rough seas. In order o realie his, irsly, under navigaion hey need o appropriaely make he use o operaional guidance in he IO second generaion inac sabiliy crieria easible. In his sudy, a novel navigaion suppor sysem using a GPS compass is inroduced o realie his purpose. A GPS compass, which was developed in recen years, is new nauical insrumens o undersand a ship course, posiion, speed and so on. Especially, he one wih buil-in a clinomeer using acceleraion sensor can also measure he ship moions such as pich moion, roll moion and heave moion, simulaneously. In his paper GPS compass wih his uncion is called he GPS+. We ocused on his uncion. ha is, by using his GPS compass, we can obain various inormaion o remain a sae navigaion in rough seas. As well known, in he research ield o seakeeping qualiy, ship moions can evaluae saisically by muliplying response ampliude operaors (RAO) based on he linear poenial heory and given direcional wave specra. hereore, i we can prepare he RAO o he ship and can give he encouner direcional wave specrum, hen we can evaluae saisical values o ship moions heoreically. In 98s, his idea had been concreely realied by many ship builders. However, in hese sysems, oicers and sailors had o inpu several inormaion which are he ship speed, saisical values o encouner waves and so on. oreover, a ransverse meacenric heigh, namely G, was also required o calculae he RAO o moions. Consequenly, hey were no popular. In order o solve one o disadvanages, in 99s, as well as wave buoy sysem, an encouner direcional wave specrum under navigaion can be evaluaed by using he knowledge o saisical science ha is especially Bayesian saisics as shown Iseki and Ohsu [994] irsly. In recen years, his procedure is called a Wave Buoy Analogy (WBA). In WBA, he direcional wave specrum can be evaluaed by using a RAO concerning ship moions calculaed heoreically and a cross specrum obained by calculaing rom measured ime series o ship moions. oreover, Iseki and erada [22] showed ha ship moions and a longiudinal bending momen can be prediced by using he esimaed direcional wave specrum. In his case, he measuremen o ship moions can be done by an Inerial easuremen Uni (IU). hereore, even i we used he WBA, he ship speed had o inpu by oicers and sailors. I should be noed ha he IU is no an equipmen

2 Proceedings o he 6 h Inernaional Ship Sabiliy Workshop, 5-7 June 27, Belgrade, Serbia 2 designaed by law, alhough here are he IU which can ake in a signal o GPS. On he oher hand, as menioned beore, he GPS+ can simulaneously measure boh o he ship speed and moions. hereore, disadvanages o he sysems developed in 98s can be solved by using he GPS+. oreover, in our recen research [erada e al. (26)], we had developed he esimaion mehod o G based on nonlinear sae space modeling procedure which is a ype o ime series modeling procedure. I means ha he esimaion o he direcional wave specrum can be auomaically achieved by he use o he GPS+. From his background, we considered ha i can be developed he navigaion suppor sysem in rough seas which has he uncion o he saisical predicion. he sysem conains he esimaion o G, he selecion o RAO corresponding he ship speed and he displacemen, he calculaion o cross specrum, he esimaion o direcional wave specrum and he predicion o ship moions. In hese iems, especially, as o he esimaion procedure o direcional wave specrum, a novel procedure using a general sae space modeling is proposed. he eaure o his is ha a he same ime he cross specrum was calculaed, he direcional wave specrum can be evaluaed based on ilering process in sae esimaion o general sae space modeling procedure. In his paper, we explain his in deail. he proposed sysem was veriied based on model experimens and onboard experimens. he sample ship is a conainer ship o coaswise navigaion. 2. OULINE OF PROPOSED SYSE Figure shows he basic concep o he proposed sysem. As menioned above, he mos imporan key echnology is he GPS+. As shown his igure, he inormaion or he ship posiion, he speed and moions, namely he pich, he roll and he heave, are simulaneously obained by i. ha is, by using he GPS+, he ime synchroniaion o each daa can be realied naurally. In his sysem, as o he roll moion, he damping coeicien and he naural requency are irsly esimaed, aer ha he G are esimaed based on erada e al. [26]. As o he deail o his process, see he reerence. In his case, i he G can be esimaed, hen he RAO or moions wih he ship speed and he G as parameers can be calculaed or seleced rom he daabase, because he ship speed are given by he GPS+. oreover, he cross specrum o moions can be done auomaically by he vecor auoregressive modeling procedure [Kiagawa, 2] based on he minimum AIC (Akaike Inormaion Crierion) [Akaike, 974] esimaion. hus, he problem o he pas research work is solved compleely in meaning o he applying o WBA. As o he mehodology o WBA, a general sae space modeling based on an ensemble Kalman iler (EnKF) [Evensen, 23] is proposed in aer secion. hereore, i an accurae direcional wave specrum can be esimaed, hen he ship responses such as moions, momen and so on can be esimaed wihou a direc measuremen, and he predicion o hem can be realied under an assumpion o saionariy wih respec o waves as well as he pas research work. Figure : Basic concep o he proposed sysem. 3. ESIAION OF DIRECIONAL WAVE SPECRU 3. odeling As menioned beore, i ship moions are considered o be linear responses o inciden waves, hen he cross specrum o ship moions and he direcional wave specrum are relaed by he RAO as ollows: Φ GPS compass (SC-3) Inormaion Posiion Speed oions Pich Roll Heave Cross specrum Calculaion oions, omen, and so on Esimaion and predicion G ec. Esimaion Super posiion RAO (oions) Calculaion or Selecion = π * mn H m ( e, χ ) H n ( e, χ) E( e, χ) π *G ec.: G, Damping coeicien, Naural requency and so on. dχ Direcional wave specrum Esimaion RAO (oions, omen, and so on) () where e is an encouner requency, E( e, χ) is he direcional wave specrum based on he encouner requency, Φ mn is he cross specrum beween he m-h and n-h componens, H m ( e, χ) is he RAO o

3 Proceedings o he 6 h Inernaional Ship Sabiliy Workshop, 5-7 June 27, Belgrade, Serbia 3 he m-h componen o he ime series, and he noaion * means he complex conjugae. On he oher hand, he direcional wave specrum expressed by absolue wave requencies are convenience because o a saisical predicion o ship moions, bending sress and so on. However, in his equaion, when he ship runs under he ollowing seas, he relaionship beween he encouner wave requency e and he absolue requency becomes riple valued uncion problem as shown in Figure 2. According o Iseki and Ohsu [994], i can be deal wih his problem appropriaely. e e = 4A A=2πUcosχ U: Ship speed χ: Wave direcion = + 2 2A regressive model expression using only he upper riangular marix: y = AF ( x) + w (3) where, y is he (9 l) cross specrum vecor which is composed o real and imaginary pars o each elemen o Φ( e ). Noed ha l is he divided number o he specrum. And A is he (9 l, k m) coeicien marix which is composed o producs o he RAO o ship moions. Noe ha k and m are he divided number o he encouner angle and he absolue wave requency. oreover, w~n(, Σ) is a (9 l) Gaussian whie noise sequence vecor inroduced or sochasic reamen and F(x) is he (k m) unknown coeicien vecor which is composed o he discreied direcional wave specrum. In he acual calculaion, he unknown parameer vecor should be expressed in he ollowing orm o avoid he esimaion o a negaive direcional wave specrum: Figure 2: Relaionship beween encouner wave requencies and absolue wave requencies. Considering his problem in he ollowing seas, he discree orm o he equaion () can be expressed by he ollowing marix expression: Φ( e ) = Η( + Η( + Η( 2 3 ) E( ) E( ) E( 2 = = 2A A 2 3 ) H( ) H( ) H( 2 3 ) ) ) * * * (2) where, 2 and 3 are he absolue wave requencies ha correspond o he encouner wave requencies e, Φ( e ) is he measured cross specrum marix, H( i ) and E( i ) (i=,2,3) denoe he marices o he RAO o ship moions and he direcional wave specrum a he, 2 and 3, respecively. I should be noed ha he number o elemens wih i = is K, and he number o elemens wih i = 2 and 3 represening he conribuion rom he ollowing seas is K(<K/2). In his equaion, since Φ( e ) is a Hermiian marix, his equaion can be reduced o a mulivariae 3 F( x) = [ exp( x ),,exp( x )] ( exp( x ) = E ( ), j =,, k m) j j J (4) where, E j ( ) = E(, χ k ), and χ k denoes a discreied encouner angle. In his case, i he cross specrum can be obained any ime sep recursively, hen he idea o WBA can be exended ino he esimaion o changing direcional wave specrum wih ime. ha is, equaion (3) can be expressed by he ollowing equaion: y ( + (5) = AF x ) w where, in his equaion he subscrip means any ime sep. In his case, consider ha equaion (4) is a nonlinear observaion model in a general sae space model. oreover, consider a smoohness prior wih respec o he change o he direcional wave specrum as a sysem model o he general sae space model. hen, he ime varying direcional wave specrum can be deal wih as he

4 Proceedings o he 6 h Inernaional Ship Sabiliy Workshop, 5-7 June 27, Belgrade, Serbia 4 problem o he ollowing general sae space modelling: x y here, x F = x + v = A F( x ) + w = [ ln( x, ),,ln( xj, )] ) = exp[ ln( x ),,ln( x )] (, J, x. (6) and, x is a sae vecor, v is a sysem noise vecor, y is an observaion vecor, A is a sae ransiion marix and w is an observaion noise vecor, respecively. As shown in equaion (6), since he observaion model is nonlinear, i should be noed ha an appropriae sae esimaion mehod mus be used. As o a nonlinear ilering heory o he sae esimaion, here are he paricle one Carlo iler [Kiagawa, 993], he ensemble Kalman iler (EnKF) [Evensen, 23] and so on. In his sudy, he EnKF is used rom he viewpoin o he compuaional ime. However, since he EnKF is a ype o he Kalman iler, equaion (6) including nonlinear observaion model canno be direcly used. In order o solve his problem, consider he exended sae vecor, he exended sae ransiion marix and he exended observaion vecor as ollows: x = (7) A F( x ) ~ A = ( I ) (8) (9 l, m k ) (9 l,9 l) x + v (, v ) = (9) AF( x + v ) As he resul, he equaion (6) can be ransormed ino as ollows: y = (, v ) ~, () = A + w and since his equaion is ormally a linear sae space represenaion, he EnKF can be used. 3.2 Sae esimaion In he EnKF, a sae esimaion can be done by using ensembles rom he probabiliy disribuion as well as a paricle one Carlo iler. Under given he general sae space model, he EnKF concreely calculaes a predicive disribuion p( y - ) and a iler disribuion p( y ) recursively using he ensemble member { } i =. According o Evensen [23], concree algorihm can be wrien as ollows: [Sep ] Generae an iniial ensemble {. = } i [Sep 2] Repea he ollowing seps or n=~n. () One-sep-ahead predicion (a) Generae an ensemble { v } i= o he sysem noise. (b) For i=,,, compue he ollowing equaion: = (, v ) () (2) Filer (a) Generae an ensemble { W } i= o he observaion noise. (b) For i=,,, compue he ollowing equaions: Vˆ = = j = i i W ) ( ) = W ( ˆ Kˆ = j = ˆ W j = j = W W ~ ( ˆ ~ A ˆ ) V A + = V (2) (3) (4) (5) ~ A (6) (c) For i=,,, compue he ollowing equaion:

5 Proceedings o he 6 h Inernaional Ship Sabiliy Workshop, 5-7 June 27, Belgrade, Serbia 5 ~ ( y + W ) = + Kˆ A 4. RESULS AND DISCUSSIONS (7) 4. odel experimens In order o veriy he proposed procedure, we irsly carried ou he ree running model experimens concerning a conainer ship a he marine dynamics basin belonging o Japan Fisheries Research and Educaion Agency. he principal perpendiculars and he phoo are shown in able and Figure, respecively. able : Principal pariculars o he sample ship. L pp 85. m G.828 m B 4. m ϕ 3.3 sec d m 3.54 m k' yy.264 W on Noe: Scale raio = /33 he waves are he long-cresed irregular waves, are reproduced by he condiions in which he signiican wave heigh H /3 is [m] and he mean period is 6[sec]. Noe ha he resuls o he model scale have been ransormed in o he value o he acual ship. As preparaion o he esimaion o he direcional wave specrum, as shown in Figure 3 he daa se rom one record o he measured ime series daa such ha he number o analysis daa always becomes 3 samples were made, because he measuremen ime in he model experimen has he consrain. I should be noed ha o use 3 samples is decided by he viewpoin o he calculaion ime. One record o he measured ime series daa ime(sec) 3 samples 3 samples Δ = sample daa se 3 samples 3 samples Figure 3: Schemaic diagram concerning he conracion o he daa se. Figure 2: Phoo o he sample ship. One o he resuls o he model experimens is shown in his subsecion. he condiions in he model experimens are as ollows: he model ship speed is corresponding o [knos] in acual ship. he encouner angle relaionship beween he ship course and he wave direcion is [degrees], ha is, he model ship ran under he ollowing seas. he measuremen device is he Fiber Opic Gyro (FOG) sensor made by amagawa seiki Co., Ld., and is sampling rae is 2[H]. I should be noed ha a verical acceleraion was used or he analysis, since in model experimens he heave can no be measured. From Figure 4 o Figure 6 show he hree kinds o characerisics, namely signiican wave heigh, wave mean period and wave direcion, obained by he inegral o he esimaed direcional wave specrum, respecively. In hese igures, he horional axis indicaes he sample daa number, and he verical axis indicaes he characerisics o he esimaed direcional wave specrum. Figure 4 shows he signiican wave heigh, Figure 5 shows he mean period, and Figure 6 shows he direcion o he wave, respecively. From hese igures, i can be conirmed ha each characerisic o he esimaed direcional wave specrum converges o he se values wih ime, even hough he condiion o he encouner angle wih respec o waves is he ollowing seas. hereore, i can be considered ha he proposed mehod or he esimaion o he direcional wave specrum is eecive.

6 Proceedings o he 6 h Inernaional Ship Sabiliy Workshop, 5-7 June 27, Belgrade, Serbia 6 are large. Here, hese daa were analyed every 3 samples (3 [sec]). I is called ha he irs 3 samples is case, he second 3 samples is case2, he hird 3 samples is case3 and he las one is case4, respecively. Figure 4: Esimaed signiican wave heigh. Figure 5: Esimaed mean period. Figure 7: Phoo o insallaion sae o he SC-3. Figure 6: Esimaed main wave direcion. 4.2 Onboard experimens One o he resuls o he onboard experimens is shown in his subsecion. he sample ship is he same one used in he model experimens. In he onboard experimens, as he GPS compass, he SC-3 made by FURUNO ELECRIC CO., LD. was used. he SC-3 was se as he Figure 7 a he upper o lying bridge o he sample ship. he daa which was measured a 4 [UC] o clock on Feb. 8, 24 is used in he analysis. In his case, he sampling ime is he. [sec]. Figure 8 shows he ship s posiion where daa was measured. Figures 9 (a) ~ (e) show he ime series beween,2 [sec] was measured by he SC-3. From op o boom, he ship course, he speed, he pich, he roll and he heave are shown, respecively. From hese igures, i can be seen ha he sample ship bounds or he eas a he ship speed abou [knos]. And, i can be also seen ha he moions Figure 8: Ship s posiion where daa or he analysis was measured. able 2 shows he resuls o he analysis and he resuls o he wave predicion in Japan eeorological Agency (JA) [JA(A), 27]. From his able, as o he signiican wave heigh, i can be seen ha he esimaed values by he proposed mehod are good agreemen wih he wave predicion values in he JA, hough he arge ime is sligh dieren. However, as o he wave mean period, boh resuls are sligh dieren, moreover as o he wave direcion, boh resuls are quie dieren. As one o his cause, i is considered ha he wave predicion mehod in he JA can no ake muli-direcionaliy ino consideraion as

7 Proceedings o he 6 h Inernaional Ship Sabiliy Workshop, 5-7 June 27, Belgrade, Serbia 7 shown Sasa e al. [25], alhough our proposed mehod can deal wih muli-direcionaliy o waves. As he reerence inormaion, we invesigaed he wind inormaion o he JA observaion poin, which is unakaa ciy, Fukuoka Preecure, closes o he ship s posiion [JA(B), 27]. According o his records, he direcion varied rom SSE o WSW, and he velociy varied rom.5 [m/s] o.[m/s], respecively. hereore, a leas, as o he wave direcion, i can be considered ha he accuracy o he wave predicion values in he JA is low, because here is he ac in which he direcion o he wind and wind waves is almos same. Noe ha as o his, i is necessary o veriy more in deail. (a) Couse [deg] 5 5 ime [sec] (b) Speed [ks] 5 5 ime [sec] (c) Pich [deg] ime [sec] (d) Roll [deg] ime [sec] (e) Heave [m] ime [sec] Figures 9: ime series or he daa analysis. able 2: Comparison wih he esimaed values by he proposed mehod and he wave predicion values in he JA. H /3 Wave direcion [m] [sec] ain 2 nd case Souh Norh case Souh NNW case Souh Norh case Souh NNW JA [UC2] NNE [UC24].6 4. NNW 5. CONCLUSIONS In his research, rom he view poin in which under navigaion ship s crews appropriaely make he use o operaional guidance in he IO second generaion inac sabiliy crieria easible, he sae navigaion suppor sysem using GPS compass is inroduced. he sysem conains he esimaion o G, he selecion o he response ampliude operaor corresponding he ship speed and he displacemen, he calculaion o cross specrum, he esimaion o direcional wave specrum and he predicion o ship moions. In hese iems, especially, as o he esimaion procedure o direcional wave specrum, a novel procedure using a general sae space modeling was proposed. he eaure o his is ha a he same ime he cross specrum was calculaed, he direcional wave specrum can be evaluaed based on ilering process in sae esimaion o general sae space modeling procedure. In order o veriy he eeciveness o he proposed mehod or he esimaion o direcional wave specrum, he model experimens and he onboard experimens are carried ou. Obained indings are summaried as ollows: () From he resuls o he model experimens, under he condiion in which he ship moions exis, i can be conirmed ha he esimaed direcional wave specrum based on he proposed mehod is good agreemen wih he se one, since he characerisics obained by he inegral o he esimaed direcional wave specrum converge he se values wih ime. (2) From he onboard experimens, as o he signiican wave heigh, i can be seen ha he esimaed values by he proposed mehod are good agreemen wih he wave predicion values in he Japan eeorological Agency, hough he arge ime is sligh dieren. However, as o he wave mean period, boh

8 Proceedings o he 6 h Inernaional Ship Sabiliy Workshop, 5-7 June 27, Belgrade, Serbia 8 resuls are sligh dieren, moreover as o he wave direcion, boh resuls are quie dieren. hereore, as a uure ask, i is necessary o veriy his reason more in deail comparison wih an onboard experimen using a wave buoy and a wave RADAR. erada, D., amashima,., Nakao, I. and asuda, A, 26, Esimaion o he meacenric heigh by using onboard monioring roll daa based on ime series analysis, Proceedings o he 5h Inernaional Ship Sabiliy Workshop, pp ACKNOWLEDGEEN his work was suppored by he commissioned projec or R&D o marine science and echnology in Nagasaki Indusrial Promoion Foundaion. Auhors would like o hank all ailiaed paries. REFERENCES Akaike, H., 974, A new look a he saisical model ideniicaion, IEEE rans. Auom. Conrol vol. 9, pp Evensen, G., 23, he Ensemble Kalman Filer: heoreical ormulaion and pracical implemenaion, Ocean Dynamics, 53, pp Kiagawa, G., 993, one-carlo ilering and smoohing or non-gaussian nonlinear sae space models, Proceedings o 2 nd U.S.-Japan Join Seminar on Saisical ime Series Analysis, pp. 3. Kiagawa, G., 2, Inroducion o ime series modeling, CRC Press. Iseki,. and Ohsu, K., 994, Bayesian esimaion o direcional wave specra based on ship moions (2 nd repor) (In Japanese), Journal o he Sociey o Naval Archiecs o Japan, No. 76, pp Iseki,. and erada, D., 22, Bayesian esimaion o direcional wave specra or ship guidance sysem, Inernaional Journal o Oshore and Polar Engineering, Vol. 2, No., pp Japan eeorological Agency, 27/4/(accessed), hp:// n/wave_poin.hml?poin=8&year=24&monh=2 (In Japanese) Japan eeorological Agency, 27/5/(accessed), hp:// hp?prec_no=82&block_no=943&year=24&monh=2& day=8&view= (In Japanese) Sasa, K., erada, D., Shioani, S., Wakabayashi, N., Ikebuchi,., Chen, C., akayama, A, Uchida,, 25, Evaluaion o ship perormance in inernaional ransporaion using an onboard measuremen sysem in case o a bulk carrier in inernaional voyages, Ocean Engineering, Vol. 4, pp