Using abductive machine learning for online vibration monitoring of turbo molecular pumps

14 Pages·2015·1.31 MB·English

253
Using abductive machine learning for online
vibration monitoring of turbo molecular
pumps
(cid:3)
R.E.Abdel-Aal andM.Raashid 1. Introduction
CenterforAppliedPhysicalSciences,Research
The350kVlightionacceleratorfacility[4]atKing
Institute,KingFahdUniversityofPetroleumand
FahdUniversityofPetroleumandMinerals(KFUPM)
Minerals,Dhahran31261,SaudiArabia employs some 15 Balzers turbo molecular vacuum
pumpsofvariouscapacitiestoachieveaminimumvac-
Received26April1999 uumlevelof1:33(cid:2)10(cid:0)4Pa.Table1givesasummary
Revised13September1999 ofthespecificationsandoperatingconditionsforatyp-
ical0.5m3/spump,modelTPU510,anditselectronic
Turbomolecularvacuumpumpsconstituteacriticalcompo- driveunitmodelTPC300.Manyofthepumpsruncon-
nentinmanyacceleratorinstallations,wherefailurescanbe tinuouslyforextendedperiods,andoperationalexperi-
costly in terms of both money and lost beam time. Catas- encehasshownthatbearingfailureswhilethepumpis
trophic failures can be averted if prior warning is given runningatfullspeedcancompletelydestroythepump.
throughacontinuousonlinemonitoringscheme.Thispaper
Such failures often occur without adequate warning
describestheuseofmodernmachinelearningtechniquesfor
signs that can be detected throughroutinemanualin-
online monitoring of the pump condition through the mea-
spection.Even in cases when thereis a changein the
surement and analysis of pump vibrations. Abductive ma-
pumpnoise, this may go unnoticedin thenoisy envi-
chinelearningisusedformodelingthepumpstatusas‘good’
ronmentoftheacceleratorvaultormayoccurafternor-
or ‘bad’ using both radial and axial vibration signals mea-
suredclosetothepumpbearing.Comparedtootherstatisti- malworkinghourswhenthefacilityisleftunattended.
calmethodsandneuralnetworktechniques,thisapproachof- Aturbopumpisanexpensivepieceofequipment,and
fersfasterandhighlyautomatedmodel synthesis,requiring pumpfailurescanalsobecostlyintermsoflostbeam
little or no user intervention. Normalized 50-channel spec- timeifthereisaneedtowaitforin-houserepairorfora
traderivedfromthelowfrequencyregion(0–10kHz)ofthe replacementpumptobeorderedfromabroad.Wehave
pump vibration spectra provided data inputs for model de- recentlyinitiatedworkonthedevelopmentofanonline
velopment.Modelsderivedbytrainingononly10observa-
monitoringschemefortheacceleratorpumpswiththe
tionspredictthecorrectvalueofthelogicalpumpstatusout-
objective of automatically detecting abnormalities in
putwith100%accuracyforanevaluationpopulationaslarge
thepumpconditionandwarningtheacceleratoropera-
as500cases. Radialvibrationsignalsleadtosimplermod-
torinadvancetoavertseriousfailures.Theimportance
els and smaller errors in the computed value of the status
ofcontinuousonlinemonitoringforcriticalmachinery
output.Performanceiscomparablewithliteraturedataona
similardiagnosisschemeforcompressorvalvesusingneural iswellestablished[21],sincemonthlyorweeklyman-
networks. ualmeasurementsmaynotbefrequentenoughorcon-
Keywords: Vibrationmonitoring and diagnostics, statistical sistentenoughtodetectdevelopingproblems.
vibrationanalysis,turbomolecularpumps,machinelearning, Vibration analysis truth tables have been used for
abductivenetworks manyyearsasaguidefordiagnosingvibrationsinro-
tating machinery, but conclusive results often require
further evidence [24]. Recent advances in computers,
instrumentation,andsignalprocessingtechniqueshave
*Correspondingauthor:R.E.Abdel-Aal,P.O.Box1759,KFUPM,
made online predictive vibration monitoring of ma-
Dhahran31261,SaudiArabia.Fax:[phone];E-mail:
[email protected]. chineryavailableandcost-effectiveapproachinmany
ShockandVibration6(1999)253–265
ISSN1070-9622/$8.00(cid:211) 1999,IOSPress.Allrightsreserved
254 R.E.Abdel-AalandM.Raashid/Usingabductivemachinelearning
Table1 whentheunderlyingrelationshipsbetweeninputsand
Summaryoftechnicaldataandoperatingconditionsforthe outputs are not known. With this approach, a model
BalzersmodelTPU510turbomolecularpumpanditselec-
isdevelopedautomaticallythroughtrainingon an ad-
tronicdriveunitmodelTCP300
equate number of solved examples. Once the model
Pump:
is synthesized, it can be used to perform fast predic-
Nominaldiameter tions of outputs corresponding to new cases. A ma-
Inlet 0.160 m jor advantage of this approach in vibration analysis
Outlet 0.040 m is that intensive computations are now required only
Volumeflowratefornitrogen 0.5 m3/s once, i.e., during training for model synthesis, rather
Compressionratiofornitrogen 108 thanbeingrepeatedforeveryvibrationrecordanalyzed
Theoreticalultimatepressure 10(cid:0)14 bar duringactualmonitoring.Using the modelto process
Speed new records becomes a simple and speedy operation
Rated 1000 s(cid:0)1 that can be implemented in real time using compact
Standby 666 s(cid:0)1 andportableapparatus.Withtheshapeofthevibration
Ratedbladepassagefrequency 40000 s(cid:0)1 spectrumasinput,theproblemisreducedtothatofau-
Run-uptimeto90%ofratedspeed 300 s tomaticpatternrecognitionwhichhasbeenappliedin
Weight 30 kg manydisciplines,e.g.,[28].
Cooling Air Numeroustechniques currently exist for the devel-
Lubricatingoil Pfeiffer opment of machine learning systems [27]. These in-
Turbooil clude statistical pattern recognition methods such as
TL011 Bayesian classifiers and discriminant functions [11],
Permissibleambienttemperature 0–35 (cid:14)C artificialneuralnetworksmodeledroughlyonhowthe
ElectronicDriveUnitTCP300: human brain is believed to function [26], as well as
methodsfortheinductionofdecisiontrees[9].These
Inputvoltage(AC) 110–240 V
techniquesvaryintheiraccuracy,complexity,compu-
Maximumpowerinput 300 VA
tational requirements during training, and their abil-
Maximumoutputvoltage 40 V
ity to provide human-like explanations for their con-
Run-upcurrent 7 A
clusions.Suchvariationshaveledtonewertechniques
Ratedfrequency((cid:6)2%) 1000 Hz
combininggoodfeaturesfromvariousmethods.Anex-
ampleofsuch‘hybrids’istheAIMabductivenetwork
situations [21].Techniquesused include time domain tool [20] which draws on statistical and multiple re-
and frequency domain analysis as well as combina- gressionanalysismethodsaswellasneuralnetworks,
tionsofboth.Univariatetimeseriesanalysis[29]and resulting in a faster and more automated approach to
multivariatelinearregressionmethods[19]havebeen model synthesis. The development of this approach
employed to model normal vibration behavior in the formachinelearningthroughself-organizationhasfol-
timedomain.Problemswiththefirstapproachinclude lowedthetrack ofthegroupmethodof datahandling
strongnonstationarityofthevibrationtimeseries,asin (GMDH)algorithm[12]andthecloselyrelatedadap-
thecaseofreciprocatingmachinery.Thesecondtech- tive learning network (ALN) technique [7]. A math-
nique suffers from difficultiesin determiningsuitable ematical description of the GMDH-ALN foundations
relevant time series that explain variations in the vi- for AIM is given in Section 2. Previous experience
brationdata,aswellasstrongcorrelationsbetweenthe with this approach in modeling and forecasting daily
various input time series. The two techniques require minimumtemperature[1]hasindicatedimprovedpre-
complexcomputationsandconsiderableuserinterven- dictionaccuracycomparedto neuralnetworkmodels.
tion for each analysis performed, which makes them Modelsynthesisisalsomoreautomated,requiringlit-
difficult to implement online using simple portable tleornouserinterventionandtheresultingmodelscan
apparatus. Frequency domain techniques use the fre- providemoreinsightintothephenomenonbeingmod-
quencyspectrumofthevibrationsignalasasignature eled. AIM models take the form of simple equations
forthepumpcondition,e.g.[8]. thatcanbeeasilyimplementedonaportableapparatus.
Arecenttrendinmanyareasofappliedscienceshas Artificialneuralnetworktechniqueshavebeenpro-
beentoresorttoamachinelearningapproachwhena posed as a new approach to automate vibration anal-
rigorousalgorithmicsolutionbecomestoocomplexor ysis, primarily in the frequency domain [5,17,19,23].
R.E.Abdel-AalandM.Raashid/Usingabductivemachinelearning 255
Oneapplicationdiagnosesacompressorvalveasgood nonlinear systems and can synthesize adequate mod-
orbadbytrainingabackpropagationnetworkusinga elswith relativelyfewdata points.Theautomationof
setoffeaturesextractedfromtheacousticspectra[5]. modelsynthesisnotonlylessenstheburdenonthean-
Kotani et al. [17] reports on the use of an acoustic alystbutalsosafeguardsthemodelgeneratedfrombe-
featureextractionauto-associativeneuralnetworkfol- inginfluencedbyhumanbiasesandmisjudgements.
lowed by a fault discriminating network to diagnose TheGMDHapproachisa formalizedparadigmfor
eight types of compressor faults, also using acoustic iterated (multi-phase) polynomial regression capable
spectra. Timeseries of the vibrationlevelsfor thero- of producing a high-degree polynomial model in ef-
tor of a 500 MW generator have been modeled using fectivepredictors.Theprocessis‘evolutionary’inna-
radialbasisfunctionneuralnetworks[19].Thispaper ture, using initially simple (myopic) regression rela-
describestheuseofGMDH-basedabductivemachine tionshipstoderivemoreaccuraterepresentationsinthe
learningto diagnosea turbomolecularpumpas good nextiteration.Topreventexponentialgrowthandlimit
or bad based on the vibrationspectrameasured using model complexity, the algorithm selects relationships
an accelerometer. Following an overview of the ma- which have good predicting powers and discards all
chine leaning approach used, the experimental set up
theotherswithineachphase.Iterationisstoppedwhen
isdescribedandmodelsarederivedforpredictingthe
the new generation regression equations start to have
pump status through training on a number of known
poorer prediction performance than those of the pre-
cases. Performance of these models in predicting the
vious generation, at which point the model starts to
pump status from new spectra is described. We com-
becomeoverspecializedandthereforeunlikelyto per-
pareresultsobtainedusingbothradialandaxialvibra-
formwellwith newdata. Itis seen that thealgorithm
tionsignalsfromthepump.Resultsarealsorelatedto
hasthreemainelements:representation,selection,and
dataintheliteratureontheperformanceofsimilarneu-
stopping. The algorithm applies abduction heuristics
ralnetworkapproaches.
for making decisions concerningsome or all of these
threeaspects.Adetaileddescriptionofthestepsofthe
classicalGMDHalgorithmcanbefoundin[12].
2. GMDH-typemodelingtechniques
ToillustratethesestepsfortheclassicalGMDHap-
proach,consider an estimation data base of n obser-
2.1. TheclassicalGMDHapproach e
vations(rows)andm+1columnsformindependent
variables(x ,x ,:::,x )andonedependentvariable
In quest for optimal objective models that look 1 2 m
y. In the first iteration we assume that our predictors
only at collected data representing system behavior,
aretheactualinputvariables.Theinitialroughpredic-
Ivakhnenko has proposed the GMDH algorithm in
tionequationsarederivedbytakingeachpairofinput
1966 [15]. He observed that physical models often
variables(x ,x ; i,j = 1,2,:::,m)togetherwiththe
require information that is not readily available and i j
input variable y and computing the quadratic regres-
are therefore subject to many assumptions and sim-
sionpolynomial
plificationswhichdegradethe qualityof theresulting
model.Othertechniquesforquantitativemodelingin-
y =A+Bx +Cx +Dx2+Ex2+Fx x : (1)
clude time-series analysis using various linear statis- i j i j i j
tical methods and multivariate regression [18]. These
techniques have difficulties in handling nonlinearities Eachoftheresultingm(m(cid:0)1)=2polynomialsiseval-
in the modeled phenomenaand in dealing with small uated using data for the pair of x variables used to
data sets, which is the case in many environmental, generate it, thus producing new estimation variables
ecological, and social applications [14]. Attempts to (z1,z2,:::,zm(m(cid:0)1)=2)whichwouldbeexpectedtode-
incorporatenonlinearrelationshipsinsuchmodelsre- scribeybetterthantheoriginalvariables.Theresulting
quire the nonlinearity forms to be presumed a priori, z variables are screened according to some selection
rather than being naturally and automatically derived criterionandonlythosehavinggoodpredictingpower
from the data. Inclusion of postulated nonlinearities are kept. The original GMDH algorithm employs an
inthiswayalsoincreasesthepossibilityofthemodel additionalandindependent‘selectionset’ofn obser-
s
curve-fittingnoiseinthedata[25].GMDH-typealgo- vationsfor this purposeand uses theregularityselec-
rithms solve these problems since they automatically tioncriterionbasedontherootmeansquarederrorr
k
determinetheinherentstructureofcomplexandhighly overtheselectiondataset,where
256 R.E.Abdel-AalandM.Raashid/Usingabductivemachinelearning
Pns(y (cid:0)z )2 sion polynomials directly requires solving 43758 ill-
l kl
rk2 = l=1 Pns , claoynedriGtioMneDdHlinmeoadreelqoubattaioinnsstshiemeuqltuainveaoleunstlyIv,wakhhinleeank3o-
y2
l polynomial by repetitively solving regression equa-
l=1
tions in 6 variables only (Eq. (1)). This reduces ill-
k =1,2,:::,m(m(cid:0)1)=2: (2)
conditioning effects (smaller matrices) and allows
GMDH to model complex relationships using only a
Only those polynomials (and associated z variables)
small numberof data points, while with conventional
thathaver belowaprescribedlimitarekeptandthe
k regressionweneedatleastasmanyobservationsasco-
minimum value, r , obtained for r is also saved.
min k efficients.GMDHalsokeepsgeneratingnewvariables
Theselectedz variablesaremoreeffectiveindescrib-
byintermixinglower-levelvariables,thusreducinglin-
ing and predictingy than the originalinputvariables,
eardependence[12].
and the corresponding columns represent a new data
baseforrepeatingtheestimationandselectionstepsin
2.2. GMDHvariationsandtheALNapproach
the next iteration to derive a set of higher-level vari-
ables.Ateachiterationr iscomparedwithitsprevi-
min
The original GMDH algorithm has been subject to
ousvalueandtheprocessiscontinuedaslongasr
min
many variations in the methods used for estimating
decreases or until a given complexity is reached. An
the partial descriptor functions and in the choice of
increasingr isanindicationofthemodelbecoming
min
decision rules for descriptor selection and criteria for
overly complex, thus over-fitting the estimation data
stoppingtheiterations.Optimizedpolynomialsaswell
andperformingpoorlyinpredictingthenewselection
as different descriptor functions have been proposed.
data.Keepingmodelcomplexitycheckedisanimpor-
Theexternalregularitycriterionusedforselectionand
tantaspectofGMDHalgorithmswhichkeepaneyeon
stopping required the splitting of the training data
the final objective of constructing the model, i.e., us-
available into two sets which reduces the amount of
ingitwithnewdatapreviouslyunseenduringtraining.
dataavailableforestimation.Moreover,resultsdepend
The best model for this purpose is that providing the
on the way the data was divided and some splitting
shortestdescriptionforthedataavailable[6].Compu-
heuristicsandclusteranalysiswereoftenrequired[7].
tationally, the resulting GMDH modelcan be seen as
A number of methodshave been proposedwhich op-
alayerednetworkofpartialquadraticdescriptorpoly-
erateonthewholetrainingdatasetforestimation,se-
nomials, each layer representing the results of an al-
lection, and stopping, thus avoiding these limitations.
gorithm iteration. The single polynomial in the final
GMDH-relatedactivitiesintheU.S.A.hasbeengener-
layer predicts the independentvariable y in two vari-
allyidentifiedastheadaptivelearningnetwork(ALN)
ables, which are themselves quadratics in two lower-
approach(AIMbeinganexample),whichemphasized
level variables, etc. The lowest-level polynomials in
the use of the predicted squared error (PSE) criterion
thefirstlayeroperatedirectlyonthemindependentin-
forselectionandstoppingtopreventmodeloverfitting.
putxvariables.Makingnecessarysubstitutionsforthe
ThePSEcriterionminimizestheexpectedsquareder-
completemodel,wecanreachahighlycomplexpoly-
rorthatwouldbeobtainedwhenthenetworkisusedfor
nomial(known as the Ivakhnenkopolynomial)of the
predictingnew data which is differentfrom that used
form:
during training [7]. For example, AIM expresses this
Xm Xm Xm PSEerroras
y=a+ bixi+ cijxixj (cid:18) (cid:19)
i=1 i=1 j=1 PSE=FSE+CPM 2k (cid:27)2, (4)
Xm Xm Xm n p
+ d x x x +(cid:1)(cid:1)(cid:1) : (3)
ijk i j k
whereFSEisthefittingsquarederrorforthemodelon
i=1 j=1k=1
the training data, CPM is a complexity penalty mul-
It is worth pointing out a number of advantages for tiplier selected by the user, k is the numberof model
theGMDHapproachcomparedtoconventionalregres- coefficients,nisthenumberofsamplesinthetraining
sionanalysis,particularlyformodelinglargeandcom- dataset,and(cid:27)2 isapriorestimateforthevariancefor
p
plex systems. For the modest case of m = 10 and the error obtained with the unknown model. This es-
order p = 8, obtaining the coefficients of the regres- timate doesnot dependon the modelbeing evaluated
R.E.Abdel-AalandM.Raashid/Usingabductivemachinelearning 257
andisusuallytakenashalfthevarianceofthedepen- rons in each layer, and the training parameters, and
dent variable y [6]. It is noted that as the model be- often a number of combinations need to be tried in
comesmorecomplex,relativeto the sizeofthetrain- search of the best solution. With the commonly used
ing set, the second term increases linearly while the standard back propagation algorithm, training times
first term decreases. Therefore,the PSE goes through can be huge and there are many training parameters
a minimum at the optimum model size which strikes to adjust which may have a major effect on the re-
a balance between accuracy and simplicity or exact- sults [27]. The algorithm is not guaranteed to con-
ness and generality. CPM has a default value of 1 in vergetoagoodsolution[10],andbecausethemethod
AIM.Lowervaluesallowmorecomplexmodelswhile may be unstable and oscillate between solutions, it
highervaluesallowsimplerones. may not be clear when to stop [27]. This makes ab-
ductive networks easier to use and considerably re-
duces the learning/developmenttime and effort. AIM
3. AIMabductivemachinelearning advantagesover back-propagationneural networks in
forecastingthedailyminimumtemperaturearedemon-
AIM is a supervised inductive machine-learning strated in [1] while large improvements in training
toolforautomaticallysynthesizingabductivenetwork speed are reported in [20]. It should be mentioned,
models from a data base of input and output values however, that improvements are becoming available
which represent a training set of example situations. whichattempttoalleviatesomeoftheproblemsasso-
Once synthesized by training on a training data set, ciated with older standard neuralnetwork paradigms.
the network can be queried with new input data to For example, using a stiff ordinary differential equa-
provide the corresponding predicted output. Abduc- tion solver with the back propagation algorithm re-
tive networks[20]combinethe advantagesof the neu- duces the number of parameters to be adjusted, cuts
ral network approach with those of advanced statisti- on training time, and improves accuracy [27]. Using
cal methods.While theprocessingelementsin neural conjugate gradient methods for unconstrained opti-
networksarerestrictedbytheneuronanalogy,abduc- mization has been suggested for ensuring guaranteed
tive networks consist of various types of more pow- and faster convergence during training [10]. A step-
erful numerical functional elements based on predic- wise construction procedure has also been proposed
tion performance. The network size, element types, forbuildingandtrainingsingle-layerneuralnetworks
connectivity, and coefficients for the optimum model without the requirement for the number of neurons
are automatically determined using well-proven opti- in the hidden layer to be fixed a priori by educated
mization criteria, thus reducing the need for user in- guesses[16].
tervention. With neural networks, the user has to ex- The work reported here used AIM version 1.0 for
periment with various architectures and there are no theMacintoshcomputer.AIMmodelstaketheformof
hard and fast design rules to determine optimum val- layeredfeed-forwardabductivenetworksoffunctional
ues for the number of hidden layers, number of neu- elements (nodes)[3], see Fig. 1. Elements in the first
Fig.1.AtypicalAIMnetworkstructureshowingvarioustypesoffunctionalelements.
258 R.E.Abdel-AalandM.Raashid/Usingabductivemachinelearning
layeroperateonvariouscombinationsoftheindepen- the actual use for which it is developed, rather than
dentinputvariables(x’s)andthesingleelementinthe simply fitting the training data. The user may option-
finallayerproducesthepredictedoutputforthedepen- ally control this trade-off between accuracy and gen-
dentvariabley.Inadditiontothefunctionalelements eralityusingthecomplexitypenaltymultiplier(CPM)
inthemainlayersofthenetwork,aninputlayerofnor- parameter[6]. Larger values than the default value of
malizers converts the input variables into an internal 1 lead to simpler models which are less accurate but
representation as Z scores with zero mean and unity are more likely to generalize well with unseen data,
variance[3], and an output layer of unitizers restores while lower values produce more complex networks
theresults to the originalproblemspace. Both theel- which overfit the training data and may therefore de-
ement type and the combination of inputs to it from grade prediction performancewith noise. An ‘Evalu-
all the previous layers are selected automatically for ate’utilityallowsevaluationoftheresultingabductive
bestpredictionperformanceaccordingtothepredicted network on an independent set of data and generates
squared error (PSE) criterion[6]. The following main a report of the results. To obtain good AIM models,
functionalelementsaresupported: thetrainingsetshouldbeagoodrepresentationofthe
problemspace.Thelearningtaskisalsosimplifiedby
(i) A white element which consists of a constant
breakingthe problem into smaller and more manage-
plus the linear weighted sum of all outputs of
ableassignments, and by utilizing any human knowl-
thepreviouslayer,i.e.,
edgeonparametersrelevanttothemodelinthechoice
of input variables to be included in the training data
Output =W +W X +W X
White 0 1 1 2 2 base.
+W X +:::+W X , (5)
3 3 n n
where X ,X ,:::,X are the inputs to the 4. Experimentalsetup
1 2 n
element and W ,W ,:::,W are the element
0 1 n
weights. Figure 2 shows the experimental setup used for
(ii) Single, double, and triple elements which im- data acquisition and analysis of pump vibration. Vi-
plement a third-degree polynomial expression bration signals are detected using a ceramic shear
with all possible cross-terms for one, two, and modeaccelerometer,PCBPiezoelectronicsInc.,model
threeinputs,respectively;forexample, 352B22[22].Table2givesasummaryofthedynamic
performance of this tansducer. Vibration perpendicu-
Output =W +W X +W X +W X2 lartotheflatmountingsurfaceofthesensorareinter-
Double 0 1 1 2 2 3 1
nallyconvertedintoshearforces.Sensitivityislowat
+W X2+W X X +W X3
4 2 5 1 2 6 1 verylowandveryhighfrequencies,withareasonably
+W X3: (6) flat response ((cid:6)3 dB variations) over the frequency
7 2
range 1 Hz to 16 kHz. Sensitivity increases steadily
The first step in solving a problem is preparing withhigherfrequenciesuptoamountedresonantfre-
a data base of input-output training examples which quencyexceeding32kHz.Theaccelerometerresponse
AIMusestoderivetheabductivenetworkmodel.This drops at frequencies above that resonant frequency.
model network is synthesized layer by layer until no Thesensorwas adhesivelymountedon thesurfaceof
further improvement in performance is possible or a thepumpbeingmonitoredthroughathinlayerofpetro
presetlimitonthenumberoflayersisreached.Within wax.Twopositionshavebeeninvestigatedformount-
each layer, every element is computedand its perfor- ingtheaccelerationsensorasshowninFig.2.Inposi-
mance scored for all combinationsof allowed inputs. tionRthesensorissensitivetoradialvibrations,while
The best network structure, element types and coeffi- inpositionAthesensorregistersaxialvibrations(par-
cients, and connectivity are all determined automati- allel to the pump axis). One of the objectives of this
callybyminimizingthePSEcriterion.Thisselectsthe work has been to compare vibration monitoring per-
mostaccuratemodelthatdoesnotoverfitthetraining formanceforthesetwotypesofvibrationsignals.AC-
data, and therefore strikes a balance between the ac- coupledsignalsfromthebuilt-inpreamplifieroftheac-
curacy of the model in representing the training data celerometer were further magnified in two timing fil-
and its generality which allows it to fit yet unseen teramplifierstypeORTEC474withnoCRorRCtim-
future data. In this way the model is optimized for ing networks inserted (for a flat frequency response).
R.E.Abdel-AalandM.Raashid/Usingabductivemachinelearning 259
Fig.2.Experimentalsetupfortheacquisitionandanalysisofpumpvibrationsignals.
Thefrequencyspectrumoftheunfilteredvibrationsig- Table2
Summary of the dynamic performance data for the PCB 352B22
nalwasobservedonaHewlettPackardspectrumana-
accelerometer
lyzermodelHP8568Bwhichshowedfrequencycom-
Voltagesensitivity((cid:6)15%) 1.02 mV/ms(cid:0)2
ponents as high as 75 kHz with the pump running at
Frequencyrange((cid:6)5%variations) 5–8000 Hz
the full speed of 1000 s(cid:0)1. It appears that the high
Frequencyrange((cid:6)10%variations) 2.5–9000 Hz
frequency response of the accelerometer extends be- Frequencyrange((cid:6)3dBvariations) 1–16000 Hz
yond the mounted resonant frequency with adequate
Mountedresonantfrequency >32 kHz
sensitivity to allow the detection of vibration signals Measurementrange (cid:6)3924 ms(cid:0)2Peak
having such higher frequency components. An anti- Resolution(broadband) 0.015 ms(cid:0)2Peak
aliasinglowpassfilterwith30dBs/octaveattenuation Amplitudelinearity (cid:6)1 %
inthestopbandwasinsertedbetweenthetwoamplifier Transverselinearity 65 %
stages. The filtered signal had a peak-to-peak ampli-
tudeofabout4V,andaDCoffsetof–4Vwasapplied 5. Dataanalysis
to this signal using an ORTEC dual sum-and-invert
Figure3shows500-samplesectionsofthevibration
amplifiermodelORTEC553.Thisconvertsthebipolar
waveformrecordsfromaTPU510pump.Therecords
signalintoaunipolar0–8Vsignalwhichwassampled
weremeasuredafterapproximately5000hoursofop-
by a LeCroy 3511 CAMAC ADC at a sampling fre-
eration (when bearing change becomes due) as well
quencyof about84 kHz (sampling interval= 12(cid:22)s).
asshortly followingbearingchange.Theformercon-
This sampling frequency is about five times the high
dition was used to represent a ‘bad’ pump, and the
end of the frequency range where the transducer re- latter a ‘good’ pump. Shown in the figure are wave-
sponseisflatwithin(cid:6)3dBs,seeTable2.Cut-offfre- formsmeasuredin both the radial and axial positions
quency on the anti-aliasing filter was selected to pre- ofthe accelerometer(positionsR and A in Fig. 2, re-
ventaliasingeffectsduetothehigherfrequencycom- spectively). It is noted that the good pump is gener-
ponents of the vibration signal. Vibration waveform allymuchquieter,wherethevibrationsignalsarelower
records, each being 4K-samples in length, were ac- inamplitudeandhavepredominantlylowerfrequency
components. It is also noted that signals at the radial
quiredbyaVAX3200workstationrunningtheXSYS
positionofthesensorarerelativelyricherinfrequency
dataacquisitionandanalysispackage[2,13].Software
components compared to the axial position. Figure 4
intheVAXcomputedthemagnitudeofthefastFourier
showsthecomplete4K-pointFFTspectrumofthe4K-
transform(FFT) of the sampled recordand generated
sample waveform record of the radial vibration sig-
databasesfortrainingandevaluatingtheAIMmodels.
nal for the bad pump. Each channel incrementrepre-
These data were transfered to a Macintosh computer, sentsafrequencyintervalof1=(4095(cid:2)12(cid:2)10(cid:0)6)(cid:25)
connectedtotheVAXasaterminal,foruseinthede- 20:35 Hz. The figure indicates that the majority of
velopmentandevaluationofAIMmodelsforvibration the frequency content of the sampled vibration sig-
monitoring. nal lies below 10 kHz. Frequency analysis in this re-
260 R.E.Abdel-AalandM.Raashid/Usingabductivemachinelearning
Fig.3.500-samplewaveformrecordsofthepumpvibrationsignals:(a),(b)attheradial(R)positionforthe‘good’and‘bad’pumpconditions,
respectively;(c),(d)attheaxial(A)positionforthe‘good’and‘bad’pumpconditions,respectively.Samplinginterval=12(cid:22)s.
gionisacknowledgedasthemosteffectivemethodfor
detecting imbalance, misalignment, mechanical reso-
nances,andloosenessinrotatingmachinery[21].This
region(channels1to500oftheFFTrecord)wasused
throughoutasthevibrationsignatureofthepumpcon-
dition. Figure 5 shows plots of this region of the vi-
bration spectracorrespondingto the cases of the four
waveformrecordsinFig.3. Thefundamentalcompo-
nentinallcasesisabout1kHz,whichisthefrequency
corresponding to the rated pump speed of 1000 s(cid:0)1.
Theplotsconfirmobservationsmadeaboveonthetime
recordsregardingrelativedensityoffrequencycompo-
nents for good vs bad pumps as well as for radial vs
axialsensorpositions.
Data bases for training and evaluation were de-
rived from the 500-channel frequency spectra shown
inFig.5throughadatareductionprocedure,sincethe Fig.4.FFTspectrumfora4096-samplewaveformrecordforthevi-
brationsignalattheradial(R)positionandthe‘bad’pumpcondi-
versionofAIMusedallowsamaximumofonly50in-
tion.1channel=20:35Hz.
putparametersforuseinmodelsynthesisandevalua-
R.E.Abdel-AalandM.Raashid/Usingabductivemachinelearning 261
Fig.5.FFTspectrainthelow-frequencyregion(0–10kHz),1channel=20:35Hz:(a),(b)attheradial(R)positionforthe‘good’and‘bad’
pumpconditions,respectively;(c),(d)attheaxial(A)positionforthe‘good’and‘bad’pumpconditions,respectively.
tion.Weemployedamethodadoptedby[5]toreduce ingsensitivityoftheresultingmodelstochangesinin-
the 500-channel spectra to 50-channel spectra. With dividual spectrum components which may result, for
thismethod,theoriginal500-channelspectrumSisdi- example,fromslightchangesinsensorlocationifthe
videdinto50 segments;S ,S ,:::,S , each consist- spectrumdatawere to be applieddirectly to theAIM
1 2 50
ingof10channels.The50-channelpercentageareara- network.Themethodalso producesnormalizedtrain-
tio spectrumR used forAIMtrainingis derivedsuch ing/evaluation data such that the models are derived
thatitsjthchannelRj containsthepercentageratioof and used with input data always in the same number
thesumofthecontentsofallchannelswithinsegment space(range0–100).Usingratiosofthespectralcom-
Sj tothetotalsumofthecontentsofallchannelsinall ponent levels, rather than amplitudes of the spectral
the50segments,whichisthetotalareaoftheoriginal components themselves, makes the resulting models
spectrumS,i.e., morerobustagainstvariationsin vibrationsignal lev-
els which are reflected directly in the spectrum am-
P10
plitude.Therefore,thenormalizedarearatiospectrum
S
ji
R =100(cid:2) i=1 : (7) used to derive the training/evaluation data bases pro-
j P50 P10 videsaspectralsignaturethatcontainsinformationon
S
ki the relative strength of frequency components in the
k=1i=1
variousregionsofthespectrum,whilebeingfairlyim-
Inadditiontosatisfyingthedatareductionrequirement mune to signal amplitude variations including those
by AIM, this averaging approach is useful in reduc- causedbygainandoffsetchanges.
262 R.E.Abdel-AalandM.Raashid/Usingabductivemachinelearning
6. AIMmodeling
As a first exercise, we considered the development
of abductive network models that continuously per-
formgo-nogochecksonthepumpconditionbyclas-
sifyingthefrequencyspectrumasrepresentingagood
orabadpump.Figure6showstypical50-channelper-
centagearearatiospectraforgoodandbadpumpsus-
ingsignalsfromboththeradialandaxialsensorposi-
tions. Ineach position,spectraforbothgoodandbad
pumpsareshownsuperimposedonthesameplottoin-
dicatetherelativeeaseofseparatingthe twopatterns.
It is seen that discrimination appears easier with sig-
nalsattheradialsensorposition,andthereforethistask
should be achieved using simpler models. A typical
databaserecordformodelingthepumpstatusinterms
ofthepercentagearearatiospectrumisgivenbelow:
Inputs: Output:
Channelcontents Logicalvariable
ofthepercentage
arearatiospectrum
Ch ,Ch ,Ch ,:::,Ch Pumpstatus
1 2 3 50
(1=‘Good’,0=‘Bad’)
Throughout this paper, the numbers of training and
evaluationobservationswillbedesignatedNTandNE,
respectively.Allmodelsweredevelopedusingthede-
faultCPMvalueof1.Modelsweresynthesizedusing
atrainingdatabaseof1000records(NT=1000)with
both good and bad pump status equally represented
(500recordseach).Structureoftheresultingnetworks
forboththeradialandaxialsensorpositionsisshown Fig.6.Percentagearearatiospectraforthe‘good’and‘bad’pump
in Fig. 7. The network for the radial case is simpler, conditionsusedfordevelopingtheAIMmodels:(a)attheradial(R)
sincethe‘good’and‘bad’spectrumsignaturesareeas- position,(b)attheaxial(A)position.
iertodifferentiateasnotedabove.Theradialnetwork
isasingle-layernetworkthatusesonlythecontentsof andCh , respectively.Both networkswere evaluated
15
channel5toachievetherequireddiscrimination,while on a mixture of 250 ‘good’ and 250 ‘bad’ new cases
discriminationintheaxialcaserequiresa2-layernet- (NE=500).Theresultinglogicalvalueforthepump
workoperatingontwovariables(Ch5 andCh15).Sub- status (ideally 1 for ‘Good’ and 0 for ‘Bad’) was de-
stitutingtheequationsshowninFig.7(a)forthevari- rived from the real number predicted by the network
ousfunctionalelementsproducesthefollowingmodel forthestatusoutputthroughsimplethresholdingat0.5.
relationshipforthepumpstatusattheradialsensorpo- Table3 lists themaximum,average,andstandard de-
sition: viation of the error in the predicted pump status out-
putaswellasthegood/badclassificationaccuracyfor
bothsensorpositions.Thetableindicates100%accu-
Status =(cid:0)0:081056+0:21675(Ch )
Radial,NT=1000 5 racyfortheAIMmodelinpredictingthepumpstatus
(cid:0)0:01076(Ch )2: (8) forthe500evaluationcases,sincetheerrorinthevalue
5
of thecomputedstatus outputneverexceeds0.5. Itis
The correspondingpolynomialexpression for the ax- noted that the maximum error is higher for the axial
ial configuration is much more complex, consisting sensorconfiguration,althoughaloweraverageerroris
of 28 terms with powers as high as 9 and 3 for Ch obtained.
5