an integrated classifier for gear system monitoring

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Contents lists available at ScienceDirect

Mechanical Systems and Signal Processing

Mechanical Systems and Signal Processing 23 (2009) 1298–1312

0888-32

doi:10.1

� Cor

E-m1 Te

journal homepage: www.elsevier.com/locate/jnlabr/ymssp

An integrated classifier for gear system monitoring

Wilson Wang a,�, Derek Kanneg b,1

a Department of Mechanical Engineering, Lakehead University, 955 Oliver Road, Thunder Bay, ON, Canada P7B 5E1b Department of Control Engineering, Lakehead University, Thunder Bay, ON, Canada P7B 5E1

a r t i c l e i n f o

Article history:

Received 25 April 2008

Received in revised form

13 October 2008

Accepted 16 October 2008Available online 5 November 2008

Keywords:

Integrated classifier

Neural fuzzy classifier

Fault diagnosis

Multi-step forecasting

Gear systems

70/$ - see front matter & 2008 Elsevier Ltd. A

016/j.ymssp.2008.10.006

responding author. Tel.: +1807 766 7174; fax:

ail addresses: [email protected] (W

l.: +1807 343 8795.

a b s t r a c t

A novel integrated classifier has been developed in this paper for real-time machinery

health condition monitoring, specifically for gear systems. The diagnostic classification

is performed by a neural fuzzy scheme; the diagnostic reliability is enhanced by

integrating the (multi-step-ahead) future states of the dynamic system. An online

hybrid training technique is adopted based on recursive Levenberg–Marquet and least-

squares estimate (LSE) algorithms to improve the classifier convergence and adaptive

capability to accommodate different machinery conditions. The viability of this new

monitoring system is verified by experimental tests under different gear conditions. Test

results show that the proposed integrated classifier provides a robust problem solving

framework; it outperforms other related data-driven classification schemes, because of

its efficient feature enhancement, formation integration, and system training.

Furthermore, the integrated classifier has been implemented for condition monitoring

in multistage printing machines; its effectiveness is verified by some primary

application practices.

& 2008 Elsevier Ltd. All rights reserved.

1. Introduction

A reliable online condition monitoring system is very useful in industries to provide accurate fault diagnosticinformation in mechanical systems to prevent machinery performance degradation, malfunction or even catastrophicfailures. On the other hand, machinery condition monitoring information can also enable the establishment of amaintenance program based on an early warning of incipient defects. This can be of great value for those machines such asairplanes, power turbines, and chemical engineering facilities, for which unexpected shutdowns can have serious economicor environmental consequences.

Fault diagnosis is a sequential process involving two steps: representative feature extraction and pattern classification.Feature extraction is a mapping process from the measured signal space to the feature space. Representative featuresassociated with the health condition of a machinery component (or subsystem) are extracted by using appropriate signalprocessing techniques. Vibration signals are used for analysis in this case. Pattern classification is the process of classifyingthe characteristic features into different categories. The classical approach, which is also widely used in industry, relies onhuman expertise to relate the vibration features to the faults. This method, however, is tedious and not always reliablewhen the extracted features are contaminated by noise; Furthermore, it is difficult for a diagnostician to deal with thecontradicting symptoms if multiple features are used. The alternative is to use analytical tools (e.g., numerical models

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. Wang), [email protected] (D. Kanneg).

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W. Wang, D. Kanneg / Mechanical Systems and Signal Processing 23 (2009) 1298–1312 1299

[1–3]) and data-driven paradigms [4]. The latter will be utilized in this work because an accurate mathematical model isdifficult to derive for a complex mechanical system, especially when it operates in noisy environments. Data-drivendiagnostic classification can be performed by reasoning tools such as neural networks [5,6], fuzzy logic [7,8], and neuralfuzzy synergetic schemes [9,10]. The authors’ research team has suggested several neuro-fuzzy (NF) schemes for dynamicsystem condition evaluations [11–13], and some positive results have been achieved in several types of machineryapplications.

Even though several techniques have been proposed in the literature for machinery condition monitoring, it stillremains a challenge in implementing a diagnostic tool for real-world monitoring applications because of the complexity ofmachinery structures and operating conditions. The objective of this research work is to develop a new technique, anintegrated classifier, for real-time condition monitoring in, especially, gear transmission systems. It is a great extension toour previous work, and it is new in the following aspects: (1) the monitoring reliability is enhanced by integrating theinformation of the object’s future states forecast by a multiple-step predictor, (2) the diagnostic scheme is adaptivelytrained by a novel recursive hybrid algorithm to improve its convergence and adaptive capability, (3) the proposedtechniques are implemented for real-time monitoring applications in multistage printing machines.

The remaining of the paper is organized as follows: Section 2 describes integrated classifier, whereas the monitoringindices are illustrated in Section 3. Section 4 discusses the hybrid training algorithm. The effectiveness of the proposedintegrated classifier is verified in Section 5 by experimental tests. An application example is illustrated in Section 6.

2. The diagnostic system

The diagnostic classifier is used to integrate the features obtained by appropriate signal processing techniques to make amore positive assessment of the health condition of the mechanical component (i.e., object) of interest. The diagnosticreliability in this suggested classifier will be enhanced by implementing the future (multi-step-ahead) states of the object’sconditions. The developed classifier is an NF paradigm, in which the diagnostic classification is performed by fuzzy logic,whereas an adaptive training algorithm, as discussed in Section 4, is utilized to fine-tune the fuzzy system parameters andstructures. The conditions of each object (machinery component or subsystem) are classified into three categories: healthy

(C1), possible (initial) damage (C2), and damaged (C3), respectively. {x1, x2,y, xn} are the input variables at the current timestep. Three membership functions (MFs), small, medium, and large, are assigned to each input variable. The diagnosticclassification, in terms of the diagnostic indicator y, is formulated in the following form:

<j : If ðx1 is A1jÞ and ðx2 is A2jÞ and . . . and ðxn is AnjÞ ) ðy � Sj with wjÞ (1)

where Aij are MFs; i ¼ 1, 2,y, n, j ¼ 1,2,y, m, m denotes the number of rules; Sj represents one of the states of C1, C2 or C3,depending on the values of the diagnostic indicator.

When multiple features (input indices) are employed for diagnostic classification operations, the contribution of eachfeature association to the final decision depends, to a large degree, on the situation under which the diagnostic decision ismade. Such a contribution is characterized by a weight factor wj which is related to the feature association in each rule. Theinitial values of these rule weights are chosen to be unity; That is, all input state variables are initially assumed to haveidentical importance to the overall diagnostic output.

Similarly, the diagnostic classification based on the predicted monitoring indices, {x01, x02,y, x0n}, is formulated as

<j : If ðx01 is A1jÞ and ðx02 is A2jÞ and . . . and ðx0n is AnjÞ ) ðy0 � Sj with wjÞ (2)

where y0 is the diagnostic indicator based on forecast input variables.The number of rules is associated with the diagnostic reasoning operations of input state variables. In general, if all

monitoring indices are small, then the object is considered healthy (C1). Otherwise, the object is possibly damaged. In thiscase, the diagnostic classification indicator y represents faulty condition only. Fig. 1 schematically shows the networkarchitecture of this integrated classifier. Unless specified, all the network links have unity weights.

The input nodes in layer 1 transmit the monitoring indices {x1, x2,y, xn} or their forecast future values {x01, x02,y, x0n} tothe next layer. These two sets of monitoring indices are input to the network and processed separately.

Each node in layer 2 acts as an MF, which can be either a single node that performs a simple activation function ormultilayer nodes that perform a complex function. The nodes in layer 3 perform the fuzzy T-norm operations. If a productoperator is used, the firing strength of rule <j is

Zj ¼Yn

i¼1

AijðxiÞ or (3)

Z0j ¼Yn

i¼1

Aijðx0iÞ (4)

where Aij( � ) denote MF grades.

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Fig. 1. The network architecture of the proposed integrated classifier.

W. Wang, D. Kanneg / Mechanical Systems and Signal Processing 23 (2009) 1298–13121300

Defuzzification is undertaken in layer 4. By normalization, the faulty diagnostic indicator will be

y ¼

PmZjwjP

mZj

. (5)

Similarly, the fault diagnostic indicator based on forecast inputs will be

y0 ¼

PmZ0jwjP

mZ0j. (6)

The states of the diagnostic indicator y (or y0) are further classified into three categories

If 0pyp0:33) HealthyðC1Þ

If 0:33oyp0:66) Possibly damagedðC2Þ

If 0:66oyp1) DamagedðC3Þ

8><>:

The final decision regarding the health condition of the object of interest is made by

ðaÞ If ðy � C1 and y0 � C1Þ or ðy � C2 and y0 � C1Þ then ðthe object is healthy C1Þ

ðbÞ If ðy � C3 and y0 � C3Þ or ðy � C2 and y0 � C3Þ then ðthe object is damaged C3Þ

ðcÞ Otherwise ðthe object is possibly damaged C2Þ. (7)

3. Prediction of monitoring indices

3.1. Monitoring indices

In general, most machinery defects are related to transmission systems, mainly for gears and bearings. In this work,gears are used as an example to illustrate how to apply the proposed integrated classifier for machinery conditionmonitoring. In operations, the fault diagnosis of a gear train is conducted gear by gear. Because the measured vibration is anoverall signal contributed from various vibratory sources, the primary step is to differentiate the signal specific to each gearof interest by using a synchronous average filter [14]. By this filtering process, the signals which are non-synchronous to therotation of the gear of interest (e.g., those from bearings, shafts, and other gears) are filtered out. As a result, each gearsignal is computed and represented in one full revolution, called the signal average which will be used for advanced analysisby other signal processing techniques.

Several techniques have been proposed in the literature for gear fault detection. However, because of the complexity inthe machinery structures and operating conditions, each fault detection technique has its own advantages and limitations,and is efficient for some specific application only [14]. Consequently, the selected features for fault diagnostics should berobust, that is, sensitive to component defects but insensitive to noise (i.e., the signal not carrying information of interest).

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In this case, three features from the information domains of energy, amplitude, and phase are employed for the diagnosisoperation: (a) wavelet energy function, using the overall residual signal which is obtained by band-stop filtering out thegear mesh frequency fRN and its harmonics, where fR is the rotation frequency (in Hz) of the gear of interest and N is thenumber of teeth of the gear; (b) phase demodulation [15], using the signal average; and (c) beta kurtosis, using the overallresidual signal. The details of these reference functions can be found from [13].

Based on the related reference functions, the monitoring indices are determined to quantify the feature characteristics.Each index is a function of two variables: magnitude and position. The magnitude of an index is determined as thenormalized relative maximum amplitude value of the corresponding reference function; the position is where themaximum amplitude is located. Usually, the maximum amplitude positions in these reference functions do not coincideexactly due to the phase lags in signal processing. Based on simulation and test observations, an influence window is definedas a period of four tooth periods in this case. Correspondingly, if all indices are located within one influence window, oneset of inputs {x1, x2, x3} is given to the classifier. Otherwise, if three indices are not within one influence window, the objecthas no fault or has more than one defect; more than one set of inputs should be provided to the classifier. For example, if x3

0 90 180 270 360-1

0

1Signal Average

Am

plitu

de (V

)

0 90 180 270 3600

1

2

Wavelet Energy Reference Function

Am

plitu

de

0 90 180 270 360

0.4

0.5

0.6Beta Kurtosis Reference Function

1 / B

K

0 90 180 270 3600

20

40

Phase Modulation Reference Function

Deg

rees

Gear Angular Position (Degrees)

0 5000 10000-2

0

2

Acc

eler

atio

n (V

)

Time Signal Samples

Part of the Original Time Signal

Fig. 2. Processing results for a healthy gear: (a) part of the original vibration signal; (b) signal average; (c) wavelet reference function; (d) beta kurtosis

reference function, and (e) phase modulation reference function.

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does not fall within the influence window determined by x1 and x2, two sets of inputs will be given to the monitoringclassifier: The first input vector is {x1, x2, x3}, where x3 is computed over the influence window determined by both x1 andx2; The second input vector is {x1, x2, x3}, where x1 and x2 are determined over the influence window around x3.

Fig. 2 illustrates an example of the reference functions corresponding to a healthy gear with 41 teeth. Fig. 2a shows partof the original vibration signal measured from the experimental setup to be illustrated in Section 5. Fig. 2b represents thesignal average of the gear of interest, which is obtained by synchronous average filtering; each wave represents a toothperiod. Fig. 2c–e represents the resulting respective reference functions of the wavelet energy, beta kurtosis, and phasemodulation. It is seen that no specific irregularities can be found from these reference functions for this healthy gear. Thecorresponding indices x1, x2, and x3 are, respectively, 0.128, 0.227, and 0.315 in this case.

Fig. 3 shows the processing results corresponding to a cracked gear with 41 teeth. It is impossible to recognize the geardamage from the original signal (Fig. 3a). A little signature irregularity can be recognized around 2001 in the signal averagegraph (Fig. 3b). However, this gear damage can be identified clearly from the proposed reference functions (Fig. 3c–e).

0 5000 10000-2

0

2

Acc

eler

atio

n (V

)

Time Signal Samples


0 90 180 270 360-1

0

1Signal Average

Am

plitu

de (V

)

0 90 180 270 3600

1

2


Am

plitu

de

0 90 180 270 360

0.4

0.5

0.6Beta Kurtosis Reference Function

1 / B

K

0 90 180 270 3600

20

40


Deg

rees


Fig. 3. Processing results for a cracked gear: (a) part of the original vibration signal; (b) signal average; (c) wavelet reference function; (d) beta kurtosis


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0 5000 10000-2

0

2

Acc

eler

atio

n (V

)

Time Signal Samples


0 90 180 270 360-1

0

1Signal Average

Am

plitu

de (V

)

0 90 180 270 3600

2

4


Am

plitu

de

0 90 180 270 3600.4

0.5

Beta Kurtosis Reference Function

1 / B

K

0 90 180 270 3600

25

50


Deg

rees


Fig. 4. Processing results for a chipped gear: (a) part of the original vibration signal; (b) signal average; (c) wavelet reference function; (d) beta kurtosis



Although the maximum peak positions are little different from one graph to another, these peaks occur within oneinfluence window. The corresponding indices x1, x2, and x3 are 0.838, 0.741, and 0.816, respectively.

Fig. 4 illustrates the processing results for a chipped gear (with 41 teeth). Some signature irregularity can be recognizedaround 2001 in the signal average graph (Fig. 4b) due to this gear tooth damage. However, this defect can be clearlyidentified from other three reference functions (Fig. 4c–e), and the monitoring indices (x1 ¼ 0.901, x2 ¼ 0.733, andx3 ¼ 0.809) are located within one influence window.

3.2. Forecasting of the monitoring indices

System state forecasting is the process to predict the future states in a dynamic system based on available observations.Several techniques have been suggested in the literature for time series forecasting. The classical methods are the use ofstochastic models [3,16] which are usually difficult to derive for mechanical systems with complex structures. More recentresearch on time series forecasting has focused on the use of data-driven paradigms, such as neural networks and neuralfuzzy schemes [17,18]. In this work, the multi-step-ahead prediction of the input variables (indices) is performed by the

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predictor as developed in [11], whose effectiveness has been verified by different simulations. The system parameters inthis multi-step predictor are trained by using a hybrid algorithm with a real-time recurrent learning and least-squaresestimate (LSE). Details about the training algorithm can be found in [11].

4. Online training of the diagnostic classifier

The developed diagnostic classifier should be optimized in order to achieve the desired input–output mapping. Severaltraining algorithms have been proposed in the literature for NF-based classification schemes [18–23]. Because mostmachinery operates in noisy and uncertain environments, whereas machinery dynamic characteristics may changesuddenly, for instance, just after repair or regular maintenance, an adaptive training will be employed in this case toaccommodate different machinery conditions. The proposed integrated classifier will be trained by a hybrid method basedon recursive Levenberg–Marquet (LM) and LSE. Such a training approach possesses randomness that may help to escapecertain local minima.

4.1. Training the premise MF parameters

The nonlinear premise MF parameters will be trained by adopting the recursive LM method. The general LM algorithmpossesses quadratic convergence close to a minimum. Its convergence property is still reasonable, even if the initialestimates are poor. In addition, the LM algorithm has been proven globally convergent in many applications by properlychoosing the step factors.

For a training data pair {x(p),d(p)}, the inputs are x(p)¼ {x1

(p), x2(p), x3

(p)}, p ¼ 1, 2,y, P; d(p) are the desired outputs {0, 0.5, 1}as x(p) belongs to C1, C2 and C3, respectively. The error function with respect to adjustable MF parameters hp at the currenttime instant, p, is

EðhpÞ ¼1

2

XP

p¼1

½yp � dp�2 ¼

1

2

XP

p¼1

r2p ¼ rT

prp (8)

where yp is the pth output determined by Eq. (5); p ¼ 1,2,y, P; dp is the desired output; and rp is the error vector. Both yp

and rp are functions of hp.By taking the Taylor series expansion and neglecting higher order terms,

hpþ1 � hp þ lðJTpJp þ ZIÞ�1JT

prp ¼ hp þ ð1� aÞH�1p JT

prp (9)

where JpARN� Z denotes the Jacobian matrix; Z is the dimension (or the number of adjustable parameters) of hp; HpARZ� Z isthe modified Hessian matrix; IARZ� Z is an identity matrix; l ¼ 1�a is the learning rate, and a is the forgetting factor. Bysome manipulations as listed in the Appendix, the recursive LM algorithm can be represented by

hpþ1 ¼ hp þUpJprp (10)

Up ¼1

a½Up�1UðaV þ UTUp�1UÞ�1UTUp�1� (11)

The denominator (aV+UTUp�1U) is a matrix with dimension 2�2; its inverse computation is simple, and can beimplemented for real-time applications. h0 ¼ 0. Up is a covariance matrix with initial condition U0 ¼ rI, where r is apositive quantity and I is an identity matrix. By simulation tests, the following initial values are given to the relatedparameters in this study: Z ¼ 0.01 (A[0.001, 10]), a ¼ 0.995 (A[0.95, 1]), and r ¼ 103 (A[102, 105]).

4.2. Implementation of the hybrid training method

In implementation, inside each training epoch, the nonlinear MF parameters in the classifier are optimized in thebackward pass by using a recursive LM method, whereas consequent linear rule weights are updated by LSE in the forwardpass. On the other hand, after training or real applications over some time period, if the updated rule weights wj aresufficiently small (e.g., wjo0.01), the contribution of the related rule to the final classification operation can be neglected,and that rule can be removed from the rule base.

5. Performance evaluation and industrial applications

5.1. Experimental setup

Fig. 5 shows the experimental setup used in this study to verify the performance of the proposed integrated classifier.The apparatus are anchored onto a massive concrete block. It consists of a 3-HP AC drive motor and a gearbox. The motorrotation is controlled by a speed controller which allows tested gears operating in the range of 20–4200 rpm. An opticalsensor provides a one-pulse-per-revolution signal which is used as the reference for the time synchronous average filtering.

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Fig. 5. The experimental setup: 1—speed controller, 2—motor, 3—optical sensor, 4—gearbox, 5—load controller, 6—loading system, and 7—sensors.

Fig. 6. Gear conditions tested: (a) healthy gear, (b) cracked gear, and (c) chipped gear.


The gearbox consists of two pairs of spur or helical gears. The shafts in the gearbox are mounted on to the housing byrolling element bearings. The load is provided by a magnetic loading system which is connected to the output shaft. Thespeed of the drive motor and the load are adjusted to simulate different speed/load operating conditions. The vibration ismeasured using ICP-accelerometers mounted on the gearbox housing along different orientations. After being properlypreconditioned (e.g., amplification, rectification, and anti-aliasing filtering), the collected signals are fed to a computer forfurther processing.

5.2. Performance evaluation

To verify the effectiveness of the proposed classifier, five gear cases are tested in this study as represented in Fig. 6: (a)healthy gears (C1); (b) gears having a tooth crack with 15% (C2), and 50% (C3) tooth root thickness; and (c) gears having achipped tooth with 10% (C2) and 40% (C3) tooth surface area removed. These simulated defects belong to localized gearfaults. From the signal property standpoint, when a localized fault occurs, some high-amplitude pulses will be generateddue to impacts, which are relatively easier for a signal processing technique to recognize. When a localized fault propagatestowards a distributed defect, the overall energy of the fault will increase, but it often becomes more wideband in natureand difficult for a vibration-based signal processing technique to detect in the presence of the other vibratory componentsof the machine. That is, it is relatively easier to detect a distinct low-level narrowband tone than a high-level widebandsignal in the presence of other signals or noises. On the other hand, a distributed fault could be detected based on analysisof acoustic signals or lubricant information.

To make a comparison, the diagnostic results from the following three classifiers are also listed:

(1)
A pure fuzzy system with a similar reasoning architecture as in Fig. 1 but without the use of predictors. The rule weightfactors are chosen as those in the integrated classifier after initial training.
(2)
Classifier-1: An NF classifier with a similar reasoning architecture as in Fig. 1 but without predictors. Its MF parametersare trained by a gradient-LSE algorithm.
(3)
Classifier-2: Same as Classifier-1, but trained by the hybrid algorithm of the recursive LM and LSE.
Given the network architectures, the initial parameters of three adaptive classifiers can be primarily trained by usingsome data sets collected in previous tests on the same test apparatus, or be initialized by experience. Then these classifierparameters are optimized in the following online training processes.

During online tests, motor speed and load levels are randomly changed to simulate general and unusual machineryoperating conditions. The tests are conducted under load levels from 0.5 to 3 hp, and motor speeds from 50 to 3600 rpm.

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In online monitoring, based on test schedule and load/speed change frequency, the monitoring time-interval is set at15 min; that is, all the monitoring schemes are applied automatically every 15 min for condition monitoring operations.Three-steps-ahead predictors (i.e., r ¼ 3) are used in the integrated classifier. The selection of data size depends on noisereduction requirement [13]; usually the data for the gear with the lowest speed should cover more than 100 revolutions.For example, if the slowest gear speed in the gearbox is 1200 rpm, the data acquisition process takes at least 5 s (15 s in thiscase). The monitoring is performed gear by gear. Three examples corresponding to healthy, cracked, and chipped gears(all having 41 teeth) have been illustrated in Figs. 2–4, respectively.

Each healthy gear condition is tested over 24 h, whereas each faulty gear condition is tested over 50 h. In total, 386 datapairs are recorded for testing purpose. Table 1 summarizes the classification performance by different diagnostic schemes.

The fuzzy classifier records 15 missed alarms and 37 false alarms, with an overall reliability of 85.3%. Its relatively poordiagnostic performance is mainly due to the lack of learning capability. In addition, fixed or human-determined systemparameters are subject to variations and are rarely optimal in terms of reproducing the desired classification outputs,which results in the fuzzy classifier not being optimized under different operating conditions.

Classifier-1 records 7 missed alarms and 21 false alarms, with an overall reliability of 92.5%. One difference between thisNF system and the fuzzy classifier is related to the rule weight factors. Each signal processing technique (and the resultingfeature) has a limited capability in fault detection. Even if the firing strengths of two fuzzy if-then rules are identical, theirdiagnostic reliabilities may be different under different machinery conditions. Therefore, rule weights play an importantrole in the diagnostic classification operations.

Classifier-2 records 7 missed alarms and 17 false alarms, with an overall reliability of 93.6%. The main differencebetween classifier-2 and -1 is related to training algorithms. It is seen that the recursive LM algorithm is superior to thegradient method in convergence, and has the randomness to reduce the chance of possible trapping due to local minima. Inaddition, each rule has its own decision (mapping) space, whereas the MFs and the rule weights are directly associatedwith the characteristics of the decision space. The efficient optimization of classifiers can adjust the boundarycharacteristics of the decision space so as to reduce misclassifications. This property is especially important for classifierwith coarse fuzzy partitions.

The developed integrated classifier generates 3 missed alarms and 7 false alarms, with an overall reliability of 97.6%.Compared with classifier-2, the integrated classifier can enhance the classification accuracy by properly implementing thefuture states of the classifier. It follows that adaptively fine-tuning of the fuzzy parameters is necessary to enhance theapproximation of the mapping from the observed symptoms to the underlying faults. In addition, the severity ofthe localized gear defects can be recognized because, to some extent, the greater the localized fault, the more pronouncedthe feature modulation, and the larger the monitoring indices will become.

The developed integrated diagnostic classifier provides a robust problem solving framework. Machinery conditions varydramatically in real-world applications, and new system conditions may occur under different circumstances. With the

Table 1Comparison of the diagnostic results from different diagnostic schemes.

Diagnostic schemes Healthy gears Cracked gears Chipped gears Overall accuracy (%)

M.A. F.A. M.A. F.A. M.A. F.A.

Fuzzy system 0 13 12 16 3 8 85.3

Classifier-1 0 7 6 9 1 5 92.5

Classifier-2 0 5 7 8 0 4 93.6

New classifier 0 2 3 3 0 1 97.6

M.A., missed alarms; F.A., false alarms.

Mon

itorin

g in

dica

tor

A

Time

I II III IV

Fig. 7. The deterioration trend of a machinery component.

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help of an adequate learning algorithm, new information can be extracted from online training, and the diagnosticknowledge base can be expanded automatically to accommodate different machinery conditions.

In general, deterioration history of most machinery components follows a ‘‘U curve’’ as illustrated in Fig. 7. It consists offour periods: the run-in stage (I), the normal operation period (II), initial (III), and advanced (IV) failure stages, respectively.Such a trend characteristic is easy for a powerful NF predictor to catch up. If a false alarm is generated during the healthyperiod II, the false alarm is induced due to noise instead of real defect. Based on the forecast result, the diagnostic stateshould lie in period III (or initial defect). However random noise will disappear in the following processing steps, and thediagnostic indicator should return to period II (or healthy). Correspondingly, this misclassification can be prevented by theintegrated classification/forecasting information. On the other hand, if an object is damaged, its diagnostic indicator shouldlie in period III (or IV). If a misclassification occurs, or the diagnostic indicator falls in period II, the forecast information willbe contradictory to that from the classifier. Comprehensive analysis in Eq. (7) can avoid this possible missed alarm so as toimprove fault diagnostic reliability. In both aforementioned examples, classifier will be updated to accommodate such anoise in the following monitoring applications.

6. An industrial application example

6.1. Overview

The proposed integrated classifier has been implemented for real-time condition monitoring applications in printingmachines.

A multistage printing machine is a complicated, high-speed, and very expensive piece of equipment. As shown in Fig. 8,a typical machine consists of several printing stages (units) identical in mechanical design; each unit prints a differentcolor to the images on the web. Each unit consists of many rollers and cylinders that are driven by a gear system housed onthe outside of the unit as shown in Fig. 9. In this example, the two printing cylinders are driven by gears #1 and #2,respectively. Gear #7 is the input pinion which is driven by a motor drive.

One of the main concerns in printing quality control is related to the doubling error (or blurring) which is a registrationerror among different printing units. It occurs whenever the impression on a printing cylinder blanket does not line upexactly with the previous image remaining on the web. Doubling is induced by any rotation non-synchronization errorsamong the printing cylinders in different units [24]. It can be caused by imperfections either within units or in linksconnecting different units, such as vibrations and mechanical damage in gears and bearings. Although electroniccompensation systems are utilized in each printing machine to offset some of print imperfections, these offset methods areinadequate to accommodate for inaccuracies caused by machine vibration and mechanical faults. Once the doubling errorexceeds a certain threshold (e.g., 0.08 mm for general printing applications), the printing quality falls below tolerance,prompting shutdowns to allow for adjustments or repairs. Unfortunately, it is usually difficult to isolate the sources of thedoubling error among hundreds of rotating components in a complex multistage machine. The machine downtime duringinspection and repair may add significant cost to the operation of the machine.

As a matter of fact, system dynamics in a printing machine is time-varying. Even for identical machines manufacturedby the same company, due to the machines’ complex mechanical structures and unavoidable manufacturing and assemblyimperfections, their initial conditions vary dramatically from one machine to another. On the other hand, in printingoperations, web material properties (e.g., web type and materials) vary from one project to another; the machinerydynamics changes correspondingly. Furthermore, the machinery characteristics may also change suddenly, for example,just after repairs and maintenance. As stated in introduction, the classical monitoring paradigms (including predictors) donot have sufficient adaptive capability to accommodate these time-varying dynamic effects.

Based on the proposed integrated classifier as well as other related techniques and tools by the authors’ research group,a novel condition monitor is developed for Mechworks Systems Inc. for real-time fault diagnostics in printing machines.Fig. 10 illustrates its block diagram. It consists of both hardware and software systems. Signals are collected by using

Fig. 8. An example of a multistage printing machine with six stages (units).

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Fig. 9. A gear system housed on the outside of a printing unit. (1)–(7): the gears to be monitored; (8)—the magnetic pickup sensor.

Gear fault Diagnosis

Rotation Synch Monitoring

Runout Detection

Post Processing

Signal Processing

Filtering

AlarmsDataAcquisition

Fig. 10. The block diagram of the developed online gear condition monitoring system.


appropriate sensors. After being properly pre-processed, the signals are fed to the computer for advanced processinganalysis.

6.2. The hardware systems

The hardware includes sensors, a data acquisition card, an alarm system, and a computer that can be either a separatePC or the main computer used in the machine.

Vibration signals are collected by 3-D smart sensors, as shown in Fig. 11, which are developed by the authors’ researchgroup. The sensing unit employs three ICP-accelerometers (PCB 320) mounted along x-, y-, and z-directions to measure 3-D

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Fig. 11. A 3-D smart sensor for vibration measurement.


vibrations. Signal conditioning circuits perform the functionalities of amplification, rectification, anti-aliasing filters, A/D,etc. The pre-processed digital signals are fed to the computer by a USB interface. The reconfigurable parameters of thesmart sensor include sensor ranges, sampling frequency, measurement ranges, etc.

The reference signals are provided by magnetic pickups (MP62TA) in this study. Compared with other proximity probes,a magnetic pickup is a self-generating sensor, requiring no external excitation and accessory devices; thus it has lower cost.But to get an appropriate signal output, the surface speed of the sensed object should not be too low (X0.25 m/s in thiscase).

Vibration signals are fed to the computer by a USB adaptor, whereas reference signals are input to the computer by anappropriate data acquisition board.

An alarm system is used to trigger alarm signals to remind users once if some defects occur. The alarms can be in eitherlight or acoustic signals.

6.3. The software system

As illustrated in Fig. 10, the Filtering Module contains the generally used filters such as low-pass, high-pass, band-pass,band-stop, or user defined filters. The Signal Processing Module is used to extract representative features of the gear by theuse of appropriate signal processing techniques. The resulting representative features are further processed in the Post-Processing Module to enhance feature characteristics and derive monitoring indices. The condition monitoring consists ofmodules of gear system fault diagnostics, rotation synch monitoring, and run-out detection. Since the proposed integratedclassifier in this work is used for gear fault diagnostics, whereas rotation synch and run-out monitoring require differenttechniques, only the module of ‘‘gear fault diagnostics’’ is discussed in this section.

6.4. Gear fault detection by the integrated classifier

Before applications, the monitoring software should be properly initialized. The necessary inputs consist of: the geartrain information, the location of the reference sensor, number of units in the printing machine, web type, monitoringinterval, system training set up, etc.

Based on maintenance record, fault detection is mainly undertaken for gears #1–7 which drive the correspondingcylinders, as shown in Fig. 9. Each unit in the printing machine uses three 3-D accelerometers (as shown in Fig. 11) on theopposite side of the gear system. The reference signal in the gear train is provided by a magnetic pickup sensor which ismounted along the radial direction to gear #2. The generated reference signal is a tooth-based signature, that is, each toothperiod generates one pulse.

Based on the developed integrated classifier, the fault diagnostic processing is performed gear by gear. Specifically, for agiven machine unit, the vibration signal of a gear of interest is obtained from a 3-D smart sensor close to the gear ofinterest, along x- or y-direction. The information along other directions is used for verification. Since a gear signal isperiodic in terms of gear’s rotation, the relevant signal for a gear of interest can be extracted by time synch average filtering[14]. The reference signals for other gears (except #2) can be obtained by the corresponding transmission ratio with respectto gear #2. By time synch average filtering, the signals non-synchronous to the rotation of the gear of interest are filteredout. The resulting signal (i.e., signal average) is represented in one-full revolution. As stated in Section 3.1, three monitoringindices {x1 x2 x3} are then determined from the respective reference functions of wavelet energy, beta kurtosis, and phasedemodulation.

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Fig. 12. An interface for gear fault diagnosis based on the developed integrated classifier.


For a given gear, the corresponding monitoring indices {x1 x2 x3} are input to the integrated classifier to determine thediagnostic indicator y by Eq. (5). If yp0.33, the gear of interest is considered healthy (C1); if 0.33oyp0.66, the gear ispossibly damaged or in initial damage (C2); and otherwise it is damaged (C3) if yX0.66.

On the other hand, the future states of the monitoring indices of {x1 x2 x3}, {x01 x02 x03}, are forecast by multi-steppredictors. In this monitoring operation, time interval for each step is set at 4 h. That is, the monitoring system isapplied automatically over every 4 h to diagnose the health condition of the gear systems. If the forecasting is for three-step-ahead prediction (i.e., r ¼ 3), then state v0+r, or x0d, represents the future state of the given monitoring index after3�4 ¼ 12 h.

For a given gear, based on the forecast input vector {x01 x02 x03}, the corresponding forecast diagnostic indicator y0

can be determined by Eq. (6). The gear of interest is believed to be healthy (C1), possibly damaged or in initialdamage (C2) or damaged (C3) if the resulting diagnostic indicator y0 falls to the range of [0, 0.33], (0.33, 0.66], or (0.66, 1],respectively.

Based on the states of the diagnostic indicator y and forecast diagnostic indicator y0, the health condition of the gear ofinterest is diagnosed by the reasoning in Eq. (7).

As an example, all the diagnostic indicator values for gears #1–7 in unit #3 of a printing machine are listed in Fig. 12 asthe current values. They are from an old printing machine which has 6 units and is undertaken repairs due to excessivedoubling problems. On the other hand, three-step-ahead forecast diagnostic indicator values for the related gears in thisunit are listed as future values. From diagnosis based on the integrated classifier, gear #4 is damaged; gear #7 has an initialdefect, whereas all other gears in this unit are healthy. Real examination has verified the diagnostic results: gear #7contains excessive tooth surface wear due to inappropriate lubrication. Gear #4 has some localized tooth damage as shownin Fig. 13.

Fault diagnostic results can also be verified by analyzing historic trends of the fault diagnostic indicators. To facilitatethe demonstration of the monitoring results to users, the gear health conditions are represented by specific colors: forexample, green for healthy (C1), yellow for possibly damaged (C2), and red for damaged (C3). The function of ‘‘GearConditions’’ in Fig. 12 is to explain the diagnostic results for the related gears. It also includes system training suggestions toaccommodate different system conditions.

It should be stated that the forecast information can be used not only to improve the diagnostic reliability, but also tohelp to schedule repair operations without routinely shutting down the machine for regular maintenance. On the other

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Fig. 13. A detected localized gear tooth defect.


hand, while in repairs, based on the diagnostic results from the integrated classifier, the damaged objects can be identifiedquickly without the need to examine all of the involved components. As a result, the maintenance cost can be furtherreduced.

7. Conclusions

In this paper, an integrated classifier is developed for gear fault diagnostics. The purpose is to provide industries with amore reliable monitoring tool to prevent machinery system performance degradation, malfunction, or even sudden failure.The classifier can properly integrate different features for a more positive assessment of the object’s health condition. Thediagnostic reliability is improved by properly integrating the future states of the gear, which are forecast by a multi-steppredictor. An online hybrid training technique based on a recursive LM and LSE is adopted to improve the classifier’sconvergence and adaptive capability to accommodate different machinery conditions. The viability of the new integratedclassifier has been verified by experimental tests corresponding to different gear conditions. Furthermore, the integratedclassifier is implemented for real-time condition monitoring in multistage printing machines, whose effectiveness has beenverified by some primary application practices.

Acknowledgements

This work was partly supported by the Mechworks Systems Inc. and Materials and Manufacturing Ontario (Canada). Theauthors want to thank Dr. F. Golnaraghi and Dr. L. Shubin at Mechworks for their support in software development andtests. Appreciation is also given to Mr. Brad Hughson in the Laboratory for Intelligent Mechatronics System at LakeheadUniversity for his help to this work.

Appendix. Derivation of the recursive LM algorithm

Start from Eq. (9), hp+1Eyp+l(JpTJp+ZI)�1Jp

Trp ¼ hp+(1�a)Hp�1Jp

Trp; the Hessian matrix can be expressed as

Hp ¼ aHp�1 � ð1� aÞðJTpJp þ ZIÞ. (A.1)

In implementation, instead of computing the Z� Z matrix ZI at each time step, a diagonal element is added at each timestep

Hp ¼ aHp�1 � ð1� aÞðJTpJp þ ZZKÞ (A.2)

where KARZ� Z has only one nonzero element located at {pmod(Z)+1} diagonal position

Lii ¼1 if i ¼ fp modðZÞ þ 1g

0 otherwise

�(A.3)

Correspondingly, (A.2) can be rewritten as

Hp ¼ aHp�1 � ð1� aÞ½UV�1UT� (A.4)

where U is a Z�2 matrix whose first column is Jp and second column consists of a Z�1 vector with one element of 1 at theposition of {p mod(Z)+1}

UT¼

JTp

0 . . . 0 1 0 . . . 0

" #and V�1

¼1 0

0 ZZ

" #.

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The computation of Hp�1 in Eq (9) is time consuming, and is not suitable for real-time applications. To solve this problem,

Eq. (9) is rewritten as

hpþ1 ¼ hp þ ð1� aÞH�1p JT

prp ¼ hp þ ð1� aÞ ðaHp�1Þ�1� ðaHp�1Þ

�1ð1� aÞU

n�½V þ UT

ðaHp�1Þ�1ð1� aÞU��1UT

ðaHp�1Þ�1o

JTprp (A.5)

Based on the matrix inversion formula (A+BCD)�1¼ A�1

�A�1B(C�1+DA�1B)�1DA�1, and by some manipulations,Eq. (A.5) becomes

hpþ1 ¼ hp þ ð1� aÞfaHp�1 þ ð1� aÞUV�1UTg�1JT

prp (A.6)

By some manipulations, the recursive LM algorithm can be represented by

hpþ1 ¼ hp þUpJprp (A.7)

Up ¼1

aUp�1 �

Up�1UUTUp�1

aV þ UTUp�1U

" #(A.8)

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