Industrial Communication Systems

68-6 Industrial Communication Systems

approximated as 2δP

M

(x)

for small δ. Alternatively, the probability under the model of equaling or

exceeding the observed value can be computed:

P x x P x d

M M

′

≥

( )

= +

∞

∫

( φ) φ

0

(68.1)

e

data

x

can

be

a

sensor

reading

such

as

an

air

pressure

sensor,

contact

sensor,

temperature

sensor,

and

so

on.

Given

a

new

data

value,

the

system

assigns

a

probability

to

this

value.

When

the

probability

is

ab

ove

a gi

ven

th

reshold,

th

e

sy

stem

co

ncludes

th

at

th

is

da

ta

va

lue

is “n

ormal.”

Given

a

sequence

of

sensor

readings

x

=

{x

1

, … ,x

T

} from times 1 to T, the system must create a model

of

“normal”

sensor

readings.

e

system

uses

an

online

version

of

the

expectation

maximization

algo-

rithm

for

maximum-likelihood

parameter ...