Real-time embedded Fault Detection Estimators in a satellite's ...

Proceedings of the International Multiconference on Computer Science and Information Technology pp. 759–766

ISBN 978-83-60810-27-9 ISSN 1896-7094

46275415 4994916C14C4C7A81DC756CAFD178161+6C47C4D1 46C7A81344D 3EC4EE

BFC.E'!4C

*FC*EF

9EECC8%FC 0>C8%F 39::C7C0FE%C;%2C(F C C?@:CC.'EE,C6F 0E CFF CED CFC %' C F C E# C  C E# C  C F!EC AE C E C  C E C FFD2 C 4F C  C EC #CEFCCC C!9C"#$49$CDCCE%CEC CFEDC>FFCEDCFC%' C#CEC F'!EDCEDCCFEDDFC%#CECC B*)CFDE2C 4C8*)CFDECFC%ECFCC%CECC B*)CFDECCFFFCFCE'DC'CF#CC! DFCFD#CE2 8F#CCCCCDDCFCECCEFC "#CFDCEF CCF#DCEF CC'CFCEC DACDCCE% CC8*)CFDECFC FECEDC"CEDCECCB*)CFDE C FCECECFFDF2C 4F C F#D C EF C FE C ED C  C  C C DCCE%CECC>FFCEDCFC%' C C CE# CE# CCCECFFD C! DF2C1CC"FCFE"CCCED C!DFECFC %'C  C"CDC  CE%C  EC'CE! DC'C 8 + 3 "#CF#DCEF % 4 C 4 = 3 2222 8 + 3 C CC#%C'7

CF&CEECEC 1 + 6 2  CC & 4 CFCC"#CFFE! C"CC 4 − "' CEC % 4 2 4 C E C E C C FED C F#D C EF C F'EC % 6 +3 C#%C'C % 6 +3 =  1 % 6 56 2

13F2

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

18@2

762

PROCEEDINGS OF THE IMCSIT. VOLUME 5, 2010

)#2C5C4C'E,CFDCECC8*)CFDE

4CDECECCFFDC1EDCEC2CCD C 6 C FC FC'CCFCEFFC A 1 CCDECFCCF!F C F!EC0,E%CC"CFECE''FC π 41 16 2 C #%C'7

π 41 16 2 = NA 1 16 + 32 H A4 16 2O ∀A4 A 1 1 

1832

 1882 4 C  C F C F'E C E C  C 0,E% C  C F π 1@2 = 4π 3 π 8 π 5 22222π 3 6 C"C 1852 C"C 16 2 FCCFC%E C ( 16 2 CFCCDE!! CDFDC%E CC 5 16 2 CFCCEECC%! E2C4CEFFCCDFDCEFC%EF C 1 6 2 C C 16 2 C F% C  C D C  C % C " C >FF C E C AE C D C  C E% C DFC  16 2 C  C  16 2 CCCCECCCF 1@2 2C1CFFEC1992 CJN2OCEFCCE''CE! E2C4C%C C A 1 CFCCCCDC 6 CFCECFC

A 1 1 6 2 = NA16 2 = A 1 O C  C  = NA3 A8 222 A3 O FFC CFCECCEFF'CFFDCDEF2C4CFFDCDC+DC EDCECFCFFDCECECCCEDCD2C1CC'C E'F%CEDCCCFC%ECE'F%EFCCC#! CEFCC2C4E CCDECEDEC F C D' C  C  C DFD C F&2 C 4 C FFDC DE C F& C F C  C  C E'F% C 0,E% C  C EDC"CCFECE''CDC π = Nπ 41 O ! FF C  C F# C D2 C 4 C FDE C FF C  C EC ED%CFFCCFCCCCFE2CC

4CEE!FFCECFC+CCCEC"FC CCECCEE"#CFEF7 12  C %FEF C E C #F C ##C EDFCCCDC 12 C#FCCC'FC%E#C 7E5C C 12 EFFCEC%FFCCCDEECE&CFCF! C'CC#FCCCEC 6" 2 4C)7*)BCF#CECC'CFFDCC'CFC F C  C E C D# C  C  C DE C F2 C 1 C EC "EF C  C %E%F C D# C " C  C ED C E C C CDECFCCCCEDCCF&CECEFC E'F%EF2CAE"CECF#CFCECDEFCECFCC EFF'CFFDCDEFCFCC,CFFCCDCDEC! E C"CFCE'D!2C4FCF#CFEC'C %C'CD#CEC%CDEFC1ED2CC FCECE%CCEFF'CFFDCDEFCCC#%C D2C4FCFFCCDECFCF#CCFCCEC DCDEC'FC)7*)B2C4ECF#CC#EECFCECDE! FC&FC!$49$4C,E"#CECEFF'CFCCCFF! D2C1CECECDCDECFDEC&FC ECCECC#EFF CCEE"#CF,FCFEC 'CDDC4367C 2 DECFCF# C '2 CFE C 2 FDCFE CC 2 1!AE2 )CFECFC"CCE'DCECF#CCDE! !'FCF%CCFCFC*DC)CECCDE! CECCECFFD2C4CFDCFECF,CED! 'FCDE!EECFDFCECE'CCE%CF! D2C4E"FCFC CCEFCEC'C%F! # CDCFE CCCEDCFEF2C4CE!  CE CA#C CF#!DE C'F C CEDC DCECDCFCECF#CDECECD!DECF! DE2C4CFDFCECECA#CCC FCECFCFC%EFCFCFDCCCE%CC CC2C1CFCFCFCCE#CCC CECEFCFCDE#CD2 AE"% C F C D C  C E C FFE C EDC "CCFFDCFCECFCDEC#F2C)ECFC! FE CC"EC'CDECECECACCC F#CC%EFCE%CFCFDCCE%CD! C"CEFCCECC#CDCDECFD! EC&2C)ECCCDECEFE#CECCFC ECEFF'C$9.CEC"CFCCCEDCE! #CDE CECCCCFC*DCC'FC ECDFDFCECEDCEC"FC#C%! EC %Eϖ 14 C C EF C C ' C , C F C C E&CEDDC%E#C%EC59CFC#C' C2#2CC J17CEEAC 4CDFCECCFC*DC! CFFEC"CCDECFCF'C'CCEE"#C ECFCFCFE7  1 16 + 32 =  1 16  1 1 6 2 5 1 16 22 +  1 16 2  1 16 2 ( 1 16 2 =  1 16  1 16 2 5 1 16 22 +  1 16 2

1892

"C  1 2ϖ)6*CCCF'FC1CCEFCC&FC #CECDECA12C4CECEFC  1 C  1 CC

NICOLAE TUDOROIU, ESHAN SOBHANI-TEHRANI, ET AL.: REAL-TIME EMBEDDED FAULT DETECTION ESTIMATORS

 C "## C D C1C DC % C  C FF C EC  C%F CE C12C 4 CEFF CEF C C DFDC EFC%EFC1CC1CC"C>FFCECAECDC"C E%CDFC  1 C 1 CF%2CC1CC CE''CECC#%CDECDFCCFFDCDEC E%FCC&CEDECECCCECC #EFF2C4,#CECECFEC'%ECECDEFC  C D CBC FF C  C  C # C D C DEC #EDCFCC#EECFD2 9EF& CECFCCEDCECC! EC#EDCFC%EC'CD#C%EFCFDFCC '##CECC2C 4CDECE''FCE%CCECECCDEC CCCC#%CD CCECCE%CC! ECECCEC"CEC2C;CF#CDEC E''FCEDE C'ECCECC#EFFC C'C%2C4FCFECD,#CEFFCFCEDC FCE#CE7

329C9EDCCD#CE%CC6 CCF C  @

8C2 C+C4E10/CCCC1C0ECEEC#CCC436C 7111F497C7A81DC4E1506#1536546/ 823C9EDCC#E'CFCF#DCEFCD7 15@2 "CCFCE%CDC C16162 C FCC CEC CDCD2CC 828 C 9ED C  C FED C #E' C F C F#D C EFC DCEDC6CEC6/37 % 6 +3 6 =  16 % 6 H6 56 2

F +7 + "'# DE # 1 4C F!5," -"'#$4C# 9 F!5," 9885$C

1582 18:2 829 C9EDCC#E' C CE% CED C6C EC 6/37

"Cµ'$#C'9,.CFFCCCECFEC%2C 4C#CFDEC#EDCFCCCC ',FCECECCC2CBCECFCFCCDC "6/0 26/3CFCFCE"C CCFCFDCCD C"6 5 @ 1 686 3 C  C F C E" C E% C D C  @ 1 686 3 C "CEDCC%C&F!FCFFFCECCCFC EDE CCCFFDECCDECECCC DFCCFFDCDE2 4C'E%CFECCFCECECCEC! 'C'CFECEDEC'ECCC1FFECEC! E2 CCEEC1"CFFECECE2 CCFAC1EC CECCC"CCF%2 CCCCE! CD2 M12 3ABCB0;B77B7C)$8-4C7B4B94163C*$-0$3C)1-4B5C B.410$465.C134B5$9413>C.45$4B>/ 4CD'CFCECC1%C0C0EC #EDCCB*)P8*)CFDEFCFCCCC! FC436!486 C496!4C62C7CECFCDEFCECC8*)C 'FCEFCFCF'C'E" CC#EDCFFC! D#CDEFCCFDCECC'ECFF2 C+C4E1,/CCCC1ECCD#CECCFDFCC436 323 9EDCCCDECE''CED C6CEC 6/3 18B2

1552

82:C9EDCCFEDC#E'CECF#DCEFC DCEDC6CEC6/37 26 +3 6 =  1 6 % 6 +3 6 56 2

π14 1 2 1 µ4 1 6 2 I 1 1 6 +3 H 6 2 µ

1592

82BC9EDCCC#E'CECEDC6CEC6/3 15:2C 82FC9EDCCDFDCFCECCDE C1 C 6/37C 1 ν 1 16 + 32 = ( 16 + 32 −  1 16 + 3H 6 2 15B2 1 " C  1 16 + 3H 6 2 C FF C  C1! C EDE C E C C C 1 #E'CCFC  16 + 3H 6 2 C1CDEC12 CC ( 16 + 32 FF C  C " C %' C DFD C E C  C %C DECC CCFC4 CDC ( 16 + 32 = (4 16 + 32

15F2

82?C9EDCC#E'CCECE%CD! C 15?2

328 9EDCCD#CE''CC67 µ41 16 2 =

1532

825 9EDCCC#E'CFCEDC6CEC6/37

+ 1 1 6 6332D + 1 1 66332 + 1

763

18F2

82CC9EDCC#E'CEFF!E%CD

325 9EDCCD#CFDCC67 18?2

15C2

764

PROCEEDINGS OF THE IMCSIT. VOLUME 5, 2010

823@C9EDCC#E'C*DCC#CC6Q3/ 19@2 7717AFF4C7A81DC4E/ 8233C8CCFCFDCC,/3 I 1 16 + 3H 6 + 32 = I 1 16 + 3H 6 2 +   1 16 + 32ν 1 16 + 32 1932 8238C8CCFCE%CDC 1982 C+C4E12/CCCC C C8C C C1CCDECE''CCC6CCQ3 C C 523C9EDCC,EECECC6Q3 1952 528C8CCDECE''CC6Q37 1992 C+C4E13/11C)CECC C C6/ C C3 CC 923C9EDCCDECE''C%ECCC6Q37

A

B

9+ 1 66332 +3 1 6633 +8 1 6 633 + 5 1 6 63 3 2 22 + 3 1 6 63 3 19:2

928C6'CCDDDC%CECCDECE''C %E7 19B2 925C7DCCCECCDDDC%CECDEC E''C%EC

12 F4. 1 9+ RR D 1 9+ 33

19F2

CF'F&CFF#7 4.#21 C+C4E14C7C)CFECSC)77CE#C C C 4F

µ 33 D > µ '$#C'9,.

CCEF

19?2 19C2

6"FCECCEF2 M112 5B$-!410BC963456-C$37C)>*BC.45$4B>/C10J-B0B34$4163 4CEECFFDCCCFCF%C C!DCFE"CC"CDDECFF C CCEFCCEC'EC#EDFCCFD#C DCFE2C3EDCCDDECFCC! DCFFDCF#CCECE#C'CCCDEFC FFCFCEECFC"FC#E2C0EE%CC! DCFFDCF#CFCCEDCEECF%C#E! # C  C DDE C FF C E C  C EE C #EDF2C AE"%CCCFCFCC!DCDDECC F#CFFC#CDECFCECEEC##C  C  C E C % C E C FE" C EEF C ,C 0$4-$;P.108-13*C"CFC54(C15!4DC(E,FE 2CCC54(4C15!4DC(E"FC4#2C4EE'EF2C 7CFC"C!DCEDFCECCDD! ECEC!DCDFCFCCF%CDCDC'C ECCECCC%CFEDC"',F C##CC #EE C F# C %" C E C  C ! C E'DF C  C EC

D#C#CC!DCDDECECCEEC FFD2 C ;# C  C !D C $9. C &F C ED C "EC F#F7CJ17CEECCFDEFCF#CFC"CFCC #CDDEF2C$CEECCFDEFCF#C F# C FED C ED C F C  C  C  C  C J17C EECCB*)CC8*)CFDEFCCF#CECE! DACFCF2 $ CDDE CF# CDCEE CF,FCFE C'C FCECCC)J>$C14#,.4$95$!AA!E,#!"#6$4 $!2CE'ECDEEFFECECEECDE2C(C%C EC,CC'ECF,CF#C,#CECECC DC%'CED#CFEF2C)FCECFCC FD# C D C C  C FE C , C E C E C  C DC EDE C D C E% C ' C  C " C F C  C EC %ECCEC"CFCEDECDCC1EEC 22 C.CCEE CCFCCC'C EEC+ CCCEFFCCEC%CCC FFDC C C FFCE CD2C4 CEFFC ECC$9.C EECF#C 5 16 2 CFCECCEECEDC C 'CECCFCEC#CCECFD#C% C CE#CCECFCCC 5 16 − 32 C"C'C C#2C.CFCFECDC"CEC! CCCFCECD CCCEC%CCEEC F# C  C ' C  C F C  C F C $9. C  C F' 5  16 2 2 C $" C F C E C '" C EE C E! DCCF,CF#C"C'C%F#CCCC "E,2C M1112.108-$4163C5B.8-4. 4 C !D C ED C F C E C ED C F C !DC FDEFC"FCC0$4-$;C58@@F'C"C.108-13*C! #CECC"ECEFFEFC(1376(. C6.CD2C4C FDECFFCCE'CECCFD#CDC C C&C EC3F C'CCCFECECCCCEC'! "CEECEDCCF,CF#C"C'CEC CCC"E,2C1CFCECC#CD'CECFEF CEC %CCE%CD#C'ECCFDEFCED C"C FCC#FC192!1:2CECCCFDECFFC ECC'EC!DCD'CCECF#F2C1C FC#FC"C"CFCCDFCECCDECE''! CCCFCCCFCFCECCC DEFCEFCCCD!CF&2CC4FC#FC %CCCFDCDCCE'FFFCECC'ECFDEFC ECCEFC%CCECCE''CD2C$FECCF! DEFCEDCEDFECFC%'CCC'! D,CFCC4'C32C 1D2 C9639-8.163. 1CFC C"C%CFCCEFF'CECF#C"EC %CDCDEFC'FCECBCC8F! C*DC)CFDEFCECCC#EFCCFC CEC"FCEC1CEECFFDC1$9.2CCC F2C4CDCE'EFCCECFCCFDD! AC'CFCEE"F7 12 7E C  C E C E C E C "C F C E C  C $9. C  C E C  C D' C E C EFF'C

NICOLAE TUDOROIU, ESHAN SOBHANI-TEHRANI, ET AL.: REAL-TIME EMBEDDED FAULT DETECTION ESTIMATORS

(a)Robustness to the noise level

(b)Robustness to the noise level 8 mode probability index

mode probability index

8 6 4 2 0

0

100 200 300 samples (c)Robustness to the noise level

6 4 2 0

4 2 0

0

100 200 300 samples (d)Robustness to the PImatrix

8 mode probability index

mode probability index

8

6

0

100 200 samples

300

6 4 2 0

0

100 200 samples

300

C)#2C9C4CEDCCDFCECDECE''FCCECE! 'FFFCFFCF#CC)7!B*)CF#C (a)Robustness to the noise level

(b)Robustness to the noise level 6 mode probability index

mode probability index

6

4

2

0

0

100 200 300 samples (c)Robustness to the noise level

4

2

0

2

0

0

100 200 300 samples (d)Robustness to the PImatrix

6 mode probability index

mode probability index

6

4

0

100 200 samples

300

4

2

0

0

100 200 samples

300

C)#2C:C4CEDCCDFCECDECE''FCCECE! 'FFFCFFCF#CC)7!8*)CF#

TABLE 1 THE PERFORMANCE COMPARISON OF THE FDKFE STRATEGIES

FEFCC#CFECCCEDFC! #CCFCDFFECECCF 1'2 1DDE C E C  C ', C E C !D C C *D C F C E C C DEF C E%# C  C &C #CFCECCDEFC,CCEDDECEFF'C FEFCECEC"CF 12 7ECC#EFFCEC'ECCCF#! CEC"CFCECCFEFC F#CC!DCB*)CC8*)CFDEC#E! DF C 12 9EDFECECEDC'FCC%! #FCEC!DC8*)CFDEC#EDC"C FCECC!DCCB*)CFDEC#ED C  12 5E'FFFCFFCEC'EC!DCFDEC! #EDFCECCFECECDECFECE'! 'F CDE#CEF CCEFCFFFCC CFEF2 4CECEEFCCFCCFCE''FCC!  C C F C FF C  C  CDE C  C  C %#C #EECCFFEC'FCCCFC! FFCCFC"CFCCC2C;FCECC! ECFFCCFCCCC'CE'F%CCC! !DC8*)CFDEC#EDCFCE'FCECDE#C! F C  C E C FFF C E C EF C DFDF C C EFFCEF2C4C'EC!DC#EDFC"E,CFDCEC C!DCC"E,CFDECCFFCDEC E C ED C FFE C )7*)B2 C 9ED C E C  C !DC C"E,CFDECCFF CC!DC8*)C FDE C#ED CEF C C CE!C # CC ,FCCF%CDECECEDECFEF2C9ED! CECC'E%CEFCC!DCB*)CFDEC #ED CC!DC8*)CFDEC#EDCEDFC 'CCFCCDCFFCEDEC'CCED!  CCCDECEFCDCF2CJFCC '##FC"',CEC%CDE!'FCEFCFC CCECCF'C&CECCEC#CCF! # C  C FFD C # C  C %ED C F C 43@6 C 43562C 0EE% CF'CE CC!DC8*) C FDEC#E! DCFCDFCCEC&FE C"CFCC! %F#E2CC$FE CC'%ECECC!DC8*)CFD! EC#EDCE C#EFFC CCF CECC##C EFFCDFCFCEC'CEC2

-C45

14FBAF5684

111111111

11

1111)

3

$ C 7#C E C C DEC F

C C C C MC #EE

CCCC>EE

1 1MC >EE

$ C 7#C E C !DEC FC

CCCCCCCC.D

CCCC.D

5

5E'FFFCE C  CDF

C C C C C 3EC 5E'F

3EC 5E'F

11C5E'F

4562

9

5E'FFF C E C C DC E''F C π

C C C C C C 3EC 5E'F

3EC 5E'F

CCCC5E'F

4962

8

5B)B5B39B. 4362 CCC/2CT#CC5E#!-CDE CK7ECC7#EFFCEC.!

CCC>EE

4862

VBD'CFDEF7C*)!.C*DC) CB*! )!BC*DC) C8*)!8FC*DC)2

765

4:62

FECC$EC)FCF#C100CBFDEL C $!C!84 "49 9  6#$9C!8#  !.  ,#8"$948 C"#AC C ME259 C 3E29 C 2C 38C5!3533 C3CC?2 CCC.2CA, !,A!4,"#$45!.3#5$!,3#"9$6C CGEC(! CUC.EF C8@@32 CCC;2C;, CKA#C)C0DC0E#CEC5EC (C JEDL C6.!8#C 4"'# 6C"$9!5"48!, 84#8#C C 3CC? C2C9?5!9CB2 CC.2CG2CGCCG2C*2C8D CK$C3"CBFECECC*DC ) CEC3EC.FDFL2 C$98##.45C9F6#$9#C#D$94 8##.45C9F"'#00"' "#$!"49!,A9C45A96#$9C!8#73#4 F#C##C45D4A5,!"49!.89"$9,C C3CCF C23?8!3C52 CCCB2C$2C( C52C0" CK4C8FC*DC)CEC3E!  C BFDEL C$98##.45C    A9C45AD $' C 9 C8@@@2

766

PROCEEDINGS OF THE IMCSIT. VOLUME 5, 2010

4B62 CCC32C4EECC*2C*EF C9)C7ECC7#E!

43@62 G2C72C;EF,E%CC*2C02C0 C8@@3 CKA'C)C4EC

FFCEC5EC(FCE C.FC$C9EEC.FDC 8F#CC;,CEC*DC)FL C$98##.45C9F  "#$!4 "49!,A9C45A945!,D84$854"C!.C"#AC C1F C5ED!  C8@@: 2C3CC!8@82 CCC32C4EECC*2C*EF CK)C7ECC7#EFFC EC.FC$C9EEC.FDCF#CC1%C0! C0EC11002C$EL C$98##.45C9F"'#89F#$#8#  989"$9,6,48!"49C C4EEE C9 C8@@:2C C C C324EE C*2C*EF CK.C)C7#EFFCF#CC ;, C E C 1# C *D C )F: C   $!C!8"49C  9 6#$9C!8#  !.  ,#8"$948  C"#AC C ME2 C 95 C 3E29 C 8@@F C 2C 3559!35:@2 CCC32C4EE CB2C.E'!4 CC*2C*EF 1K1! %C;,CEC8FC*DC)FCEC)C7ECC 1FEECC5EC(C$EFCEC.C$C9E! EC.FDLD 8-3;D'#?