Neural Networks Modelling for Aircraft Flight Guidance Dynamics

HAL Id: hal-01002817

https://hal-enac.archives-ouvertes.fr/hal-01002817

Submitted on 6 Jun 2014

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Neural Networks Modelling for Aircraft Flight Guidance

Dynamics

Wen-Chi Lu, Walid El-Moudani, Téo Cerqueira Revoredo, Felix Mora-Camino

To cite this version:

Wen-Chi Lu, Walid El-Moudani, Téo Cerqueira Revoredo, Felix Mora-Camino. Neural Networks Modelling for Aircraft Flight Guidance Dynamics. Journal of Aerospace Technology and Man-agement, Departamento de Ciência e Tecnologia Aeroespacial (DCTA), 2012, 4 (2), pp 169-174. �10.5028/jatm.v4i2.152�. �hal-01002817�

INTRODUCTION

The sustained increase of air transportation over the last GHFDGHVKDVOHGWRWUDI¿FVDWXUDWHGVLWXDWLRQV7RPDQDJH VDIHO\ DQG HI¿FLHQWO\ VXFK WUDI¿F QHZ PDQHXYHULQJ capabilities are needed on board civil aviation aircraft to SHUIRUPDGYDQFHG'WUDMHFWRULHVZKLOHSUHGLFWLYHWRROV JLYHQUHIHUHQFH'WUDMHFWRULHVDUHQHFHVVDU\WRHVWLPDWH DFFXUDWHO\WKHLULPSDFWVLQWHUPVRIEXUQHGIXHODQGQRLVH HPLVVLRQV%RWKREMHFWLYHVUHTXLUHWKHDELOLW\RISHUIRUP LQJDLUFUDIWÀLJKWG\QDPLFVLQYHUVLRQ'LIIHUHQWLDOÀDWQHVV a concept introduced by the school of Fontainebleau (Fliess et al  KDV SURYLGHG QHZ RSSRUWXQLWLHV WR GHVLJQ DGYDQFHG PDQDJHPHQW DQG VXSHUYLVLRQ VFKHPHV IRU QRQOLQHDU V\VWHPV $FFRUGLQJ WR WKLV WKHRU\ JLYHQ WKH GHVLUHG WUDMHFWRU\ IRU ZKDW LV FDOOHG D ÀDW RXWSXW LW EHFRPHVVWUDLJKWIRUZDUGWRGHULYHWKHFRUUHVSRQGLQJLQSXW 6RPH DXWKRUV KDYH DOUHDG\ JLYHQ VRPH LQVLJKW LQWR WKH

GLIIHUHQWLDO ÀDWQHVV RI DLUFUDIW ÀLJKW G\QDPLFV /DYLJQH

et al0DUWLQZKLOHRWKHUVKDYHFRQVLGHUHG

LWVSRWHQWLDODSSOLFDWLRQVWRDLUFUDIWWUDMHFWRU\PDQDJHPHQW /Xet al

 ,QWKLVFRPPXQLFDWLRQ¿UVWO\DVLPSOL¿HGSURRIRIWKH LPSOLFLW GLIIHUHQWLDO ÀDWQHVV RI ÀLJKW JXLGDQFH G\QDPLFV LV GLVSOD\HG 6HFRQGO\ D IHHGIRUZDUG QHXUDO QHWZRUN VWUXFWXUHLVGHYHORSHGWRLQYHUWWKHÀLJKWJXLGDQFHG\QDP LFV,VVXHVUHODWHGWRWKHHIIHFWLYHWUDLQLQJRIVXFKVWUXFWXUH DUHGLVFXVVHGDQGQXPHULFDOUHVXOWVUHODWHGWRDUHIHUHQFH DLUFUDIW PRGHO DUH GLVSOD\HG7KHVH UHVXOWV VKRZ WKDW WKH SURSRVHGDSSURDFKDOORZVWKHLGHQWL¿FDWLRQRIÀDWQHVVSURS HUW\RIÀLJKWJXLGDQFHG\QDPLFVUHVXOWLQJLQDQXPHULFDO WRROIRUQHZDLUFUDIWWUDMHFWRU\PDQDJHPHQWDSSOLFDWLRQV

DIFFERENTIAL FLATNESS OF NONLINEAR SYSTEMS

 7ZRGH¿QLWLRQVRIGLIIHUHQWLDOÀDWQHVVDUHLQWURGXFHGRQH UHODWHGWRV\VWHPVIRUZKLFKFDXVDOUHODWLRQVKLSVRILQWHUHVW DUHDQDO\WLFDOO\GLVSOD\HGDQGDQRWKHURQHZKHUHWKHVHFDXVDO

Neural Networks Modelling for Aircraft Flight Guidance

Dynamics

Wen-Chi Lu1_{, Walid El-Moudani}2_{, Téo Cerqueira Revoredo}3,*_{, Felix Mora-Camino}4

_{1DWLRQDO)RUPRVD8QLYHUVLW\<XQOLQ±7DLZDQ}

_{/HEDQHVH8QLYHUVLW\)DFXOW\RI%XVLQHVV7ULSROL±/HEDQRQ}

_{8QLYHUVLGDGHGR(VWDGRGR5LRGH-DQHLUR5LRGH-DQHLUR5-±%UD]LO} _{eFROH1DWLRQDOGHO¶$YLDWLRQ&LYLOH7RXORXVH±)UDQFH}

Abstract: The sustained increase of the air transportation sector over the last decades has led to traffic

satu-rated situations, inducing higher costs for airlines and important negative impacts for airport surrounding communities. The efficient management of air traffic supposes that aircraft trajectories are fully mastered and their impacts can be accurately forecasted. Inversion of aircraft f light dynamics, which are essentially nonlinear, appears necessary. Aircraft f light dynamics is shown to be differentially f lat, which is a property that has enabled the development of new numerical tools for the management of complex nonlinear dynamic systems. However, since in the case of aircraft f light dynamics this differential f latness property is implicit, a neural network is introduced to deal with its numerical inversion. Results related to the developed neural network training are displayed, while potential uses of the proposed tool are discussed.

Keywords:1HXUDOQHWZRUNV'LIIHUHQWLDOÀDWQHVV$LUFUDIWÀLJKWG\QDPLFV

5HFHLYHG $FFHSWHG DXWKRUIRUFRUUHVSRQGHQFHWHRUHYRUHGR#\DKRRFRPEU

'HSDUWPHQWR GH (OHWU{QLFD H 7HOHFRPXQLFDo}HV ± )DFXOGDGH GH (QJHQKDULD±8(5-±5XD6mR)UDQFLVFR;DYLHUQƒ

UHODWLRQVKLSV DUH LQWURGXFHG WKURXJK LPSOLFLW IXQFWLRQV$ JHQHUDOQRQOLQHDUV\VWHPZKRVHG\QDPLFVDUHJLYHQE\(T

 

ZKHUHFLVDVPRRWKPDSSLQJH[SOLFLWO\ÀDWZLWKUHVSHFWWRWKH output vector ZLIZ is an mthRUGHUYHFWRUZKLFKFDQEHH[SUHVVHG

DQDO\WLFDOO\DVDIXQFWLRQRIWKHFXUUHQWVWDWHWKHFXUUHQWLQSXWDQG its derivatives and also such as the state and the input vectors can EHDQDO\WLFDOO\H[SUHVVHGDVDIXQFWLRQRIZDQGLWVGHULYDWLYHV 7KHUHDUHVPRRWKPDSSLQJVGxGu and GzDVLQ(T , , , Z G X U U( ) z f p = ^ h_{ D} , , , X G Z Z Z( ) x f q = ` o j <sub>E</sub> , , , U G Z Z Z( ) U f q 1 = ` o + j  F ZKHUHp and qDUHLQWHJHUQXPEHUV9HFWRUZLVFDOOHGDÀDW RXWSXWIRUWKHQRQOLQHDUV\VWHP$OWKRXJKWKHUHLVQRV\VWHP DWLFDOZD\WRGHWHUPLQHWKHÀDWRXWSXWWKHFRPSRQHQWVRIWKH ÀDWRXWSXWXVXDOO\SRVVHVVVRPHSK\VLFDOPHDQLQJ  7KHH[SOLFLWÀDWQHVVSURSHUW\LVRISDUWLFXODULQWHUHVWIRUWKH VROXWLRQRIDPDQDJHPHQWSUREOHPZKHQDPHDQLQJIXOÀDWRXWSXW FDQEHUHODWHGWRLWVREMHFWLYHVIRULQVWDQFHLQPDQ\VLWXDWLRQV WKH PDQDJHPHQW SUREOHP FDQ EH IRUPXODWHG DV D ÀDWRXWSXW WUDMHFWRU\WUDFNLQJSUREOHP+RZHYHUIRUPDQ\V\VWHPVQR FRPSOHWHDQDO\WLFDOPRGHOVDUHDYDLODEOHWRGHVFULEHWKHLUIXOO G\QDPLFV6RPHRIWKHLUFRPSRQHQWVPDNHXVHRILQSXWRXWSXW QXPHULFDOWDEOHVGHULYHGERWKIURPWKHRU\DQGIURPH[SHULPHQWDO GDWD,QWKHVHFDVHVWKHDYDLODEOHWKHRU\SURYLGHVLQJHQHUDOWKH PDLQPDWKHPDWLFDOSURSHUWLHVRIWKHVHLPSOLFLWIXQFWLRQVZKLOH H[SHULPHQWDOGDWDDUHXVHGWREXLOGDFFXUDWHLQSXWRXWSXWQXPHUL FDOGHYLFHV7KLVKDSSHQVIRULQVWDQFHZKHQÀLJKWG\QDPLFV PRGHOLQJLVFRQVLGHUHGHLWKHUIRUFRQWURORUVLPXODWLRQSXUSRVHV VLQFH LQ SUDFWLFH WKH LQYROYHG DHURG\QDPLF FRHI¿FLHQWV DUH REWDLQHGWKURXJKLQWHUSRODWLRQDFURVVODUJHVHWVRIORRNXSWDEOHV  $QRQOLQHDUV\VWHPJLYHQE\DJHQHUDOLPSOLFLWnth _order GLIIHUHQWLDOUHSUHVHQWDWLRQ(T ( , , ) , , F X X Uo ₌0 X_!R Un _!Rm  

ZKHUH F LV D UHJXODU LPSOLFLW PDSSLQJ ZLWK UHVSHFW WR X ̙ ZKLFKLVVDLGLPSOLFLWO\ÀDWRYHUDQLQWHULRUQRQHPSW\GRPDLQ ¨ŽRn+m

LILWLVSRVVLEOHWR¿QGDQmth order vector ZWKDWPHHWV

FRQGLWLRQ(TVDQGDDQGFRQGLWLRQLQ(T/pYLQH

( , , , , , ) 0

G X U Z Zo _f Z( )r ₌

 

ZKHUHGLVORFDOO\LQYHUWLEOHRYHU¨ZLWKUHVSHFWWRX and U

rLVDQLQWHJHU$JDLQYHFWRUZLVVDLGWREHDÀDWRXWSXW7KH

local invertibility of GLVJXDUDQWHHGLIWKHGHWHUPLQDQWRIWKH -DFRELDQRIGLVQRW]HURDFFRUGLQJWRWKHWKHRUHPRILPSOLFLW IXQFWLRQVOLNHLQ(T/pYLQH ( / ( , ) det 2G 2 X U !0_{ }  ,QWKLVFDVHJLYHQDWUDMHFWRU\RIWKHÀDWRXWSXWZLWLV SRVVLEOHWRPDSLWQXPHULFDOO\LQWRWKHLQSXWVSDFHWRGHULYH FRUUHVSRQGLQJFRQWUROVLJQDOVVRWKDWRQHRIWKHPRUHLQWHUHVW LQJSURSHUWLHVRIGLIIHUHQWLDOO\ÀDWV\VWHPVLVVWLOOPDLQWDLQHG

FLIGHT GUIDANCE DYNAMICS AND DIFFEREN-TIAL FLATNESS

 ,QWKLVVWXG\RQO\WKHJXLGDQFHG\QDPLFVRIWUDQVSRU WDWLRQ DLUFUDIW LH WKH WHPSRUDO WUDMHFWRU\ IROORZHG E\ LWVFHQWHURIJUDYLW\LVFRQVLGHUHG,WLVDVVXPHGWKDWWKH DLUFUDIWLVHTXLSSHGZLWKDEDVLFDXJPHQWDWLRQV\VWHPDQG DXWRSLORWZKLFKGHDOHI¿FLHQWO\ZLWKLWVIDVWG\QDPLFVDQG FRQWUROVLWVDWWLWXGHDQJOHVșzȥZLWKUHVSHFWWRDORFDO (DUWKIUDPHDVZHOODVLWVWKUXVWUHJLPH1+HUHWKH ÀLJKWYDULDEOHVDQG1DUHWDNHQDVWKHLQSXWVIRUWKHJXLG DQFHG\QDPLFV)LJXUHGLVSOD\VWKHUHVXOWLQJVWUXFWXUHIRU WKHZKROHÀLJKWJXLGDQFHG\QDPLFV  7KXV LQ VWHDG\ ZLQG FRQGLWLRQV WKH ÀLJKW JXLGDQFH G\QDPLFV FDQ EH H[SUHVVHG LQ WKH DHURG\QDPLFV UHIHUHQFH IUDPHDV(T/Xet al cos cos xo =Va } c_{ D} sin cos yo=Va } c_{ E} sin zo= -Va c F /X:et al Flight guidance dynamics

ș

x

y

z

N

1

z

)LJXUH ,QSXWRXWSXWDLUFUDIWÀLJKWJXLGDQFHVWUXFWXUH

ZKHUHȖLVWKHJURXQGSDWKDQJOH7KHPRGXOXVRIWKHLQHUWLDO DQGWKHDHURG\QDPLFVSHHGVDUHJLYHQE\(T Va x y z 2 2 2 = o + o + o _{ D} ( ) ( ) Va x wx y wy z wz 2 2 2 = _^o- _h + o- + o-  E ZKHUHwxwy and wzDUHWKHZLQGFRPSRQHQWV

 $VVXPLQJWKDWWKHVLGHVOLSDQJOHȕLVYHU\VPDOODQGWKDWș and

zYDU\VORZO\WKHIROORZLQJHTXDWLRQVFDQEHZULWWHQDV(T

/ cos

cos sin sin cos cos

V D T m g a a a i a z i = - + - - + o _^ ^ h h D ( ) / ( ) ( / ) ( ) sin

sin sin cos cos cos

L T mV g V a a a c a a i a z i = + - + o  E ZKHUHȖaLVWKHDHURG\QDPLFSDWKDQJOHZKLFKLVUHODWHG to ȖE\(T sin sin Va c-wz=Va ca   ,QFRRUGLQDWHGWXUQPDQHXYHUWKHKHDGLQJUDWHLVUHODWHG WRWKHEDQNDQJOHWKURXJKWKHIROORZLQJUHODWLRQ(T ( / ) tang Va }o = z  

 7KHGUDJDQGWKHOLIWIRUFHVD and LDUHUHVSHFWLYHO\ FRQVLGHUHG WR EH IXQFWLRQV RI DOWLWXGH z DLUVSHHG Va DQG

DQJOHRIDWWDFNĮ:KLOHWKHWKUXVW7FDQEHFRQVLGHUHGIXQF WLRQRIDOWLWXGH]DLUVSHHGDQGHQJLQHUHJLPH1(T ( , , ) ( , , ) ( , , ) D D z V L L z V T T z V N a a a 1 a a = = =  

 )RU ORFDO JXLGDQFH SXUSRVHV WKH ÀLJKWSDWK DQJOH Ȗ is XVXDOO\WDNHQDVWKHFRQWUROSDUDPHWHU:KHQȕLVVPDOOșz

ȕ and ȖDUHUHODWHGE\(T

( )

sin sin cos cos_Vcos sin V W

a a z c= i a- z i a -  D ZKLFKLVUHGXFHGWR a=i-c _{ E} WKDWLVLQJHQHUDOWKHFDVHIRUDWUDQVSRUWDWLRQDLUFUDIW$ XQLTXHVROXWLRQLQĮ corresponds to values of ș and z

Once x(ty(tDQGz(tDUHNQRZQLWLVSRVVLEOHWRXVHWKHPDQG WKHLUGHULYDWLYHVWRH[SUHVVDOOWKHJXLGDQFHYDULDEOHVDVIROORZV  %\UHDUUDQJLQJWKHNLQHPDWLFDOHTXDWLRQV(TVDEDQG FLWLVSRVVLEOHWRH[SUHVV(TVDQG ( / ) sin 1 z Va c =- - _o   ( / ) tan 1 y x } = - _{o o}  

The state variables V_aȖ and ȥ can obviously be functions RILQHUWLDOSRVLWLRQRIWKHDLUFUDIWZKLOHWKHFRQWUROYDULDEOHV VDWLVI\WKHUHODWLRQVLQ(T

( ) /

( )

cos

cos sin sin cos cos

V D T m g 0 a a a i a z i - - + + - + = o  D ( ) / ( ) ( / ) ( ) sin

sin sin cos cos cos

L T mV g V 0 a a a c a a i a z i - + + + = o  E ( / ) tang Va 0 }o - z=  F

ZKHUHĮ and ȖaFDQEHH[SUHVVHGDVIXQFWLRQVRIzș and Ȗ

DFFRUGLQJWRWKHUHODWLRQVLQ(TVDQG  7KHIROORZLQJQRWDWLRQVDUHDGRSWHGIRUWKHSRVLWLRQRIWKH FHQWHURIJUDYLW\RIWKHDLUFUDIWDQGIRUWKHJXLGDQFHLQSXWV(T ( , , ) and ( , , ) Z x y z T U N 1 i z = = _{ }  2QFHWKHYDULDEOHVLQ(TDUHUHSODFHGZLWKWKHLUH[SUHV sions in ZDQGWKHLU¿UVWWZRGHULYDWLYHVWKHVHHTXDWLRQVFDQ EHUHZULWWHQDVLQ(T ( , , , , ) GN1 Z Z Z U W =0 o p _{ D} ( , , , , ) Gi Z Z Z U Wo p =0 E ( , , , , ) Gz Z Z Z U Wo p =0 F

 +HUH ZH VXSSRVH WKDW HLWKHU WKH ZLQG VSHHG YHFWRU LV H[DFWO\NQRZQRUQXOO6XEVHTXHQWO\WKHDUJXPHQWWZLOOEH GHOHWHGIURPWKHGiIXQFWLRQV7KHVHLPSOLFLWIXQFWLRQVDUH

ORFDOO\LQYHUWLEOHZLWKUHVSHFWWRWKHLQSXWYHFWRUVLQFHIRU QRUPDOÀLJKWFRQGLWLRQVWKHGHWHUPLQDQWRIWKHLU-DFRELDQLV QRW]HUR(T

G G G G G G N G N G N G N N N 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 i i i z z z i z i z i z  D  2QFHWKLVFRQGLWLRQLVHTXLYDOHQWWR . ( .sin .cos ) . , N T T D L 0 1 2 2 2 2 2 2 2 2 ! a a a a i a - +` + j  E ZKLFKLVVDWLV¿HGVLQFHLQJHQHUDODOORILWVWHUPVDUHGH¿QLWH SRVLWLYH  +HQFHZ=(x,y,tTLVDÀDWRXWSXWYHFWRUIRUWKHFRQVLGHUHG ÀLJKWJXLGDQFHG\QDPLFV7KHWLPHHYROXWLRQRIWKHVHÀDW RXWSXWVUHSUHVHQWVWKHWUDMHFWRU\IROORZHGE\WKHFHQWHURI JUDYLW\RIWKHDLUFUDIW7KHQDFFRUGLQJWRWKLVWKHRU\IURPWKH NQRZOHGJHRIWKLVWUDMHFWRU\LWVKRXOGEHSRVVLEOHWR¿QGWKH FRUUHVSRQGLQJLQSXWV

NEURAL NETWORK INVERSION OF THE FLIGHT GUIDANCE DYNAMICS  $VDFRQVHTXHQFHRIWKHÀDWQHVVSURSHUW\JLYHQDVPRRWK UHIHUHQFHWUDMHFWRU\IRUWKHÀDWRXWSXWVVXFKDV , ( ), ( ) , , , Z_c xc yc zc t t T 0 ! x = x x x x ^ h ^ ^ h h 6 @  

WKH FRUUHVSRQGLQJ UHIHUHQFH LQSXW YDOXHV DW WKH LQVWDQW t

U_c(t z_c(tș_c(tN_c(tTDUHWKHVROXWLRQV ( ( ), ( ), ( ), ( )) GN1 Z tc Z tc Z tc Uc t =0 o p  D ( ( (, ( ), ( ), ( )) Gi Z tc Z tc Z tc Uc t =0 o p  E ( ( ), ( ), ( ), ( )) Gz Z tc Z tc Z tc Uc t =0 o p  F  :KHUHZc(tZ ̙ c(tDQGZ ̙̙ c(tDUHWKHFXUUHQWSDUDPHWHUV  ,QJHQHUDOLWZLOOEHYHU\GLI¿FXOWWRREWDLQDQRQOLQHQXPHUL FDOVROXWLRQWRWKLVVHWRILPSOLFLWHTXDWLRQVVRLWLVXVHIXOWRJHW DQDGHTXDWHQXPHULFDOGHYLFHWRVROYHLW7KLVDGHTXDF\FDQEH VSHFL¿HGPDLQO\LQWHUPVRIFRPSOH[LW\DQGDFFXUDF\  7KHGLIIHUHQWLDOÀDWQHVVSURSHUW\RIDG\QDPLFDOV\VWHP SRLQWVRXWLQDUHYHUVHZD\WKHFDXVDOUHODWLRQEHWZHHQLWV LQSXWVDQGHYHQWXDOO\ÀDWRXWSXWV6LQFHQHXUDOQHWZRUNVDUH SDUWLFXODUO\ZHOODGDSWHGWRUHSURGXFHFDXVDOUHODWLRQVHYHQ LQWKHFDVHRIYHU\FRPSOH[V\VWHPVLWLVLQWHUHVWLQJWRWU\ EXLOGLQJDQHXUDOQHWZRUNZLWKWKLVREMHFWLYH2QFHFRUUHFWO\ WUDLQHGWKHQHXUDOQHWZRUNVKRXOGEHDQLQSXWRXWSXWGHYLFH ZKHUHWKHLQSXWVDUHSURYLGHGE\WKHUHIHUHQFHWUDMHFWRU\ZKLOH WKHRXWSXWVDUHWKHQRPLQDOÀLJKWFRQWUROSDUDPHWHUV)LJ  0XOWLOD\HUQHXUDOQHWZRUNV0/11KDYHEHHQVKRZQWR EHDEOHWRSHUIRUPJHQHUDOIXQFWLRQDSSUR[LPDWLRQWKURXJK WKHVHOHFWLRQRIDQHXUDOQHWZRUNVWUXFWXUHDVVRFLDWHGZLWK D OHDUQLQJ SURFHVV +D\NLQ  7KH VHOHFWLRQ RI WKH VWUXFWXUH DQG RI D OHDUQLQJ DOJRULWKP VWURQJO\ GHSHQGV RQ HPSLULFDOUXOHVZKLOHQXPHURXVFDQGLGDWHQHXUDOQHWZRUNV VWUXFWXUHVDQGOHDUQLQJDOJRULWKPVDUHDYDLODEOH,QRUGHUWR DFKLHYHDQDFFHSWDEOHDFFXUDF\DQGDVXI¿FLHQWJHQHUDOL]D WLRQFDSDELOLW\DODUJHDPRXQWRIWUDLQLQJGDWDLVQHFHVVDU\ +HUHLQWKHWUDLQLQJGDWDDUHFRPSRVHGRIVHWVRIWUDMHFWRULHV for Z and UZKLFKFDQEHSURYLGHGIURPHLWKHUÀLJKWWHVWGDWD RUHYHQIURPFRPPHUFLDOÀLJKWGDWDLQZKLFKPDQHXYHUVDUH SHUIRUPHGPDQXDOO\RUE\WKHDXWRSLORWHQJDJHGLQDEDVLF DWWLWXGHKROGLQJPRGHLQRUGHUWKDWQRJXLGDQFHORRSLVDFWLYH DWWKDWWLPH0RUD&DPLQR  6LQFHIRUPRGHUQDLUFUDIWRQERDUGQDYLJDWLRQV\VWHPVDUH DEOHWRHVWLPDWHZLWKJRRGDFFXUDF\WKHFXUUHQWDLUFUDIWSRVLWLRQ LQHUWLDOVSHHGDQGZLQGVSHHGWKHLUUHFRUGVFDQEHXVHGDVDEDVLV IRUWKHWUDLQLQJRIWKHQHXUDOQHWZRUN$VLPXODWLRQPRGHORID OLJKWDLUFUDIWWKH1DYLRQ6FKPLGWZLWKDSLVWRQSURSHOOHU HQJLQHDQGDEDVLFFRQWUROOHUIRUDWWLWXGHKROGLQJKDVEHHQXVHG IRU WKH JHQHUDWLRQ RI WUDLQLQJ GDWD DQG YDOLGDWLRQ SXUSRVHV 3UHOLPLQDU\VLPXODWLRQUHVXOWVKDYHEHHQREWDLQHGLQWKHFDVHRI PDQHXYHUVLQWKHYHUWLFDOSODQH,QWKLVVWXG\WKHFRQYHQWLRQDO (UURU%DFN3URSDJDWLRQQHXUDOQHWZRUNZLWKRQO\RQHKLGGHQ OD\HUKDVEHHQVHOHFWHGWRSHUIRUPWKHLQYHUVLRQRIÀLJKWJXLG DQFHG\QDPLFVDOWKRXJKPDQ\RWKHUQHXUDOQHWZRUNVWUXFWXUHV KDYHEHHQLQYHVWLJDWHG/X)LJXUHGLVSOD\VVRPHRIWKH WUDMHFWRULHVWKDWKDYHEHHQFRQVLGHUHGWRJHQHUDWHWUDLQLQJGDWD  7KHVWUXFWXUHRIWKHUHWDLQHGQHXUDOQHWZRUNFRPSULVHV VHYHQLQSXWVQRGHVDERXWQHXURQVLQWKHKLGGHQOD\HU ZLWK D K\SHUEROLF WDQJHQW DFWLYDWLRQ IXQFWLRQ DQG WKUHH RXWSXW QRGHV ZLWK OLQHDU WUDQVIHU IXQFWLRQV 7KH VHYHQ

(t)

(t)

(t)

Neural networks

ș

N

1c

z

)LJXUH 5HIHUHQFHLQSXWJHQHUDWRUE\QHXUDOQHWZRUNV /X:et al

LQSXWVDUHDOWLWXGHWKUHHFRPSRQHQWVRILQHUWLDOYHORFLW\ DQGWKUHHFRPSRQHQWVRILQHUWLDODFFHOHUDWLRQ7KHWKUHH outputs are the pitch șWKHUROOz and N_WKHHQJLQHUHJLPH )LJXUHVDQGGLVSOD\H[DPSOHVRIWUDLQLQJSHUIRUPDQFHV IRUGLIIHUHQWVWUXFWXUHVDQGVL]HVRIWKHWUDLQLQJGDWDEDVH  2QFH WKH ZHLJKWV RI D QHXUDO QHWZRUN KDYH EHHQ RSWLPL]HGWKHWUDLQLQJRIWKHQHXUDOQHWZRUNPXVWEHYDOL GDWHGXVLQJDQLQGHSHQGHQWYDOLGDWLRQGDWDEDVH7DEOH GLVSOD\V DQ H[DPSOH RI YDOLGDWLRQ GDWD SHUIRUPDQFHV ZKHUHL(ELVWKHWRWDOPHDQVTXDUHHUURURIWKHQHXUDO QHWZRUNIRUDJLYHQLQWHUQHXURQVZHLJKWLQJSDWWHUQDQG FRPSXWHGHLWKHURYHUWUDLQLQJGDWDRUYDOLGDWLRQGDWDS LVWKHQXPEHURIQHXURQVLQWKHKLGGHQOD\HUDQGn is the QXPEHURIHIIHFWLYHFRQQHFWLRQVEHWZHHQQHXURQV 7DEOH ([DPSOHRIWUDLQLQJDQGYDOLGDWLRQGDWD

S n L(E WUDLQLQJ L(E 9DOLGDWLRQ

  î _î   î _î   î _î   î _î   î _î  $UHOHYDQWYDOLGDWLRQRIWKHQHXUDOQHWZRUNLVREWDLQHG ZKHQLQQRPLQDOFRQGLWLRQVQRPLQDOÀLJKWPRGHOQRZLQG YDULDWLRQWKHRXWSXWVRIWKHQHXUDOQHWZRUNVDUHVXEPLWWHGDV UHIHUHQFHYDOXHVWRDQDXWRSLORWRSHUDWLQJLQEDVLFPRGHVDWWL WXGHDQJOHVDQGHQJLQHUHJLPHWUDFNLQJ)LJXUHGLVSOD\VWKH UHVXOWLQJUHIHUHQFHDQGUHVSRQVHWUDMHFWRULHVRIWKHVLPXODWHG DLUFUDIWDVZHOODVWKHWUDMHFWRU\HUURU )LJXUH $VHWRIWUDLQLQJWUDMHFWRULHV )LJXUH 7UDLQLQJSHUIRUPDQFHZLWKGLIIHUHQWQXPEHURIQHXURQV LQWKHKLGGHQOD\HU )LJXUH 7UDLQLQJSHUIRUPDQFHIRUGLIIHUHQWVL]HVRIWKHWUDLQLQJ GDWDEDVH

)LJXUH ([DPSOH RI RSHQORRS FRQWURO SHUIRUPDQFH IRU ÀLJKW WUDMHFWRULHV

CONCLUSIONS  7KLVSDSHUKDVVKRZQKRZQHXUDOQHWZRUNVFDQEHXVHG WRWDNHSUR¿WRIWKHLPSOLFLWGLIIHUHQWLDOÀDWQHVVSURSHUW\RI WKHDLUFUDIWÀLJKWJXLGDQFHG\QDPLFV'LIIHUHQWLDOÀDWQHVVLV DFKDUDFWHULVWLFVKDUHGE\PDQ\QRQOLQHDUV\VWHPVDQGLQ WKHFDVHRIFRPSOH[V\VWHPVWKLVSURSHUW\PD\DSSHDULQDQ LPSOLFLWZD\,QWKLVVWXG\WRPDNHWKLVSURSHUW\YDOXDEOHIRU DLUFUDIWWUDMHFWRU\PDQDJHPHQWDIHHGIRUZDUGQHXUDOQHWZRUN VWUXFWXUH KDV EHHQ SURSRVHG WR LQYHUW WKH ÀLJKW JXLGDQFH G\QDPLFV7KHSHUIRUPHGQXPHULFDOH[SHULPHQWVVKRZWKDW E\DGRSWLQJFODVVLFDOQHXUDOQHWZRUNVVWUXFWXUHVDQGOHDUQLQJ VFKHPHVLWLVSRVVLEOHWRDFKLHYHTXLWHHDVLO\WKLVREMHFWLYH 7KLVDSSURDFKDOORZVDQDGHTXDWHLGHQWL¿FDWLRQRIWKHLQYHUVH LQSXWRXWSXWUHODWLRQVDVVRFLDWHGZLWKWKHÀDWQHVVSURSHUW\RI ÀLJKWJXLGDQFHG\QDPLFV  7KLVDSSURDFKUHVXOWVLQDXVHIXOQXPHULFDOWRROIRUPDQ\ DSSOLFDWLRQV VXFK DV QHZ WUDMHFWRU\ WUDFNLQJ ÀLJKW FRQWURO VWUXFWXUHVDVGLVSOD\HGLQ)LJDQGQHZVRXQGH[SRVXUHOHYHO FRPSXWDWLRQVFKHPHVVXFKDVWKHRQHVGLVSOD\HGLQ)LJ  +RZHYHUPDQ\LVVXHVUHPDLQRSHQIRUIXUWKHUUHVHDUFKZRUNV ‡ GH¿QLWLRQRIDPLQLPXPVHWRIWUDMHFWRULHVIRUJHQHUDWLRQ

RIDGHTXDWHWUDLQLQJGDWD

‡ VHDUFK IRU PRUH HI¿FLHQW G\QDPLFV LQYHUVLRQ QHXUDO QHWZRUNVWUXFWXUHV

‡ VHWWLQJRIDFOHDUEDODQFHEHWZHHQWKHQHXUDOLQYHUVLRQ DFFXUDF\DQGWKHDPRXQWRIFRPSXWDWLRQIRUWUDLQLQJDQG ‡ JHQHUDWLRQRIHI¿FLHQWUHIHUHQFHWUDMHFWRULHV

REFERENCES

)OLHVV 0 et al  ³)ODWQHVV DQG GHIHFW RI QRQOLQHDU V\VWHPV WKHRU\ DQG H[DPSOHV´ ,QWHUQDWLRQDO -RXUQDO RI &RQWURO9RO1RSS +D\NLQ6³1HXUDO1HWZRUNVD&RPSUHKHQVLYH)RXQ GDWLRQ´0DFPLOODQ3XEOLVKLQJ&RPSDQ\1- /DYLJQH/et al³0RGHOLQJRI/RQJLWXGLQDO'LVWXUEHG $LUFUDIW0RGHOE\)ODWQHVV$SSURDFK´LQ$,$$*XLGDQFH1DYL JDWLRQDQG&RQWURO&RQIHUHQFHDQG([KLELW7H[DV$XVWLQ86$ /pYLQH-³2QQHFHVVDU\DQGVXI¿FLHQWFRQGLWLRQVIRU GLIIHUHQWLDO ÀDWQHVV´ $SSOLFDEOH $OJHEUD LQ (QJLQHHULQJ &RPPXQLFDWLRQDQG&RPSXWLQJ9RO1RSS /X:&³&RQWULEXWLRQDX6XLYL$XWRPDWLTXHGH7UDMHF WRLUHVSDUXQ$YLRQ&RPPDQGH3ODWHHW5pVHDX[GH1HXURQHV´ 3K'7KHVLVeFROH1DWLRQHOHGHO¶$YLDWLRQ&LYLOH)UDQFH /X :& et al  ³)OLJKW 0HFKDQLFV DQG 'LIIHUHQ WLDO )ODWQHVV´ LQ ',1&21  ,OKD 6ROWHLUD %UD]LO SS

/X :& et al  ³1HXUDO *XLGDQFH &RQWURO IRU $LFUDIW %DVHG RQ 'LIIHUHQWLDO )ODWQHVV´$,$$ -RXUQDO RI *XLGDQFH &RQWURO DQG '\QDPLFV 9RO  1R  SS

0DUWLQ 3  ³&RQWULEXWLRQ j O¶pWXGH GHV V\VWqPHV GLIIpUHQWLHOV SODWV´ 3K' 7KHVLV eFROH GHV 0LQHV GH 3DULV)UDQFH

0RUD&DPLQR)³$YLRQLTXH´OHFWXUHQRWHV(1$& 6FKPLGW /9  ³,QWURGXFWLRQ WR $LUFUDIW )OLJKW '\QDPLFV´$,$$(GXFDWLRQ6HULHV Neural network Trajectory generation Flight dynamics Auto pilot

Fast control feedback

ș

z

N

_1c

x

c

y

c

z

c

x y z

)LJXUH 7UDMHFWRU\WUDFNLQJLQFOXGLQJQHXUDOLQYHUVLRQ Neural inversion of flight mechanics Aircraft attitude and thrust Receiver position Sound exposure level computation Sound exposure level Aircraft trajectory and position )LJXUH 1RLVHH[SRVXUHOHYHOHVWLPDWLRQVFKHPH /X:et al