Third International Workshop on Advanced Computational Intelligence August 25-27,2010 - Suzhou, Jiangsu, China

On-line Bearing Fault Diagnosis Based on Signal Analysis and Rough Set

Xin Chen, Yuhua Chen, Guofeng Wang, Dong Hu

Abstract-Bearing defects are categorized as localized and distributed. For on-line bearing fault diagnosis, in this paper, the time-domain kurtosis calculation and the frequency

domain wavelet analysis are used to extract the transitory

features of non-stationary vibration signal produced by the bearing localized defects. To distributed defects, bearing fault diagnosis is built on the reducing decision based on rough set. This algorithm, making use of conditional entropy and the

importance of it, without calculating the attribute core, get the optimization and minimum reduction set, and improves the on­line diagnosis speed and increases the fault diagnosis reliability. The feasibility and the robustness of this algorithm is

demonstrated in a real-world application.

I. INTRODUCTION

ROLLING element bearings are parts widely used in industrial applications, many breakdowns of machinery

are to do with rolling bearings. Accordingly, a reliable bearing fault diagnosis technique is very useful to a wide array of industries. Fault diagnostics involves two sequential processes: feature extraction and decision-making [1]. Feature extraction is to use appropriate signal processing techniques to extract representative features corresponding to the condition of a bearing, Several techniques have been proposed in the literature for faulty feature extraction, in WhICh the analysis can be performed in the time domain [2, 3], the frequency domain [4, 5], or the time-frequency domain [6, 7]. In recent years, some research efforts have been devoted to the formulation by using the evolutionary computation techniques such as genetic algorithms [8], particle swarm optimization [9], and genetic programming [10]. Each of these techniques has its own merits and limitations, and can be used for some specific bearing application.

An on-line bearing fault diagnosis technique, based on the signal process and the rough set, is developed in this work. The on-line bearing fault diagnosis system, in practice, collects amount of data from bearings measuring, and detects real-time bearing fault without a human interpreter.

This paper introduces the method of detecting bearing defects in on-line bearing fault diagnosis system (OBFDS).

Backgrounds are first presented on both the characteristic of the fault frequencies of rolling element bearings, detecting equipment, and bearing fault detection. This presentation is followed by the attribute reduction algorithm before

X. Chen, Y.H. Chen and G.F. Wang are with the Information Science an� Technology College, Dalian Maritime University, Dalian, PR China(e­mall: ch931105@Yahoo.cn, yuhuach@sina.com, gfwangsh@163.com).

D. Hu is with the Technical-Testing Center, Wafangdian Bearing Group Corporation, Dalian, PR China(e-mail: hwts@tom.com).

978-1-4244-6337-4/10/$26.00 @2010 IEEE 233

introducing it in the use of the practical bearing fault diagnosis.

II. BEARING F AUL T SIGNATURE AND TESTER

A. Characteristic of the Fault Frequencies The main components of rolling bearings (see Fig. 1) are

Outrring

Inner ring

Cage

Rolling elements -����

Figure I. Components of a rolling element bearing

the inner ring, the outer ring, the rolling elements, and the cage. The inner ring is mounted on a rotating shaft, and the outer ring to a stationary housing. The rolling elements may be balls or rollers. The cage separates the rolling elements, preventing contact between them during operation. It also helps to prevent poor lubrication conditions and, in many cases, holds the bearing together during handling. Roller bearings are generally used for applications requiring high load carrying capability, but radial ball bearings are the most common type of rolling element bearing [11]. If one among of the main components of rolling bearings is flawed, each time the rolling elements roll over the flaw, a high-level short duration force is incurred that causes the bearing to vibrate at its natural frequency, a response that decays quickly because of damping. The response occurs each time the rolling elements roll over the flaw, so that the fundamental frequency of the response waveforms is the rate at which the elements roll over the flaw. It is this fundamental frequency that is of interest in the fault diagnosis of rolling bearings.

Different frequencies are obtained for flaws in an outer race, inner race, on one of the balls, or in the cage [12]. For an angular contact ball bearing in which the inner race rotates and the outer race is stationary, the four characteristic frequencies are:

(1)

N B F[ (HZ) = S (-)(1 + -cos <1» • (3) 2 P

P B2 FB (HZ) = S (-)(1- -cos 2 <1» • (4) 2B p2

Where Fe is the cage fault frequency, F 0 the outer raceway fault frequency, FJ the inner raceway fault frequency, FB the ball/roller fault frequency, B the ball or roller diameter, P the pitch diameter, N the number of the rolling elements, and S the shaft rotation rate in hertz, and <I> the ball contact angle (zero for the roller).

These formulas are theoretical, and in real-world applications, vibrations measured on a bearing are dominated by high-level imbalance and misalignment components and include random vibrations associated with friction and other sources. Imbalance vibration occurs at the shaft rate of rotation; misalignment shows up at the fundamental and its harmonics. Therefore, the observed vibration signal on engineering usually is very complicated, in which they may include impacting, modulation, channel characteristic and noises.

As a rule, bearing defects may be categorized as localized and distributed. Localized defects, typically occurred as cracks, pits and spalls on the rolling surfaces, are always visible that appear on the raceways, and produce one of the four characteristic frequencies (e.g., Fe, Fa, FJ and FB) depending on which surface of the bearing contains the fault elements. Distributed defects include surface roughness, waviness, misaligned races and off-size rolling elements. Commonly in industry, the defects are usually generalized such as a coarse, rough track in contacted surface of components in rolling element bearings, and as long as reach an advanced stage, the bearing is near failure. An OBFDS must be able to detect both localized and distributed faults for real-world applications.

B. Bearing Tester An accelerated bearing life tester (ABLT, See Fig. 2) is a

kind of equipment for accelerated endurance testing of rolling element bearings reliability and analysis of bearing fatigue life. The shaft is driven by a 3-hp motor. The motor can run from 1000 rpm to 10000 rpm which is changeable by an embedded system (See Fig. 3). Four tested rolling element bearings are fitted in the ABL T, and piezoelectric accelerator sensors, each mounted in the outer ring, are installed to measure the vibration of bearing. Table I summarizes the main parameters of ABL T.

In OBFDS, the embedded system acquires the data of vibration at 100 kHz sample frequency, where the number of signal samples is adjustable according to bearing type and speed. To detect incipient faults, after sampling the signal of vibration, the embedded system's microprocessor identifies

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Figure 2. Accelerated Bearing Life Tester (ABL T)

TABLE I. TABLE TYPE STYLES

Bearing Types Ball & roller bearings

Bore Diameter(mm) <1>10 -<1>60

Tested Bearings 2 or 4 pieces

Changeable Tested Speed( r/min ) 1000 - 10000

Max Radial Load ( kN ) 100

Max Axial Load ( kN ) 50

Power I Spindle Motor 380V, 50Hz, 3k W

Supply I Pump Motor 380V, 50Hz, 0.37k W

Ambient Temperature 10°C - 40°C

the localized faults by the sample data, and almost simultaneously transmits these data in lower thread than the process to the database server (See Fig. 3).

III. BEARING F AUL T DETECTION

At the beginning of testing, the embedded system gradually improves the speed in the course of testing, and while collects the data of bearings to transmit it to the database server without detecting bearing defects, owing to the healthy status of the new bearings installed on the ABL T. The inspecting bearing flaws is followed. As discussed above, bearing defects include localized and distributed. In OBFDS, localized defects are detected by the embedded system, and distributed defects are identified by the application server.

A. Localized Defects Localized defects are visible that appear on the raceways,

rolling elements, or cage, and produce one of the four characteristic frequencies (e.g., Fe, Fo, FJ and FB) depending on which surface of the bearing contains the fault. But defect signals are not obvious. The sample signals from the sensor include the structure vibration and background noise. Bearings are mechanically coupled to other supporting structures, radial loaded rolling element bearings generate vibrations even if they are geometrically perfect, owing to a fmite number of rolling elements to carry the load with bearing rotation and the elastic deformation on contact points. And therefore defect signals are often submerged in structure

local area network

Industrial Ethernet

Figure 3. floor chart of ABL T's in OBFDS

noise and background noise (e.g., background vibrations, rubs, electrical noise), especially at the incipient stage when the related signals are usually short in duration and weak in amplitude. Fig. 4 shows a bearing vibration signal in time domain. In order to improve the signal-to-noise ratio and make the signal analysis more effective, the band-pass filtering is necessary. The band-pass filter can reject the low­frequency high-amplitude signals associated with imbalance and misalignment and eliminate random noise outside the pass-band. In OBFDS, the time-domain kurtosis calculation and the frequency domain wavelet analysis were used to extract the transitory features of non-stationary vibration signal produced by the bearing distributed defects. The kurtosis is sensitive to the pulses trend induced by bearing defects and has proven effective in the rolling element bearing diagnostics, and the wavelet transform provides powerful multi-resolution analysis in both time and frequency domain and thereby becomes a favored tool to extract the transitory features of non-stationary vibration signal produced by the faulty bearing.

Owing to a part of parameters the application server supplying to the embedded system at incipient testing stage, which are used in the kurtosis calculation and wavelet analysis, the mature techniques about localized defects of bearings are not detailed.

B. Destributied Defects The aforementioned method is effective to localized

defects, but not adapted for distributed defects. As discussed above, distributed defects include surface irregularities like roughness, waviness or off-size rolling elements. Distributed defects are caused by manufacturing error, improper installation or abrasive wear [13, 14]. The variation in contact force between rolling elements and raceways due to distributed defects results in an increased vibration level. For example, generalized roughness is the most common damage occurring to rolling bearings. It produces a frequency spreading of the characteristic fault frequencies, thus making it difficult to detect with spectral or envelope analysis, and general statistical analyses of typical bearing faults is quite time-consuming in on-line measure. To distributed defects, in this paper, based on the reducing decision of rough set, the

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application server identifies the bearing fault diagnosis according to the samples in the database server.

1) Model and Approximate Reduction Rough set theory is a mathematical technique used to

analyze imprecise, uncertain, or vague information [15, 16]. This technique has been used for decades in fields such as information system analysis, artificial intelligence, decision­making systems, data mining, pattern recognition, fault diagnosis and so on [17-19]. A rough set, characterized by a pair of lower and upper approximations, may be viewed as an approximate re-presentation of a crisp set in terms of two subsets derived from a partition on the universe.

In rough set theory, an information system is defmed as S= (U. A. V, j), where U is a fmite set of objects called the universe; A is a fmite set of attributes; V = UVa. Va EA, Va is the value region of the attribute a; f U X A -+ V which appoints the attribute value of every object x in U is an information function. A decision table is an information system, where A = CUD and enD = <P. C is the set of condition attributes and D is the set of decision attributes. Some defmitions are followed.

2) Knowledge granularity Suppose U is a fmite nonempty domain, R indicates an

equivalence relation on U, X is a classical set, according to R and X can get the UIR, the classical set Xi EUIR, then establish the a classical set UIR = {Xl. X2• " .• Xn}, the knowledge granularity of X is

G(Xi) = I Xi 1I1v]· (5) Where, I • I is the cardinality of a set.

Suppose the R is the knowledge in the information system, K = (0. R). u/R = { Xj, X2• " •• Xn }, then the knowledge granularity of R is.

n n

G(U I R) = I G(XJI I U I = II X I I I U 12. (6) ;=1 ;=1

3) Information entropy The entropy is also a kind of generous character of the

knowledge granules. The bigger granularity is, the more rough its demarcation toward object is, then the value of entropy is smaller; the smaller granularity is, the thinner its divide the object is, then the value of entropy is bigger [20].

If u/R = { Xj, X2 •• ". Xn } is a classical set on U domain, the Information entropy is defmed as

n H (U I R) = - L G (X; ) log G (X;) . (7)

;=1

Suppose T=<o, CUD> is decision table system, and P � c, Q � D, where both P and Q the indiscernible relationship, The condition entropy of knowledge u/IND(P) = {Xj, X2 •• ". Xn} relative to UIIND(Q) = {Xj, X2• " •• Xm} is defmed as

n m

H(Q I P) = -LG(X;) LG(� / X;)log(G(� / X;)).(8) i=1 j=1

Where G(lj /XJ = IY; nx; III X;I, i= 1,2, ... , n;j= 1,2, ... , m.

4) Attribute Rduction An infOlmation system is defmed as S = ( U, A, V, f ), P

c c, 'if a E C -P, its importance to D is denoted by SGF(a, P, D), which is defmed as

SGF(a,P,D) = H(D I P)-H(D I (PU{a}». (9)

According to the importance of attribute, and on the basis of the above ideas, the attribute reduction algorithm is presented based on information entropy. Different from most traditional algorithms, this algorithm need not to compute the attribute core, the optimization and minimum reduction set can be output directly. The algorithm as follows:

Input: Decision table T=<U,C UD>, Output: Reduction attribute set P. Step 1: Calculate the conditional entropy of D relative to

C: H (DIc); Step2: Calculate the conditional entropy of D relative to

each attribute ai EC : H(DI{a;}), then P= ai, ai is correspondence with the maximum of H(DI{ ai }) ;

Step3: Repeat

End

Calculate the importance SGF (aj, P, D), If SGF (aj, P, D) = 0, then delete aj from the attribute set C. Else if

P = P U {a;J ; where aj is correspondence with the maximum of {SGF (aj, P, D) },

If H (DI P) = H (DI C), stop; goto Repeat

IV. BEARING FAULT DIAGNOSIS

In OBFDS, the original features of bearings are also from the kurtosis calculation and the wavelet transform as above depiction, but the distributed fault samples from the fault sample database. The excessive fault samples can not satisfy the requirement of the real-time signal processing, and therefore the attribute reduction is necessary.

Consider an example to explain the attribute reduction algorithms just discussed where the sample data were dispersed, the decision table is displayed in Table II.

In the decision table, U is the universe to represent the sample number, c], C2, C3 and C4 are all condition attributes, d is the decision attributes. The course and result of attribute reduction are proposed as:

H ({d) I (cd) = 0.48072, H ({d) I (C2}) = 0.63150, H ({d) I (C3}) = 0.54651, H ({d) I (C4}) = 0.61840, H ({d) I (c2}»H({d}I{C4}) > H({d} I (c3}»H({d}I{CI}) P = {C2}. Calculate the importance:

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SGF (cI,P,d)=H({d) I ( C2}) - H({d} I P U{ CI}).

Where P U{ cd = { C2, CI}, and

U/IND ({C2, cd) = {{7}, {9}, {12}, {I, 2}, {3, 13}, {5, 6}, {8, II}, {4, 10, 14}},

SGF (c 1, P, d) = 0.29706. Similarly,

U/IND ({C2, C3}) = {{13}, {1O, ll}, {I, 2, 3}, {5, 6, 7, 9}, {4, 8, 12, 14}},

SGF (C3, P, d) = 0.13640. u/IND ({C2, C4}) = {{2}, {5, 9}, {6, 7}, {I, 3, 13},

{4, 8, 1O}, {ll, 12, 14}}. SGF (C4, P, d) =0.12329. And go on, the optimization and minimum reduction set

is {c], C2, C4}

V. CON CLUSION

This paper introduces the method of detecting bearing faults in OBFDS. Bearing defects are categorized as localized and distributed in this system. The literature focus on detection of distributed faults, which used attribute reduction algorithm from the point of view of information entropy. This algorithm, making use of conditional entropy and the importance of its, without calculating the attribute core, get the optimization and minimum reduction set, and improves the on-line diagnosis speed and increases the fault diagnosis reliability, the feasibility and the robustness of this algorithm is demonstrated in a real-world application.

REFEREN CES

[1] O. Ondel, E. Boutleux, and G. Clerc, "A method to detect broken bars in induction machine using pattern recognition techniques," IEEE Transactions on Industry Applications, vol. 42, no. 4, pp. 916-923, 2006.

[2] R. B. W. Heng and MJ.M. Nor, "Statistical analysis of sound and vibration signals for monitoring rolling element bearing condition," Applied Acoustics, vol. 53, pp. 211-226, 1998.

[3] J. Vass, R. Smid, R. B. Randall, P. Sovka, C. Cristalli, and B. Torcianti, " Avoidance of speckle noise in laser vibrometry by the use of kurtosis ratio: Application to mechanical fault diagnostics," Mechanical Systems and Signal Processing, vol. 22, pp. 647-671, 2008.

[4] J.R. Stack, R.G. Harley, and T.G. Habetler, "An amplitude modulation detector of fault diagnosis in rolling element bearings," IEEE Transactions on Industrial Electronics, vol. 51, no. 5, pp. 1097-1102, Oct. 2004.

[5] J.R. Stack, T.G. Habetler, and R.G. Harley, "Fault-signature modeling and detection of inner-race bearing faults," IEEE Transactions on Industry Applications, vol. 42, no. 1, pp. 61-68, 2006.

[6] J. Liu, W. Wang, F. Golnaraghi, and K. Liu, " Wavelet spectrum analysis for bearing fault diagnostics," Measurement Science and Technology, vol. 19, pp. 1-9,2008.

[7] J. Liu, W. Wang, and F. Golnaraghi, "An extended wavelet spectrum for bearing fault diagnostics," to appear (in press) in IEEE Transactions on Instrumentation and Measurement, 2008.

[8] B. Sarnanta, "Artificial neural networks and genetic algorithms for gear fault detection," Mechanical Systems and Signal Processing, vol. 18,no. 5,pp. 1273-1282,2004.

[9] H. Firpi and E. Goodman, "Swarmed feature selection," Proceedings of 33rd Applied Imagery Pattern Recognition Workshop, pp. 112-118, 2004.

[10] H. Guo, L. B. Jack, and A.K. Nandi, "Feature generation using genetic programming with application to fault classification," IEEE Transactions on Systems, Man and Cybernetics, vol. 35, pp. 89-99, 2005.

[I I] SA McInerny and Y. Dai, " Basic Vibration Signal Processing for Bearing Fault Detection," IEEE Transactions on Education, vol. 46, pp. 150-151,2003.

[12] 1.1. Taylor, The Vibration Analysis Handbook, 1st ed. Tampa, FL: Vibration Consultants, Inc, 1994.

[13] C.S. Sunnersjo, "Rolling bearing vibrations-geometrical imperfections and wear," 1. Sound Vibr. , 1985; 98(4): 455-74.

[14] M. W. Washo, "A quick method of determining root causes and corrective actions of failed ball bearings," Lubric Eng 1996; 52(3): 206-213.

[15] Z. Pawlak, "Rough Sets," International Journal of Computer and Information Sciences , 1982 ( I I): 341 - 356.

(16] Z. Pawlak, "Rough Sets: Theoretical Aspects of Reasoning about Data," Boston, MA, Kluwer Academic Publishers, 1991.

(17] 1. Wang, X. Y. Peng, and Y. Peng, "Efficient rough-set-based attribute reduction algorithm with nearest neighbourearchin," Electronics Letters, 2007, 43(10), pp. 563-564.

[18] S. Liu, Q. Sheng and B. Wu, "Research on efficient algorithms for rough set methods," Chinese 1. Computers. , 2003, 26(5), pp. 524-529.

[19] Ivo Duntsch, Gunther Gediga, "Uncertainty mesaures of rough set prediction," Artificial Intelligence, 1998, 106, pp. 109-137.

[20] G. Y. Wang, H. Yu and D. C. Yang, "Decisin Table Reduction based on Conditional Information Entropy," Chinese 1. Computers, July 2002,25(7), pp. 759-766.

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Figure 4. Vibration Signals. (a). before filtering; (b). after filtering

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