1、 l : 2001-06-21; : 2002-01-08 “:t b9 ?( 62. 2. 2. 1) “c: http: / / www. hkxb. hkxb/ 2002/ 04/ 0294/cI|: 1000-6893(2002) 04-0294-04 I MYET / MY#O1, 2,Z1, 1( 1. 2t bt?v , 2210016)( 2. 2t bt?v t, 2210016)MODAL PARAMETER EXTRACTION USING FREQUENCY DOMAINPOLY-REFERENCE METHOD UNDER OPERATIONAL CONDITION
2、SSHEN Fan1, ZHENG Min2, CHEN Huai-hai1, BAO Ming1( 1. Institute of Vibration Engineering Research,Nanjing University of Aeronautics andAstronautics,Nanjing 210016,China)( 2. College of Civatation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)K1: L= f ,V LYWM1f m,w aT / I
3、 MYE, Bf ZE kb1oM: MY;T ;M1f ; q ; ms |: V214.3+ 3DS M :AAbstract: It is difficult to measure the input forces of some operating structures. Only the operating responsedata can be used to identify modal parameters. A frequency domain poly-reference modal identificationmethod under operational condit
4、ions was presented on the basis of the cross-correlation function of measuredresponses to solve the only-output problem. T he proposed method in this paper was applied to an airplanemodel.Key words: modal identification; operational conditions; cross-correlation function; cross-power spectraldensity
5、; unknown excitation L=, af fV 3;t b?#QqT / +, 4 ;Btv, Z a B a ?v L, 4 E k,y1 Pt 31 Fv ,/ 8 , H ? / |Y , Y MYb “ -T / H MYZE, ITD/ h E 1aKvE 2a0 bW LC E 3aARMA 4, ZE , q E 5aKl Z wL EE 6b q E T / LYW q wL 9 ,Y1 p P ! Ll,7 O q aE D1 v H,ZE a bKl Z wL EEY dL5, p bVYWM1f m,w aT / I MYE, X q EKl Z wL EE
6、 bBf T kq,ZEr kb1 1. 1M1f ll f l(t)/,n 3Yynl( t)p 3Yyp l( t)WM1f R npl(T) = Eynl(t + T )ypl(t) ( 1): f l(t) l) ; R npl(T ) l /,np 3YWM1f; T HWW; EV U ; ynl(t) l /n 3Y; ypl(t) l 23 4 2002 M7t bACT A AERONAUTICA ET ASTRONAUT ICA SINICAVol.23 No. 4July 2002/p 3YbL ! |. 2 O4NM1, I n l,l= 1, 2,l, L,l p,
7、Vnp) LYWM1f 1Rnp(T ) = 2Nr= 17 nrQp reKrT ( 2): Rnp( T)np) LYWM1f ; N ; 7 nr r n ;Kr r+; Qp r B ,Qpr = 2Ns= 1 Ll= 1- Al7 lr7 p s7 lsaras(Kr + Ks) ( 3): L “; al, ar, as bTlNYP IYWM1f R(T ) =R11(T ) R12(T ) R1P(T )R21(T ) R22(T ) R2P(T ) RN1(T ) RN2(T ) RNP(T )( 4)* T( 2), VR(T ) = 7e+TQ ( 5): 77 nrFN
8、2N+_ ;+KrF2N2N+ ;QQprF2NP b1. 2 I MYE/ VZ(5)M1f VrT?,wT / I MYEb| T(5) HT fMG(s) = 7(sI - +) - 1Q ( 6):G(s)M1f R(T ) fM,I b| T(5)T pB VR (T ) = 7+e+TQ ( 7)| TM fG (s) = 7+(sI - +) - 1Q ( 8):Gc(s) Rc(T ) fMb| T(6) T( 8)FB Z,G(s)G (s) =77+ O(s) ( 9):O(s)= (sI- +) - 1Qb+ +_ ,BiB A 7 , P TA7 + 7+ = 0 (1
9、0) ,| TAI 77+ = 0 (11)Z HO(s) , VAI 77+ 0(s) = O (12)| T(9) TAIG(s)G (s)= 0 (13)T(13)9 V / TAG(s) + G (s) = 0 (14)6,G (s) = sG(s) - R(T )T = 0 (15)T = 0 H, T(5) VR(T )T = 0 = 7Q (16)yN, T(15) VG (s) = sG(s) - 7Q (17)| T(17) T( 14),AG( s) + sG(s) - 7Q= 0 (18)7s= jX, TMAG(jX) + jXG(jX) - 7Q= 0 (19)7AG
10、(jX) - 7Q= - jXG(jX) (20)W |K q,X1, X2,l, XK, * VKZAG(jXk) - 7Q= - jXkG(jXk), k = 1, 2,l, K(21)7D= G( jX1)G( jX2)lG(jXk), 8= - diagjX1IjX2IljXkI , * KZ VA- 7Q DI IlI = D8 (22)D8 L q # qXkf , X ,yN VYV p TA- 7Q = D8 DIIlJ+(23) A, A- 7 Q -N b , +V Ul Ib T( 10), A p+5 V“d+ +_ 7,2954 #O: I MYET / MYV7“d
11、 b“dr 7 r 7r _ ,r1 qXnrE D1NrsYXnr = Re(Kr) 2 + Im( Kr) 2, Nr = - Re(Kr)Xnr: Re( Kr) Kr L, Im(Kr) Krb2 k 4ZE M L V,Bf k, m1 Ubm1f Fig. 1The airplane model h,1000mm,tZ1100mmbYV3+ 7| + ,HP3562|? 3 3. 2 |, P HEV-20 t,f 24F . Y|,64YMVMAS-3 s“d “bn5 aE 18 ( 8 ), qE D1 V1 U, m2 UbNT I ,L I MYET1 bm2f - (
12、a)B ; ( b)= (P: aE,: MYE)Fig. 2The 1st and 2nd mode shapes of airplane model( left: Pure mode method; right: Frequency-domain method) H “,“ q|512Hzbt 1, 2T I, I MYE4 | kq qE D1,T V1 U, 9 ZE WMACb IMYE m2 UbVV1T V A,ZE9 MY “ ,170Hz173Hzbf kTV ,4T / I MYE ? z LY 4 | bV1 aE MYE f Table 1Modal parameter
13、s from two methods Q/Q aE MYE q/ HzE D1/ % q/ HzE D1/ %M AC/ %114. 8 5. 14 15. 3 4. 76 98. 22Q23. 6 0. 86 24. 2 0. 36 99. 13Q35. 1 4. 25 36. 2 4. 05 98. 6445. 0 1. 67 44. 9 2. 01 99. 25Q52. 5 3. 11 52. 4 3. 53 98. 4663. 4 1. 50 64. 7 1. 61 99. 07Q69. 2 1. 45 69. 6 1. 70 96. 7874. 8 6. 56 75. 3 5. 05
14、 83. 29Q91. 5 1. 02 92. 3 1. 35 92. 11098. 7 1. 36 97. 6 0. 92 98. 811Q107. 3 0. 93 107. 3 0. 96 89. 312Q112. 9 1. 58 111. 7 1. 05 90. 913143. 5 0. 70 143. 4 0. 82 96. 514151. 5 0. 39 150. 7 0. 54 98. 815Q158. 3 0. 48 158. 2 0. 39 99. 016170. 2 1. 05 170. 8 0. 88 97. 617Q173. 3 0. 54 173. 4 0. 52 82
15、. 518185. 5 0. 50 186. 2 0. 67 96. 83 4 sZE X q EKl Z wL EE ,M1/, /:(1) B I MYEb( 2) H LY , 8,yN B 98 MYEb(3) ? MY “ b( 4)YV p+5, V H“d b(5) pVe,i O9 lb(6)L| L q f wL q f wLB 1 , V Lb296t b23 ID 1Chiang D Y, Cheng M S. Modal parameter identificationfrom ambient response J . AIAA J, 1999, 37( 4) : 51
16、3-515. 2Desforges M J, Cooper J E, Wright J R. Spectral andmodal parameter estimation from output-only measure-ments J . Mechanical Systems and Signal Processing,1995, 9( 2) : 169- 186. 3Lardies J. A stochastic realization algorithm with applica-tion to modal parameter estimation J . Mechanical Sys-
17、tems and Signal Processing, 2001, 15( 2) : 275- 285. 4Hermans L , Auweraer H V, Mathieu L. Modal parameterextraction from in-operation data A . Proceedings of the15th SEM IMAC C . 1997. 531- 539. 5Luz E, Wallaschek J. Experimental modal analysis usingambient vibration J . TheInternational Journal of
18、 Analyt-ical and Experimental M odal Analysis, 1992, 7( 1) : 29-39. 6Chalko T J, Haritos N. Scaling eigenvectors obtained fromambient excitation modal testing A . Proceedings of the15th SEM IMAC C . 1997. 13- 19. 7 , #O,Z,. M1f / s J .t b, 2000, 21( 6) : 535- 537.( Zheng M, Shen F, Chen H H, et al.
19、Modal parametersextraction with cross-correlation function under ambientexcitation J . Acta Aeronautica et Astronautica Sinica,2000, 21( 6) : 535- 537. )Te:#O( 1971- ) 3, , =,C 2t bt?v Tb1Z_: k# e, 3|) b “: 025-4893082, Email: shen-fanzm 163. com ( 1972- ) o, ! ,C 2t bt?v tV YTb1Z_: k# 3|) b “: 025-4893501, Email: zhengminsf 163. comZ( 1965- ) 3, , q,C 2t bt?v Tb1Z_: kb “:025-4893082b ( 1939- ) 3, ,p V 3 =,C 2t bt?v Tb2974 #O: I MYET / MY
