new method in determining rotor crack depth by using multi-scale

Transcription

1 9-59 mme.modares.ac.ir * - - mnouri@srttu.edu68858 * () -.. % : 9 9 : 9 8 : newmethodindeterminingrotorcrackdepthbyusingmulti-scale permutationentropyandanfisnetwork MehrdadNouriKhajavi * MohamadRezaBavir, EbrahimFarrokhi DepartmentofMechanicalEngineering,ShahidRajaeeTeacherTrainingUniversity,Tehran,Iran P.O.B.68858Tehran,Iran,mnouri@srttu.edu ARTICLEINFORMATION ABSTRACT OriginalResearchPaper Received9March5 Accepted8April5 AvailableOnline8May5 Keywords: PermutationEntropy TimeSeries ANFIS TransverseCrack RotatingShaft In statistics, Entropy is measure of time series disorder. Entropy is used in physiologic signal analysis.inphysiologicscience,entropyisusedforperformanceanalysisofbodyorganssuchas heartandbrain.epilepticpatientshavebeendiagnosedwiththistechnique.inthispaperforthe firsttime,entropyisusedtodeterminethehealthconditionofmechanicalsystems.specialkind ofentropy,namelypermutationentropyisusedforthispurpose.toperformtheexperimentan apparatus consisting of motor coupled with shaft has been designed and manufactured. Vibration signals from support bearing of this system in different shaft states, namely healthy shaft, and shafts with, and mm crack were gathered with vibration data analyzer. The vibrationsweretakenfromsensorsmountedonbearingsupportsoftheshaft.shaftwas subjected to constant bending moment. The vibration signals were preprocessed by permutation Entropy method. Nine different features were extracted from the Entropy signals whicharefedtoanadaptiveneurofuzzyinferencesystem(anfis).thedesignedanfiswas capableofclassifyingdifferentshaftstateswithanoverallprecisionof96% Pleasecitethisarticleusing: : M.NouriKhajavi,M.R.Bavir,E.Farrokhi,newmethodindeterminingrotorcrackdepthbyusingmulti-scalepermutationEntropyandANFISnetwork,ModaresMechanical Engineering Vol.5,No.,pp.-9,5(InPersian)

2 [] () DC AC.. CTC (). 9. CK5(SAE5 mm MPa 8 MPa. -MultiscalePermutationEntropy -Adash [].[] [] [5] [] [6]..... [] [8] [9] % [] Entropy salgorithm -ShannonEntropy -ApproximateEntropy -Dimension 5-TimedelayVector 6-MultiScaleSampleEntropy -AdaptiveNeuroFuzzyInferenceSystem 8-Permutation 9-PermutationEntropy -EEG

3 DDS - -. / / /6/5 -. :[] (). [, ) x ) ()...[,] ()/() = ((), ), () =.. ()....[] () ().. ().[5] -ElectricalDischargeMachining(EDM) -SymbolicSynamicalSystems () --. () mm kg 95mm /9mm 5 mm 6mm 59

4 () () () () () () () () () () () () (j) () () () () () () () () () () () () = = = =5 = =8 = = =.5 = d= = = (,, 5, 8) = = (,,, 6) = =(,5, 8, ) = =(,, ) = 5 = (5, 8,,.5) = 6 = (, 6,, ) 59 (j) t= (). (8. = = (,,, ) () (8) (9) (= ) < (= ) < (= 5) < (= 8) (,,, () (9) () = = (,,5,8) (,,, ) = = (,,, 6) (,,,) = = (, 5,8,),,, ) = = (,, 6, ) (,,, ) = 5 = (5,8,,. 5) (,,, ) = 6 = (, 6,, ) (,,,) ()!..!..!! ()... ).,, }.. [6].. [] (t) A= } () = { (), (), (),, () }, = : ( ) > () ). (,,,, ) (, ) (). ) () < () < () < < <. ) (6) (5) () = () < A ( () (5) (6) -Takenz -Sequentialpattern -Delaytimevector -Dimension

5 [9] Coarsegrained -Whitewave -Mamdani 5-Sugeno.!.!.. ). (.!....[] #{()} () = () =,,,,=!! (, ) = () log () : () () () () j () - (). (, ) log! j (). () =!..() (, ) ( = ) log! () ).[] --.[]. = ().( 5) (5) (5) -Nomalize 5 59

6 8 59 = { } (). y () : x (5) = () Followingparameters 5-(LSE) 6-Reducedgradientalgorithm. yx. 8 f B y A x ( fpqr B y A x ( fpqr } Bi Ai () :(.. (6)..[8] (), = () =,, = () =, (6)..... (8) () ( ) = exp ( ) = () () (8) ={} (5-) (-) :( ) () = () () =,.(9) (9) () (). () : ) () = + () :(). () = ( + + ).() () -Gaussianfunction -Bellfunction -AdaptiveParameters 6

7 (). = ( ) = ( ).[] () /9.. - ) M M M.[9] (. )..[8] : ) (5 9 T = (x ) T = max(x ) T = min(x ) T = (x ) n T = n (x T ) T = (x T ) T = 5 6 T (x T ) T = n (x ) T 8 T = (x ) 9 9 -FuzzyC-meansclustering 8-Generatefuzzynferencesystem(genis) 9-Anfis -Rootmeansquareerror(RMSE) -ConfusionMatrix 5 5 -Minimum -Mean -Geomean -Rootmeansquare(RMS) 5-Skewness 6-Kurtosis 59

8 Column 6 8..[] Series Column : - :.- : -. 96/ Softcomputing 5- Hardcomputing -Specificity -Precision -Sensitivity 8

9 [8] R.Yan,R.X.Gao,ApproximateEntropyasdiagnostictoolformachine healthmonitoring,mechanicalsystemsandsignalprocessingpp.8 89,() [9] L.ZhangG.XiongH.LiuH.ZouW.GuoBearingfaultdiagnosisusing multi-scale entropy and adaptive neuro-fuzzy inference, Expert Systems with Applications pp ,,http// locate/eswa [] C. Bandt, B. Pompe, Permutation entropy natural complexity measure for time series, Institute of Mathematics and Institute of Physics DOI:./PhysRevlett.88.9April. [] R. Yan, Y. Liu, R.X. Gao, Permutation entropy: nonlinear statistical measure for status characterization of rotary machines, Mechanical SystemsandSignalProcessing9pp. 8, [] V. Rajagopalan, A. Ray, R. Samsi, J. Mayer, Pattern identification in dynamical systems via symbolic time series analysis. Pattern Recognition,VolumeIssuepp.89-9,November [] R.Asok.Symbolicdynamicanalysisofcomplexsystemsforanomaly detection.signalprocessing8, pp.5, [] I.Veisi,V.Pariz,A.Karimpour,FastandRobustDetectionofEpilepsyin NoisyEEGSignalsUsingPermutationEntropy,IEEEpp.-,- Oct. [5] R. Badii, A. Politi, Complexity Hierarchical Structures and Scaling in PhysicsCambridgeNonlinearScienceSeries,vol.6,CambridgeUniversity Press99 [6] F. Takens, Detecting strange attractors in turbulence, In D.A. Randand L.-S. Young,Dynamical Systems and Turbulence, Lecture Notes in Mathematics,vol.898,Springer-Verlagpp.66 8,98 [] X.Chen,N.JinA.Zhao,Z.K.Gao,L.S.ZhaiB.Sun,Theexperimental signalsanalysisforbubblyoil-in-waterflowusingmulti-scaleweighted- permutationentropy,statisticalmechanicsanditsapplicationspp.-, 5,www. sciencedirect. com /science/ article/ pii/ S886 [8] J.S.RJang,ANFIS:Adaptive-network-basedFuzzyInferenceSystem.IEEE TransactionsonSystemsMan andcyberneticpp [9] E. Dogan, Reference evapotranspiration estimation using adaptive neuro-fuzzy inference system, Journal of Irrigation and Drainage volume 58, pp. 6-68,8, journal /./(ISSN)5-6 [] M.Rostaghi,M.N.Khajavi,Detectionofsizeandlocationofcrackinpipes underfluidpressurebyneuralnetworks,mme.modarespp.5-, July [] R.Safdari,G.saeedi,Comparingperformanceofdecisiontreeandneural network in predicting myocardial infarction Mashhad Journal of RehabilitationMedicineautumnwinter(InPersian) [] E. Ebrahimi, k. Mollazade, Intelligent Fault Classification of Tractor Starter Motor using Vibration Monitoring and Adaptive Neuro-Fuzzy Inference System Insight Non-Destructive Testing and Condition Monitoring5()pp , %96/5 %9/ %9/ % % %9/ %9/ % % 5. %96/5 - [] W. Mayes, W.G.R. Davies, the Vibrational behaviour of rotating shaf systemcontainingtransversecrack,institutionofmechanicalengineers Conference Publication Vibration in Rotating Macninery PP. 68-6, 96. [] R.Gasch,Dynamicbehaviourofsimplerotor,Institutionofmechanical Engineers Conference Publication, Vibration in Rotating Machinery pp. 6-8,99. [] T.A.Henry,B.E.Okah-Avae,Vibrationincrackedshaft,Institutionof mechanical Engineers conference Publication, Vibration in Rotating Machinerypp.6-6,96. [] H.D.Nelson,C.Natraraj,Thedynamicsofrotorsystemwithcracked shaft, American Society of Mechanical Enginees Jornal of Vibration, Acoustics,Stress,andReliabilityinDesign8pp.89-96,986. [5] L.A.Papadopoulos,A.D.Dimarogonas,CoupledLongitudinalandbending vibrationsofrotatingshaftwithanopencrackjournalofsoundand Vibrationpp.8-9,98 [6] L.A.Papadopoulos,A.D.Dimarogonas,Couplingofbendingandtorsional vibration of cracked Timoshenko shaft, IngenieurArchiv,pp.5-66, 98 [] S.M.PincusApproximateentropyasmeasureofsystemcomplexity ProcNatlAcadSciUSA88,pp.9-,March