Available online at ScienceDirect. Procedia Computer Science 103 (2017 ) 67 74

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1 Available olie a ScieceDirec Procedia Compuer Sciece 03 ( XIIh Ieraioal Symposium «Iellige Sysems» INELS Ocober 06 Moscow Russia Real-ime aerodyamic parameer ideificaio for he purpose of aircraf iellige echical sae moiorig O.N. Korsu a * M.H. Om b K.Z. La b A.. Sulovsii a a Sae Isiue of Aviaio Sysems Moscow 7 icoreo Sree 539 Russia b Moscow Aviaio Isiue (Naioal Research Uiversiy Moscow 7 oloolams Road 5993 Russia Absrac he repor deals wih he problem of desig he ew geeraio of aircraf echical sae moiorig sysems usig mehods of arificial iellec. he ey poi i he iellecual suppor is he heory of sysem ideificaio applied o he problem of aerodyamic parameer esimaio from he fligh daa. he repor cosiders he specific aspecs of he parameer ideificaio problem as a par of real-ime iellige moiorig sysem. he aircraf model wih he objec oise ad he ideificaio algorihm wih esimaio of ideificaio accuracy are formulaed. he preseed algorihms are esed hrough processig he daa geeraed usig a moder aircraf simulaio faciliy. 07 he Auhors. Published by by Elsevier Elsevier B.. B.. his is a ope access aricle uder he CC BY-NC-ND licese (hp://creaivecommos.org/liceses/by-c-d/4.0/. Peer-review uder resposibiliy of he scieific commiee of he XIIh Ieraioal Symposium «Iellige Sysems». Peer-review uder resposibiliy of he scieific commiee of he XIIh Ieraioal Symposium Iellige Sysems Keywords: echical sae; sysem ideificaio; aerodyamic parameer esimaio. Ideificaio of aerodyamic coefficies ca be a effecive mehod of esimaig he echical sae of he aircraf. I his paper he aircraf moveme model is formulaed which icludes also he amospheric urbulece fligh parameer sesors ad he aircraf corol sysem. he ideificaio of he aircraf aerodyamic parameers usig he coiuous-discree exeded Kalma filer is also discussed. For he simulaio of amospheric urbulece i is recommeded o use for example he Dryde model accordig o which he specral desiy of he urbule wid i he verical logiudial ad laeral direcios is give by: *Correspodig auhor address: marmoo@rambler.ru he Auhors. Published by Elsevier B.. his is a ope access aricle uder he CC BY-NC-ND licese (hp://creaivecommos.org/liceses/by-c-d/4.0/. Peer-review uder resposibiliy of he scieific commiee of he XIIh Ieraioal Symposium Iellige Sysems doi:0.06/j.procs

2 68 O.N. Korsu e al. / Procedia Compuer Sciece 03 ( L 3 L S ( L L S ( U U U L ( L 3 L S ( L where - aircraf velociy m/s; - agular frequecy /s; U - sd. deviaios of wid gus velociies m/s; L LU L - urbulece scales m; he urbulece scales a he fligh aliude H 55m L L L 55m. A aliude H 55m 3 L H L L 435 H I addiio we have he relaio: U U U ( L L L U o esimae he ifluece of urbulece o he closed-loop coour he models of aircraf moveme ad aircraf corol sysem mus be coupled wih he Dryde urbulece model. I his case he liearized model is accepable for example i he viciiy of a sraigh ad horizoal fligh. Le us cosider he logiudial moio of he aircraf equipped wih he fly-by-wire sysem i urbulece. he simplified model of he fly-by-wire sysem ca be approximaed by elemes providig feedbac sigals of overload ad agular velociy. he appropriae rasfer fucios are as follows K Т p ( p ( p K p p. I his case he deviaio of sabilizer is give by: B( P( ( ( (3

3 O.N. Korsu e al. / Procedia Compuer Sciece 03 ( here P ( - deviaios due o he acios of he pilo. Afer rasformig he rasfer fucios io he model i he sae space we obai: K ( ( ( ' y K e( e( z ( ( e( K z ( Equaios which form filer for he verical compoe of urbule guss of wid are he followig u( u ( u ( u ( u ( ( Le us combie he above equaios wih he model of shor-period logiudial moio give i deviaios relaive o seady moio. For accouig he dyamic compoes of measureme errors le us addiioally iroduce models of he agular velociy ad overload sesors as a secod order differeial equaio. he sesor models are also used as formig filers for measureme oises. As a resul we obai he followig sysem of equaios. qs qs ( z( cy ( u( u( cy B( m 3 m z ' a qsb A qsba mz qsba ba z( mz a( u( u( mz B ( z ( Jz 3 Jz Jz u( u ( u ( u ( u ( ( ( z изм ( 0 z изм 0 ( a ( a ( a ( ( (4 ( ( y изм ( a ( a ( a ( ( 0 y изм 0 y K ( ( ( ' yизм K e( e( z изм ( z where - aircraf velociy m/s; q - dyamic pressure Pa; m - mass g; S - equivale wig surface m ; b A - mea aerodyamic chord m;

4 70 O.N. Korsu e al. / Procedia Compuer Sciece 03 ( J z - mome of ieria / L g m ; M - urbulece spaial frequecy /s; ( ( e( - supplemeary variables; a a 0 sesors - dampig coefficies of sesors; ( ( - sesor oupu sigals; z изм y изм a a - parameers of he agular velociy ad overload 0 ( ( ( - ormal radom processes of he whie oise ype wih zero meas ad iesiies. S 3 S a a S a a 0 0 where - sd. deviaio velociy of he verical compoe urbulece m/s; - sd. deviaio of radom errors of he agular velociy sesor (/s ad of he overload sesor (overload uis; ( - he deviaio of he ormal overload relaive o seady-sae pah defied by he formula y qs qs y( cy ( u( u( cy B(. m 3 g m g I he differeial equaios sysem (4 he sabilizer deviaios are calculaed hrough he formula (3 which feed-bac compoe ( has he form: ( e( K z изм ( I equaio (4 i is also assumed ha he agle of aac caused by he ifluece of urbulece is give by he expressio: ( ( where ( u( u( - velociy of verical guss of urbule wid m/s. 3 I is assumed ha he correcio of sysemaic measureme errors of agle of aac is carried ou accordig o he mehod [45]. Simulaio of sochasic sysems (4 are carried ou as follows. his sysem is a case of he followig sysems: y( f( y( a u( ( he performig he simulaio i s ecessary o solve he followig equaios a each discreizaio ierval dy( f ( y( a u(

5 O.N. Korsu e al. / Procedia Compuer Sciece 03 ( df ( A( F ( where df ( y( a( u( A( (5 dy( d ( A( ( ( A( S (. Marix S ( of he iesiies of objec oise for he sysem (4 has he form S( S diag( a0a 0 a0a 00 Afer calculaig he predicio esimae of he sae vecor y ( ad he correlaio marix of he equivale discree oise ( he value of sae vecor is calculaed accordig o he formula y ( y ( G (6 where - idepede sequece of -dimesioal ormal vecors wih zero mea ad ui correlaio marix N(0 E G - riagular marix correspodig o equaio ( G G (7 For ideificaio algorihm he coiuous-discree exeded Kalma filer is chose because i aes io accou he objec oise. Model of objec ca be formulaed as; y( f( y( a u( ( (8 a 0 I s obvious ha i equaio (8 he assumpio of cosacy of he ideificaio parameers is iroduced. Discree model of he observaios is give by he equaio: z ( h( y ( a u ( ( (9 i i i i Prior o ideificaio algorihm i is ecessary o se he iiial values of he geeralized sae vecor x ( 0 y( 0 a0 ad he correspodig correlaio marix ( 0. o fid he esimaes x ˆ( 0 he followig compuig operaios are performed a each discreizaio ierval 0 N deermiaio of predicio esimaes of he sae vecor ad parameers dy ( f ( y( ˆ a( u( a ( ˆ a ( (0 wih iiial codiio y ( y ˆ( ; he calculaio of he rasiio marix F( of dimesio ( p hrough he soluio of he equaio

6 7 O.N. Korsu e al. / Procedia Compuer Sciece 03 ( df ( A( F ( 0 ( A( ( wih iiial codiio F ( E( 0 ( p where f ( y( ˆ a( u( A ( ( y ( f ( y( ˆ a( u( A ( ( p deermiaio of he correlaio marix ( of a ˆ( equivale discree oise of objec by solvig he equaio d ( A( ( ( A( S ( ( wih iiial codiio ( 0( ; deermiaio of he predicio error correlaio marix P F F (3 where F( 0 F 0 E ( ( p ( p ( pp - filer gai calculaio: K P H H P H R ( (4 where H hx ( ( u ( x ( correlaio marix of he error of curre esimaes of he sae ad parameers - marix of observaios of dimesio r( p ; calculaio of he ( K H E P ( K H E K R K (5 deermiaio of he curre esimaio of he sae vecor ad he ideifiable parameers x ˆ( x ( K ( z ( hx ( ( u ( (6 he processig of he simulaio daa cofirmed he sabiliy of ideificaio algorihm especially i urbule codiios. Le us cosider he classical problem of parameric ideificaio - ideificaio of aerodyamic coefficies. Assume ha he laeral roll mome is defied by a liear model:

7 O.N. Korsu e al. / Procedia Compuer Sciece 03 ( L L x y FL Н mx mx mx x mx y mx FL mx Н here - slip agle x y- agular velociies - Differeial deflecio of flaperos FL Н - Deflecio of he rudder. o obai esimaes of he parameers Kalma filer which has bee discussed above muliple liear regressio maximum lielihood mehod [4] or frequecy domai maximum lielihood mehod [6] ca be used. Sice he objec is geerally a o-saioary he ideificaio should be performed o a slidig ierval. e ivesigae he relaio of he accuracy of esimaes ad he legh of he ierval. he esimaes correcess ca be checed by comparig hem wih he correspodig values obaied by he processig he aircraf wid uel aerodyamic characerisics. I his case we assume ha he mach of he esimaes obaied from wo differe sources shows heir correcess. Le us examie relaio bewee he aerodyamic coefficies esimaes ad legh of he slidig ierval accordig o he fligh experime dmx mx(d(ba (mxd*d s Fig.. Relaio of ime pahs of he roll mome esimaes due o deflecio of he rudder obaied a 9 s slidig ierval (purple lie ad from he ba of aerodyamic characerisics (blue lie dmx mx(d(ba (mxd*d s Fig. Relaio of ime e pahs of he roll mome esimaes due o deflecio of he rudder obaied a 0 s slidig ierval (purple lie ad from he ba of aerodyamic characerisics (blue lie.

8 74 O.N. Korsu e al. / Procedia Compuer Sciece 03 ( dmx mx(d(ba (mxd*d s Fig. 3. Relaio of ime pahs of he roll mome esimaes due o deflecio of he rudder obaied a he ierval legh equal o he whole area (68 s (he purple lie ad from he ba of aerodyamic characerisics (blue lie. e ca see i Figures - 3 he legh of he seleced ierval has a sigifica effec i evaluaig he sigal. he he legh of he ierval 9 secods we ca see a good eough mach o sigal peas bu sigifica oises geeraed by he isabiliy of esimaes are oiceable. By icreasig he legh of he movig ierval o 0 secods sigifica oises are decreased ad he qualiy of he desired sigal is high eough. By icreasig he legh of he ierval o 68 secods (he eire area oises are almos compleely smoohed ou bu here are mismaches i he useful sigal. ha idicaes he presece of osaioariy. hus i is possible o choose he opimal legh of he ierval which esures low oise level ad good accouig of useadiess o he reaed area. I his example he opimal legh of he slidig ierval is 0 secods. Preseed example also shows a good mach of available ba of aerodyamic characerisics wih fligh daa. his wor was suppored by he Russia Foudaio for Basic Research (RFBR a projec. Refereces. Klei Morelli EA. Aircraf sysem ideificaio: heory ad pracice. Reso: America Isiue of Aeroauics ad Asroauics р.. Jaegaoar R. Fligh vehicle sysem ideificaio: A ime domai mehodology. Reso: America Isiue of Aeroauics ad Asroauics р. 3. Korsu ON. Poplavsy BK. Approaches for fligh ess aircraf parameer ideificaio. Proc. of he 9 Cogress of Ieraioal Coucil of he Aeroauical Sciecies. Sai Peersbourg. 04. Paper Korsu ON Poplavsii BK. Esimaio of sysemaic errors of oboard measureme of agle of aac ad slidig agle based o iegraio of daa of saellie avigaio sysem ad ideificaio of wid velociy. Joural of Compuer ad Sysems Scieces Ieraioal. 0. Т p Korsu ON Niolaev S Pushov SG. A algorihm for esimaig sysemaic measureme errors for air velociy agle of aac ad slidig agle i fligh esig. Joural of Compuer ad Sysems Scieces Ieraioal (3 pp Кorsu ON. A ideificaio algorihm for dyamic sysems wih a fucioal i he frequecy domai. Auomaio ad Remoe Corol (5 pp

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