Physics-based Learning for Aircraft Dynamics Simulation

Transcription

1 Physics-based Leaning fo Aicaf Dynaics Siulaion Yang Yu 1, Houpu Yao, and Yonging Liu 3 1 School fo Engineeing of Mae, Tanspo & Enegy, Aizona Sae Univesiy, Tepe, AZ, 8581, USA yang.yu@asu.edu School fo Engineeing of Mae, Tanspo & Enegy, Aizona Sae Univesiy, Tepe, AZ, 8581, USA houpu.yao@asu.edu 3 School fo Engineeing of Mae, Tanspo & Enegy, Aizona Sae Univesiy, Tepe, AZ, 8581, USA yonging.liu@asu.edu ABSTRACT The accuae pedicion of fligh ajecoies is cucial fo he eal-ie pognosics of ai anspoaion syse. Howeve, he copuaion coss of pedicions can be expensive o even pohibiive especially fo a lage nube of aicafs in he ai affic syse. This sudy poposes he concep of physics-based leaning, a hybid appoach based on daa-diven leaning and physical odels, as a copuaionally efficien ehod fo he siulaion of aicaf dynaics. The physics-based leaning inegaes he undelying physics of dynaical syses ino leaning odels such as neual newoks o educe he aining and siulaion coss. The applicaion of physics-based leaning fo siulaing aicaf dynaics is deonsaed using a ecenly inoduced physics-awae newok known as he deep esidual ecuen neual newok (DR-RNN) on a Boeing aicaf. The aicaf dynaics ae descibed using a six degees-of-feedo aicaf odel. The DR-RNN is fis ained using he siulaed esponses of he aicaf and hen he ained newok is used o pedic he esponse of aicaf unde abiay conol inpus and disubances. The esuls show ha he DR-RNN can accuaely pedic aicaf esponses and has excellen exapolaion capabiliies. Moeove, he DR-RNN exhibis supeio copuaion efficiency copaed wih a classical nueical ehod, he fouh-ode Runge-kua ehod, highlighing is suiabiliy in seving as suogaing odels fo aicaf dynaical syses. safey. The aicaf dynaical syse is govened by he equaions of oion of he aicaf ha can be solved using nueical ehods. Howeve, he copuaion coss of hese opeaions can be expensive o even pohibiive especially fo a lage nube of aicafs in he ai affic syse. Theefoe, a copuaionally efficien ehod is needed fo he siulaion of aicaf dynaical syses. Recuen neual newok (RNN) is a class of aificial neual newoks whee unis ae conneced o fo a dieced gaph. RNNs have achieved gea success in any diffeen aeas such as language odeling, speech ecogniion, and ie seies pedicion (Hinon e al., 01; Gaves, 013). The geneal RNN achiecue is illusaed in Figue 1. RNN uses is inenal saes (s -1 shown in Figue 1) as eoies o lean he ie dependencies and hus i is capable o odel he evoluion of dynaical syses. One of he advanages of RNNs is ha he weighs of he newok ae shaed acoss all ie seps. Theefoe, he sae opeaions ae pefoed a each sep wih diffeen inpus, which significanly educes he nube of paaees duing aining. n he pas, hee have been applicaions on using RNNs as suogae odels o siulae dynaical syses (Tischle & D Eleueio, 016). Neveheless, a ajo challenge of using RNNs o siulae dynaical syses is he high aining coss. This is because he leaning using os RNNs is puely daa-diven, which usually equies significan aoun of aining daa and a lage nube of aining paaees. 1. NTRODUCTON The pedicion of aicaf ajecoies hough he siulaion of aicaf dynaical syses povides ipoan infoaion fo he isk assessen of ai anspoaion Yang Yu e al. This is an open-access aicle disibued unde he es of he Ceaive Coons Aibuion 3.0 Unied Saes License, which peis unesiced use, disibuion, and epoducion in any ediu, povided he oiginal auho and souce ae cedied. Figue 1. llusaion of he RNN achiecue (Biz, 015) 1

2 ANNUAL CONFERENCE OF THE PROGNOSTCS AND HEALTH MANAGEMENT SOCETY 018 n his sudy, he concep of physics-based leaning is poposed. Physics-based leaning is a hybid appoach ha uilizes boh he daa-diven leaning and he undelying physics of dynaical syses o achieve oe efficien leaning and pedicion. Specifically, he undelying physics of he dynaical syse is inegaed ino he leaning odels such as RNNs o povide addiional consains fo he leaning and pedicion of dynaical syse behavios. By doing so, he physics-based leaning ehod is able o gealy educe he aining coss associaed wih puely daadiven ehods. The ained odel can seve as suogae odels fo aicaf dynaical syses and hus educe he high copuaion coss of diecly solving he syse. Fuheoe, he inegaion of he physics will enhance he exapolaion pefoances of he leaning odel. This is consideed as a desiable feaue since he long-e esponses of dynaical syses unde abiay inpus ae ofen of inees. Recenly, a physics-awae RNN achiecue known as he deep esidual RNN (DR-RNN) was inoduced (Kani & Elsheikh, 017). The DR-RNN foulaes an ieaive schee o iniize he esidual funcion ha is copued using he undelying physics of he dynaical syse. n his sudy, he DR-RNN will be adoped o handle leaning of aicaf dynaics. The objecive of his sudy is o inoduce he physics-based leaning fo he siulaion of aicaf dynaics. The aicaf dynaical syse is epesened as a six degees of feedo (DOFs) odel. The deivaion of he equaions of oion of he aicaf is pesened. Then, he sandad RNN achiecue is biefly eview, which leads o he inoducion of he DR-RNN as a fo of physics-based leaning. To deonsae he applicaion, he DR-RNN is ained o lean he dynaical behavio of a lage anspo aicaf, he Boeing 747. The ained newok is used o pedic he esponses of he aicaf unde abiay conol and disubances, and he copuaion efficiency of he DR- RNN fo siulaing aicaf dynaics is analyzed.. PHYSCS-BASED LEARNNG.1. Sandad Recuen Neual Newoks The sandad RNN achiecue can be wien as (Goodfellow e al., 016): whee h anh Wh Ux b (1) 1 o Vh c () x is he inpu a ie insan ; h is he inenal sae a ie insan ; o is he oupu a ie insan ; b and c ae he biases of he RNN; W, U, and V ae he weigh paaees of he RNN. can be seen ha he cuen inenal sae is copued using he cuen inpu and he inenal sae a he pevious ie sep which seves as he eoy of he RNN. The paaees of RNN, i.e., θ W,U,V,b,c, ae esiaed by iniizing he loss funcion. Fo ie seies pedicion, he loss funcion can be wien as: whee S N T 1 ped ue L( θ) y y (3) TSN s 1 n 1 y and ped y ae he pediced and ue ue esponses of he dynaical syse a ie insan, especively; T is he nube of ie seps; N is he nube of feaues (nube of saes of he dynaical syse); S is he nube of aining saples. Duing aining, he values of RNN paaees ae updaed using back-popagaion hough ie (Webos, 1990). Howeve, i was found ha he sandad RNN achiecue ofen has difficulies in leaning long-e dependencies due o he vanishing o exploding gadien poble (Pascanu e al., 013). To addess his poble, gaed RNN achiecues such as long sho-e eoy (Hocheie and Schidhube, 1997) and gaed ecuen uni (Cho e al., 014) wee inoduced... Deep Residual Recuen Neual Newoks Fo dynaical syses, he physics is efleced in hei govening equaions whose geneal fo can be wien as: dy f(, ) d y (4) whee y is he sae of he dynaical syse. Tadiionally, Eq. (4) can be solved eihe analyically o nueically o obain he esponse of he dynaical syse. Fo exaple, he sae a ie insan +1 can be obained using he iplici Eule ehod as: y y h f ( 1, y ) (5) 1 1 whee h is he ie sep size. Fo Eq. (5), a esidual funcion can be foulaed as: y y h f ( 1, y ) (6) The DR-RNN achiecue is designed o ieaively iniize he esidual funcion given in Eq. (6) by sacking K newok layes (Kani & Elsheikh, 017): y y W anh( U ), fo k = 1 ( k ) ( k 1) ( k ) y y G ( k ) ( k 1) k ( k ) k, fo k > 1 ( k) whee k is he laye nube; 1 is he esidual a ie insan +1 in he kh laye; he opeao denoes eleenwise uliplicaion; W, U, and ae he weigh paaees of he DR-RNN; is a sall nube o avoid division by zeo; and G is he exponenially decaying squaed no of k he esidual calculaed as: G k 1 k1 (7) G (8)

3 ANNUAL CONFERENCE OF THE PROGNOSTCS AND HEALTH MANAGEMENT SOCETY 018 whee and ae he facion facos and hei values ae ofen se as 0.1 and 0.9, especively (Tielean & Hinon, 01). n his sudy, he DR-RNN is ipleened in Tensoflow TM and he Ada opiize (Kinga and Ba, 014) is adoped o iniize he loss funcion given in Eq. (3). n his case, y ped and y ue ae hee-diensional ensos wih he shape of [N, M, H] whee N is he bach size; M is he nube of ie seps; and H is he nube of saes of he dynaical syse. n addiion, i can be seen fo Eq. (7) ha he DR-RNN is explici in ie wih a consan copuaional cos a each ie sep. 3. ARCRAFT DYNAMCS 3.1. Six DOFs Aicaf Model n aicaf dynaics, he aicaf is usually assued as a igid body and a six DOFs aicaf odel shown in Figue can be adoped o siulae he aicaf behavio. Choosing he sabiliy axes as he body axes, he equaions of oion of he aicaf can be wien as: X ( u qw v) Y ( v u pw) (9) Z ( w pv qu) L p q( ) pq xx xz zz xz M q p( ) p xx zz xz N p p( ) q zz xz xx xz (10) 1 sin an cos an p 0 cos sin q (11) 0 sin sec cos sec xe u y e T v (1) z e w whee (X, Y, Z) ae he axial, side, and noal foces applied o he aicaf, especively; (L,M,N) ae he olling, piching, and yawing oens applied o he aicaf, especively; (u,v,w) ae he linea velociies in he x, y, z diecions, especively; (p,q,) ae he oll, pich and yaw aes of he aicaf, especively;,, ae he oll, pich and yaw angles of he aicaf, especively; (x e, y e, z e ) ae he noh, eas posiions and he negaive aliude of he aicaf wih espec o he eah, especively; xx, and, zz ae he oens of ineial abou (x, y, z) axes, especively; xz is he poduc of ineial; and [T] is he ansfoaion aix given as: cos cos sin sin cos cos sin cos sin cos sin sin cos sin sin sin sin cos cos cos sin sin sin cos sin sin cos cos cos 3.. Sall-disubance Theoy Eqs. (9) and (10) can be lineaized unde sall peubaions o he an equilibiu fligh condiion (Ekin and Reid 1996). n his sudy, he efeence (equilibiu) fligh condiion is assued o be in longiudinal i wih no angula velociy, i.e., v0 p0 q The sabiliy axes ae seleced so ha lif and dag ae aligned wih he Z and X Figue. Six DOFs aicaf odel (Pee, 010) axes, i.e., w0 0. A efeence fligh condiion, he aicaf is assued o have velociy u0 and pich angle. Applying 0 he above condiions and ignoing high-ode es in Eqs. (9) and (10), he longiudinal and laeal oions of he aicaf can be decoupled and lineaized equaions of oion can be epesened in sae space fos as: 1) Fo longiudinal oion: 3

4 Xu Xw 0 g cos( 0) u Zu Z Z w q u0 sin( 0) u w Zw Zw Zw Z w w q q 1 M 1 1 M w( Zq u0) wz u M wz w M wg sin( 0) M u M w M q Zw Zw Zw ( Zw) X X e h Z Z e h e Zw Zw h M M e wz M M e h wz h ( Zw) ( Zw) 0 0 ) Fo laeal oion: Y Y v p Y Y Y a ( u0) gcos( 0) 0 v v L Lv p L p xznv xzn p xzn 0 0 p L L a x x xzn a xzn x x x a N N v p N xzlv xzlp xzl 0 0 N N a z z xzl a xzl z z z 0 1 an( 0) sec( 0) / and x xx zz xz zz / z xx zz xz xx / xz xz xx zz xz whee e, h, a, and ae he elevao deflecion, hus, aileon deflecion, and udde deflecion of he aicaf, especively. n Eqs. (13) and (14), he noaion of foce o oen wih a subscip of he aicaf sae o conol inpu denoes he aeodynaic sabiliy o conol deivaive. Fo exaple, X denoes he deivaive of he u aeodynaic foce in he x diecion wih espec o he linea velociy u of he aicaf. The coplee sae and conol vecos of he aicaf ae expessed as: x u w q v p (15) T e h a δ (16) T 4. DEMONSTRATON 4.1. Aicaf Daa (13) (14) The applicaion of physics-based leaning fo siulaing aicaf dynaics is deonsaed hee using a lage anspo aicaf, he Boeing (Figue 3). n his sudy, he efeence fligh condiion is se as seady level fligh a 1,19 (40,000 f) and Mach 0.8. The aicaf popeies and aeodynaic deivaives of he Boeing a he efeence fligh condiion ae given in Table 1, Table and Table 3. Figue 3. Boeing (Wikipedia, 018) 4

5 ANNUAL CONFERENCE OF THE PROGNOSTCS AND HEALTH MANAGEMENT SOCETY 018 Table 1. Boeing daa a efeence fligh condiion (Ekin and Reid, 1996). Noe: W is he weigh of he aicaf; S is he wing aea; b is he wing span; c is he sandad ean chod of he wing; u is he efeence fligh velociy; is he ai densiy. 0 Table. Longiudinal sabiliy and conol deivaives of Boeing a efeence fligh condiion (Ekin and Reid, 1996). Noe: is a diensionless nube beween 0 and 1. h Table 3. Laeal sabiliy and conol deivaives of Boeing a efeence fligh condiion (Ekin and Reid, 1996). he aining conol inpu is given as a one degee elevao sep funcion and fo he laeal oion, he aining conol inpu is given as one degee udde sep funcion. Fo boh longiudinal and laeal oions, ando iniial disubances following a unifo disibuion fo o 0.05 ae used when geneaing he aining daa. Five hunded saples of aining daa fo he duaion of 10 seconds wee geneaed and used o ain he DR-RNN. should be noed ha since he longiudinal and laeal oions of he aicaf ae decoupled, wo DR-RNNs ae used o lean he longiudinal and laeal dynaics of he aicaf, especively. The aining sep sizes fo longiudinal and laeal oions ae 0.1 s and 0.05 s, especively. The aining was ipleened in Tensoflow which calculaes he gadiens sybolically based on he copuaion gaph. Also, i is noed ha fo he aining of neual newoks, lage diffeences of feaue scales could cause aining difficulies (Ba e al., 016). Theefoe, he linea velociies of he aicaf ae noalized wih espec o he efeence fligh velociy befoe he aining and he sae veco of he aicaf becoes: u x q p (17) u0 whee u / u0 is he noalized velociy in he x diecion; an w/ u is he angle of aack; and 0 0 an v/ u is he sideslip angle. Duing aining, he aining daa is divided ino baches wih a bach size of 16 and i was found ha using a wo-laye DR-RNN can each sufficien accuacy. The loss funcion fo longiudinal and laeal oions conveged o aound 5.5e-8 and.e-5 afe 0 inues of aining on GPU device Nvidia Gefoe GTX Figue 4 shows he convegence of he loss funcion fo he laeal oion of aicaf. T 4.. DR-RNN Taining Wih he aicaf daa given in he pevious secion, he equaions of oion can be solved o obain he aicaf esponses. n his sudy, he aining daa is obained by solving Eqs. (13) and (14) given ando iniial disubances and specified conol inpus. Fo he longiudinal oion, Figue 4. Convegence of loss funcion fo he laeal oion (one bach fo each ieaion) 5

6 ANNUAL CONFERENCE OF THE PROGNOSTCS AND HEALTH MANAGEMENT SOCETY Pedicion using Tained DR-RNN The ained DR-RNNs ae adoped o pedic he esponses of aicaf unde abiay disubances and conol inpus. Fo deonsaion puposes, a oal of five pedicion cases ae consideed in his sudy and he descipion of hese cases is given in Table 4: (1) Cases 1 and involve only Case nube niial disubance o saes Table 4. Descipion of cases consideed fo pedicion. Conol inpus conol inpu and disubance o he longiudinal oion of he aicaf; () Cases 3 and 4 involve only conol inpu and disubance o he laeal oion of he aicaf; (3) Case 5 involves conol inpus o boh longiudinal and laeal oions. The pedicion duaion is chosen o eflec he oscillaions of aicaf esponses befoe he syse eaches he seady sae. Elevao Thus Aileon Rudde Pedicion duaion Case 1 =0.15 ad/s N.A. N.A. N.A. N.A. 800 s Case N.A. N.A. 1/6 sep inpu N.A. N.A. 800 s Case 3 =0.1 ad/s N.A. N.A. N.A. N.A. 00 s Case 4 N.A. N.A. N.A. Case 5 N.A. 1 degee 5-sec double inpu 1/4 50-sec inpu 1 degee -sec ipulse inpu 1 degee -sec double inpu N.A. 1 degee -sec ipulse inpu 00 s 800 s Figue 5 shows he pediced esponses of he aicaf fo Cases and 3. can be obseved ha he pediced esponses ached vey well wih he ue esponses. Table 5 gives he pedicion eos calculaed using Eq. (3) fo all pedicion cases. The sall eo values sugges ha he DR-RNN is able o accuaely pedic he esponse of aicaf unde diffeen conol inpus and disubances. Fuheoe, he pedicion esuls indicae ha he DR- RNN has exapolaion capabiliies since: (1) he pedicion duaion is uch lage han he aining daa duaion of 10 s; () he conol inpus given fo he pedicion ae diffeen fo hose given duing aining. The good exapolaion pefoances of he DR-RNN ae aibued o he inegaion of he undelying physics of he dynaical syse ino he leaning odel. Table 5. Pedicion eos of consideed cases. Case nube Pedicion eo Case e-7 Case 3.17e-7 Case 3 1.4e-4 Case e-5 Case 5.63e-4 (a) (b) Figue 5. Tue and pediced esponses of he aicaf using ained DR-RNNs fo: (a) Case ; (b) Case 3. 6

7 Fo bee visualizaion, he pediced fligh ajecoy of Cases 5 is calculaed using Eq. (1) and ploed in Figue 6. The accuacy of pedicion is confied by he good ach beween he siulaed and ue fligh ajecoies. n addiion, in ode o es he aining obusness of he DR- RNN, he aining was conduced wih he Gaussian whie noise added o he aining daa whee he signal o noise aio of he aining daa is se as 50. Figue 7 shows he copaison beween he pediced longiudinal esponses and aining daa using he ained newok. can be seen ha while hee exiss soe eos in he pediced esponses, he DR-RNN is sill able o pedic he geneal end of he esponses wih sufficien accuacy. (c) Figue 6. Tue and siulaed fligh ajecoies using ained DR-RNNs fo Case 5: (a) Noh locaion; (b) Eas locaion; (c) Aliude (a) (b) Figue 7. Pedicion esuls using newok ained wih noisy daa 4.4. Copuaion Efficiency Copuaion efficiency is a ciical index o evaluae he pefoances of suogae odels. n his sudy, he copuaion efficiency of he DR-RNN is copaed wih ha of a classical nueical ehod, he fouh-ode Runge-kua (RK) ehod. Fo boh ehods, he esponses ae obained using wo diffeen ie sep sizes of 0.05 s and 0.1 s. Figue 8 plos he esponses of he sideslip angle of he aicaf obained using he DR-RNN and he RK ehod fo Case 4 along wih he ue esponse. can be seen ha fo boh sep sizes, he DR-RNN is able o accuaely pedic he ie hisoy of he sideslip angle. Howeve, he esponses obained using he RK ehod showed uch lage eos han hose pediced using he DR-RNN. This is caused by he nueical insabiliy of he RK ehod. n fac, Figue 8 shows ha he esponse obained using he 7

8 ANNUAL CONFERENCE OF THE PROGNOSTCS AND HEALTH MANAGEMENT SOCETY 018 RK ehod ends o gadually convege o he ue esponse wih salle sep sizes. Neveheless, fo explici ehod, a vey sall ie sep size is soeies needed in ode o achieve nueical sabiliy. n pacice, a sall sep size would consideably educe he copuaion efficiency. Fo his pespecive, he DR-RNN can efficienly educe he siulaion coss since i is able o use ie scales lage han hose equied fo nueical sabiliy. (b) Figue 8. Tie hisoies of sideslip angle fo diffeen ie sep sizes obained using he DR-RNN and he RK ehod: (a) sep size = 0.1 s; (b) sep size = 0.05 s n ode o bee deonsae he copuaion efficiency of he DR-RNN, one hunded siulaions of Case 4 wih ando iniial disubances o he aicaf saes wee conduced on a achine wih nel i CPU and 16 GB of RAM using boh he DR-RNN and he RK ehod. Table 6 liss he copuaion ie fo boh ehods as well as he aveage pedicion eo. The sep size of he RK ehod is chosen such ha is pedicion eo is copaable wih ha of he DR-RNN. Fo Table 5, i can be seen ha he pedicion using he DR-RNN is abou 80 ies fase han (a) ha of he RK ehod wih a sep size of 0.00 s and abou 30 ies fase han ha of he RK ehod wih a sep size of s. Also, i can be seen ha he DR-RNN has he leas pedicion eo aong he hee cases. Theefoe, he DR-RNN is consideed o be suiable fo he suogae odeling of aicaf dynaical syses fo is supeio copuaion efficiency. Table 6. Copaison of copuaion ie and accuacy beween he DR-RNN and he RK ehod. DR-RNN (sep size = 0.1 s) RK (sep size = 0.00 s) RK (sep size = s) Copuaion ie (s) Aveage pedicion eo.60e e-4 5.7e-4 5. CONCLUSONS n his sudy, he concep of physics-based leaning is poposed and inoduced o siulae aicaf dynaics. A physics-awae RNN known as he deep esidual RNN (DR- RNN) is adoped o lean he aicaf dynaical behavio. The ained DR-RNN was used o pefo pedicions of aicaf esponses unde abiay conol inpus and sae disubances. The pedicion esuls show ha he DR-RNN has excellen exapolaion capabiliies in ha: (1) i can accuaely pedic esponses of uch longe duaion han ha of he aining daa; () i can accuaely pedic esponses unde conol inpus and disubances diffeen fo hose given duing aining. The excellen exapolaion capabiliies of DR-RNN ae aibued o he inegaion of he undelying physics of dynaical syses ino he leaning odel. Also, i was discoveed ha he DR-RNN is obus in aining since i is able o lean he aicaf dynaical behavio using aining daa conainaed wih noise. Fuheoe, he DR-RNN deonsaes supeio copuaion efficiency copaed wih a classical nueical ehod, he fouh-ode Runge-kua (RK) ehod. The ain eason is ha he DR-RNN is able o pedic he aicaf esponses using elaively lage ie scales ha violae he nueical sabiliy condiions. Also, since he DR-RNN is explici in ie, he copuaional cos a each ie sep is fixed. Theefoe, he DR-RNN is consideed o be suiable fo he suogae odeling of dynaical syses. n addiion, since he gadien infoaion can be explicily obained hough he aining pocess, physicsbased leaning can be poenially applied fo syse idenificaions of dynaical syses, which will be invesigaed in fuue sudies fo he diagnosics and pognosics of dynaical syses. should be noed ha in his sudy, he leaned odel is a lineaized odel of he non-linea diffeenial equaions, ade a an iniial cuise condiion. Fuue sudy will focus 8

9 ANNUAL CONFERENCE OF THE PROGNOSTCS AND HEALTH MANAGEMENT SOCETY 018 on siulaing he enie fligh envelop by using seveal leaned odels coesponding o diffeen sages of he fligh. n addiion, he pefoances beween adiional RNNs (wihou physics) and DR-RNN will be copaed in he fuue wok. ACKNOWLEDGEMENT The eseach epoed in his pape was suppoed by funds fo NASA Univesiy Leadeship niiaive poga (Conac No. NNX17AJ86A, P: Yonging Liu, Pojec Office: Kai Goebel). The suppo is gaefully acknowledged. REFERENCES Ba, J.L., Kios, J.R., & Hinon, G.E. (016). Laye Noalizaion. axiv pepin, axiv: [sa.ml]. Biz, D. (015) Recuen Neual Newoks Tuoial, Pa 1: noducion o RNNs. hp:// Cho, K., van Meienboe, B., Gulcehe, C., e al. (014). Leaning Phase Repesenaions using RNN Encode- Decode fo Saisical Machine Tanslaion. axiv pepin, axiv: [cs.cl]. Ekin, B, & Reid, L. (1996) Dynaics of Fligh Sabiliy and Conol. Hoboken, NJ: John Wiley and Sons, nc. Goodfellow,, Bengio, Y, and Couville, A. (016). Deep Leaning. Cabidge, MA: MT Pess. Gaves, A. (013) Geneaing sequences wih ecuen neual newoks. axiv pepin, axiv: Hinon, G., Deng, L., Yu, D., e al. (01). Deep neual newoks fo acousic odeling in speech ecogniion: The shaed views of fou eseach goups. EEE Signal Pocessing Magazine, vol. 9(6), pp Hocheie, S. & Schidhube, J. (1997). Long sho-e eoy. Neual copuaion, vol. 9(8), pp Kani, J.N., & Elsheikh, Ahed. (017). DR-RNN: A deep esidual ecuen neual newok fo odel educion. axiv pepin, axiv: Kinga D.P. & Ba, J. (014) Ada: A Mehod fo Sochasic Opiizaion, 3d nenaional Confeence fo Leaning Repesenaions, May 7-9, 015, San Diego, CA. Pascanu, R., Mikolov, T., & Bengio, Y. (013). On he difficuly of aining ecuen neual newoks. Poceedings of he 30h nenaional Confeence on nenaional Confeence on Machine Leaning, vol. 8, pp Pee, M.M. (010). Lecue 9: 6-DOF Equaions of Moion. MAE441: Spacecaf and Aicaf Dynaics. Tielean, T., & Hinon, G. (01). Lecue 6.5-spop: Divide he gadien by a unning aveage of is ecen agniude. COURSERA: Neual Newoks fo Machine Leaning, 4(). Tischle, & A.P., D Eleueio, G. (016). Synhesis of ecuen neual newoks fo dynaical syse siulaion. Neual Newoks, vol.80, pp Webos, P.J. (1990). Backpopagaion hough ie: wha i does and how o do i. Poceedings of he EEE, vol. 78(10), pp Wikepedia. (018, 05 10). Boeing 747. Reieved fo WKEPEDA: The Fee Encyclopedia: hps://en.wikipedia.og/wiki/boeing_747 BOGRAPHES Yang Yu is a posdocoal eseach associae in he School fo Engineeing of Mae, Tanspo & Enegy a Aizona Sae Univesiy. He eceived his Ph.D. in Civil Engineeing in 017 fo Louisiana Sae Univesiy and his Bachelo s degee in Civil Engineeing in 014 fo Hunan Univesiy, China. His eseach ineess include applicaions of achine leaning, sucual healh onioing, sucual safey and eliabiliy, and sucual dynaics. Houpu Yao is cuenly a Ph.D. candidae in Aeospace Engineeing a Aizona Sae Univesiy, Tepe, Aizona. He eceived his bachelo degee fo Nohwesen Polyechnical Univesiy, Xi'an, Shanxi, in 013. His pevious eseach ineess include sucual dynaics, copuaional echanics and acousics, bounday eleen ehods and fas ulipole ehods, paallel copuaion, deep leaning and copue vision. His cuen eseach inees is in bidging he gap beween deep leaning and copuaional echanics, designing neual newoks o solve vaious physics pobles. Yonging Liu is a pofesso in he School fo Engineeing of Mae, Tanspo & Enegy a Aizona Sae Univesiy. He copleed his PhD a Vandebil Univesiy in 006, and obained his Bachelos and Mases degees fo Tongji Univesiy in China in 1999 and 00, especively. His eseach ineess include pobabilisic ehods, diagnosics and pognosics, isk anageen, aeials and sucues. He has published ove 100 jounal aicles in he geneal aea of pognosics and healh anageen. He has seved on any echnical coiees in AAA, ASME, and ASCE. He is an associae fellow of AAA. 9