a probabilistic model for sensor validation

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lbargiiengoytia, Sucar, and Vadera

A PROBABILISTIC MODEL FOR SENSOR VALIDATION

L.E. Sucar

S. Vadera

Institute de Investigaciones

Institute Tecnologico y de

University of Salford

P.H. lbargiiengoytia Electricas, A.P. 1-475

Estudios Superiores de Monterrey

Dept. of Mathematics

Cuernavaca, Mor., 62001, Mexico

Campus Morelos, A.P. 99-C

and Computer Science

[email protected]

Cuernavaca, Mor., 62050, Mexico

Salford, M5 4WT, U.K.

[email protected]

[email protected]. uk

Abstract

considered as general, the specific application is in the power plants domain.

The validation of data from sensors has be­ come an important issue in the operation and control of modern industrial plants. One ap­ proach is to use know ledge based techniques

The approach proposed in this paper has two layers: •

pected values of the sensors and identify

to detect inconsistencies in measured data. the detection of such inconsistencies. Based able to find the existence of a possible fault

potential

faults;

This article presents a probabilistic model for on probability propagation, this method is

a prediction layer: which is used to predict the ex­



a constraint satisfaction layer:

which is used to

distinguish the faulty sensor(s) from the appar­ ently faulty ones.

among the set of sensors. That is, if an er­

apparent

Both layers make use of a probabilistic network model.

fault due to the propagation from the sen:.

A probabilistic or Bayesian network [Pearl, 1988] is a

sor(s) with a real fault. So the fault detection

directed acyclic graph (DAG) whose structure corre­

ror exists, many sensors present an

mechanism can only tell if a sensor has a

po ­

tentwl fault, but it can not tell if the fault is

sponds to the dependency relations of the set of vari­ ables represented in the network (nodes), and which is

real or apparent. So the central problem is to

parameterized by the conditional probabilities (links)

develop a theory, and then an algorithm, for

required to specify the underlying distribution. In this

distinguishing real and apparent faults, given

case, the nodes correspond to the sensors that consti­

that one or more sensors can fail at the same

tute the model. The structure of the network makes

time. This article then, presents an approach

explicit the dependence and independence relations

based on two levels: (i) probabilistic reason­

between the variables.

ing, to detect a potential fault, and (ii) con­ straint management, to distinguish the real fault from the apparent. ones. The proposed approach is exemplified by applying it to a

In this approach, with the use of probability propaga­ tion, a prediction is made of a variable's value based on other parameters.

If this predicated value devi­

power plant model.

ates from the actual value given by a sensor, by some predefined margin, then some fault can be assumed.

INTRODUCTION

sensor has a

But the fault detection mechanism can only tell if a

1

Computing is playing an increasingly important role in domains like communications, medicine, and industry. Examples of industrial applications include the control of advanced manufacturing plants, power generation, power distribution, and chemical processes. These ap­ plications require the utilization of several method­ ologies that have emerged from the area of artificial intelligence (AI). In general, AI methods are moving towards more realistic domains that require coopera­ tion between several fields of research. This paper de­

potential fault, but it can not tell if the

fault is real or apparent. The central problem is to de­ velop a theory, and then an algorithm, for distinguish­ ing real and apparent faults, considering that one or more sensors can fail at the same time. For this, the structure of the model is considered, which produces a set of constraints that has to be solved to determine the faulty sensor( s). This article then, presents an ap­ proach based in two levels: (i) probability propagation, to detect a potential fault, and (ii) constraint manage­ ment, to distinguish the real faulty from the apparent ones.

of AI methods to solve the problem of sensor valida­

The paper is organized as follows. Section 2 in­ troduces the problem and summarizes previous ap­

tion. Although the techniques presented here can be

proaches.

scribes an ongoing research project in the utilization

Section

:3 presents the approach with the

A Probabilistic Model for Sensor Validation

Section 4 presents the ideas Section 5 describes a real example that shows

ports a fa ulty sensor, it is impossible to define which

the

perature sensor fails and it is uti li zed to d e tect a fault

aid of a simple example. formally.

the complete

technique. Finally, section 6 presents

conclusions and future work.

sensor was the faulty one. In t his example , if the tern­

in the velocity, the system will certainly report a fail­ ure on the velocity reading.

2

333

This could be a wrong

conclusion.

SENSOR VALIDATION

Such an approach , of course , requires the help of do­ The validation of data from sensors has become an imp ortant issue in the operation and control of modern industrial plants. Usually, the control system can not

main experts to identify the dependencies of the vari­ ables and must also take into account of the fol l ow i ng characteristi c s:

detect signifi cant deviations from the expected values g i ven the design working point, for example of the gas turbine in a power plant. Conversely, an experienced operator is capable of detecting such deviations of a



The sensors can provide erroneous informa tion.



Information is available all the time, i .e., all sen­ sors can be observed as evidence or considered as

variable by direct observation of the related variables

an h ypoth esis at any time .

and consequently, avoids false plant trips. T his proj ect



proposes the modelli ng of the operator's experience in

The system must respond within a real time en­ vironment.

the detec ti on of sensor failures.



Typical solutions to this problem, particularly in criti­ cal systems where security is essential, include the use

The applic ation considers the possibility of mul­ tiple faults.

of: •

Hardware redundancy

and majority voting:

w here

hardware is dupli cated and a voting algorithm is used to exclude faulty sensors. This is possible in applications such as civilian aircraft or part of the nuclear industry [Yung and

C l arke,

1989].

How­

ever, for many industria l plants, these tech n iques are not feasible where , for example , adding fur­ ther sensors might we a k en the walls of the pres­ •

3

THE APPROACH PROPOSED

This section presents the approach proposed through a very simple example. Assume the model of the gas turbine in a power plant shown in Fig. 11 . The root node

m

represents the rea d in g of the Megawatts gen­

erated in the plant.

The temperature is represented

by node t and the pressure by p.

F inal ly,

g represent s

the fue l supplied to the combustion chamber. The val­

sure vessels.

idation process starts assumin g that th e sensors, one

Analytical redundancy: in which all process, actu­

by one, are suspect.

ators and sensors are monitored centrally. Exam­

system deci des if the reading of the sensor is correct

ples of these tech niques are generalized likelihood ratio (GLR) [Willsky an d Jones, 1976], and failure

process is carried out for each one of the variables that

sensitwe filters [Massoumnia, 1986].

By probabilistic reasoning, the

based on the values of the most related variables. This is required to be validated. The most closely related

However, these approaches can require the develop­ ment of mathematical or knowledge based models whose solution require expensive computer power. Ad­

d itionally, they are very expensive and dem and an enormous amount of expertise to use them in a differ­ ent process or even make a itored system.

m odifi cat i on

of the mon­

Modern techniques, from where this

project is motivate d , include a decentralised and hier­

archical approach [Yung and Clarke,

1989].

A survey

of some of these techniques can be found in [Basseville,

1988].

Previous stages in the development

of this

proj ect in­

cluded some experiments in the validation of signals

in power plants [I barg iiengoytia et al., 1995]. These experiments were bas ed on the following assumption:

each sensor is validated independently, i.e., each vari­ able was considered as the hypothe sis while some other variables were considered as correct evidence.

How­

ever , a real solution of the prob l em requires a different set of assu mptions to be taken.

For example, if the

turbine velocity is validated u tilizing only the signals of temperature and pressure, and if the re as oning re-

Figure l: Simple tree representing the turbine gener­ ati on

.

m o d el

variables for each sensor consist of the Markov blanket of the sensor variable. A Markov blanket is defined as the set of variables that make a variable i ndependent 1This is

a

simplified model of the gas turbine.

directions of the arcs do not imply causality.

The

334

lbargiiengoytia, Sucar, and Vadera

from th e

others.

even after the probabilistic reasoning,

ing t hree

sets

In a B ayesi an network, the follow­ of neighbours is suffi cient for forming a Markov blanket of a node : the se t of direct. prede­ cessors direct successors, and the direct predecessors

fusion: which

,

of the

successors

(i.e

parents, children, and spouses).

The set of variabl es that constitu tes the Markov blan­ ket of a variable can be seen as a p r ote cti o n of this variable against. ch ange s of vari able s outside the blan­ ket. Tlus rnea.ns that, in order t.o analyze a variable, it is only needed to kno w the value of all variables in its blanket. For exarnple, in Fig. l a Markov blanke t of t is { m, g}, while a blanket of g consists of { t} only. Tab le l shows the Ma rk ov blankets of each one of the variables in the rnodel of Fig. 1.

Table I: Mark o v

blankets of

process variable

p

blankets, probabilistic

area of rnaniff:'st.ation which forms a con­ The contexts can be arranged in a lattice as show n in Fig. :) The lower nod!:' represents the no fault contf:'xt of t.he sys te rn The upp!:'r layers repre­ .

.

m

is s h o w n

where t he absence of g i nd i cates that this variable is out. of m.'s Markov blanket.. ln (b), the mod el to pre­

dict t indicat.es t.hat thf:' chang f:'s of pare not r onsi clf:'red giwn a value of m. The sanw for p and gin (c) and (d).

top node represents a conte xt where all .

reported faulty

.

mtpg l ( mtg I :··:-.,_. ..

(

mt

'

)

Figure

(b)

(a)

tp



. 1· p

)

( tpg ) T



tg. )

pg

1

(. g

F igu r e 2: E qui valf:'nt models p,

for the and (d) for y.

Lattice with the

four v ariab les

,

m,

t, p,

and

Every step in the probabilist.ic rf:'asoning generates a

the final d e tec tion of the sensor in fail. bottom of the lattice of Fig. 3, eac-h step will rnake a tran siti on between thf:' nod es of the lattice. Figure 4 shows the transitions from thP bottom node (cp) to thf:' final node : {m,l,y}.

constraint. for

S tarting at the

g fails

t fails

(d)

(c)

:3:

g, for the model in Fig. 1 .

r r 7 rz 0 0 9 0 0 0

m

fails

variables. (a) for

A�sunH' tha t. the tf:'lnpera.ture sensor suffe rs catas­

t.roplllr d anmge

sensors. The the Sf:'nsors are

Sf:'nt an incremental assumption of faulty


cut.. Starting the Validation jli'UfPSS with Ill, Slllrf:' f jJarftcipafCS i ll the

Figure

4:

Trajectory

followed in the la ttice by the

probabilistic reasoner"

.

[se simple turbine m o del .

proct>:s�

variable

Markov blanket

lattice node

{t,p} {in,g} {m} {t}

{m,t,p} {m,t,g} {m,p} {t,g}

m

p !I

the

axioms of ronditiona! independencl:' and

So1mdnc.5.s theorem [Pearl d al., 1990]. Although there may b e ot h er Markov blankets, only this type of t.lw

blankets are considered.

In using a Bayesian network representation for sensor validation, the following assu m p tions are m ade: 1. Observability: all the variables (sensors) can be 2.

measured directly With this llH'chani:ml, e v en if there exist rnany appar­ e n t faults. t.he p rop agati o n on t.ht> l a t tice distinguishes w hi ch

ers

union of its dir ec t parents

P A(X), its d ire c t successors .')U(X), and all direct

lows from

Table 2:

wnt.ains

setJsor

t.ht> re al

only single f fuel

in tlw combustion charnber. The control val v e i s cotnrnanded by the control system or by t h e oper­ a t or in t h e rn anua.l o p eration mode, and its ap ert u re ran be read by a p o s i t i o n sensor. The temperature at the b l ade p at h which i s t h e rnost cr i t i c a l variable. taken along tlw c i rcumfe re n c e of the t u r b i n e . .

A m o n g all var i a b l e :s t h at participate in

is

the gas tur­ a few are directly 1n e asure d by t h e sensors. b l ade path temperature is the most crit ical variable. i t is obtai n io> given by as t h P l a t. t i r:e model can only ensurE'

the same

t h at there exi :-;t:-; a fa u l t in pr b u t i t can not distin­ guish t h e d u u h l t' fau l t in pt and dp.

tlw

r e a d i n g s of sensors in i n d us t r i al T h is ap p ro ac h . b ased on Bayes ian networks

con::; ist.Pnc iPs i n

and constraint satisfaction , p ossPsses al s o tlw advan­ tage that m u c h

of

the p r o ce ss i n g

b efore t h e system op erate�

t he

c h a racteris t i c w i l l h e l p in

ttuired in n w s t

IS

performed off

line.

th e plant.

This

in

r e a l time p e rfo r m an c E'

uf t. h e i n d ustrial ap p l i cations.

re­

With the

u s e of p ro h ah i li ty p rop ag at i o n , a p redi ction is 1n ade of

other pararnf'ters .

a vari a b l e ' s val u e b ased o n

predi cated

Vv i l i s co nsi d e r P d , which p r o d u c es a se t of constramts t h at. h as t o he solved to df'terrnine the fau lty sensor( s ) . Tlw app roach is b ase d o n two IPv­ els: ( i ) p robabil i ty p r o pagation , to detect a p o t e n t i a l fault , and ( i t ) run:> t t·a.iut managenwnt. to dist i n g u is h tht:> real fanlts front d w a p p ar P n t o n t:> s . T h e uwt hod w as ap p liPd to a s i t u p lifi,..cl rn odPI o f a gas turlHn w i t h pot('ntial fau l t s .

Tht:>

no

c ases w lwn

m ar i z e cl as fo llows: •

two



a d o n h i e fau l t otlwr.

or 1 1 1 0 1'ration has d iffP r en t p h asPs, ( e . g . , st a r t up, s y n­ chroni zation , stt:>ady st a t e , a n d stop) different proba­

rnoclels are

b i l is t i c

required .

For exarn p l e , d ur ing the

s t a r t u p p h ase, t h e v e lo c i t y of t h e t u r b i n e able t h at.

will

changes in the probab i listic [n

add i

work well

D iffPrent prob a b i l i s t i c

is

t h e vari­

be s u b st i t u t e d by the M egawatts g e n­

erated d u r in g other p h ases. A m e c h an i s m

t i o n to

rno del is

to det.Pct

that al l ow s

required .

t he two l e vels of d P c i s i o n , a

r t:> aso ni n g is r e q u i rP d

new

level of

w hen tllf' fault is i n tlw

proces s , and not in the readi ngs of the i nst.rmnent.s .

For ex am p l e ,

thP sen so r

r ead i n g

roneous

valid at.or may

frorn the t u r b i n e

detect an e r­ ve l o c i ty g i ven t h e

temp erature an d prt:>ssure rneasures . H oweve r , i t may

be

the case that t h P r e is a SPrious rnechanical p rob­

with t h e generator which may velocity to go to a ve ry low val u e .

lem

the l as t stf'p

F i n ally,

c ause that the re al

i n t h e p r oj e c t w i l l be t h e con­

struction of a pro t o ty p e w hi c h performs in el ect ri cal

a

thermo­

power plant. Th is p ro t oty p e r e q u i res a re al time response. Fo r this reason, d ifferent mechanisms of sc h ed u l in g h ave to be d ev e l o p ed , e.g . . any t z m e al­ go r i t hrns [Ibargiiengoytia d al. , 1 9 9 .'i ] . A eknow ledgtnen t s S p e c i al thanks to E d u ar d o M o r ale� w h o p r o v i d e d

val u ab l