Signal Trend Identification with FUZZYMethods/67531/metadc625319/... · Signal trend identification is an important part of computer-based monitoring, diagnostic and control systems

Submitted to the IEEE International Conference on Information, Intelligence and Systems (ICIIS),Washington, DC, Nov. 1-3,1999

EThe submitted manuscript has been authored

Signal Trend Identification with FUZZYMethods .“der contract ~~. ~.~1.1~~~~~.ss.by a contractor of the U. S. Government

Accordingly, the U. S. Government retains anonexclusive, royalty-free license to publish

Xirl Wang or reproduce the published form of thiscontribution, or allow others to do so, for

School of Nuclear Engineering, Purdue UniversityW.Lafayette, Indiana47907-1290

Em& [email protected]

Thomas Y. C. WeiArgonne National Laboratory, Reactor Engineering Division, Argonne, Illinois 60439

Jaques ReifmanArgonne National Laboratory, Reactor Analysis Division, Argonne, Illinois 60439

]q~=%~~~.~~

Lefteri H. TsoukakwSchool of Nuclear Engineering, Purdue University

W.Lafayette, Indiana47907-1290 OCT I 21!)99

Abstract

A@~-logic-based methodology for on-line signal trend identification is introduced. Although signal trendidentification is complicated by the presence of noise, jiuzy logic can help capture important features ofon-line signals and classifi incoming power plant signals into increasing, decreasing and steady-statetrend categories. In order to veri? the methodology, a code named PROZ%!?Nis developed and testedusing plant data. l%e results indicate that the code is capable of detecting transients accurately, identifyingtrends reliably, and not misinteqn-eting a steady-state signal as a transient one.

I. INTRODUCTION

Signal trend identification is an important part ofcomputer-based monitoring, diagnostic andcontrol systems. In many applications it is anessential first step in the reliable and timelydiagnosis of complex systems, such as nuclearpower plants and industrial processes. Althoughconventional methods have been widely appliedfor signrd trend identification, these methods aregenerally signal- and process-dependent, andhence, cannot be easily ported to other processesand plants. Here, we describe a new fizzy-logic-based method, which is signal- and process-independent, that performs signal trendidentification.

Argonne National Laboratory (ANL) and PurdueUniversity are collaborating on the developmentof a novel operator advisory knowledge-baseddigital system called IGENPRO.l It is anadvanced plant- and thermal-hydraulic process-

independent system for nuclear power planttransient diagnostics and management.

There are three major modules in IGENPRO:PROTREN, PRODIAG and PROWA. Thefirst module (PROTREN) performs signalprocessing. Each individual signal trend isclassified as increasing, decreasing or constantand the results are fed to the second module.l’ 2The second module (PRODIAG) performs plant-level diagnostics. It is based on a knowledgebase of generic thermodynamic first principles,such as mass, momentum, and energyconservation equations. The PRODIAGknowledge base does not follow a conventionalevent-based approach, but rather a genericfunction-based approach with a comprehensivealthough compact, knowledge base.3 The thkdmodule (PROMANA) recommends a series ofoperations for plant recovery.

In this paper, we describe the theoreticalconcepts of the fuzzy-logic-based PROTREN

1

—.—. ..—4. ..

DISCLAIMER

This report was prepared as an account of work sponsoredby an agency of the United States Government. Neither theUnited States Government nor any agency thereof, nor anyof their employees, make any warranty, express or implied,or assumes any legal liability or responsibility for theaccuracy, completeness, or usefulness of any information,apparatus, product, or process disclosed, or represents thatits use would not infringe privately owned rights. Referenceherein to any specific commercial product, process, orservice by trade name, trademark, . manufacturer, or

otherwise does not necessarily constitute or imply itsendorsement, recommendation, or favoring by the UnitedStates Government or any agency thereof. The views andopinions of authors expressed herein do not necessarilystate or reflect those of the United States Government orany agency thereof.

—--- ——. ,. *..—.. .,, ,, ,.. \,..&,.4..,,......../ ,,.-........ .. . .:,:-—qyj~-— .— --.—-—— -.—-.

DISCLAIMER

Portions of this document may be illegiblein electronic image products. images areproduced from the bestdocument.

original

,--— - .,, ,, ,“-.?r.-, _ . ...+—w--=— -7. . . . .,.,.ri,

. . . . . . . . . . . . . . . . . . ,A- ...~,--T--7 ~, ~--T---- .. _____,., ., .ti. .


module for signal trend identification and show the results of validation tests with plant data.

“[A

1

YI

Fig.1. Flowchart of the methodology

II. BACKGROUND AND BASICCONCEPTS

1. Outline of the methodology

For the purpose of on-line classification of anincoming plant signal trend as increasing,decreasing, or constant, some preprocessingneeds to be performed to extract useful signalfeatures. In PROTREN, five parametersrepresenting several features of the signal areextracted. In order to incorporate all theinformation included in these features, theparameters are transformed into fuzzy numberswhich are then synthesized into one final fuzzynumber representing, in an approximate way, thedegree to which the current constellation offeatures offers evidence for the onset of atransient.4 Then, based on the final fuzzy numberand the use of t%zzy logic, a trend identification

decision is made. The basic structure of thetechnology discussed below is shown in Fig.1.

2. Development of final fuzzy number

The information on signal trends is assumed tobe represented by the final fuzzy number that

.summarizes the important features of the signal.This is performed through the following three-step process.

2.1. Definition of the five parameters

The definition of the five parameters is based onthe assumption that during steady-state processoperation the plant signals are normallydistributed with mean value p and standarddeviation 6. The values of p and o can becomputed off-line based on steady-statehistorical data before they are used on-line, at

2

—— -—-——..————————. — ——— . .

Submitted to the IEEE International Conference on Information, Intelligence and Systems (ICIIS),Washington, DC, Nov. 1-3, 1999

each sampling time, to compute the fiveparameters. For each sampling signal, themathematical description of the parameters is asfollows:

(a) Probability density function( pa’!’)

(%-PI’

‘d*“ =i%exp2“’(1)

where,

tc=current time step

stC=signal value at k

/l =mean value of the steady-state signal

0 =standard deviation of the steady-state signal

Sample points belonging to off-normal stateshave small pd!vrdues. Thus, this parameter candetermine the deviation of the signal fromsteady-state operation.

(b) Cumulative probability density function(CW7Z _ pdf )

w 1. - fw [..,avgd *C= (3)t= - t=-,

where,

This parameter represents the time rate of changeof the variable avg, which is defined as theweighted sum of the sampled signal values overthe time window of length n: In Eq.(4), k is apositive constant.

(d) Relative deviation (ravg )

W3t= –Pravg ~==

P(5)

This parameter represents the deviation of avgfrom the signal mean steady-state value and isindependent of the amplitude of the signal. Thesign of this parameter is used to differentiatebetween increasing and decreasing trends.

(e) Sample derivative (sd )

cum _ pdf,= = 2 pdft.-,iza

(2)

s, —Stc-,

sd, = ‘. t= – tc-l(6)

where n represents the length of the timewindow. Small signal changes are accumulatedand recorded in this parameter. By accumulatingsmall signal changes, it becomes possible tomake decisions based on not only theinstantaneous signal changes, e.g., the pdf, butalso on the recent history of the signal.

(c) Average derivative ( avgd )

Thk parameter is used to capture theinstantaneous rate of change of the originalsignal without any smoothing since smoothhghides the occurqmce of local peaks.

2.2. Fuzziilcation of the five parameters

In order to synthesize the information describedby the five parameters, they are transformed intofuzzy numbers and mapped into a [0,1] truthdomain!

3

~...,m ——,—.. . ,.m---- -——.. ... . .

.


As shown in the conversion table, Table.1, the the [0,1] truth domain according to thetruth of a parameter is computed according to its conversion map.actual value. Then a fuzzy number is set up on

Ta’

Parameter

pdf

cum-pdf

avgd

ravg

sd

?.1. Conversion table for transforming a crisp number into a fuzzy number

Converting a crisp number into a

Finding the truth having membership 1

’111

:.Uu “-.” “ “

“

“

“

.

$:.um-----...,.......

-,,,--- ---- -,---‘=-- -T%-= .,<..2-, -..~- , , ~,-?r,’..-. ,<.~ :.. . .. .. . . .. ., -<. . ::,.”<.. . . ---- ,.. —.. . .

=. ..:

“

.

,,

0’‘Ezll“--“,

.

u’.! ,

,L.ls.. A.””””

uzzy number

Setting up fuzzy number

“~

.‘N-1-

“.“

“.”” :“”’”

“‘M—..1“

“

“

“.””:” ,

!,

‘m.—”.

!’.*“.”” :“’”

!,

‘Egf “-”“M

“

%02 ..0,” ,,,

4


2,3. Formulation of the final fuzzy numberwith the MAX operation

A final fuzzy number is computed to incorporatethe information provided by the five fizzynumbers associated with the five parameters.Here, the final fuzzy number is computed by theMAX operator. 5

(a”,b” )= (mm ,=,-,(a~), mm ,=l-,(b~)) (7)

where,

aa =the left point of the of a-cut of the finalfuzzy number

ba =the right point of the of a-cut of the finalfuzzy number

# =the left point of the of a-cut of the ith fuzzy

number

b; =the right point of the of a-cut of the ith

fuzzy number

The final decision isnew fuzzy number.

made on the basis of this

3. Trend evaluation

The trend inference is obtained based whetherthe signal trend pertains to ‘steady state’ or‘transient state’. Because ‘steady’ and ‘transient’are both fuzzy concepts, a fuzzy decision

strategy is developed. The methodology has twoparts: detizzification and tizzy decision.

3.1. Computing the dissembhzce index andthe confidence conj?d

In order to draw a conclusion concerning thefinal fuzzy number, i.e., defizzification, thedistance between the membership function of thefinal fuzzy number and prototype membershipfunctions are calculated. The distance is alsocalled the dissemblance index (DO of two fuzzynumbers A and B, 6(A,B), and is defined as: 6

where,

(8)

~ is used to normalize the value of DI to [0, 1]

a: ( b: ) = the left point of the a-cut of a fuzzy

number of A (B)

a; (b:)= the right point of the a-cut of a fuzzy

number A (B)

The two prototype membership functions arefuzzy numbers O and 1 which represent steadystate and transient signals respectively. TheZadeh diagrams of these numbers are shown inFig.2?

5

.-T .,~-:--—-nT.---m- ,- — .,~.>r.~ . . . . . . .. —.-—-


“o 0.2 0.4 0.6 0.8 1

truth domain

Fig.2. Fuzzy number Oand 1

Next, we define the parameter conjld, which isused to infer the confidence in the decision.

8,conjid = —

30+ 3,(9)

unstable (i.e., oscillatory) trend inferences. Forexample, if the signal trend is not wellestablished, the value of conjid can oscillateabout 0.5, resulting in conflicting inferences. Toavoid this undesirable behavior, we propose theuse of the following fuzzy decision strategy.

3.2. Fuzzy decision strategg

where,

61= distance or DIfrom the final fuzzy number totizzy 1

80= distance or DI fiorn the final fuzzy numberto fuzzy o

Two decision methods in which the parameterconjid plays different roles are considered. Thefust one is a non-fuzzy decision method whilethe second one is a fuzzy decision method.

In the non-fuzzy decision method, the decision ismade on the basis of the value of conjld. If thevalue of confid is huger than 0.5, it means thatthe final fuzzy number is closer to O than to 1indicating a steady-state trend. On the otherhand, a confid of less than 0.5 indicates achanging signal trend.

Because of the crisp nature of this decisionmethod, under certain conditions, it can provide

The fuzzy decision strategy is composed ofseveral rules. First, we use three rules to identifythe trend of the signal:

●

●

●

If conjid indicates that the fuzzy number isapparently close to fuzzy number O,then thesignal trend is not changing.

If conjid indicates that the fuzzy number isapparently close to fuzzy number 1, then thesignal trend is changing.

If the decision cannot be made confidently,i.e., 60is close to S1, then the history of thechange in conjid is used.

According to these rules, a decision is made onlywhen confid is close to O or 1, i.e., the result isrelatively clear. If the final fuzzy number falls


within the fizzy region as mentioned in the thirdrule, two additional rules are used.

. If the value of conjid is continuouslydecreasing, then the signal is not constant.

● If the value of con,d is oscillating orincreasing, the signal is assumed to beconstant,

One major characteristic of the strategy is thatthe decisions made are not only dependent on thevalues of 6., 61 and conjid, but also on theprevious values of conj%i.Actually, in manycases, the changing trend of confid is even moreimportant than the parameter itself.

For example, suppose 80 is a little less than &but the value of conjld is decreasingcontinuously throughout the last sample points.In this case, 60 larger than 61can be predicted tooccur within the next few steps and a changinginference can be made. On the other hand, if thevalue of conjid is oscillating violently, thestrategy most likely identifies a signal as steadystate even when r50larger than &

Monitoring the past values of confid does notimpair the performance of the overall strategy.Off-line signal analysis shows that the changingtrend of conjid for steady-state is much differentthan that of transient state even for slow andsmall changes. Therefore, this strategy is veryuseful in determining to which state the currentsample point pertains and contributes to quickerresponse and more stable results.

m. RESULTS

This methodology has been incorporated into thecode PROTREN, which is the signal processingmodule of the computer-based diagnostics andmanagement system IGENPRO.

Figures 3 and 4 show two flow signal data fromthe Chemical Volume Control System of apressurized water reactor power plant sampled at5s intervals. Fig.3 illustrates the changing pumpdischarge header flow and Fig.4 illustrates theoutlet flow of the letdown heat exchanger.

The signal shown in Fig.3 is a transient one.PROTREN begins to provide the transient resultabout 15s after the onse~ when the change isabout 0.3% It is apparent that the methodologydoes not deduce transients for steady statesignals and can provide detection of transientsfor actual transient signals.

Due to the difficulties involved in obtainingactual data from power plants, many validationexperiments with simulated signals wereperformed. Although it is difficult forconventional methods to differentiate betweensmall and slowly changing transient signals andnoisy steady-state signals, PROTREN can makecorrect and stable decisions. Figures 5 shows thePROTREN response to simulated datarepresenting a slowly increasing signal trend. Ittakes PROTREN about ten minutes to get thecorrect and stable decision. Figure 6 shows theresponse for a fast transient resulting in a smallmagnitude increase in the signal value. In thiscase the correct inference is made in one timestep from the onset of the transient and withoutany oscillatory behavior.

7

,..,,....--_rT—. , ,, ..m. -. z.qw,m .+ , .,——. . . . . . . . - ----—— -


140CHARG PMP DISC+ HDR

I & t , ,

’39 -“””’””’”’’””””~- ~ ~ 1:

. . . .. ......+.. ............................ ......... . ...................... ....................... ...... .... ..... . .. .. ............ ..

3

ik -

~ 138 . ...................j .....................j .......?tinsl~. .................- ........ '- ...................j ....................... ..................

&Z4

137 - ..................... . . ......................... ............. ..... . ....... ..... ... .. . ........ ..........

1381 I-35 -30 -25 -20 -15 -lo -5 0 5

CHARG PMP DISCH HDR

time

Fig.3. PROTREN resuhs for a decreasing signal trend

LEDOWN1-XLEDOWN~, t , , ,

lm.4 . ....................~ ................ . ..w . ....." ..... ............t . ....." ..... ....i . .... . .. .. . .

g 120.2- ;~f; ,j~ ;Lj~[~~&J ~

......... .........+_ ..5 .......... ........ ....... .. . . ............... .............. .:.. ....... ........ ........... ......... . ........

ii,, .....!q ...... .......<J... ~... 1...,. ...fl.+...... ....... . ... ..... .............-s 120 - ...................+.......

3

119.8 - ............................................................. ..... ............. ...... . ................. . .... .. .. ... .... . ............... .... ......... .. . ...

119.6-35 -30 -25 -m -15 -lo -5 0 5

time

Fig.4. PROTREN results for a unchanging signal trend

8


slowWllielltI

120.s ...................~. . ....................+. ....................4. .....................~. . ....... ......... “........~ . ..... ...........

;;

~:h~!~iFii~d

.ti~~y~=l:

1.....!.. ..... .... ......\.....................”...... ............" . ........ ............" ... .." . ......."-

119.8 - ............................................ ...................... ............... ..... ....: t mti .. . ...... .................................i ...................-t I 1

I , t t , 1-s5 -30 -25 -20 -15 -lo -5 0

time

-35 -20 -25 -20 -15 -lo -5 0 5

Result of PROTREN

5

Fig.5. PROTREN results for a slowly increasing signal trend

Smti transient

120.6 ----”+-.-’-- ,. -y- ..... ... .. .. .. . -.i . .. . ... .. ~-. .“.. ...... -~. . . ... ..- “+---

120.2: ..................#ih)kkbl#ibq~

!#i~fi[~---:

120.4 - ..................-.-. ,

........ .. . .. . ... : .: . .. --”.; .. . ........... ...

120 - ..................... :.................. ............... i.. . .. ... ................. . ......... ......... .. .. ........ .. ....... .. .. .... . ...... . ....... .. . ......

119.8 - ...................+.....tms @ ........ ............ ......... ............. ........... .......... . ................ . ....." ..............i............-

— ,. -.=,-...=~.-.J7-.-- , .,,. .< ,. 4.. . . . .,...~,,, -m ....mPT . ,:A .RT-7’3..: *.,.,. .? ,., ,.. . .,.1 .>..—- —.. . . .

.

-25 -20 -25 -20 -15 -lo -5 0 5

Resultof PROTREN1

1 ....................1 :I , ,

. . . . . . . . . .

0.5 - ................ .... .....t mA ... ............ ...... ......................~......... .... ..... . .. .. .... .... ..... ..... ............ .. .... . .. . ........

o . ...................9 .................i...................... ....................... ...................... ................. .............................................

-0.5 - ....................... ........................................... ...................... ......... .................. ..... ...........................................

-1 . ....................i......................i....................... ....................... ......................~"...............................-.............................

-35 -20 -25 -20 -15 -10 -5 0time

Fig.6. PROTREN results for a fast but snudl signal trend

I

9


Iv. CONCLUSIONS

A fbzzy-logic-based methodology for signaltrend identification is presented in this paper. Itdiffers from conventional methods in severalaspects.

●

●

9

In order to perform on-line estimation ofsignal trends, five parameters are definedand transformed into a final fuzzy number.The trend identification is based on theanalysis of the final fuzzy number. ‘

A fuzzy decision strategy is used to infer thesignal trend when the final fuzzy numberfalls within a fuzzy region.

Simmls with chamzimztrends can be deducedqu;ckly and insta~li~es in the final decisionare reduced significantly. At the same time,signals with unchanging trends are notmisinterpreted.

PROTREN has been validated through numeroustests including both simulated and actual plantdata. Preliminary results indicate that theproposed method is capable of earlyidentification of signal trends in the presence ofnoisy data. Future research will involve furtherimprovement of the algorithm and qualitativedetermination of its sensitivity.

ACKNOWLEDGMENTS

Work is supported by the U.S. Department ofEnergy, Office of Nuclem Energy, Science andTechnology, under contract W-31 -109-ENG-38.The authors also wish to thank CommonwealthEdison Company for providing plant signal data.

REFERENCES

1. J. A. Mormam, J. Reifman, J. E. Vitela, T.Y. C. Wei, C. A. Applequist, P. Hippley, W.Kuk and L. H. Tsoukalas, “IGENPROKnowledge-Based Digital System forProcess Transient Diagnostics andManagement,” Proceedings of the IAEAMeeting on Advanced Technologies forImproving Availability and Reliability ofCurrent and Future Water Cooled Nuclear

2.

3.

4.

5.

6.

Power Pkmts, Argonne, IL, September 8-11,213-224,1997.

J. Reifman, “Survey of ArtificialIntelligence Methods for Detection andIdentification of Component Faults inNuclear Power Plants; NuclearTechnology, 119,76-97,1997.

Jaques Reifman, Thomas Y. C. Wei,“PRODIAG: A Process-independentTransient Diagnostic System-k TheoreticalConcepts:’ Nuclear Science andEngineering, 131,1-19,1999.

Jin Chai and L. H. Tsoukalas, “AnInvestigation of Fuzzy Trend Algorithms forNuclear Power Plant Transients,” School ofNuclear Engineering, Final Repor6 1998.

Ead Cox, l%e FUW Systems Handbook,Boston, 1994.

Arnold Kaufmann and Madan M.Introduction to Fuzzy An”thmetic:and Application, New York, 1991.

Gupta,Theory -

10

Documents

Signal Trend Identification with FUZZYMethods/67531/metadc625319/... · Signal trend identification is an important part of computer-based monitoring, diagnostic and control systems