A Prediction Model for Night Recovery of Embarked Aircrafts Based on System Dynamics

Transcription

1 doi: 1.528/jam.v9i4.648 A Predicion Model for Nigh Recovery of Embarked Aircrafs Based on Sysem Dynamics iangliang Cheng 1,3, Kuizhi Yue 1,2, Zhenghao Huang 2 ABSTRACT: In order o make a sensible predicion on he air raic flow managemen wih condiions of wave-o and boler, a sysem dynamic model for he nigh recovery operaions of embarked aircrafs is buil o ensure he adapion of air raic flow wih he capaciy of air conrol a each phase of he recovery operaions. The model aims a he characerisics of muliple feedbacks, delays and complex ime varying, builds a sock flow diagram and operaion model wih impac facors of he nigh recovery sysem, and is simulaed in Vensim Personal earning Ediion 5.9. The simulaion shows a reasonable predicion resul for he nigh recovery of embarked aircrafs wih condiions of boler and wave-o and can provide a heoreical basis for scheduling he air raic flow managemen of embarked aircrafs formaion recovery. KEYWORDS: Air raic flow managemen, Recovery, Embarked aircrafs formaion, Sysem dynamics, Complex sysem modeling. INTRODUCTION Aircraf Carrier Aack (CVA), wih he abiliy of fas oversea power projecion, becomes he main comba force of modern navies. For a large number of aircrafs in he process of formaion recovery, secure, eicien and sequenial air raic flow managemens are necessary o make full use of he capaciy of airspace and fligh deck, improve he uilizaion of ime and space, and provide he laes informaion for he carrier-aircrafs sysem. The issue on civil air raic flow managemen has been well sudied by researchers boh a home and abroad. Taking he complexiy of he air raic managemen sysem (Zhang e al. 29) ino consideraion, researchers presened 3 approaches o solve he air raic flow managemen problem: air raic capaciy managemen (Yang and Hu 21), ground holding managemen (Ye and Hu 21) and fligh schedule opimizaion (Zhang and Hu 21). Meng e al. (212) sudied he problem of air raic flow managemen in uncerain severe convecive weaher and esablished a dynamic reroue planning model based on geneic algorihms. In iu and Hu (211), an aucion-based marke mehod was proposed o solve he congesion problem of airspace in he sage of pre-acic and acic air raic flow managemen, and a decision-making model for airline company was analyzed based on game heory. Bersimas e al. (28) used an ineger opimizaion mehod o research he air raic flow managemen while DeArmo e al. (21) sudied he preliminary benefis of he analysis of air raic flow managemen. Weigang e al. (28) sudied a decisionsuppor sysem of he acical air raic flow managemen. 1.Beijing Universiy of Aeronauics and Asronauics School of Aeronauic Science and Engineering Deparmen of Aircraf Design Beijing China. 2.Naval Aeronauical Universiy Deparmen of Airborne Vehicle Engineering Sa Room of Aircraf Yanai/Shandong China. 3.Naval Aeronauical Universiy Deparmen of Carrier-Based Engineering Aviaion Mainenance Teaching Group Huludao/iaoning China. Auhor for correspondence: Kuizhi Yue Naval Aeronauical Universiy Deparmen of Airborne Vehicle Engineering Sa Room of Aircraf 188 Erma Road Yanai/Shandong 2641 China yuekuizhi_2@sohu.com Received: Mar. 22, 216 Acceped: Mar. 14, 217

2 496 Cheng, Yue K, Huang Z A dynamic model for air raic flow managemen and a research abou he fligh deck scheduling based on disribued nework were presened in Mukherjee and Hansen (29) and Dasidar and Frazzoli (211), respecively. Ryan e al. (211) designed an ineracively local and global decision-suppor sysem for aircraf carrier deck scheduling. In Yue e al. (213a), he sock flowchar and he mahemaical model of he complex ime-varying sysem for dynamic handling of embarked aircrafs were buil based on sysem dynamics (SD) afer discussion of he process of aircraf urnaround and ransferring of embarked aircrafs among he fligh deck, hangar and elevaors. In Yue e al. (213b), o make a reasonable schedule of recovery considering wave-o and boler of aircrafs, an operaion model on embarked aircraf recovery in good weaher was buil. Wesonga (215) presened a pracical sochasic opimizaion model for air raic flow managemen (ATFM) of airpors, considering he airpor delay based on mulivariae saisics. The uncerainy of eecive measures in ATFM was esimaed wih mulivariae probabilisic collocaion mehod (PCM) in Zhou e al. (214). The issue of deermining he sochasic capaciy of airspace in ATFM was discussed in Clarke e al. (213). The heaing eec of je blas from 4 embarked aircrafs on ake-o zone of he fligh deck was sudied in Yue e al. (215a) based on CFD echnique and, similarly, he impac of he je blas on he je blas deflecor (JBD) was discussed based on CFD heory in Yue e al. (215b). Neverheless, researches on he sysem modeling problems of ATFM model, like muliple feedback facors, ime delay and complex ime-varying, are no suicien. In addiion, he sudy on he dierences of ATFM beween he aircraf carrier and civil airpor brough by dieren environmens and plaforms is also inadequae. For example, due o he high risk of nigh recovery of embarked aircrafs, an accurae recovery schedule is necessary o ensure he securiy. However, if boler or wave-o happens due o landing misses, he ime schedule of recovery will be disruped, recovery will be delayed, reducion of eiciency will be consequen, and he recovery securiy will be even harmed. In order o solve he exising problems in he previous models, a sysem dynamic mehod is applied in his sudy o build an ATFM model of embarked aircraf nigh recovery. I is expeced ha i provides a viable soluion o solve such ATFM problems. PREDICTION MODE Sysem dynamics is an inegraed science of sysems heory and compuer simulaion focusing on he sysem feedbacks and acions (Yue e al. 211). I is inroduced ino various fields, such as economic, miliary, and ecological o solve he problems of complex non-linear gian sysems wih feedback srucures (Wolsenholme 23; Thompson and Tebbens 27). The predicion model based on sysem dynamics heory has 4 pars: he analysis of nigh recovery process of embarked aircraf formaion, he sysem boundaries deerminaion and basic assumpions, sock flow diagram analysis and equaion seups. Nigh Recovery Process of Embarked Aircraf Formaion Analysis Nigh recovery of embarked aircraf is quie dieren from ha in he dayime, because his operaes under he Case I weaher condiion while nigh recovery is conduced under he Case III one. The process of nigh recovery of embarked aircraf formaion includes he arrival, approach, final approach, deck landing, boler or wave-o phases (Figs. 1 and 2). Wave-o means he maneuver of nose-up for climbing of he embarked aircraf before ouching he deck. I happens generally in adverse meeorological condiions of landing, inappropriae manipulaing of he pilo, excessive deck moion ec. Boler happens if he ail hook of he aircraf bouncing above he arresor cable when ouching he deck or he aircraf misses all he cables on he arresing area when landing. In his case, he aircraf mus be powered up immediaely o climb for safey. h/m 2, 1, E D C B R [km] Figure 1. Fligh cross-secional view of he nigh recovery of embarked aircraf formaion. A

3 A Predicion Model for Nigh Recovery of Embarked Aircrafs Based on SD km Boler or wave-o phase Deck landing phase 2 km Final approach phase 24 km 38 km Approach phase 4 km Arrival phase Sock Flow Diagram Analysis The sock flow diagram is buil o disinguish he variables, clarify he logical relaionships among he various elemens, feedback forms and conrol laws of he sysem. I is a represenaion mehod wih inuiive symbols for furher research on he sysem. The sock flow diagram of he predicion sysem is a srucural descripion of he arrival holding paern, approach and final approach, landing roue, wave-o, boler, arresing gear area, deck landing area and emporary spos. I holds much more informaion han wrien saemens can do and is clearer and more accurae in logic. The diagram consiss of 9 sae variables, 11 rae variables and 23 auxiliary variables (Fig. 3). Figure 2. Verical view of nigh recovery paerns for embarked aircrafs. The Deerminaion of Sysem Boundaries and Basic Assumpions The sysem boundaries of he predicion model depend primarily on he scope and span of he variables and ime, being deermined according o he sae variables. The subjec of his paper is he number of embarked aircrafs a each phase of he nigh recovery. Only he relaed eniies are concerned, including he number of embarked aircrafs a he menioned phases (A arrival; B approach; C final approach; D deck landing; E boler or wave-o; Fig. 1), deck arresor gear area, fligh deck landing area and emporary spos. The connecions of he eniies form he enire sysem discussed here. Various uncerainies exis in he nigh recovery process during over-sea operaions. The primary concerns of his research include key facors such as spinning of he embarked aircrafs, arge acquisiion wih landing direcor radar and opical landing aid sysem, wave-o, boler, ouching he deck, arresing, and axiing. The following assumpions are presened o simplify he predicion sysem: The nigh recovery sysem of embarked aircrafs is coninuous over ime. The remaining fuel of aircrafs is suicien for landing, waving-o and boler. Fligh accidens are excluded from he model. Equaion Esablishmen The operaion of he predicion sysem has he characerisics of complex ime-varying. Figure 3 presens he explanaions of he sysem, which can improve he undersanding of Eqs. 1 o 24. d = cdd djj = c dd ld dzhjj = ld + + yqr d = gx( ) cj d = d = cj zl y dy = y yqr dl = zl hx dlsj = hx( ) gx (1) (2) (3) (4) (5) (6) (7) (8) (9)

4 498 Cheng, Yue K, Huang Z where: is he number of embarked aircrafs in arrival holding paern; represens ime, in min; is he flow rae of arriving embarked aircrafs; cdd is he flow of embarked aircrafs deparing from he spin holding paern; jj is he number of aircrafs in approach phase; ld is he flow rae of embarked aircrafs capured by landing direcor radar; zhjj is he number of embarked aircrafs in final approach; is he flow rae of embarked aircrafs from wave-o o final approach; yqr is he flow rae of aircrafs from boler o final approach; gx is he flow rae of embarked aircrafs capured by opical landing aid sysem; is he number of embarked aircrafs deck in landing paern; is he flow rae of embarked aircrafs waving o; cj is he flow rae of embarked aircrafs ouching he fligh deck; is he number of embarked aircrafs waving o; is he number of embarked aircrafs in he arresing gear area; Time in which a wave-o occurs Time from wave-o o final approach Flow rae of embarked aircrafs from wave-o o final approach Number of embarked aircrafs waving-o Flow rae of embarked aircrafs waving-o Disance a approach phase Disance a final approach phase Final approaching speed of embarked aircrafs Approaching speed Time of radar capure Capure ime Number of aircrafs a approach phase Number of embarked aircrafs in arrival holding paern Flow rae of embarked aircrafs capured by landing direcor radar Flow of embarked aircrafs deparing from he spin holding paern Delay ime Arrival speed Disance a arrival phase Expeced number of embarked aircrafs in each bach Flow rae of aircrafs from boler o final approach Number of embarked aircrafs a final approach Time from boler o final approach Arrival ime Number of embarked aircrafs boling Flow rae of embarked aircrafs capured by opical landing aid sysem anding speed Flow rae of embarked aircrafs boling Time of boler Probabiliy of boler Arresed ime Disance of he landing paern Time from landing o ouching he fligh deck Number of embarked aircrafs deck in landing paern Number of embarked aircrafs in he arresing gear area Flow rae of embarked aircrafs arresed Probabiliy of wave-o Flow rae of embarked aircrafs ouching he fligh deck Number of embarked aircrafs in deck landing area Flow rae of arriving embarked aircrafs Number of recovering embarked aircrafs Flow rae of embarked aircrafs axing on deck Time of axiing for each aircraf Number of embarked aircrafs on emporary aircraf spos Figure 3. Sock flow diagram of he predicion sysem for he nigh recovery of embarked aircrafs.

5 A Predicion Model for Nigh Recovery of Embarked Aircrafs Based on SD 499 zl is he flow rae of embarked aircrafs arresed; y is he flow rae of embarked aircrafs boling; y is he number of embarked aircrafs boling; l is he number of embarked aircrafs in deck landing area; hx is he flow rae of embarked aircrafs axing on deck; lsj is he number of embarked aircrafs on emporary aircraf spos. ( ) = mhs PUSE(,1) cdd PUSE ( l yc = v + ld = ηgd cdd, ld, l ld = v jj jj yc, n db ) < (1) (11) (12) (13) (14) where: m hs is he number of recovering embarked aircrafs; is he arrival ime, in min; PUSE(,1) is he single impulse funcion wih a sar poin and a lengh of 1; yc is he delay ime, in min; n db is he expeced number of embarked aircrafs in each bach; l is he disance in arrival phase, in m; v is he arrival speed, in m/min; η gd (.,.,. ) is he pipeline delay funcion; ld is he ime of radar capure, in min; l jj is he disance in approach phase, in m; v jj is he approaching speed, in m/min; bh is he capure ime, in min; l zhjj is he disance in final approach phase, in m; v zhjj is he final approaching speed of embarked aircrafs, in m/min; is he ime from wave-o o final approach, in min; yqr is he ime from boler o final approach, in min; is he probabiliy of wave-o; xh is he ime when a wave-o occurs, in min; xhcj is he ime from landing o ouching he fligh deck, in min; l is he disance of he landing paern, in m; v is he landing speed, in m/ min; λ y is he probabiliy of boler; y is he ime of boler, in min; zl is he arresed ime, in min; hx is he ime of axiing for each aircraf, in min. gx = η gd ld + + yqr, bh, l bh = v zhjj zhjj = η gd,, ( )) = η (( ), ), yqr ( gd y yqr ( ) cj( ),, λ / xh (1 λ )/ xhcj < < (15) (16) (17) (18) (19) (2) SIMUATION CASES AND ANAYSIS The model according o Eqs were simulaed in Vensim Personal earning Ediion 5.9. In his secion, he model of nigh recovery is simulaed based on he Russian aircraf carrier Kuznesov. The iniial values of he facors of he predicion sysem are: ) =, jj ) =, zhjj ) =, ) =, ) =, ) =, l ) =, lsj ) =, m hs = 8, = 1 min, n db = 8, l = 6 km, v = 8 km/h, l jj = 25 km, v jj = 38 km/h, l zhjj = 9 km, v zhjj = 28 km/h, = 6 min, yqr = 6 min, λ =.2, xh = 1 s, l = 1 km, v = 24 km/h, λ y =.3, y = 3 s, zl = 3 s and hx = 3 s. The conrol parameer = ~ 9 min. = xhcj l v y zl ( ) = / hx l λ / y y (1 λ ) / hx y zl < < (21) (22) (23) (24) Wave-O or Boler The mahemaical model of nigh recovery is a nonlinear ime-varying complex gian sysem wih delays and feedback loops. The probabiliy of wave-o and boler is relaively high in nigh recovery. The simulaion resuls of he number of aircrafs a each sage of he nigh recovery for an 8-aircraf formaion wih λ =.2 and λ y =.3 are shown in Fig. 4. In Figs. 4 and 5, he abscissa represens he ime poins of he embarked aircrafs in he recovery process and he verical axis represens he quaniy of embarked aircrafs.

6 5 Cheng, Yue K, Huang Z Figure 4a shows he quaniy of embarked aircrafs during nigh recovery a he arrival, approach, final approach and landing paern phases. A he arrival phase, embarked aircrafs are assumed o ener when = 1 min and i is compleed when = 11 min; when = 14.5 min, embarked aircrafs in he 8-aircraf formaion begin o wihdraw from spin holding paern in urn, and he phase is finished when = 22.5 min. The arrival phase has a range of 6 km for he spin holding paern, and he wihdrawing rae of aircrafs can be conrolled a 1 aircraf per min. When = 14.5 min, he formaion of embarked aircrafs eners he approach phase in urn. For he relaively small range abou 25 km for he approach sage, a maximum of 4 aircrafs can be held in his phase. When = 18.4 min, aircrafs will be capured by landing direcor radar and hen ener he final approach phase. The whole approach phase will be finished a = 26.4 min. The saus a his phase becomes complex he maximum number of aircrafs can reach 2, bu for he aircrafs re-enering from wave-o or boler, he quaniy can be divided ino 7 levels. The number reduces below.1 from = 59.4 min. The quaniy of embarked aircrafs a he landing paern phase is also complex he phase begins a = 2.4 min and, for he disance of landing paern, i is abou 1 km; he aircrafs only spend.25 min a a speed of 24 km/h in he paern. Then he maximum number of aircrafs is.25 per min. The quaniy of aircrafs of his phase also has 7 levels for he same reason of wave-o and boler. The number of aircrafs reduces below.1 per min from = 61.1 min. Figure 4b shows he quaniy of embarked aircrafs a each phase of he nigh recovery operaions. The case of wave-o and boler makes he saus complex and divides he quaniy of embarked aircrafs ino 7 levels. Embarked aircrafs ener he emporary spos when = 21 min; when = 45.1 min, he quaniy of embarked aircrafs enering ino he deck emporary spos is 7 and, when = 64 min, ha number reaches 7.8, which means ha 97.5% of embarked aircrafs are recovered in probabiliy. (a) jj zhjj (b) y l lsj [min] [min] Figure 4. The quaniy of embarked aircrafs a each phase in he case of wave-o or boler. (a) Embarked aircrafs in ouch before he fligh deck; (b) Embarked aircrafs afer ouching he fligh deck. (a) 8 (b) jj zhjj 6 4 y l lsj [min] [min] Figure 5. The quaniy of embarked aircrafs a each sage wihou wave-o or boler. (a) Embarked aircrafs before ouching he fligh deck; (b) Embarked aircrafs afer ouching he fligh deck.

7 A Predicion Model for Nigh Recovery of Embarked Aircrafs Based on SD 51 Wihou Wave-O and Boler The simulaion resuls in he case wihou wave-o and boler, which means λ = and λ y = are shown in Fig. 5. I can be derived ha, for an 8-aircraf formaion, 12.5 min are spen a he arrival phase, 12 min a he approach phase, and he ime spen a he final approach, landing paern, arresor gear area, landing area and emporary spos are 9.875; 8; 8; 8 and 1 min, respecively. The simulaion resuls in boh cases have a high reliabiliy according o he capaciy of ATFM of he Kuznesov carrier during nigh recovery of embarked aircraf formaion. CONCUSIONS The predicion model of nigh recovery of embarked aircraf formaion can provide receivable simulaion resuls for air raic forecasing in he case of boler and wave-o o ensure ha he flow of aircrafs a each phase of recovery is in accordance wih he capaciy of ATFM. The implemen of air raic schedule and fligh plan can benefi from he simulaion resuls so ha delays, holding ime and oher bolenecks of he recovery process will be minimized. The resuls can provide he heoreical and echnical basis for he developmen and implemenaion of ATFM of embarked aircrafs recovery. The following resuls were achieved hrough he research: A sensible predicion model for nigh recovery of embarked aircraf formaion can be esablished based on he mehod of sysem dynamics. The characerisics of muliple feedbacks, delays, complex ime varying, non-lineariy and dynamics of he recovery sysem are well refleced in he model. The simulaion resuls correspond o he case of fligh es of embarked aircrafs. ACKNOWEDGEMENTS The auhors hank he Naional Naural Science Foundaion of China. AUTHOR S CONTRIBUTION Concepualizaion, Yue K and Cheng ; Mehodology, Yue K, Cheng, and Huang Z; Invesigaion, Cheng and Huang Z; Wriing Original Draf, Yue K and Huang Z; Wriing Review & Ediing, Cheng and Yue K; Funding Acquisiion, Yue K; Resources, Cheng and Huang Z; Supervision, Yue K. REFERENCES Bersimas D, Guglielmo, Odoni A (28) The air raic flow managemen problem: an ineger opimizaion approach. Proceedings of 13h Inernaional Conference; Berinoro, Ialy. Clarke JPB, Solak S, Ren, Vela AE (213) Deermining sochasic airspace capaciy for air raic flow managemen. Transpor Sci 47(4): doi: /rsc Dasidar RG, Frazzoli E (211) A queueing nework based approach o disribued aircraf carrier deck scheduling. AIAA Proceedings of he Infoech@Aerospace; S. ouis; USA. DeArmo J, Wanke C, Greenbaum D (21) Probabilisic ATFM: preliminary benefis analysis of an incremenal soluion approach; [accessed 217 Jan. 16]. hp:// iu FQ, Hu MH (211) Aucioning mehod for airspace congesing resource allocaion and game equilibrium analysis. Transacions of Nanjing Universiy of Aeronauics and Asronauics 31(3): Meng H, Xu XH, i SM (212) Dynamic reroue planning under uncerain severe convecive weaher. Journal of Souhwes Jiaoong Universiy 47(4): Mukherjee A, Hansen M (29) A dynamic rerouing model for air raic flow managemen. Transporaion Research Par B: Mehodological 43(1): doi: 1.116/j.rb Ryan JC, Cummings M, Roy N, Banerjee A (211) Designing an ineracive local and global decision suppor sysem for aircraf carrier deck scheduling. AIAA Proceedings of he Infoech@Aerospace; S. ouis; USA. Thompson KM, Tebbens RJD (27) Eradicaion versus conrol for poliomyeliis: an economic analysis. ance 369(957): doi: 1.116/S (7) Weigang, Souza BB, Crespo AMF (28) Decision suppor sysem in acical air raic flow managemen for air raic flow conrollers. J Air Transpor Manag 14(6): doi: 1.116/j. jairraman Wesonga R (215) Airpor uiliy sochasic opimizaion models for air raic flow managemen. Eur J Oper Res 242(3): doi: 1.116/j.ejor Wolsenholme EF (23) Towards he definiion and use of a core se of archeypal srucures in sysem dynamics. Sys Dynam Rev 19(1):7-26. doi: 1.12/sdr.259.

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