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(k)(k)
istics of a synthetically generated indicator series: dcc, ab and tb controlling
(k)(k)(k)
the edge process, Kc, ac , qc and pc controlling the trend process, dcw,
(k)(k)(k)
Kw, aw , qw and pw controlling the white noise process, and gs controlling the outlier process. By assigning speci.c values or probability distributions to these parameters, indicator progressions similar to those associated with various mechanical conditions can be generated.
Figure
6.4
shows
a
.ow
chart
of
the
indicator
model.
The
collection
boxes
(double boxes) used for sigmoids and steps signi.es that zero or more tran-sitions are generated. In the cases where more shapes a produced, these are simply added together in the sum blocks following each sigmoid and step block. When several shapes a produced by a collection block, the control parameters for each transition are tagged with transition index (k) in super-script,
as
shown
in
equation
6.3,
6.4
and
6.7.
The operator ">" produces zero for false and one for true. The intermediate results gw, w, s, b, c, d and r are labeled in the .gure.

Figures
6.5
to
6.10
show
synthetically
generated
progressions
represent-
ing normality, a maintenance action and a fault propagation. Each .gure

6.2. PROGRESSION ANALYSIS
is accompanied with the distributions from which their model parameters where chosen. All con.guration parameters associated with steps and tran-sitions are generated from random uniform distributions ru(from, to). For the counters Kw and Kc, the integer uniform distribution run(from, to) is used, to that {Kw,Kc}∈N .

Symbol  Value  Symbol  Value 
dcw  0.5  dcc  5 
Kw  .  Kc  . 
a(k) w  .  a(k) c  . 
q(k) w  .  q(k) c  . 
p(k) w  .  p(k) c  . 
gs(t)  2gw(t)  ab  . 
pb  . 

Table 6.1: Normal state model parameters

6.2. PROGRESSION ANALYSIS

Symbol  Value  Symbol  Value 
dcw  0.5  dcc  5 
Kw  .  Kc  . 
a(k) w  .  a(k) c  . 
q(k) w  .  q(k) c  . 
p(k) w  .  p(k) c  . 
gs(t)  2gw(t)  ab  ru(1, 4) 
pb  100 
Table 6.2: Step change model parameters.

 

 

Symbol  Value  Symbol  Value 
dcw  0.5  dcc  5 
Kw  run(1, 4)  Kc  run(1, 4) 
a(k) w  ru(0, 1)  a(k) c  ru(.5, 5) 
　
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