Research on Simplifying the Motion Equations for Submarine Training Simulator based on Sensitivity Index

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1 Secon nenaional Sympoium on nelligen nfomaion echnology Alicaion Reeach on Simplifying he Moion Euaion fo Submaine aining Simulao bae on Seniiiy nex Zhao Lin,Zhu Yi,Lu Zhihong 3,Zhang Jing 4 College of Auomaion, Habin engineeing unieiy, Habin, Heilongjinag,5000,China huyi985@gmail.com Abac Submaine aining imulao uilie he high echnology eice o ain he ailo in he afe, highefficiency an ealiic enionmen hile eucing he angeou ualiy an fun in acual aining. Soling he ix imenion moion euaion of ubmaine play a ignifican ole in he aining imulao. A he 08 hyoynamic coefficien ae ha o acuie compleely, an he lo oling pee becaue of he complex euaion, i i neceay o implify he euaion in he ange of accepe eiaion. n hi pape, he ubmaine moion moel i analye, he moion euaion i implifie, a eniiiy inex i inouce, an hee ypical maneue imulaion e ae choen a he eeach ubjec. he influence of hyoynamic coefficien fo he maneueabiliy i ealuae. he imulaion eul pe he feaibiliy of he implifie meho.. noucion he mahemaical moel [] of he maneue an conol fo ubmaine conain hyoynamic foce an momen expee in em of a e of hyoynamic coefficien. Hyoynamic coefficien ongly affec he ynamic pefomance of ubmaine. he main objecie of he aining imulao i aining he ailo o be familia ih he ubmaine maneueabiliy. i iffeen o he eal aining in he acual ubmaine. he imulao ge he moion aiue accoing o oling he moion euaion. he geneal euaion [] ae ey complex. conain 08 hyoynamic coefficien, o acuiing he hole coefficien i ahe ha. Many eeache implify he ana moion euaion accoing o manipulae expeience an he hyoynamic coefficien analyi. he expeimen an imulaion eul[][3][4] ho ha he main effec o he ubmaine pace moion epen on ome coefficien no he hole coefficien; heefoe e coul conie he paicula pimay coefficien influence on ubmaine moion an ignoe he le effecie coefficien. hi pape implify he moion euaion uing he manipulae expeimen imulaion eul of coefficien eniie inex.. Submaine pace moion euaion he cooinae an ymbol ule ae comply ih he ell knon geneal ix-egee-of feeom euaion of ele [] m u + x( + ) + y( p ) + ( p + ) = X m p + u y( + p ) + ( p) + x( p + ) = Y m u + p ( p + ) + x( p ) + y( + p) = Z xp + y + m y u + p p + u = K y+ x p + m u + x u + p = M + y x p+ m x p+ u y u + = N n he abe, upepeen,,,,, he anlaional an oaional elociie in he boy yem. x, y, i he cooinae of he cene of gaiy. m i ma an xx, xy,ec., enoe he aiou pincipal an comomen momen of ineia of boy. he lef-han ie of abe euaion i exac. XYZKMN,,,,,, epeen he eulan foce an momen. he igh-han ie of abe euaion ha conain exenal foce an momen ae unceain an aoximae in he ynamic moel. hey ae expee in em of a e of hyoynamic coefficien uch a X p hich ae ha o eimae o eemine exacly. W, B, epeen he eigh an buoyancy of boy. φ, θ, ϕ, epeen he oll, pich an ya angle epeciely /08 $ EEE O 0.09/A

2 Suge: 4 X = ρ L X + X + X p p 3 + ρ L X uu X X ρ L uu X u + X + X + ρlu X X X b b b + + au + buuc + cu c ( W B) in θ Say: 4 Y = ρl + + p p + p p+ + 3 p p Yu up p + + ( + ) + ρl Yu ( ) 0 + Yu u u + ( W B)coθin φ Heae: 4 Z = ρl + p + + p p+ 3 p + u+ + p 3 + ρl ( + ) 0u + u+ u + ρl ( + ) + ( + ) + 3 u u + u b + ( W B) coθco φ Roll: b 5 + p p+ 4 p + up+ u 4 K K K ρl Ku ( ) Ku ρl K u + ( yw yb) coθcoφ ( W B)coθ in φ 5 K = ρl Kp p+ K + K p p C Pich: 5 M = ρl M + M p + M + M + M p p 4 + ρl M ( ) M u M M p p M ρl[ M 0u + M u+ M u ] 3 + ρl M ( + ) + M ( + ) + M 4 3 M u + ρl M u + M u b b ( xw xb) coθcoφ ( W B) in θ C C Ya: 5 N = ρl + N' p p+ p p + + p p+ 4 + ρl [ pup + + u] 4 L N ( ) + ρ + p p ρl ( ) 0u + u u + ρl u + ( xw xb) coθinφ + ( yw y B) in θ C C n he abe, he ix egee of feeom euaion of ubmaine i ahe complex an non-linea hich exi coupling beeen hoional plane an eical plane. he numbe of he hyoynamic coefficien of he euaion i 08. A fa a he aining imulao i concene, calculaing he euaion oul co a moun of ime an yem eouce. Hoee he main pupoe in aining ailo i ha achieing he coeponing ue effec accoing o manipulae he ue, bo an en in em of epaaely o combine eeing ih iual C 78

3 inumen. n coneuence, hi pape implifie he complex euaion o impe he calculaing efficiency of imulao an opimie he yem eouce. 3. ypical eeing e n hi pape, ypical eeing e e ecie o chooe ae ehoo maneue in he eical plane, ehoo maneue in hoional plane an uning cicle maneue in he hoional plane. hough he e, e can ge a e of maneue paamee hich enoe eenial chaaceiic. he efiniion of maneue paamee i he ame a []. Oehoo maneue in hoional: 0 / 0 ue, he maneue paamee ae a, a, ψ,. uing cicle maneue in hoional: 35 ue, he maneue paamee ae,, A,, Oehoo maneue in eical: 0 en, pich angle 6, he maneue paamee ae e, θ, ζ. 4. he eniiiy inex he eniiiy inex - S ae inouce fo meauing he eniiiy exen of manipulae paamee o he hyoynamic coefficien. he efiniion i a follo: * * * S = R R / R =ΔR/ R ( ) R epeen he manipulae paamee, R * epeen he coeponing manipulae paamee ha i calculae on he ana hyoynamic coefficien. S epeen he hyoynamic coefficien eniiiy exen o he manipulae paamee. he moe enible in ubmaine moion,he highe alue of S. ha mean hyoynamic coefficien play a ignifican ole in he manipulaing imulaion. 4.. he eniiiy calculaion of hyoynamic coefficien he poceue of expeimen in hi aicle ae a follo: () By chooing one of he ypical manipulae e, efining he oiginal iuaion, e imulae he moion in paicula ue egee ihin he iniial hyoynamic coefficien an calculae a eial of manipulae paamee a he ana alue. () efine he ih hyoynamic coefficien a 0, o he ame expeimen in (), ge he change manipulae paamee an calculae he coeponing eniiiy inex. An hen change he ih coefficien ino he oiginal coefficien. Repea he imulaion expeimen unil all he hyoynamic coefficien ee change, he manipulae coefficien ae acuie an he coeponing eniiiy inex ae calculae compleely. (3) Chooe anohe ypical manipulae e o o he ame ep in () an analyi in () (4) Ue he hee ype of coefficien o make a able ha conain he oiginal hyoynamic coefficien, manipulae paamee an eniiiy inex. (5) Calculae he elaie eo of maneue paamee. 4.. Pa of hyoynamic coefficien eul he imulaion of manipulae e bae on he malab7.0. he hee able,,3 ho he eniiiy inex hoe alue i geae han 3% in he hee ypical e epeciely. inf epeen infinie. coef able Seniie inex imulaion eul of ehoo maneue in hoional plane a ψ p inf inf inf inf inf inf inf inf 79

4 Coef able Seniie inex imulaion eul of uning cicle maneue in hoional A p inf inf inf inf inf Y K Coef able 3 Seniie inex imulaion eul of ehoo maneue in eical plane e θ ζ Z Z inf inf inf M M M inf inf inf M inf inf inf 4.3. Analye of eul n hi pape, e eee he eniiiy inex hoe alue i geae han 3% in hee e. he 3% inicae ha he maximum influence oul no beyon 3%. We euce he numbe of he hyoynamic coefficien o 3 hile he fome numbe i 76. Figue,, 3 ho he imulaion eul (oe line efe o implifie imulaion cue, oli line efe o oiginal imulaion cue). able 4 ho he elaie eo of he maneue expeimen able 4 Simplifie moel manipulae ealuae inex elaie eo a ψ A e θ ζ 70

5 5. Concluion hi pape inouce a ne meho ha implifie he ubmaine moion moel bae on he analye of coefficien eniiiy. hee ypical ype of manipulae expeimen an i expeimen coefficien ha ealuae he manipulaion ae icue, eemine he inex an e poceue, imulae he algoihm in malab, acuie he imulaion cue an eul, implify he euaion. Refeence Figue uing cicle maneue in hoional plane Figue ehoo maneue in hoional plane [] ebabaa Sen(000). A uy on eniiiy of maneueabiliy pefomance on he hyoynamic coefficien fo ubmege boie. Jounal of Ship Reeach, Vol. 44, No. 3, : [] Shi henga. Conollabiliy of Submaine. Beijing: Naional efence nuy Pe. 995(in Chinee). [3] Wang yan fei, Zhu Jun, Zhang hen han(005). A meho of ealuaing he influence of hyoynamic coefficien on conollabiliy of ubmaine. Jounal of Ship Mechanic, Vol. 9, No.5.:6-68 [4] W.Y.Hang(980) Alicaion of yem ienificaion o hip maneueing M Ph.. hei [5] Le,M,,Nguyen, -H(000), Eimaion of hip hyoynamic coefficien in habo maneue an i alicaion, Poc of FAC Conol alicaion of Opimiaion. Vol., No., :7-3 [6] Foen,,(994) uiance an conol of Ocean Vehicle, John Eiley&Son, UK [7] H.K.Yoon, K.P. Rhee(004), Eimaion of oll elae coefficien of a hip by uing he yem ienificaion meho he Sociey of Naal Achiec of Koea, Vol.4, No.4.:53-58 [8] S.Y.Kim(004), Eimaion of maneueing coefficien of a ubmege boy by paamee ienificaion Ph. hei Seoul Naional Unieciy Figue 3 ehoo maneue in eical plane A hon in Figue,, 3 an able 4, he influence fo implifying he euaion i lile afe ignoing he mall alue eniiiy inex., heefoe implifying he euaion bae on eniiiy inex i feaible. he maximum elaie eo i 7.7%. Simplifie euaion oul eceae in an amoun of calculaing ok. 7