Safety analysis in process facilities: Comparison of fault tree and Bayesian network approaches
Multiple Approaches to Comparison Structure Analysis
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s.i.(ICV 1,ICV 2) = 6 i=1 (ICV 1 i - ICV 2 i ) 2
Transcript of Multiple Approaches to Comparison Structure Analysis
s.i.(ICV 1, ICV 2) =
!""#6$
i=1
(ICV 1i ! ICV 2i)2
dp(x, y) = (n$
i=1
|xi ! yi|p)1/p
d : XxX " R
d(x, y) # 0d(x, y) = 0 x = yd(x, y) = d(y, x)d(x, y) $ d(x, y) + d(y, z)
(1, 1, 2, 1, 1, 2, 1, 1, 2, 4) (1, 2, 1, 1, 2, 1, 1, 2, 4, 1)
(1, 1, 2, 1, 1, 2, ...)
Preprocessing: e.g. selection of the
suitable segmentation cardinality
INPUT: Note event list
Preprocessed event list
Segment classificationAutomated segmentation
Straigh analysis with
segment classes
Calculations with the
similarity functionComparison structure(s) RESULTS: Time series plots etc.
(2, 1, 1) (4, 2, 2)n ·(2, 1, 1) q
T ww = (w1, w2...wk) k = |w|
w w[1...k] w[2..10]w w[2] w[10]
(2, 1, 1)2 == (2, 1, 1, 2, 1, 1)w w(r) w = (1, 1, 2, 4)
w(1) = (1, 2, 4, 1) w(0) = w(4)
q T T|q| q
q Tq
T|q|
|q| . . . 2
|q| < |T |i si
(1, 2) (2, 1)
w |w| ! 2 w (1, 2)(2, 1) |w| = 3
w = (1, 1, 2) w(1,2) (1, 2, 1)(2, 1, 1)
(1, 2) (1, 1)T S d
q si (% S)
d(q, si) = 1! q·si|q||si|
dr r i si
dr(q, si) = min(d(q, s(r)i )) 0 $ r < |q|
q[1...l] ll m = 0
ql ! m m = 1
l ! mq[1...(l ! m)] q[(m + 1)...l]
ml!m = 2
q = (2, 2, 4, 2, 2, 4, 2, 2, 4, 8)
T(2, 1, 1, 2, 1, 1, ...)
(1, 1, 2, 1, 1) w(1!4)
(1, 2, 1, 1, 1) (2, 1, 1, 1, 1) (1, 1, 1, 2, 1) (1, 1, 1, 1, 2)(2, 2, 4)
((2, 2, 4)3, 8) (22, (4, 2, 2)2, 4, 8)
q = (2, 2, 4, 2, 2, 4, 2, 2, 4, 8) |q|
0 100 200 300 400
0.0
00.1
00.2
00.3
0
Bar
Cosi
ne d
ista
nce
Exposition Repetition Development Recapitulation
2nd subj. group
0 100 200 300 400
02
46
8
Bar
Subse
t dis
tance
Exposition Repetition Development Recapitulation
2nd subj. group
(2, 2, 4, 2, 2, 4, 2, 2, 4, 8)
q = |q| ! 2
q
Tn
Tn
Tn
[000000]
sub(xi) i xsub((5 ! 2A)2)
ix y
REL(x, y) =
%349i=2
&sub(xi) · sub(yi)'%349
i=2 sub(xi) ·%349
i=2 sub(yi)
REL(4!1[0, 1, 2, 3], 4!5A[0, 1, 2, 6])
[(0)3210002110000000000000000100...zeros...]
[(0)210111100001010000100000000000010...zeros...]
REL(4! 1, 4! 5A) =
&3 · 2 +
&2 · 1 +
&2 · 1&
11 · 11' 0.48
(nk
)= n!
k!(n!k)! nk
REL(X, 7!35)0sREL(X, 7 ! 1)0s ' 0.45
REL(X, 7! 1)889s = 1
Seconds
RE
L(X
,Co
mp.S
et!
Cla
ss)
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900
0.5
0.7
0.9
1
’Medieval’ ’Renaissance’ ’Baroque’ ’Romantic’ ’Post!tonal’
REL(X, 7 ! 1) REL(X, 7 ! 35)REL(X, 7 ! 31B) > 0.8
889s
REL(X, 7 ! 31B) > 0.8
Tn
{0, 4, 9}
tp pcset
tp = vpcsetM/|pcset|
vpcset = (v0, v1, ...v11)vi i
{0, 4, 9} vpcset = (1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0).
tp1 tp2
{0, 4, 9}
tp1 tp5 tp10 tp17 tp22
corwkk(tp1, tp2) = 1! !(tp1, tp2)
!(tp1, tp2) =
%24i=1(tp1i ! ¯tp1)(tp2i ! ¯tp2)'%24
i=1(tp1i ! ¯tp1)2%n
i=1(tp2i ! ¯tp2)2
{0, 2, 4, 6, 7, 9, 11}
4.941.39 5.04 sd = 1.27
400 410 420 430
0.0
0.5
1.0
1.5
Bar
corw
kk(X
,{0
,2,4
,6,7
,9,1
1})
400 405 410 415 420 425 430 435
00
.51
1.5
corwkk(X, {0, 2, 4, 6, 7, 9, 11})
400 410 420 430
0.0
0.5
1.0
1.5
Bar
Co
rr.
dis
tan
ce
400 405 410 415 420 425 430 435
00
.51
1.5
!"! !"# $"! $"#
$"!
$"$
$"%
$"&
$"'
$"#
()*+,,!-.*/0.)12
3)*45167/28*5-6)
the number of cases in DNL · (536/565)/the number of cases in DAL
Tn/I
s1 = (43, 62, 74, 83) s2 = (43, 59, 74, 83)sum(s1) = 262 sum(s2) = 259
s1 s2 s2 ! s1 = 259! 262 = !3
sum(r) = 0 r
Bar
Co
rre
latio
n
1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30
!0
.50
0.5
1
sum(sn+1) ! sum(sn)
Bar
Ba
r
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
13
57
91
11
41
72
02
32
62
9
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
13
57
91
11
41
72
02
32
62
9
Bar
Ba
r
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
13
57
91
11
41
72
02
32
62
93
2
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
13
57
91
11
41
72
02
32
62
93
2
< 4
Tn
r = min(dens1/dens2, dens2/dens1) r $ 1
3 · 3 · 3
x ci
U(x, ci) =%K
k=1 U(xk,ci)(d(x,xk)!2/(m!1)
%Kk=1 d(x,xk)!2/(m!1)
xk kth x d(x, xk)x kth m > 1
KU(xk, ci) xk ci
C%C
i=1 U(x, ci)) = 1x
> 1d(x, y)!2/(m!1)
m = 2
(2 $)K $ 6
! "!! #!! $!! %!! &!!
!'!
!'#
!'%
!'(
!')
"'!
*+,-
./001*+,!23+014+563-
! "! #!! #"! $!! $"!
!%!
!%$
!%&
!%'
!%(
#%!
)*+,
-.//0)*+!12*/03*452,
p ) 0.01
