13 3 20095 EL ECTR ICMACH IN ESANDCON TROL Vol113 No13 May 2009 FPN,, (, 150001) :,,Petr( FPN ), BP, FPN,,,, : ; ; Petr; : U661 : A : 1007-449X (2009) 03-0464- 07 System s vulnerablty assessment of a rcraft guarantee system based on mproved FPN YAO Xong2lang, FENG L n2han, ZHANG A2man (College of Shpbuldng and Engneerng, Harbn Engneerng Unversty, Harbn 150001, Chna) Abstract: Accordng to the characterstcs of vulnerablty assessment of arcraft guarantee system on board, a vulnerablty assessment model s p resented. Consderng the fuzzy and random characterstcs of equpm ents falure and the sophstcated logc relatonshp s among equpm ents on board, on the bass of fuzzy reasonng algorthm n fuzzy Petr net ( FPN), an mp roved FPN model whch can be app led to e2 valuate vulnerablty of comp lex system s on board was constructed, combned w th layered thought and B P algorthm w th nonlnear feedback. The new model s able to make a great num ber of uncertan parameters n the system whch gets rd of the dependerue on experence. The selecton of model param eters was ds2 cussed n detal, and then the model was used to evaluate vulnerablty of arcraft guarantee system. The results comparson between the p resented m ethod and dam age tree analyss method demonstrates exhaus2 tveness and ratonalty of ths assessment model. The model would be app led to sophstcated system as2 sessm ent on board. Key words: arcraft guarantee system; vulnerablty; mp roved fuzzy Petr net; assessment model 1,,, : 2007-01 - 01 : (50779007) ; (50809018) ;( 200801104) ; (20070217074) : (1963 - ),,,,; (1981 - ),,, ; (1968 - ),,,,
3 FPN 465 [ 1 ],,, Petr( fuzzy Petr net, FPN ), 311 [ 2, 3 ] [ 4, 5 ] FPN,,, FPN, R =,BP { R 1, R 2,, R m }, R ( = 1, 2,, m ), [ 3 ] 312FPN 2, : A: ; B : ; C: ; D :,, Z = R - S = 0, (1) : R ; S Z < 0, Z > 0 [ 0, 1 ],, p P M ( p ), P d = P ( Z < 0) = P ( (R - S ) < 0) (2),; Th: T [ 0, 1 ],,S, t ( tt ) Th ( t), Th ( t) =, ; W = { w 1, w 2,, w r } R = P (R <S ) = f s ( s) - s f R ( r) dr ds, (3) - f s ( s) f R ( r),, Z,,,,, 3FPN FPN,,, [ 6 ], FPN 1 FPN, FPN = { P, T, D, I, O, M, Th, W, f, }, P = { p 1, p 2,, p n }, ; T = { t 1, t 2,, t m }, ; D = { d 1, d 2,, d n }, P = D, P T D = g ; I (O ) : T P, ( ),, ; M : P,, ; f: T[ 0, 1 ],, f ( t), f ( t) =, ; : P D,, FPNThf W,, 2p I ( t), tt, p t,t, p t p j O ( t), tp j,t, p j t
466 13 FPN, FPN,, 3 Π tt,π p Ij I ( t), M ( p Ij ) j w Ij Th ( t), ( j = 1, 2,, n), t 4, t,, p f ( t) = M ( p Ij ) w Ij, p Ij I ( t) 5 FPN,t 1, P I ( t 1 ), t 2, P O ( t 2 ), P, h x 4 + 313 1 + e - b ( h - x 4 ) 1 + e - b ( x 4 - h) (5) [ 5 ],,,FPN FPN,, [ 7 ] 314FPN S( 1, ),,, 1 y ( x) = 1 + e - b ( x -, (4),FPN k), bb, x > k, y ( x), 1; x < k, y ( x)001, FPN,, (BP )FPN,,, FPN F g. 1 1H ll functon curve 1), 3,x = n M ( p ) w, k =Th ( t) b =1, x > k, y ( x)1, t ;x < k, y ( x)0, t,y ( x) 4, y ( x) f ( t) n M ( p ) w =1 2) y ( x), b, : t =max ( x 1, x 2 ) x 1 + 1 + e - b ( x 1 - x 2 ) 1 + e - b ( x 2 - ; x 1 ) h =max ( x 1, x 2, x 3 ) =max (max ( x 1, x 2 ), x 3 ) = max ( t, x 3 ) t x 3 + 1 + e - b ( t - x 3 ) 1 + e - b ( x 3 - ; t) g =max ( x 1, x 2, x 3, x 4 ) =max ( h, x 4 ) x 2, BP,, ;,,,,,, [ 8 ] BP
3 FPN 467,, 31411FPN BP FPN FPN, FPN BP, FPN FPN n, bp j ( j = 1, 2,, b) r, E = 1 2 r b =1 j =1 [M ) - M 1 2, (6) M ) M 1 ) p j,fpn, [ 9 ], dw ( n) x d[m n ( p = ( n) j, x = 1, 2,, m - 1; (7) dw ( n) x d[m n ( p = ( n) j ; (8) d ( n) d ( n) d ( n) d[m n ( p = ( n) j ; (9) d ( n) ( n) = (10) d[m n, t ( n) FPN n, t ( n) T n, t ( n) w ( n) 1, w ( n) 2,, w ( n) m, t ( n) ( n), t ( n) ( n) p ( n) O ( t ( n) ), p ( n) n - 1,p ( n - 1), (7) ( 10),, n - 1 dw ( n - 1) x d[m n - 1 ( p = ( n - 1) j, x = 1, 2,, m - 1; d ( n - 1) d ( n - 1) dw ( n - 1) x (11) d[m n - 1 ( p = ( n) j ; (12) d ( n - 1) d [M n - 1 ( p = ( n - 1) j ; (13) ( n - 1) = d ( n - 1) d[m n ( p ( n) j (14) d[m n - 1,n - 2, n - 3,, 1 dw x, x = 1, 2,, m - 1; q = d x d x n - 2, n - 3,, 1 FPN,,,(5), : = ( q + 1) d[max ( u, v du bue - b ( u - v) [ 1 + e - b ( u - v 2 - = ( q + 1) 1 + 1 + e - b ( u - v) bve - b ( v - u) [1 + e - b ( v - u 2, (15) u v q 31412 BP,,,, t, w x (k +1) =w x (k) - dw x +f[w x (k) - w x (k - 1, x = 1, 2,, m; q = n, n - 1,, 1 (16) f ( z) = tanh ( a z) e - dz2 ; (17) z =w x ( k) - w x ( k - 1) (18) ad, : w m - 1 m ( k + 1) = 1 - w x =1 ( k + 1) = ( k) - + d x ( k + 1) ; (19) f [ ( k) - ( k - 1; (20) (k +1) = (k) - + d f [ (k) - (k - 1 (21) FPN,,, 4FPN 411, 2 [ 10 ]
468 13,,, FPN 412 2,, F g. 2M a n equ pm en ts of a rcraft guaran tee system, on board,:, 1) : FPN,,0; FPN 3 2) FPN :, FPN :P 1, P 3 P 5 P 7,P 2 P 4 P 6 P 8, P 33, f ( t) = 1, t ( = 13, 16, 36) P 34,P 10 P 13,P 22, P 25,P 14 P 16 P 18 P 20,P 15 P 17 ; P 19 P 21, P 26 3) FPN, n [ 6 ] ;,,, 4) FPN t ( = 1, ; 2,, 36) 1, t ( = 1, 2,, 35, 13, 5) r, 4, 16, 36)( 0),, 51 ; 6) (6) E, E <,, 8) ;,; 7), ( 7) ( 21),, 5) ; 8), FPN, 5),, 9) ; 9), 10), 2) ; 10), 5 511FPN F g. 3FPN 3FPN m odel for system vulnerab lty a ssessm en t of a rcraft guaran tee system, (A, B, C, D ),,FPN t 13 t 16 t 36, 3 r 1 r 2 r 3,,,FPN, Th f, [ 9 ] b a dfpn, 50,,,
3 FPN 469 b a d, 40, 1, = 10-6 : b a, d,, b a,d b 1 0002 000, a 015016, d 011012, FPN 1 FPN Table 1 Performance of FPN model under var ous parameters FPN 512 3,, FPN = 10-6, = 012, b = 2 000, a = 016, d = 011,,4,, BP,,, FPN, 4 F g. 4Performance ndex E versus tra n ng cycles,,, FPN, 2, 3, (DTA) 2 Table 2 Test sam ple of fa lure probab lty of equ pm en ts n a rcraft guaran tee system
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