VRdissertation Gr
of 80
description
Τα τελευταία χρόνια, έχει σημειωθεί μια μεταστροφή από τους κλασικούς στό-χους του αυτομάτου ελέγχου όπως είναι η ευστάθεια και η απόδοση συστήματος,σε λιγότερο παραδοσιακούς, όπως είναι η σθεναρότητα και η ανοχή στα σφάλματα.Ο λόγος γι’ αυτή την μεταστροφή είναι η αναγκαιότητα να αντιμετωπιστεί αποτε-λεσματικά η αναπόφευκτη εμφάνιση σφαλμάτων στα συστήματα ελέγχου. Με τονόρο σφάλμα εννοούμε τη μη αποδεκτή αλλαγή μιας τουλάχιστον χαρακτηριστικήςιδιότητας ή παραμέτρου του συστήματος από την φυσιολογική, συνήθη κατάστασήτου
Transcript of VRdissertation Gr
-
: 250
2010
-
,
-
ii
-
. . , , , , . , , .
, , . , , . - , , . , - , , .
- , , , , , , . , . - . , .
- , - , , , -, , , , , , , . , . , , , .
iii
-
, , .
, - IBM Memory and Probe Technologies Group, StorageTechnologies. . , Storage Technologies . , Memoryand Probe Technologies Group, . . Abu Sebastian, . . Deepak R. Sahoo, .
-, -. , . . - , 23 , . , - , .
, , - . . , . , .
iv
-
- . (C.152).
. 08-25/05/2010 -, 40% .
v
-
vi
-
xiii
1 11.1 1
1.1.1 . . . . . . . . . . . . . . . 31.1.2 . . . . . . . . . . . . . . . . 6
1.2 - . . . . . . . . . . . . . . . . . . 8
1.3 . . . . . . . . . . . . . . . . 10
2 132.1 . . . . . . . . . . . . . . . . . . . . . . 132.2 . . . . . . . 14
2.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.2 . . . . . . . . . . . 15
2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3.1 . . . . . . . . . . . . . . . . . . . . . 162.3.2 . . . . . . . . . . . . . . . . . . . . . 17
2.4 . . . . . . . . . . . . . . . . . . . 182.4.1 182.4.2 19
2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.5.1 . . . . . . . . 212.5.2 . . . . . . . . . . . . . . . . . . . . . . . 21
2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 233.1 . . . . 233.2 . . . . . . . . . . . . . . . . . . 243.3 . . . . . . . . . . . . . . . . . . 26
3.3.1 . . . . . . . . . . . . . 283.3.1.1
. . . . . . . . . . . . . . . . . . . . . 29
vii
-
3.3.1.2 . . . . . . . . . . . . . . . . . . . 30
3.3.2 . . . . . . . . . . . . . 303.3.2.1 303.3.2.2 30
3.4 : . 313.4.1 . . . . . . . . . . . . . . 313.4.2 . . . . . . . . . . . . . . . . . . . . . 32
3.4.2.1 . . . . . . . 353.4.2.2 . . . . . . . 36
3.5 . . . . . . . . . . 373.5.1 . . . . . . . . . . . . . . . . . . 37
3.5.1.1 - . . . . . . . . . . . . 37
3.5.1.2 - . . . . . . . . . . 37
3.5.2 . . . . . . 383.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4 - 434.1 . . . . . 434.2 . . . . . . . . . . . . . 484.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5 53
57
viii
-
1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 . . . . . . . . . . . . . . . . . . . . . 31.3 . . . . . . 51.4 ) , ) -
[1]. . . . . . . . . . . . . . . . . 71.5 . . . . . . 81.6 . . . . . . . . . . . . . 10
2.1 (n=2): a) , b) - . . . . . . . . . . . . . . . . . . . . . 15
2.2 (n=2) . . . . . . . 172.3 W(i) -
: ) ) (n=2) 192.4 -
(n=2) . . . . . . . . . . . . 202.5 -
(n=2) . . . . . . . . . . . . . 20
3.1 (n=2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 : ) , ) (n= 2). . . . . . . . . . . . . . . . . . . 25
3.3 : ) ,) (n= 2). . . . . . . . . . . . . . . . . 25
3.4 (n= 2). . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.5 (n= 2). . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.6 (n= 2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.7 - id j = i f j (n= 2). . . . . . . . . . 33
ix
-
3.8 - (n= 2) . . . . . . . . . . . . . . . . . . . . . 36
3.9 (n= 2) . . . . . . . . . . . . 373.10 Undetected fault case (n= 2). . . . . . . . . . . . . . . . . . . . . . 383.11 (n= 2). . . . . 393.12 -
(n= 2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.1 ) , ) -- . . . 44
4.2 - q 1 , . . . 46
4.3 - q 2 , . . . 46
4.4 - q 3 , . . . 47
4.5 . . . . . . . . . . 48
4.6 (B) (D) - . . . . . . . . . . . . . . . . . . 51
x
-
4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 . . . . . . . . . . . . . . . . . . . 45
4.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
xi
-
xii
-
W(i)
W(i1 j i0) WQ(i1 j i0) Q(i1 j i0)Wu(i1 j i0) W(i1 j i0) u WQu (i1 j i0) WQ(i1 j i0) u Q(i)
X(i)
Xu(i) X(i) u
W(i)
Wr(i)
Ww(i)
WQ(i) Q(i)
Wu(i) W(i) u
WQu (i) WQ(i) u
f(i)
fm(i)
Q(i)
q c(i) Q(i)
Qr(i)
xiii
-
Qw(i)
q (i)
q u (i) u q (i)
q cXu(i) Xu(i)
qXu(i); q+Xu(i) X(i)
q cX(i) X(i)
q cWQ(i) WQ(i)
q cWQu (i) WQu (i)
qWQu (i); q+WQu
(i) WQ(i)
q cWu(i) Wu(i)
qWu(i); q+Wu(i) W(i)
q cW(i) W(i)
ey(i)emaxy
( )
efu(i)emaxfu
u
( )
F(i)
n
P(i) Q(i)
S(i)
Snp(i)
Sp(i)
w(i)
wu(i);wminu ;w
maxuu w(i)( )
y(i)
ym(i)
Q(i1 j i0)
xiv
-
1
1.1
, - , , . - . , [1]. : ) - / , ) - , ) , , . - , , - . , , .
. , . , -.
1
-
1.
, , , .
- , . - :
Y (t) = g(U(t);x(t);q) ; (1.1)
Y (t); U(t); x(t) , q . , -, [2]. 1.1 - [1],
Y (t) = Y (t)+DY (t) = Y (t)+ f (t) (1.2)
, , , [2]. 1.1 [1], .. q = a
Y (t) = (a+Da(t))U(t) = aU(t)+Da(t)U(t) = Y (t)+ f (t)U(t): (1.3)
+
f(t)=(t)
o (t) (t)a
f(t)=a(t)
U(t) (t)
pi
() ()
1.1: .
- . , : ) , -
2
-
1.1
( ) (- ) ( 1.2) [3], ) , (1.2) [4], ) , - ( 1.2) [5].
f(t)
t
f(t)
t
f(t)
t()
pipi
() ()
pi
1.2: .
1.1.1
, - - . - [1]. , -. , , . - , . , , .
, (1.3). , . ,
3
-
1.
( ) ( ) - , -. [6], [7]. - , , [8], [9].
. , Fourier, , , ARMA , , , [10], [11], [12]. , - , , , .
- , [13]. , [14]. , - . . , , , [15],[16]. - [17]. -, , - :
y= fTq ; (1.4)
y , f q . , .
- .
4
-
1.1
U(t) pi + Y(t)
e(t)
pipi
pi
pi
pi
1)
2)
1) pi
2)
3) pi
/
4)
5)
1) Fourier
2)
pi
3)
4)
5) ARMA pi
6)
pi
f(t) f(t) f(t)
1) pi
2)
3) pipi
1) pi/
2) pi
3)
4) pi
pipi 1) 2) pi pi
3)
4) pi
pi
pi
-
1)
2)
3)
/
1.3:
. -
5
-
1.
, - , - .
- , , . , , . , - , . - .
1.1.2
,
S 2 Sns M!F 2 Fn f ; (1.5)
S , F M .
- -. : ) , ) , 1.4. -, , - . -, , , . .
. , ,
6
-
1.1
1 2
pi 1
pi
pi
() ()
pi 2 pi 3 pi 4
1 2
pi 1 pi 2 pi 3 pi 4
1.4: ) , ) - [1].
. - : ) [18], ) - Bayesian [19], ) , ) - [20], ) , [21].
- , . - - : . [22]. - , - [23]. , - , ( ), [24].
, - . -, - -, - ( ). ,
7
-
1.
- , . - [25], [26].
1.5 - .
pi
1) ,
2)
3)
pi
pi pi
pi
pi
pi
1.5:
1.2 -
() , - . . , - [27], [28], [29], [30], [31], [32], [33], .
8
-
1.2
, , . - . - , [34], [35]. , [36]. , , .
, [37]., . CAD , CARAMEL, - [38]. , . , [39]. - . - . , [40].
, , [41], [42]. - , . , , [43]. , [44],[45], Kalman [46], RLS [47] - [48].
9
-
1.
1.3
- , , 1.6. , -, .
0
( )f i
i1fi
( )4ff i( )1ff i( )3ff i
( )2ff i
2fi 3fi 4fi 5fi
1.6:
, - , - :
y(i) = f(i)Tq (i); (1.6)q (i) = q (i1)+w(i)+ Dq (i)Dq i f j ; i f j < i i f j+1 ; (1.7)ym(i) = y(i)+ ey(i); (1.8)
fmu (i) = fu(i)+ efu(i); (1.9)
ym(i) 2R; fm(i) 2Rn - , ey(i) 2 R ( / ) y(i), efu(i) 2 Rn - fu(i).q (i) 2Rn , w(i) 2Rn -, Dq (i) 2 Rn .
. ,
10
-
1.3
, - ( )., - , , - . - . - , : ) ( ), ) ( ).
- ( ) . , - , . - .
- : ) - , ) . , - , . , , . -, . - , , . , , -, , , ,
11
-
1.
. - , , , . , - , , . , - . , - .
12
-
2
2.1
:
y(i) = f(i)Tq (i); (2.1)q (i) = q (i1)+w(i); (2.2)
y(i) 2 R , f(i) 2 Rn , q (i) 2 Rn - , w(i) 2 Rn is the -. y(i) f(i) = [f1(i); : : : ;fn(i)]T .
ym(i) = y(i)+ ey(i); (2.3)
ey(i) 2 R , / . , u :
fmu (i) = fu(i)+ efu(i); (2.4)
efu(i) 2 R; u = 1; : : : ;n . ey(i) efu(i) ,
jey(i)j emaxy ; (2.5)efu(i) emaxfu : (2.6)13
-
2.
emaxy ; emaxfu
. w(i)
, -:
wu(i) 2wminu ;w
maxu; 8i; u= 1; : : : ;n (2.7)
wminu ; wmaxu
.
F(i), - q (i) ((2.1)& (2.2)), ((2.3) & (2.4)) - ((2.5) & (2.6)) (2.7). , , . , . , .
2.2
2.2.1
, :
W(i) =
8>:q :264 q
W1(i)...
qWn(i)
3754 q 4264 q
+W1(i)...
q+Wn(i)
3759>=>; : (2.8)
2.1. u :
Wu(i) = proju
(W(i)) =nqu : qu 2
hqWu(i); q
+Wu(i)
io;8 u 2 f1; : : : ;ng; (2.9)
proju
(X) X u
:
q cWu(i) =q+Wu(i)+q
Wu(i)
2; u= 1; : : : ;n: (2.10)
14
-
2.2
1
2
min ( ( )) P i
max ( ( )) P i
(b)
( )c i
1 ( ) i
2 ( ) i
1( )
i
1( ) +
i
2( )
i
2( ) +
i ( ) i
( ) i
1
2
1( )
i
2( )+
i
2( )
i
1( )+
i
( )
c i
(a)
1 ( ) i
2 ( ) i
( ) i
2.1: (n=2): a) , b)
, W(i) :
q cW(i) =q cW1(i); : : : ; q
cWn(i)
T: (2.11)
2.2.2
:
Q(i) =nq : (q q c(i))T P(i)1 (q q c(i)) 1
o; (2.12)
q c(i) P(i) 0 -, 2.1. , r (q jQ(i)) :
Q(i) = fq : hq;qi r (q jQ(i))g ; 8 q 2 Rn; (2.13)
[49]:
r (q jQ(i)) = supq2Q(i)
hq;qi= hq;q c(i)i+ hq;P(i)qi1/2 ;q 2 Rn; (2.14)
hi .
, WQ(i). WQ(i) -, ,
WQ(i) =
(q :
2n\u=1
hqou;qi r (qou jQ(i)))
; (2.15)
15
-
2.
qou = [0; : : : ; 0; 1; 0; : : : ; 0]T ; qou+n =qou (2.16)
1 u, u= 1; : : : ; n. , - :
q+WQu (i) = r (qou jQ(i)) ; (2.17)
qWQu (i) = rqou+n jQ(i)
: (2.18)
, qWQu (i); q+WQu
(i)
WQ(i) u, Q(i) u :
WQu (i) = proju
WQ(i)
= proj
u(Q(i)) =
nqu : qu 2
hqWQu (i); q
+WQu
(i)io
;8 u 2 f1; : : : ;ng:(2.19)
2.3
, q (i) , S(i),
q (i) 2 S(i); (2.20) (2.1) (2.2), (2.3) and (2.4) (2.5) (2.6). : ) Sp(i), ) Snp [50], [51], [52], [53].
2.3.1
:
Sp(i) =q : ym(i) emax(i) fm(i)Tq ym(i)+ emax(i) : (2.21)
emax(i) e(i) = ey(i)ef1(i); : : : ;efn(i)
q (i)
i
emax(i) = emaxy +n
u=1
emaxfu maxqZu(i) ; q+Zu(i): (2.22)
qZu(i);q+Zu(i) q u (i),
Zu(i) Z(i), - , u. , Sp(i) ,
Sp1(i) =q : fm(i)Tq = ym(i) emax(i) ; (2.23)
Sp2(i) = fq : fm(i)Tq = ym(i)+ emax(i)g: (2.24)
16
-
2.3
2.3.2
, - . , Snp(i), :
Snp(i) =nq : ym(i) emaxy fA(i)Tq ; fB(i)Tq ym(i)+ emaxy
o; (2.25)
fA(i) =fm1 (i)+ sgn(q 1 (i))emaxf1 : : : f
mn (i)+ sgn(q n (i))emaxfn
; (2.26)
fB(i) =fm1 (i) sgn(q 1 (i))emaxf1 : : : fmn (i) sgn(q n (i))emaxfn
: (2.27)
Snp(i) ( 2.2(a)),
Snp1 (i) = fq : fA(i)Tq = ym(i) emaxy g; (2.28)Snp2 (i) = fq : fB(i)Tq = ym(i)+ emaxy g: (2.29)
- 2.2(b) E. 2.2(a), .
1
2
( )m i
max( ) ( )( )
m
m
y i e ii
max( ) ( )( )
+ m
m
y i e ii
1 ( )pS i
2 ( )pS i
( )pS i
( ) i
(a) -
(n=2)
1
2
( )iA
( )iB
2 ( )npS i
1 ( )npS i
max()
)(
m
yy ei
i
+
B
max()
)(
m
yy ei
i
A
( )npS i( ) i
(b) -
(n=2)
2.2: (n=2)
17
-
2.
2.4
- , , ,
q (i) 2 W(i);8 i (2.30)
q (i) 2 Q(i);8 i: (2.31)
q (i) 2 S(i).
2.4.1
W(i) , :
W(i) = argW
nW :W
W(i)
\S(i)
o; (2.32)
qu (i) = minqu : qu 2 proj
u(W(i))
; (2.33)
q+u (i) = maxqu : qu 2 proj
u(W(i))
: (2.34)
W(i) , :
W(i) = argWfW :W=W(i1)Wwg (2.35)
Minkowski Ww , :
Ww =
8>:q :264 w
min1...
wminn
3754 q 4264 w
max1...
wmaxn
3759>=>; : (2.36)
(2.32)-(2.34) - . , 2n :
qWu(i) = minqf Tu q ; (2.37)
q+Wu(i) = minq fTu+nq ; u= 1; : : : ;n (2.38)
18
-
2.4
2(n+1)
A(i)q b(i); (2.39)qWu(i) q q+Wu(i); 8u 2 f1; : : : ;ng (2.40)
fu u f = [Inn; Inn], I n n A(i) = [fm(i); fm(i)]T b(i) = [ym(i)+ emax(i); ym(i)+ emax(i)]T , S(i) = Sp(i), A(i) =
fA(i); fB(i)T b(i) = ym(i)+ emaxy ; ym(i)+ emaxT , S(i) = Snp(i). W(i) 2.3.
S
S
(a) (b)
2.3: W(i) : ) ) (n=2)
2.4.2
Q(i) :
Q(i) = argQ
hmin
nvol(Q) : Q
hQ(i)
\S(i)
ioi; (2.41)
Q(i) , [54], [55]:
Q(i) = argQ
[minfvol(Q) : q(i1)+w(i) 2Q;q(i1) 2Q(i1); w(i) 2Qw)g] : (2.42)
Qw , Qw Ww. Q(i)
Optimal Volume Ellipsoid (OVE) [51], [56]. Q(i) Q(i)TSp(i) 2.4.
19
-
2.
1
2
1 ( )pS i
2 ( )pS i
( )i
( )i
( 1)i
( ) i
( 1) i
( )F i
2.4: - (n=2)
Q(i)
OVE. -
Q(i) 2.5. ,
, OVE
, 2.5 2.5.
1 1
2 2
2 ( )npS i
1 ( )npS i
(a) (b)
12 ( )h i
( )i
2 ( )npS i
1 ( )npS i
12 ( )h i
21( )h i ( )i
22 ( )h i
11( )h i1
2
2 ( )npS i
1 ( )npS i
(c)
21( )h i
( )i ( )i
( )i ( )i
( ) i
( ) i ( ) i
2.5: - (n=2)
20
-
2.5
2.5
2.5.1
,
w(i) = [w1(i); : : : ;wn(i)]T = [0; : : : ;0]T ; (2.43)
q (i) = q (i1) = q (0) = q ; 8 i; (2.44)
y(i) = f(i)Tq : (2.45)
:
Q(i) = Q(i1); (2.46)W(i) = W(i1): (2.47)
, Q(i1) W(i1). , sgn(q u (i)) = sgn(q u (i1)) = sgn(q u ) ; 8 i; u.
2.5.2
- , / :
ym(i) = f(i)Tq (i)+ e0y(i) (2.48)
e0y(i) e0maxy ; (2.49) e0maxy .
21
-
2.
2.6
, - . - , - . , - , . , (-), . - n 2(n+ 1). - . - Optimal Volume Ellipsoid(OVE), - . - .
22
-
3
3.1 -
, :
y(i) = f(i)Tq (i); (3.1)q (i) = q (i1)+w(i)+ Dq (i)Dq i f j ; i f j < i i f j+1 ; (3.2)
y(i) 2 R , f(i) 2 Rn - , q (i)2Rn , Dq (i)2Rn , i f j , f j . , (2.3) (2.4), (2.5), (2.6) (2.7). -,
Lf j = argLf j
nLf j = i
f j+1 i f j :
Dq i f j + iDq i f j
= 0; i 2 n0; : : : ;Lf j 1oo : (3.3) Lf j , - Dq
i f j 8 i f j Lmin
f jLf j .
3.1 n= 2.
23
-
3.
0
1( )i
i
( )11 fi
( )31 fi
( )51 fi
0
2 ( )i
i1fi
( )12 fi
( )32 fi
( )22 fi
2fi 3fi 4fi 5fi
L L L L L
3.1: (n= 2).
-:
q u (i) 2qminu ;qmaxu
;8i; u= 1; : : : ;n: (3.4)
q u (i) u q (i). / q u (i) , -. (3.4), 8 u 2 f1; : : : ;ng
Dqu (i)Dqui f j
= q (i)q (i1)w(i) 2 gminu ;gmaxu ; 8 i f j (3.5)gminu = qminu qmaxu wmaxu ; (3.6)gmaxu = qmaxu qminu wminu : (3.7)
3.2
.
24
-
3.2
1 ym(id j); fm(id j),
Zid j\
Sid j= /0; (3.8)
id j , d j -, S
id j ( ) Z
id j
id j , id j1 < i f j id j . - 3.2 3.3, .
2
()jd
np
Si
2
1 1
( )jd
pS
i +
+
+
+
+
( ) jdi( ) jdi
( ) jdi
( ) jdi ( ) jdi
(a) (b)
3.2: : ) , ) (n= 2).
2
()jd
np
Si
2
1
( ) jdi ( ) jdi
1
( ) jdi
( ) jdi
( ) jdi
( )jd
pS
i +
+
+
+
+
(a) (b)
3.3: : ) , ) - (n= 2).
25
-
3.
3.3
, - . , Z
id j
Sid j ,
Zid j
! Zrid j; (3.9)
Sid j
! Srid j; (3.10)
q id j 2 Zr id j
q id j 2 Sr id j
9=;) Zrid j\Srid j 6= /0: (3.11) q
id j .
. , - .
3.3.1 q id j 1+wid j 2 Wid j, q id j 2Wr id j,
Wrid j=
8>>>:q :2664q rW1
id j
...
q rWnid j37754 q 4
2664q r+W1
id j
...
q r+Wnid j37759>>=>>; (3.12)
q rWuid j
= qWuid j+ gminu ; (3.13)
q r+Wuid j
= q+Wuid j+ gmaxu ; (3.14)
qWuid j, q+Wu
id j -
Wid j.
. - .
26
-
3.3
3.3.2 q id j 1+wid j 2 Qid j, q id j 2 Qr id j,
Qrid j :
q crid j
= q cid j
(3.15)
Prid j
= Uid jSrid jUT
id j; (3.16)
Srid j
= Sid j+2gS
id j1=2
+ g2I; (3.17)
Pid j
= Uid jSid jUT
id j; (3.18)
g =
sn
u=1
max(jgminu j ; jgmaxu j): (3.19)
. Sid j=
Spid j Sr
id j ,
(2.21). emaxid j,
,
emaxid j= emaxy +
n
u=1
emaxfu maxq rWu id j ; q r+Wu id j (3.20)
q rWuid j,q r+Wu
id j (3.13) (3.14), -
,
,
emaxid j= emaxy +
n
u=1
emaxfu maxq rWQu id j ; q r+WQu id j (3.21)
q rWQu
id j
= rqou+n
Qrid j (3.22)q r+WQu
id j
= rqouQrid j (3.23)
qou; qou+n (2.16).
Sid j= Snp
id j,
qminu 0 qmaxu 0; 8 u, , Sr
id j= Snp
id j,
27
-
3.
qminu < 0< qmaxu
sgnq rWu
id j
= sgnq r+Wu
id j
; 8 u; (3.24)
sgnq rWQu
id j
= sgnq r+WQu
id j
; 8 u; (3.25)
Srid j= Snpr
id j, Snpr
id j (2.25)(2.27),
(3.24) (3.25) sgnq id j.
u qminu < 0< qmaxu (3.24) (3.25), Snpr
id j
(2.21) (3.20) (3.21).
() - , - () 3.4 ( 3.5).
( ) ( )
( ) S
( ) }( ) S
( )
}
3.4: - (n= 2).
3.3.1
, - ( ) , [57].
28
-
3.3
( ) jdr i
( ) jdi
( ) ( )1j jd di w i +
( ) ( )1j jf fi i
( ) jdi
()j
dp
r iS
( )jdi
( )jd
pi
S
3.5: - (n= 2).
3.3.1.1
3.3.1 u -, iu,
Wuiujid j 1
\Wu (iu) = /0: (3.26)
Wuiujid j 1 Wu iujid j 1.
3.3.2 u , iu
Wuiujid j 1
\Wu (iu) =Wu (iu) : (3.27)
Wuiujid j 1 Wu iujid j 1.
Wuiujid j 1 :
Wiujid j 1
= arg
W
nW :W=Wd iW
id j 1
o; (3.28)
d i= iu id j 1 ; d i 1 Wd i =WwWw : : :Ww| {z }d i
.
29
-
3.
3.3.1.2
3.3.3 u - iu
WQuiujid j 1
\WQu (i
u) = /0; (3.29)
WQuiujid j 1 Qiujid j 1.
3.3.4 u iu
WQuiujid j 1
\WQu (i
u) =WQu (iu) ; (3.30)
WQuiujid j 1 Qiujid j 1.
Qiujid j 1
Qid j 1 Qd i=Qwd i wc;d i2 Pw, d i= iuid j 1 ; d i
1 wc;Pw - Qw.
3.3.2
3.3.2.1
u (u = 1; : : : ;n) - , , Dqu
i f jDqu i f j1,
dqu(iu) = q cWu (i
u)q cWu
id j 1
+d i
wmaxu +wminu
2
; (3.31)
d i= iu(id j1), iu u .
3.3.2.2
u (u = 1; : : : ;n) - , , Dqu
i f jDqu i f j1,
dqu(iu) = q cu (iu) q cu
ijid j 1
: (3.32)
d i= iu(id j1), iu u .
30
-
3.4 :
3.4 : -
, , :
y(i) = f(i)Tq +Dq
i f j1
; for i f j1 i< i f j ;
y(i) = f(i)Tq +Dq
i f j
; for i f j i< i f j+1 ; (3.33)
,
q u +Dqui f j 2 qminu ;qmaxu ; 8 i f j ;u= 1; : : : ;n (3.34)
Dqui f j 2 gminu ; gmaxu ; 8 i f j ; (3.35)
gminu = qminu qmaxu ; (3.36)gmaxu = qmaxu qminu =gminu : (3.37)
3.4.1
, - (3.8) :
Zid j 1
\Sid j= /0; (3.38)
Zid j 1 Wid j 1 Qid j 1,
. -
, . :
X(i) =i\
t=1
WQ(t); (3.39)
,
X(i) = X(i1)\WQ(i): (3.40)
X(i) - :
Xu (i) = proju
(X) =nqu : qu 2
hqXu (i) ;q
+Xu
(i)io
(3.41)
31
-
3.
:
q cXu(i) =q+Xu(i)+q
Xu(i)
2; u= 1; : : : ;n: (3.42)
X(i) :
q cX(i) =q cX1(i); : : : ;q
cXn(i)T
: (3.43)
- [58].
2 ym(id j); fm(id j),
Xid j= X
id j 1
\WQ
id j= /0: (3.44)
id j , d j id j , id j1 < i f j id j .
Qid j 1
\Sid j= /0: (3.45)
- 3.6, (3.44) 3.7.
3.4.2
3.3 - .
: ) Zid j 1!
Zrid j 1, ) Sid j 1! Sr id j 1
q +Dqi f j 2 Zr id j
q +Dq
i f j 2 Sr id j
9=;) Zrid j\Srid j 6= /0: (3.46)
32
-
3.4 :
( )3 jfi
( )3 jfi ( )2 jfi
( )2jfpS i
( )2X jfi( )2 jfi
( )1jfpS i
( )1X jfi
( )1 jfi
( )1 jfi
3.6: (n= 2).
( )1 + jfi
( )1X jfi
( )1 jfi( ) jfi( ) + jfi
( ) jfi
3.7: - id j = i f j (n= 2).
33
-
3.
. - , W
id j 1
.
3.4.1 q +Dqi f j1
2Wid j 1, q +Dq i f j2Wr id j 1, Wrid j 1
=
8>>>:q :2664q rW1
id j 1...
q rWnid j 1
37754 q 42664q r+W1
id j 1...
q r+Wnid j 1
37759>>=>>; (3.47)
q rWuid j 1
= qWu
id j 1
2gmaxu ; (3.48)
q r+Wuid j 1
= q+Wu
id j 1
+2gmaxu : (3.49)
. - , - .
3.4.2 q +Dqi f j1
2Qid j 1, q +Dq i f j2Qr id j 1, Qr
id j 1 :
q crid j 1
= q c
id j 1
; (3.50)
Prid j 1
= U
id j 1
Srid j 1
UT
id j 1
; (3.51)
Srid j 1
= S
id j 1
+4gS
id j 1
1=2+4g2I; (3.52)
Pid j 1
= U
id j 1
Sid j 1
UT
id j 1
; (3.53)
g =
sn
u=1
jgmaxu j: (3.54)
Qrid j 1
.
3.4.3 q +Dqi f j1
X
id j 1
Qid j 1, q +Dq i f j Xr id j 1
34
-
3.4 :
and Qrid j 1, Xrid j 1
=
8>>>:q :2664q rX1
id j 1...
q rXnid j 1
37754 q 42664q r+X1
id j 1...
q r+Xnid j 1
37759>>=>>; (3.55)
q rXuid j 1
= qXu
id j 1
2gmaxu ; (3.56)
q r+Xuid j 1
= q+Xu
id j 1
+2gmaxu (3.57)
Qrid j 1
= arg
Q
hmin
nvol(Q) : Q Xr
id j 1
oi; (3.58)
Lwner-John Xrid j 1 [59].
. - 3.3. - Wrid j 1,Qr id j 1 ;Xr id j 1,
Sprid j Snpr
id j.
3.8.
3.4.2.1
- :
q 2 Xid1 1 Wid1 1, q +Dq
i f j 2 Xid j + i Wid j + i, 8 i 2 0; id j+1 id j
X(i1) X(i); (W(i1)W(i)) 8 i.
3.4.1 u -, iu
Zu
id1 1
\Zu (iu) = /0;
iu id j
; (3.59)
35
-
3.
( )jfi + ( )1jfi +
( )jdiX
max
12
( )1jr di X
( )1jr di
( )jdi
( )jdi
( )1jdi X
max
12
max
22
max
22
( )jdiS
( )jr diS
3.8: (n= 2)
Zu(i) = Xu(i) - Zu(i) = Wu(i) .
3.4.2 u(u= 1; : : : ;n) - , iu
Zu
id1 1
\Zu (iu) = Zu (iu) ;
iu id j
; (3.60)
Zu(i) = Xu(i) - Zu(i) = Wu(i) .
3.9, , , q2 - -, . -, q1 .
3.4.2.2
u -, Dqu
i f j
dqu(i) = qcZu(iu+ i)q cZu
id1 1
; (3.61)
36
-
3.5
2
1
( )1 1 di
2
1
2
1
()
*
2
i ( )* i
()
12
1
d i
( )11 1 di
( )*1 i
1d
2d
( )1 1 di
( )* i
( )11 1 di
( )*1 i
()
*
2
i(
)1
21
d i
()
*
2
i(
)1
21
d i
( )11 1 di
( )*1 i
( )* i
( )1 1 di
(a) (b) (c)
3.9: (n= 2)
0 i < id j+1 iu q cZu(i) = q cXu(i) q cZu(i)= q
cWu(i) -
. q cXu(i), qcWu(i)
(3.42) (2.10), .
3.5
3.5.1
, - . q +Dq
i f j2Zi f j + ` ; `= 0; : : : ;L,
Z(i) .
3.5.1.1 -
3.5.1 q +Dqi f j 2 Wi f j + ` ; ` = 0; : : : ; i f j+1 i f j
q +Dqi f j 2Wi f j 1.
3.5.1.2 -
-, q +Dq
i f j 2 Qi f j + ` ; ` =
0; : : : ; i f j+1 i f j , q +Dq i f j 2 Qi f j 1, 3.10.
37
-
3.
( )1jfi +( )1 jfi
( )jfp iS
( )jfi
( )jfi +
3.10: Undetected fault case (n= 2).
3.5.1 q +Dqi f j 2Qi f j
q +Dqi f j1
2 Qi f j 1 ; and
Dq i f jDq i f j1
a2+
qa22 4a1a32a1
; and
a3 < 0;
a2 = 2 s(i f j )d (i f j )s(i f j )pG(i f j )
fT (i f j )q1p
G(i f j )
+ d (i
f j )t(i f j )s(i f j )
pG(i f j )
f(i f j)
+2qlmax[P(i f j1)]lmin[P(i f j1)]
,
a3 = 1+ d (if j )
s(i f j )
f(i f j )T q1p
G(i f j ) t(i f j)
2 d (i f j), q1 = q + Dq
i f j1
qc i f j 1, a1 =d (i f j )
lmin[P(i f j )].
3.5.2
id j - i f j [60]. - id j+1 . id j+1 id j < L, - L- - . , id j . .
q +Dqi f j1
2 Wi f j 1 ( ) - i f j Dq
i f jDq i f j1= [d1;0]T , ( (3.11))
L= 3.
38
-
3.5
q +Dqi f j W
i f j 1, -
Snpi f j( )
Wi f j 1. ,
Wi f j( ) ,
q +Dqi f j q +Dq
i f j1
.
id j = i f j +1, Snpi f j +1
TWi f j 6= /0, Snp i f j +1 -
. - Wr
i f j( ), -
(3.4.1), Wi f j +1
.
, Snpi f j +2
( )
Wi f j +1
id j+1 = i f j + 2 < i f j + 1+L = id j +L. , id j = i f j + 1 . - , .
( )1
max2
( ) ( )1 + jfi ( ) +
jfi
( ) ( )S
( )S +
( )S +
( ) +
2
max2
3.11: (n= 2).
, id j , id j = id j 1 - W
id j1 Wr id j1. -
id j; : : : ; id j+1
, Snp
id j+1
W
id j+1 1.
, id j =
id j 2; : : : ; id j L,
. (3.12) . , ,
39
-
3.
, id j = id j 1, S
id j+1
TWid j+1 1 6= /0.
( )
( ) ( )1 +
jfi ( ) + jfi
( )
( ) +
( )S
( )S +
( )S +
3.12: (n= 2).
3.6
, - . - , , . , - , - . , - . , -. , - - . . .
40
-
3.6
- , - . , - . , ) , ) - , .
41
-
3.
42
-
4
4.1 -
4.1, -. , . V . -- . 4.1.
:
mz+ cz+ kz=eaAV 2
2(z zmax)2= Fel : (4.1)
z , zmax - , m , k , c , A , ea Fel .
43
-
4.
(a) (b)
Serpentine
springs
fuses
X
X
X
X
Movable plate
V electronics
Actuator
electrode
Sensor
electrode
V
maxzz
k c
substrate
m
elF
4.1: ) , ) -- .
:
Fel(i) = [z(i); z(i);z(i)]
24 mck
35) y(i) = fT (i)q : (4.2) q = [q 1 ;q 2 ;q 3 ]
T = [704:96 mNmsec2
mm ;10mNmsecmm ;
0:8 mNmm ] . ym(i);fm1 (i);fm2 (i); fm3 :
ym(i) = Fmel (i) = Fel(i)+ ey(i); jey(i)j emaxyfm1 (i) = zm(i) = z(i)+ ef1(i);
ef1(i) emaxf1fm2 (i) = zm(i) = z(i)+ ef2(i);
ef2(i) emaxf2fm3 (i) = zm(i) = z(i)+ ef3(i)
ef3(i) emaxf3 ;(4.3)
ey(i); efu(i);u = 1;2;3 emaxy ; e
maxfu -
SNR=55dB. [47],
, , 4.1. gmax1 = 30%q 1 , gmax2 =40%q 2 gmax3 = 30%q 3 , L= 500.
- 4.1, -:
44
-
4.1
4.1: -
i f j 2001 3001 4001 5001 6001 7001j 1 2 3 4 5 6Dmm 0.05 0.10 0 0 0 0Dkk 0 0 0.05 0.1 0 0Dcc 0 0 0 0 0.3 0
(A) ,
(B) ,
(C) ,
(D) ,
q +Dqi f j; j= 1; : : : ;6
id j j = 1; : : : ;6, 4.2.
4.2:
j 1 2 3 4 5 6i f j 2001 3001 4001 5001 6001 7001
((A) (D)) id j 2001 3001 4001 5004 6001 7003
4.2, 4.3 and 4.4 [] (A)q+Wu(i) [q
Wu(i)] (() [] ), (B)q
+Wu(i) [q
Wu(i)] ((-
) [] ), (C)q+Xu(i) [qXu(i)] (()
[] ), (D)q+Xu(i) [qXu(i)] (() [] ),
u= 1;2;3. q u +Dqui f j
id j - .
45
-
4.
2001 3001 4001 5004 6001 7003
704.96
740.208
775.456
iterations
1(
Ns
ec2/
m)
(A)-+1
(i)
(A)-1
(i)
(B)-+1
(i)
(B)-1
(i)
(C)-+X1
(i)
(C)-X1
(i)
(D)-+X1
(i)
(D)-X1
(i)
4.2: q 1 , - .
2001 3001 4001 5004 6001 7003
10
13
iterations
2(
Ns
ec/
m)
(A)-+2
(i)
(A)-2
(i)
(B)-+2
(i)
(B)-2
(i)
(C)-+X2
(i)
(C)-X2
(i)
(D)-+X2
(i)
(D)-X2
(i)
4.3: q 2 , - .
46
-
4.1
2001 3001 4001 5004 6001 7003
0.8
0.84
0.88
iterations
3(
N/
m)
(A)-+3
(i)
(A)-3
(i)
(B)-+3
(i)
(B)-3
(i)
(C)-+X3
(i)
(C)-X3
(i)
(D)-+X3
(i)
(D)-X3
(i)
4.4: q 3 , - .
47
-
4.
4.2
-
. 4.5. , (Lc: , bc: , hc: ) (Rt : , lt : ) , .
-
, yin. , -
,
.
Split-diode
photodetector
Mirror
Mirrored Prism
Diode laser &lens
PZT tube scanner
Sample
Cantilever
Piezo
Holder
( )in t
tsFtip
( ),ct L t
4.5:
:
y t(Lc; t)+Cy y t(Lc; t)+Kyy t(Lc; t) =1 4
p
yin(t)+
w1Qc
yin(t)+w21yin(t) (4.4)
48
-
4.2
Cy =w1Qc
+2cllt2
rIrLc; (4.5)
Ky = w21 +2kllt2
rIrLc: (4.6)
w1 , Qc - , r , Ir , kl; cl - . kl ,kl = 8G
pRt (a0d0), G , a0
d0 .
:
y t(Lc; i)U(i) =y t(Lc; i) y t(Lc; i) Cy(i)Ky(i)
)
y(i) = fT (i)q (i); (4.7)
U(i) =1 2b1Lc
yin(i)+ w1Qc yin(i)+w
21yin(i), i2 [1; : : : ;10000]
:
q 1 (i) =w1Qc
+2lt2
rIrLccl(i) = b1+b
2cl(i); (4.8)
q 2 (i) = w21 +16G
p(a0d0)lt2rIrLc
pRt(i) = b3+b
4
pRt(i); (4.9)
. ym(i)=y t(Lc; i)+e1(i), ym(i)= y t(Lc; i)+
e2(i), ym(i) = y t(Lc; i)+ e3(i), eq(i); q = 1;2;3 -, emaxq SNR=55dB. , cl Rt :
cl(i) = cl(i1)+wcl (i); jwcl (i)j 0:0005cl(0)| {z }wmaxcl
Rt(i) = Rt(i1)+wRt (i); 0 wRt (i) 0:0001Rt(0)| {z }wmaxRt
:(4.10)
cl(i) 2cminl ;c
maxl
= [4 107Nsec/m;12
107Nsec/m] Rt(i) 2Rtmin;Rtmax
= [10nm;30nm], 8 i.
49
-
4.
- [61], Rt i f1 = 3501 and i f2 = 6501 Rt
i f1=
Rti f1 1+wRt i f1+0:4Rt i f1 1 Rt i f2=Rt i f2 1+wRt i f2+0:25Rt i f2 1.
4.1 (4.7) q (i) - q 1 (i); q 2 (i). 4.3.
4.3: -
j i f j (A)&(B)-id j (C)&(D)-id j
1 3501 3501 3519
2 6501 6501 6518
q 1 (i); q 2 (i) cl(i),Rt (i), - (B) (D).
4.6(a) cl(i) ( ), (B)[(D)]c+l (i), (B)[(D)]c
l (i) (
[], ) - (B)[(D)]c+l (ijid j 1), (B)[(D)]cl (ijid j 1) ( [], ). , 4.6(b) Rt(i) ( ), (B)[(D)]R+t (i), (B)[(D)]R
t (i) (
[], ) - (B)[(D)]R+t (ijid j 1), (B)[(D)]Rt (ijid j 1) ( [], ).
4.3
- - . , ,
50
-
4.3
3501 65011.5
1
0.5
0
0.5
1
1.5
2
2.5
3x 106
iterations
c l(K
gr/se
c)
cl(i)
(B)-c+l
(i)
(B)-cl
(i)
(B)-c+l
(i|idj 1)
(B)-cl
(i|idj 1)
(D)-c+l
(i)
(D)-cl
(i)
(D)-c+l
(i|idj 1)
(D)-cl
(i|idj 1)
(a) cl(i)
3501 6501
10
15
20
25
30
X= 3500Y= 11.7622
iterations
Rt
(nm
)
X= 6500Y= 17.9528
Rt(i)
(B)-R+t
(i)
(B)-Rt
(i)
(B)-R+t
(i|idj 1)
(B)-Rt (i|idj 1)
(D)-R+t
(i)
(D)-Rt
(i)
(D)-R+t (i|idj 1)
(D)-Rt
(i|idj 1)
(b) Rt(i)
4.6: (B) (D)
51
-
4.
- - . -, , , - . , - , .
52
-
5
, , . , . , : ) - , ) .
, - , , , . H - . . - , -, - . .
53
-
5.
, . , - , .
- , . , - , . , , - . , , . , - . - - , - , . , . , - , .
- (), - . -, - , , ., - , . , - . ,
54
-
, - . , , , , - , . , - . , - .
, . 2, - . , -. .
- . , , 1 [62]. , , , . , y(i) 2 R f(i) 2 Rn. - y(i) 2 Rr1 f(i) 2 Rrn [63].
3, - . , - , - / . [64].
55
-
5.
[65], [66] - . [67]. , .
, 5, - - . , - , . , , -, .
56
-
[1] R. Isermann, Fault-diagnosis systems: an introduction from fault detection to fault tolerance. Springer
Verlag, 2006.
[2] J. Gertler, Fault detection and diagnosis in engineering systems. Marcel Dekker, New York, 1998.
[3] M. Basseville and I. Nikiforov, Detection of abrupt changes: Theory and application. Prentice Hall
Inc, 1993.
[4] C. Jiang and D. Zhou, Fault detection and identication for uncertain linear time-delay systems,
Computers and Chemical Engineering, vol. 30, no. 2, pp. 228242, 2004.
[5] P. Smith, C. Furse, and J. Gunther, Analysis of spread spectrum time domain reectometry for
wire fault location, IEEE Sensors Journal, vol. 5, no. 6, pp. 14691478, 2005.
[6] I. Izadi, S. Shah, D. Shook, and T. Chen, An Introduction to Alarm Analysis and Design, in
Proceedings of the 7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes,
Barcelona, Spain, 2009, pp. 645650.
[7] K. Huang and N. EvaWu, Change Detection for the NASA Generic Transport Aircraft Model,
in Proceedings of the 7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical
Processes, Barcelona, Spain, 2009, pp. 277282.
[8] Y. Tharrault, G. Mourot, and J. Ragot, WWTP diagnosis based on robust principal component
analysis, in Proceedings of the 7th IFAC Symposium on Fault Detection, Supervision and Safety of
Technical Processes, Barcelona, Spain, 2009, pp. 13421347.
[9] J. Vanlaer, G. Gins, and J. Van Impe, Comparison of MPCAV, ARPCA, and BDPCA fault detec-
tion performance in a fed-batch penicillin fermentation process, in Proceedings of the 7th IFAC
Symposium on Fault Detection, Supervision and Safety of Technical Processes, Barcelona, Spain, 2009,
pp. 840845.
[10] W. Zanardelli, E. Strangas, and S. Aviyente, Identication of Intermittent Electrical and Me-
chanical Faults in Permanent-Magnet AC Drives Based on Time-Frequency Analysis, IEEE
Transactions on Industry Applications, vol. 43, no. 4, pp. 971980, 2007.
[11] F. Previdi and T. Parisini, Model-free actuator fault detection using a spectral estimation ap-
proach: the case of the DAMADICS benchmark problem, Control Engineering Practice, vol. 14,
no. 6, pp. 635644, 2006.
[12] M. Galvez-Carrillo and M. Kinnaert, Fault detection and isolation in current and voltage sensors
of doubly-fed induction generators, in Proceedings of the 7th IFAC Symposium on Fault Detection,
Supervision and Safety of Technical Processes, Barcelona, Spain, 2009, pp. 13601365.
57
-
[13] R. Isermann, Model-based fault-detection and diagnosisstatus and applications, Annual Reviews
in control, vol. 29, no. 1, pp. 7185, 2005.
[14] S. Rajakarunakaran, P. Venkumar, D. Devaraj, and K. Rao, Articial neural network approach
for fault detection in rotary system, Applied Soft Computing Journal, vol. 8, no. 1, pp. 740748,
2008.
[15] C. Edwards, S. Spurgeon, and R. Patton, Sliding mode observers for fault detection and isolation,
AUTOMATICA OXFORD, vol. 36, pp. 541553, 2000.
[16] G. Hendeby and F. Gustafsson, Fundamental fault detection limitations in linear non-Gaussian
systems, in Proceedings of the 44th IEEE Conference on Decision and Control, Seville,Spain, 2005,
pp. 338343.
[17] J. Sakellariou and S. Fassois, Vibration based fault detection and identication in an aircraft
skeleton structure via a stochastic functional model based method, Mechanical Systems and Signal
Processing, vol. 22, no. 3, pp. 557573, 2008.
[18] L. Hartert, M. Sayed Mouchaweh, and P. Billaudel, Dynamic Fuzzy Pattern Matching for the
monitoring of non stationary processes, in Proceedings of the 7th IFAC Symposium on Fault Detec-
tion, Supervision and Safety of Technical Processes, Barcelona, Spain, 2009, pp. 516520.
[19] V. Sugumaran, V. Muralidharan, and K. Ramachandran, Feature selection using Decision Tree
and classication through Proximal Support Vector Machine for fault diagnostics of roller bearing,
Mechanical Systems and Signal Processing, vol. 21, no. 2, pp. 930942, 2007.
[20] S. Pirooz Azad, Bahrampour, B. S., Moshiri, and K. Salahshoor, New Fusion Architectures for
Performance Enhancement of a PCA-Based Fault Diagnosis and Isolation System, in Proceedings
of the 7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, Barcelona,
Spain, 2009, pp. 852857.
[21] C. Isaza, A. Orantes, T. Kempowsky-Hamon, and M.-V. Le Lann, Contribution of fuzzy classi-
cation for the diagnosis of complex systems , in Proceedings of the 7th IFAC Symposium on Fault
Detection, Supervision and Safety of Technical Processes, Barcelona, Spain, 2009, pp. 11321139.
[22] A. Barner, J. Bredau, and F. Schiller, Ecient Fault Detection in Safety-related Pneumatic Con-
trol by Conceptual Encapsulation, in Proceedings of the 7th IFAC Symposium on Fault Detection,
Supervision and Safety of Technical Processes, Barcelona, Spain, 2009, pp. 11681173.
[23] E. Nemeth, R. Lakner, I. Cameron, and K. Hangos, Fault diagnosis based on hazard identication
results, in Proceedings of the 7th IFAC Symposium on Fault Detection, Supervision and Safety of
Technical Processes, Barcelona, Spain, 2009, pp. 15151520.
[24] R. Razavi-Far, H. Davilu, V. Palade, and L. Caro, Neuro-Fuzzy based Fault Diagnosis of a Steam
Generator, in Proceedings of the 7th IFAC Symposium on Fault Detection, Supervision and Safety of
Technical Processes, Barcelona, Spain, 2009, pp. 11801185.
[25] V. Puig, J. Quevedo, T. Escobet, and B. Pulido, On the integration of fault detection and isolation
in model-based fault diagnosis, in Proceedings of the 16th International Workshop on Principles of
Diagnosis (DX-05), Pacic Grove, CA, USA, 2005, pp. 227232.
[26] J. Meseguer, V. Puig, and T. Escobet, Fault Diagnosis using a Timed Discrete Event Approach
based on Interval Observers, in Proceedings of the 17th IFAC World Congress, Seoul, Korea, 2008,
pp. 69146919.
58
-
[27] D. Panescu, Mems in medicine and biology, IEEE Engineering in Medicine and Biology Magazine,
vol. 25, no. 5, pp. 19 28, 2006.
[28] J. Leclerc, Mems for aerospace navigation, IEEE Aerospace and Electronic Systems Magazine,
vol. 22, no. 10, pp. 31 36, 2007.
[29] N. de Rooij, S. Gautsch, D. Briand, C. Marxer, G. Mileti, W. Noell, H. Shea, U. Staufer, and
B. van der Schoot, Mems for space, in Proceedings of the 15th International Conference on Solid-
State Sensors, Actuators and Microsystems, Denver, Colorado, USA, 2009, pp. 17 24.
[30] J. Hilbert, Rf-mems for wireless communications, IEEE Communications Magazine, vol. 46, no. 8,
pp. 68 74, 2008.
[31] J. Wang, G. Li, , Y. Lu, X. Gao, Y. Zhang, and K. Tao, Vehicle supervision system based on mems
geomagnetic sensor, in Proceedings of the 4th International Conference on Nano/Micro Engineered and
Molecular Systems, Shenzhen, China, 2009, pp. 331 334.
[32] E. Eleftheriou, T. Antonakopoulos, G. Binnig, G. Cherubini, M. Despont, A. Dholakia, U. Durig,
M. Lantz, H. Pozidis, H. Rothuizen, and P. Vettiger, Millipede - a mems-based scanning-probe
data-storage system, IEEE Transactions on Magnetics, vol. 39, no. 2, pp. 938 945, 2003.
[33] D. Sahoo, W. Haberle, A. Sebastian, H. Pozidis, and E. Eleftheriou, High-throughput intermittent-
contact scanning probe microscopy, Nanotechnology, vol. 21, pp. 17, 2010.
[34] M. Dardalhon, V. Beroulle, L. Latorre, P. Nouet, G. Perez, J. Nicot, and C. Oudea, Reliability
analysis of CMOS MEMS structures obtained by Front Side Bulk Micromachining,Microelectronics
reliability, vol. 42, no. 9-11, pp. 17771782, 2002.
[35] S. Lee, R. Ramadoss, M. Buck, V. Bright, K. Gupta, and Y. Lee, Reliability testing of exible
printed circuit-based RF MEMS capacitive switches, Microelectronics Reliability, vol. 44, no. 2, pp.
245250, 2004.
[36] Z. Tao and B. Bhushan, Surface modication of AFM silicon probes for adhesion and wear
reduction, Tribology Letters, vol. 21, no. 1, pp. 116, 2006.
[37] S. Mir, Integrated circuit testing: From microelectronics to microsystems, in Proceedings of the
5th IFAC Symposium on Fault detection, supervision and safety of technical processes, Washington, DC,
USA 2003, pp. 1324.
[38] A. Kolpekwar, T. Jiang, and R. Blanton, CARAMEL: Contamination and reliability analysis of
MicroElectromechanical layout, Journal of Microelectromechanical Systems, vol. 8, no. 3, pp. 309318,
1999.
[39] R. Rosing, A. Lechner, A. Richardson, and A. Dorey, Fault simulation and modelling of micro-
electromechanical systems, Computing & Control Engineering Journal, vol. 11, no. 5, pp. 242250,
2000.
[40] M. Lubaszewski, E. Cota, and B. Courtois, Microsystems testing: an approach and open prob-
lems, in Proceedings of the Design, Automation and Test in Europe, Paris, France, 1998, pp. 524529.
[41] B. Caillard, Y. Mita, Y. Fukuta, T. Shibata, and H. Fujita, A highly simple failure detection
method for electrostatic microactuators: application to automatic testing and accelerated lifetime
estimation, IEEE Transactions on Semiconductor Manufacturing, vol. 19, no. 1, pp. 3542, 2006.
[42] A. Dhayni, S. Mir, L. Rufer, A. Bounceur, and E. Simeu, Pseudorandom BIST for test and char-
acterization of linear and nonlinear MEMS, Microelectronics Journal, vol. 40, no. 7, pp. 10541061,
2009.
59
-
[43] B. Charlot, S. Mir, F. Parrain, and B. Courtois, Generation of electrically induced stimuli for
MEMS self-test, Journal of Electronic Testing, vol. 17, no. 6, pp. 459470, 2001.
[44] R. Asgary and K. Mohammadi, Initialized RHPNN for fault detection in MEMS, in Proceedings
of the 8th International Conference on Pattern Recognition and Information Processing, Minsk, Russia,
2005, pp. 449453.
[45] J. Tanha and R. Asgary, An Intelligent BIST Mechanism for MEMS Fault Detection, in Proceedings
of MEMSTECH 2007 International Conference on the Perspective Technologies and Methods in MEMS
Design, Lviv, Ukraine, 2007, pp. 1214.
[46] A. Izadian and P. Famouri, Fault Diagnosis of MEMS Lateral Comb Resonators Using Multiple-
Model Adaptive Estimators, IEEE Transactions on Control Systems Technology, vol. PP, no. 99, pp.
18, 2010.
[47] A. Izadian, P. Khayyer, and P. Famouri, Fault Diagnosis of Time-Varying Parameter Systems
With Application in MEMS LCRs, IEEE Transactions on Industrial Electronics, vol. 56, no. 4, pp.
973978, 2009.
[48] H. Nguyen, C. Berbra, S. Lesecq, S. Gentil, A. Barraud, and C. Godin, Diagnosis of an Inertial
Measurement Unit Based on Set Membership Estimation, in 7th Mediterranean Conference on
Control and Automation, Thessaloniki, Greece, 2009, pp. 211216.
[49] A. Kurzhanskiy and P. Varaiya, Ellipsoidal Toolbox (ET), in Proceedings of the 45th IEEE
Conference on Decision and Control, San Diego, CA, USA, 2006, pp. 14981503.
[50] T. Clement and S. Gentil, Reformulation of parameter identication with unknown-but-bounded
errors, Mathematics and Computers in Simulation, vol. 30, no. 3, pp. 257270, 1988.
[51] J. Gassman and S. Yurkovich, An ellipsoid algorithm for parameter set estimation, in IEEE
Conference on Control Applications, Dayton, OH, USA, 1992, pp. 835840.
[52] G. Belforte, Parameter identication for models with bounded errors in all variables, Systems
and Control Letters., vol. 19, no. 6, pp. 425428, 1992.
[53] V. Cerone and D. Regruto, Parameter bounds for discrete-time Hammerstein models with
bounded output errors, IEEE Trans. on Automatic Control, vol. 48, no. 10, pp. 18551860, 2003.
[54] F. Chernousko, Optimal Guaranteed Estimates of Indeterminacy With the Aid of Ellipsoids-Part
I, Engineering Cybernetics, vol. 18, no. 4, pp. 19, 1980.
[55] J. Watkins and S. Yurkovich, Parameter set estimation algorithms for time-varying systems,
International Journal of Control, vol. 66, no. 5, pp. 711732, 1997.
[56] M. Cheung, S. Yurkovich, and K. Passino, An optimal volume ellipsoid algorithm for parameter
set estimation, IEEE Transactions on Automatic Control, vol. 38, no. 8, pp. 12921296, 1993.
[57] V. Reppa and A. Tzes, Fault Detection and Diagnosis relying on Set Membership Identication
for Time-Varying Systems, in Conference on Control and Fault-Tolerant Systems, Nice, France, 2010,
pp. (to appear, Paper FrA1.2).
[58] , Fault Detection and Diagnosis based on Parameter Set Estimation, IET Control Theory and
Appl., 2010, (to appear).
[59] S. Boyd and L. Vandenberghe, Convex optimization. Cambridge University Press, 2004.
60
-
[60] V. Reppa and A. Tzes, Fault Detection and Diagnosis based on Parameter Set Estimation for
Measurements corrupted by Bounded Noise, in 18th Mediterranean Conference on Control and
Automation, Marrakech, Morocco, 2010, pp. 460465.
[61] , Fault Detection relying on Set-Membership techniques for an Atomic Force Microscope,
in 7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, Barcelona,
Spain, 2009, pp. 11861191.
[62] A. Ingimundarson, J. Bravo, V. Puig, T. Alamo, and P. Guerra, Robust fault detection using
zonotope-based set-membership consistency test, International Journal of Adaptive Control and Signal
Processing, vol. 23, no. 4, pp. 10991115, 2008.
[63] V. Reppa and A. Tzes, Fault Detection based on Orthotopic Set Membership Identication for
Robot Manipulators, in in the Proceedings of the 17th IFAC World Congress, Seoul, Korea, 2008,
pp. 73447349.
[64] , Application of set membership identication for fault detection of MEMS, in Proceedings
2006 IEEE International Conference on Robotics and Automation, Orlando, FL, USA, 2006, pp.
643648.
[65] V. Reppa, M. Vagia, and A. Tzes, Fault Detection using Set Membership Identication for Micro-
Electrostatic Actuators, in IEEE International Conference on Control Applications, Singapore, 2007,
pp. 789794.
[66] , Fault Detection and Diagnosis Enhanced by a Reconguration Control Scheme for a Micro-
Electrostatic Actuator, in 18th Mediterranean Conference on Control and Automation, Marrakech,
Morocco, 2010, pp. 477482.
[67] K. Astrom and B. Wittenmark, Adaptive control. Addison-Wesley Longman Publishing Co., Inc.
Boston, MA, USA, 1994.
61
-
62
1 1.1 1.1.1 1.1.2
1.2 1.3
2 2.1 2.2 2.2.1 2.2.2
2.3 2.3.1 2.3.2
2.4 2.4.1 2.4.2
2.5 2.5.1 2.5.2
2.6
3 3.1 3.2 3.3 3.3.1 3.3.1.1 3.3.1.2
3.3.2 3.3.2.1 3.3.2.2
3.4 : 3.4.1 3.4.2 3.4.2.1 3.4.2.2
3.5 3.5.1 3.5.1.1 3.5.1.2
3.5.2
3.6
4 4.1 4.2 4.3
5
