A Rough Sets Based Classifier for Induction Motors Fault Diagnosis

Transcription

1 A ough Sets Based Classiier or Induction Motors Fault Diagnosis E. L. BONALDI, L. E. BOGES DA SILVA, G. LAMBET-TOES AND L. E. L. OLIVEIA Electronic Engineering Department Universidade Federal de Itajubá Av. Pinheirinho, BPS. CEP: Itajubá MG BAZIL Abstract This paper describes the ongoing research on ough Sets based classiier applied to Induction Motors ault diagnosis through Motor Current Signature Analysis (MCSA). The results o mechanical ailures detection and how a ough Sets based classiier is used as a monitoring system using current signature analysis in predictive maintenance are also described in this paper. Key-Words: Predictive Maintenance; Three-phase induction motor; Motor Current Signature Analysis; ough Sets based classiier; Fault diagnosis. 1 Introduction Nowadays there is a great concern about the reliability o the productive process in order to reduce production costs and increase productivity in the industrial area. This act makes maintenance techniques a very important issue. The highlights o the moment are predictive maintenance techniques. These techniques consist o using continuous monitoring systems. Their use is justiied in the presence o ailures, in general randomly, o complex equipment with a large amount o components. Such ailures usually have serious economic or human consequences. Since induction motors are oten critical components in the industrial process, they deserve special attention rom the plant maintenance department. This paper presents a method o improving ault detection in induction motors through current signature analysis using a ough Sets based Classiier. Normally, the number o inormation available to reach the proper diagnosis is large enough to complicate ast human analysis. This is not an easy task or the expert. It is even more complicate or a technician to deal with all available data, normally a huge number o measurements that must be manipulated and clustered in order to visualize the current state o the equipment. In this particular point, the use o ough Sets helps the human operator to cope with all available inormation and cluster it in a reasonable and comprehensible way, which is normally done in ordinary Expert Systems. This paper presents an ongoing approach to ault detection and diagnosis that copes with the analysis perormed by the classiier and tries to make a classiication with two outputs. The irst output is the ailure mode and the second one is the operational mode in one o the three states, namely: normal, warning and emergency. In the irst state, all signals and all measurements are within the nominal rates. In the second state, all signals continue to be acceptable although some o the measurements may be above the nominal rates. For the emergency operational state, the signals are above the nominal rates and the maintenance is mandatory. The primary results obtained by the application o the methodology o ough Sets give us the hope that this technique can be used as a powerul tool toward a robust classiier in ault diagnosis. This paper is divided in three parts. The irst one gives a concise description o the Motor Current Signature Analysis approach and the mechanical aults that have been used. The second part shows the laboratory tests. The third part presents the application o ough Sets based classiier and the results obtained. 2 Overview o Motor Current Signature Analysis and the Detected Faults MCSA is a noninvasive technique which diagnosis problems in induction motors. It consists o utilizing the results o spectral analysis o the stator one-phase current signal. When a ailure is present, the requency spectrum o the line current becomes dierent rom that o a non-aulted one. Such ault modulates the airgap and produces rotating requency harmonics in the sel and mutual inductances o the machine. Since the lux linkages oscillate at only the electric supply requency, these harmonic inductances result in stator

2 current harmonic at rotating requency sidebands o the line requency [1]. The characteristic requencies o ailure are very well known and have been described by many authors. However, this paper section intends to introduce in a concise manner the general idea o the theory, and because o that, the characteristic requencies o each studied mechanical ault will be presented. 2.1 otor Asymmetry When a rotor asymmetry is present in an induction motor, the air-gap lux density is disturbed. This disturbance rotates at shat speed, generating characteristic components in the requency spectrum given by [2]: 1 s = k ± s (1) as p / 2 Where: is the supply requency; s is the slip per unit; p is the number o poles; and k = 1,2 3, 2.2 otor Unbalance In the case o dynamic eccentricity that varies with the rotor position, what happens is an oscillation in the air-gap length, causing variations in the air-gap lux. This act, in turn, aects the machine instantaneous inductance, producing stator current harmonics in [2]: 1 s = k ± 1 p / 2 ru (2) 2.3 Air-gap Eccentricity There are two methods or the detection o air-gap eccentricity. The irst one monitors the behavior o the sidebands present in the current spectrum near the slot requency. The associate requencies with this ailure, using this irst method, are given by: 1 s ( k ± necc ) ± n slot / ecc = s p / 2 (3) hand, by using this method o monitoring, it is possible to separate broken bar eects rom eccentricity eects. The second method consists o monitoring the behavior o the sidebands around the undamental requency. These ailure characteristic requencies are given by: 1 s = 1 ± k (4) ecc p / 2 The great advantage o this second approach is that it s not necessary to know the rotor construction aspects to accomplish an evaluation o the health o the motor [3]. 2.4 Broken Bars The detection o broken bars through the stator current spectrum can be accomplished by observing two particular components around the undamental component. When broken bars are present, the current spectrum presents two components equally spaced o 2..s rom the undamental requency. The let component ( -2s) results rom the ailure. The right component results rom the speed ripple. This way, the characteristic requencies o broken bars are given by [4]: bq = ( 1 ± 2 s) (5) 2.5 Bearing Damages The monitoring o bearing damages is very important in a predictive maintenance system since they are responsible or 4% o the ailures in induction machines. There are several causes or bearing damages. Since this is not the objective o this work, the paper will present just the characteristic components o ailure in the outer and inner races, and rolling elements. The ormulations o these characteristic components depend on the bearing dimensions. Fig. 1 presents the dimensions involved in the requency calculations: Where: is the number o rotor bars; n ecc is the eccentricity order number; n s is the supply requency harmonic rank; and k = 1, 2, 3, The great disadvantage o this method is the need or the constructive aspects o the machine. On the other Fig 1: Bearing dimensions

3 The characteristic requencies o ailures in the rolling element, inner race and outer race are respectively given by [5]: re PD = ± m BD rm BD 1 cos β PD 2 (6) n BD = ± m 1 + cos β (7) ir rm 2 PD or n BD = ± m rm 1 cos β 2 PD (8) However, the characteristic race requencies can be approximated or most bearings with between six and twelve balls by: = ±. 6 n (9) = ±. 4 n (1) ir rm or rm Where: rm is the rotor speed in hertz; n is the number o rolling elements; and m = 1, 2, 3 3 Laboratory Tests This work investigates some mechanical aults such as air-gap eccentricity, load unbalances, broken bars and bearing damage. Laboratory tests have conirmed the technique eiciency in monitoring the status o three-phase-induction motors. The tests conducted are described below in order to provide a better understanding o the approach. The requency spectra were obtained and the tendency curve was plotted. Fig. 3a presents the requency spectrum o normal condition and Fig. 3b presents the requency spectrum o level-three severity. Fig. 4 presents the tendency curve Hz 31.5Hz 53.7Hz 88.3Hz Hz Fig. 3a: Spectrum o normal condition 24.7Hz 31.7Hz 52.9Hz 81.1Hz 88.1Hz Hz 144.5Hz 172.7Hz Fig 3b: Spectrum o level-three severity 2.9Hz 3.1 Load Unbalance A load unbalance was imposed to the motor by installing a metal disc with three holes in the shat. It was created three levels o ailure severity by adding a small mass o 8 grams in each hole placed 7 mm (d 1 ), 9 mm (d 2 ) and 11 mm (d 3 ) rom the shat respectively. Fig. 2 illustrates the process. Fig. 4: Tendency curve The severity levels are: 1) non ault condition; 2) motor plus unbalanced disc without mass; 3) mass placed in d 1 ; mass placed in d 2 ; mass placed in d Bearing Damage Fig. 2: Laboratory assembly to simulate load unbalance In order to analyze the eects o bearing damage a hole was drilled through the outer race as Fig. 5 illustrates. According to the equation (1), presented in section II, the three irst pairs o characteristic requencies were 43.3 and Hz, (component that responded to the ailure) and Hz, and

4 368.7 Hz. Fig 6 presents the obtained spectra with zoom in the area where a characteristic component appeared. The monitoring system responded very well to the ailure presence and the increase o the severity level. Figure 8 presents the tendency curve: Angular Misalignment -3 x Fig. 5: Bearing with a hole in the outer race 146.3Hz x 1-3 Fig. 6a: Spectrum o normal condition Hz Fig. 6b: Stator current spectrum o a motor with a hole in the outer race o the shat-end bearing 3.3 Air-gap Eccentricity In order to simulate an air-gap eccentricity, angular (horizontal) misalignments were created by rotating the induction motor at speciic angles rom the original position, which was very well aligned with the coupled load. Three levels o severity were tested: θ 1 (or D=1.36mm), θ 2 (or D=2.18mm) and θ 3 (or D=2.73mm). See Fig. 7: Motor Support Laser Projection Overall Level (*1) Severity Level Fig. 8: Tendency curve The severity levels are 1) reerence condition; 2) angular misalignment θ 1, 3) angular misalignment θ 2 and 4) angular misalignment θ 3 : 3.4 Broken Bars Because o the constructive aspects o the rotor that was tested, small holes were drilled through the surace o the rotor instead o breaking a bar. The obtained response was the same as broken bars and can be visualized in igures 9a, 9b e 9c Hz 63.3Hz Fig. 9a: otor in good conditions 56.5Hz 63.3Hz Fig. 9b: otor with one holed bar Laser.4 DC Machine θ Induction Motor D Initial Position Position Ater otation Hz 63.7Hz 3 cm 25 cm Fig.7: Horizontal misalignment Fig. 9c: otor with two holed bars

5 The tendency curve shows very well the increase o the imposed ailure (ig 1). Overall Level (*1) Broken Bars Fig. 1: Tendency curve The tests show that the MCSA approach responded very well to the imposed ailures. This act pushes the research toward a development o a robust and reliable classiier to ault diagnosis. 4 ough Sets Based Classiier 4.1 Overview o ough Set Theory The objective o this paper section is to present the undamental concepts o the rough set theory. The main idea is to transorm a set o examples in a set o rules that represents the operational state o an induction motor Inormation System An inormation system can be deined as a 4-tuple K=(U,,V,ρ), where U is a inite set o objects (search space), is a inite set o attributes (state o each signal, currents and vibration), V is the domain o each attribute o, and ρ is a total unction (named inormation unction) that deines the ollowing application: ρ :U V, i.e., the examples. The concept o inormation system is not exclusive o the rough set theory and has been extensively used in inormation theory Approximation Sets Severity Level One o the main contributions o ough Set Theory is to automatically transorm data into knowledge [6]. This theory uses lower and upper approximation o a set, as shown in Fig. 11 [7]. There are ive regions (or sets) o interest: X and X, and POS ( X ), BN ( X ) and NEG ( X ). Each one o these is deined below. Let a set X U, be an equivalence relation, and K=(U,{}) be a knowledge base. Two subsets can be associated to these: a) -lower: X = U {Y U/ : Y X} b) -upper: X = U {Y U/ : Y X Ø} These deinitions mean that the elements that belong to the X set can be, with certainty, classiied as elements o X; while the elements belonging to the X set can be, only possibly, classiied as elements o X. In the same way, POS ( X ), BN ( X ) and NEG ( X ) are deined as [8]: c) POS ( X ) = X certainly member o X d) NEG ( X ) = U - X certainly non-member o X e) BN ( X ) = X - X possibly member o X X X NEG (X) BN (X) POS (X) Fig. 11: Deinition o -approximation sets and - regions. Based on the above deinitions, the concept o accuracy measure (α ( X )) can now be presented, which numerically characterizes the inaccuracy o the knowledge, using the cardinality o X and X sets, i.e., card X α ( X ) = (11) card X where α ( X ) is deined in the interval [,1]. When α ( X ) =1, the set X is named -deinable, and the BN ( X ) region is empty. In this case, the rough set theory is reduced to classical Cantor set theory educt and Core o Knowledge The concepts o reduct and core are important in the knowledge base reduction. Let be a amily o equivalence relations. The reduct o, ED(), is deined as a reduced set o relations that conserves the same inductive classiication o set. The core o, COE(), is the set o relations that appears in all

6 reduct o, i.e., the set o all indispensable relations to characterize the relation. 4.2 Knowledge Base eduction One o the most common approaches to get knowledge rom an expert is by examples. The idea behind the knowledge base reduction is a simpliication o this set o examples. This can be obtained with the ollowing procedure: a) Calculate the core o the problem b) Eliminate (or substitute) a variable using another one; and c) edeine the problem using new basic categories. The algorithm that provides the reduction o conditions has been proposed in [8,9] and can be represented by the ollowing steps: Step 1: Eliminate the dispensable attributes. Step 2: Compute the core o each example. Step 3: Compose a table with reduct value. Step 4: Merge possible examples. 4.3 Algorithm Extension A more sophisticated system or ault diagnosis can be developed redeining the band or the attributes related to each acquired values o analog variables according to a certain metric, creating a new and more lexible database. By applying the algorithm described beore in this modiied database, it is possible to obtain a more detailed and speciic classiication o the operating point o the Induction Motor under study. Beore the presentation o the algorithm, we need to remember two major concepts in ough Set Theory, reduct and core. These concepts are important in the knowledge base reduction. Let be a amily o equivalence relations. The reduct o, ED(), is deined as a reduced set o relations that conserves the same inductive classiication o set. The core o, COE(), is the set o relations that appears in all reduct o, i.e., the set o all indispensable relations to characterize the relation. The algorithm that provides the reduction o conditions has been proposed in [8,9], and can be represented by the ollowing steps: Previous Steps: Transorm continuous values in ranges. Eliminate identical attributes. Eliminate identical examples. Step 1: Eliminate dispensable attributes. Step 2: Compute the core o the decision table. Step 3: Compose a table with reduct value. Step 4: Merge possible examples. Final Step: Compose the inal set o rules. 4.4 Description o the Problem The idea is to transorm a set o examples in a set o rules that speciies the kind o ailure (Broken bars, bearing damage, air-gap eccentricity) and represents the operational state o an induction motor. For the sake o explanation, some assumptions and reductions are made. The operational state o the induction motor and the ailure mode, shown in Fig. 12, depend on the inormation obtained rom the data acquired rom one phase o the stator current (shat speed, characteristic requencies, etc), parameters related to motor eatures (rated power, current, voltage and speed) and other attributes generated by other digital signal processing techniques. These attributes are used in a decision table in order to provide a more suitable way o accomplishing the ough Sets Algorithm. Fig. 12: Operational state o an Induction motor and changing o operational point Table 1 presents a partial set o examples relating the dierent attributes with their values categorized in ranges. Table 1: Set o examples A B C D E F G H O1 O2 1 N N N S U UL C1 N N N 2 N N N S U UL C1 C N N 3 N N N S U UL C1 G N N 4 N N N S U UL C1 N N N 5 N N N S U UL C1 C N N 6 N N N S U UL C1 G N N

7 7 N N N S U UL C2 N N N 8 N N N S U UL C2 C N N 9 N N N S U UL C2 G N N 1 N N N S U UL C2 N N N 11 N N N S U UL C2 C N N 12 N N N S U UL C2 G N N 13 N N N C1 N N N 14 N N N C1 C N N 15 N N N C1 G N N 16 N N N C1 N N N 17 N N N C1 C N N 18 N N N C1 G N N 19 N N N C2 N N N 2 N N N C2 C N N 21 N N N C2 G N N 22 N N N C2 N N N 23 N N N C2 C N N 24 N N N C2 G N N 25 W N N S U UL C1 N Ecc W 26 W N N S U UL C2 N Ecc W 27 W N N C1 N Ecc W 28 W N N C2 N Ecc W 29 W N N F O OL C1 N Ecc W 3 W N N F O OL C2 N Ecc W 31 E N W S U UL C1 N Ecc E 32 E N W S U UL C2 N Ecc E 33 E N W C1 N Ecc E 34 E N W C2 N Ecc E 35 E N W F O OL C1 N Ecc E 36 E N W F O OL C2 N Ecc E 37 N W N S U UL C1 N B W 38 N W N S U UL C2 N B W 39 N W N C1 N B W 4 N W N C2 N B W 41 N W N F O OL C1 N B W 42 N W N F O OL C2 N B W 43 W E N S U UL C1 N B E 44 W E N S U UL C2 N B E 45 W E N C1 N B E 46 W E N C2 N B E 47 W E N F O OL C1 N B E 48 W E N F O OL C2 N B E 49 N N W S U UL C1 N BB W 5 N N W S U UL C2 N N N 51 N N W C1 N BB W 52 N N W C2 N N N 53 N N W F O OL C1 N BB W 54 N N W F O OL C2 N N N 55 W N E S U UL C1 N BB E 56 W N E S U UL C2 N BB E 57 W N E C1 N BB E 58 W N E C2 N BB E 59 W N E F O OL C1 N BB E 6 W N E F O OL C2 N BB E The condition attributes are: Speciic current components: A Overall level o those components related to eccentricity; B Overall level o those components related to bearing damage; C Overall level o those components related to broken bars. A, B and C are classiied in one o the three ranges, namely: Normal (N), Warning (W) or Emergency (E). Motor eatures: D slip; E undamental current amplitude; F input power; D is classiied as ast (F), rated () or slow (S). E is classiied as underrated (U), rated () or Overrated (O). F, in turn, is classiied as underload (UL), rated () or Overload (OL). D, E and F are per unit values related to rated values. General Attributes: G related to kind o load; H - related to load and environment conditions. G is classiied as C1 (constant load) or C2 (pulsating load). H is classiied as good (G), normal (N) or critical (C). The decisions attributes are: O1 - Failure mode (air-gap eccentricity (Ecc), bearing damage (B) or broken bars (BB)); O2 - Failure severity (Normal (N), Warning (W) or Emergency (E)). The set o examples o table 1, when inally reduced, generates the ollowing reduced set showed in table 2. The indication - in some cells means that the attribute is unnecessary or the classiication.

8 Table 2: educed Set A B C G O1 O2 1 N N N - N N 2 N N - C2 N N 3 W N N - Ecc W 4 E Ecc E 5 - W - - B W 6 - E - - B E 7 N - W C1 BB W 8 N - W C2 N N E - BB E Final Step: according to the table 2, one can express the knowledge present in table 1 by the ollowing set o rules: I (A is N and B is N and C is N) or (A is N and B is N and G is C2) or (A is N and C is W and G is C2) then (O1 is N and O2 is N) I (A is W and B is N and C is N) then (O1 is Ecc and O2 is W) I (A is E) then (O1 is Ecc and O2 is E) I (B is W) then (O1 is B and O2 is W) I (B is E) then (O1 is B and O2 is E) I (A is N and C is W and G is C1) then (O1 is BB and O2 is W) I (C is E) then (O1 is BB and O2 is E) 5 Conclusion This paper presents the results o a systematic approach to detect superluous input variables and unnecessary conditions in a set o examples in order to classiy speciic problems o induction motors. The size o the knowledge base represents an important challenge or reliable diagnosis in Predictive Maintenance. In this case, a systematic and rational reduction o a knowledge base, by keeping only the core o the knowledge, is desirable. The method described in this paper to reduce the knowledge base is based on ough Set theory, and it tries to create an automatic approach to transorm data into knowledge. The methodology developed is applied to induction motor predictive maintenance. Although the described technique is still under development, the obtained results are encouraging. eerences: [1].. Obaid, T. G. Habetler, D. J. Gritter A Simpliied Technique or Detecting Faults using Stator Current in Small Induction Motors, In Proceedings o the 35th Annual Meeting and World Conerence on Industrial Application o Electrical Energy, July 2. [2] M. H. Benbouzid, M. Vieira, and C. Theys. Induction Motor's Faults Detection and localization Using Stator Current Advanced Signal Processing Techniques. IEEE Transactions on Power Electronics, Vol. 14, No. 1, January 1999, pp [3] M. H. Benbouzid. A eview o Induction Motors Signature Analysis as a Medium or Faults Detection. IEEE Transactions on Industrial Eletronics, Vol. 47, No. 5. October 2, pp [4] W. T. Thomson and M. Fenger, Current Signature Analysis to Detect Induction Motor Faults, IEE Industry Applications Magazine, July/August 21, pp [5].. Shoen, T. G. Habetler, F. Kamram and. G. Bartheld. Motor Bearing Damage Detection Using Stator Current Monitoring. IEEE Transactions on Industrial Eletronics, Vol. 31, No. 6, November/December 1995, pp [6] Z. Pawlak - "ough Classiication", International Journal on Man-Machine Studies, Vol. 2, pp , [7] G. Lambert-Torres, A.P. Alves da Silva, V.H. Quintana & L.E. Borges da Silva - "Classiication o Power System Operation Point using ough Set Techniques", 1996 IEEE Int. Con. on Systems, Man and Cybernetics. [8] Z. Pawlak - "ough Sets - Theoretical Aspects o easoning about Data", Klumer Academic Publishers, [9]. Slowinski & J. Steanowski - "ough Classiication in Incomplete Inormation Systems", Mathematical and Computing Modeling, Vol. 12, No. 1/11, pp , 1989.