Towards an automatic diagnostics system for

Towards an automatic diagnostics system for gearboxes based on vibration measurements A. P. Ompusunggu 1 , B. K. Y’Ebondo 1 , S. Devos 1 , F. Petr´e 1 1 Flanders’ Mechatronics Technology Centre (FMTC), Celestijnenlaan 300 D, B-3001, Heverlee, Belgium e-mail: [email protected]

Abstract On-line condition monitoring systems for gearboxes that can efficiently generate a diagnostic conclusion without manual interpretation of measurement data by an expert have long been desired by industries. It is in hope that such an automatic diagnostic system can reduce the total cost for implementing a Condition Based Maintenance (CBM) strategy, that has been proven in modern industries as an effective maintenance strategy, on machines/systems equipped with gearboxes. Nowadays, a number of commercial systems that can serve as automatic diagnostic systems for gearboxes have been made available on the market. However, these commercial solutions are in general closed black box, i.e. they are not open to allow gradual improvements for specific applications. This suggests that there is still a constant awareness from industrial users to build their own (automatic) diagnostic system for improved diagnostics. To fill this substantial gap, this paper aims at providing a framework for developing a gearbox diagnostic system with the following properties: (1) automatic generation of the diagnostic conclusion (2) scalable solution where the diagnostic system can be easily extended with other faults or applied to different gearbox configurations, (3) effective to detect frequent fault in gearboxes, and (4) robust in a large variety of operational conditions.

1

Introduction

Gearboxes are widely used in rotating machinery including production machines, wind turbines, automotive transmissions, etc. As critical devices, an unexpected failure occurring in gearboxes can thus lead to an unexpected total breakdown that eventually leads to unscheduled maintenance for machines/systems equipped with gearboxes. This undesirable situation can: (i) put human safety at risk and (ii) possibly cause long-term downtimes, that eventually result in lost production (hence loss of financial income) and high maintenance costs. Condition Based Maintenance (CBM) strategy has been proven in modern industries as an effective strategy that can avoid unscheduled maintenance and minimize machine/system down-times due to unexpected breakdown. To realize this strategy in practice, a condition monitoring system with automatic diagnostics capability is thus required. Vibration based techniques are commonly used for diagnostics of gearboxes due to several reasons such as (i) relatively easy installation of vibration sensors, (ii) fast data collection, (iii) more intuitive interpretation on the relation between the nature of faults and vibration signals, etc. Nowadays, a number of commercial systems that can serve as automatic diagnostic systems for gearboxes using vibration signals have been made available on the market, such as VIBXPERT of Pr¨ uftechnik, CSI machinery health analyzer of Emerson, etc. As built-in settings of these commercial systems are tuned by the developers for generic purposes, it is not surprising that these systems may not work optimally for specific applications, which is confirmed by the authors’ experience. However, these commercial solutions are in general closed-black box, implying that

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gradual improvements for specific applications are difficult for the end users. Much research effort has been spent for decades and published in literature for developing automatic diagnostics systems for gearboxes based on vibration signals. Two major issues have been identified for the development of such diagnostics systems, namely (1) signal processing in conjunction with feature extraction and (2) classification in conjunction with diagnostic agent. Hence the performance of an envisaged gearbox diagnostic system can be optimized at different levels. One may optimize the diagnostics performance either at the signal processing/feature extraction level, or the classification/diagnostic agent level, or the two levels. As the computational power has increased, incorporation of different machine learning (ML) techniques, such as Neural Networks (NNs), Support Vector Machines (SVMs), Decision Trees (DTs), Fuzzy Classification, etc, in development of automatic diagnostic systems for gearboxes has been active research since the last decade [1, 2, 3, 4, 5]. Despite successful implementations, the applicability of gearbox diagnostic systems based on ML techniques is limited to specific applications. In general, ML based diagnostic systems reported in the literature utilize features including both statistical and specific features that are typically calculated with sub-optimal signal processing. In this approach, a large amount of data collected both from healthy and faulty states are required for training ML techniques in order to determine “optimal” features that significantly separate two classes of healthy and faulty states in specific applications. Data collected from a faulty state are typically not available in many applications. Hence, ML based approach would not be appropriate in such cases. When data collected from healthy state (hereafter called baseline data) are only available or possible to obtain, an approach based on physically-inspired features calculated with optimal signal processing steps are favorable. As we rely only on baseline data, an envisaged diagnostics system can be realized as early as possible and it can be gradually improved when faulty components become evident. In Ref. [6], development of a diagnostics system based on physically-inspired features is discussed. However, this diagnostics system uses traditional signal processing techniques for features calculation that may lead to sub-optimal diagnostic results. In addition, a method to determine a threshold that can lead to automatic diagnostics results is not discussed in the aforementioned publication. A number of signal processing techniques inspired from the physics of gearbox faults (e.g. bearing and gear faults) have been developed and optimized for calculating effective features representing health condition of gearboxes [7, 8]. However to the authors’ knowledge, a methodology that integrates the optimized signal processing steps/feature calculation with a fault classification/diagnostic agent for developing an automatic diagnostics system of gearboxes using baseline data only is still lacking. To fill this gap, this paper aims at providing a framework for developing a gearbox diagnostic system with the following properties: (1) automatic generation of the diagnostic conclusion (2) scalable solution where the diagnostic system can be easily extended with other faults or applied to different gearbox configurations, (3) effective to detect frequent fault in gearboxes, and (4) robust in a large variety of operational conditions. The remainder of this paper is organized as follows: Section 2 discuss a framework proposed for developing an automatic diagnostics system for a specific gearbox application. For validation and demonstration purposes, the description of a gearbox setup and the test procedure carried out are discussed in Section 3. Section 4 demonstrates the performance of a developed diagnostics system for a gearbox and discusses the experimental results. Section 5 concludes important remarks drawn from the study and suggests recommendation for future work.

2

Proposed framework

This section provides a framework for efficiently developing a vibration-based diagnostic system for gearboxes. This proposed framework is divided into three levels, namely (1) feature development, (2) threshold setting and (3) diagnostic report generation. This framework was developed with a main focus on detecting major faults typically occurring in rolling-element bearings and gears as shown in Figure 1.

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Bearing faults

Misaligned shaft

inner & outer race / rolling element  also for low speeds < 400rpm

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Eccentric gear

Gear pitting

Chipped tooth

Tooth profile error Worn gears

Gear backlash

Missing tooth

Figure 1: Bearing and gear faults tackled within this framework.

2.1

Feature development and selection

Relevant and robust features are essential for developing a diagnostics system. In this section, guidelines for developing and selecting fault features, and then for assessing their robustness for specific gearbox applications are discussed. 2.1.1 Procedure of relevant feature development Figure 2 shows a guideline for finding and selecting fault features. The master words should be: ”First start with simple solution”, i.e simple solutions will be generally privileged. By simple solution, it means the use of well known developed and validated features. A simple solution can comprise Stewart Figures Of Merit (FOM), Sideband Index (SI) or Sideband Level Factor (SLF) [7] and statistical features defined from vibration signal filtered in adequately chosen frequency bands (RMS, kurtosis, crest factor,...). In parallel, the knowledge of vibration manifestation of the fault can be used to derive a fault feature. This knowledge may come from literature or from experts. A short literature survey can be enough for knowing whether the fault is described in literature along with its vibration manifestation. In case where no information has been found, an advanced review can be needed for scanning literature. When possible, the use of advanced signal processing and/or classification methods can also be considered. We have made an assumption throughout this study that only a limited amount of data are available for feature development. In particular, measurements on machines with faults are often not a priori available; such as prototypes, newly installed machines. Our approach is based on physical understandings, implicitly and explicitly expressed, of what the vibration manifestation of a fault is. Purely statistical or data-driven approaches which need a large amount of data were not privileged in this study. Note that these data-driven methods could also be based on the output of a simulated accelerometer readings from a physics-based model. However, physics-based modeling was not considered since the significant effort/cost that would be required for simulation and also for validation to guarantee that the simulated data is representative for real measurement data. Concerning the use of statistical features, the drawback is that they are rarely specific, i.e. they can be sensitive to several faults and thus, not fulfill the attributes of good features as given in [9]: (1) computationally inexpensive, (2) mathematically definable, (3) explainable in physical terms, (4) characterized by large interclass mean distance and small intra-class variance, (5) insensitive to extraneous variables, (6) uncorrelated with other features.

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Fault

Short literature scanning

N

Indepth literature review

Is the vibration manifestation well known and well described?

Y N Gear fault? Y Traditional gear fault features (FOM) Advanced signal processing

Gear fault feature based on vibration manifestation

Signal processing to compute the feature

Derive fault feature

N

N Bearing fault?

Y Bearing fault feature based on characteristic frequencies

Shaft fault?

Y Shaft fault feature based on described manifestation

Vibration data

Evaluate relevance and robustness of the feature

Relevant and robust fault feature found?

Y Useful Feature

Figure 2: Methodology of fault feature development. 2.1.2 Feature robustness assessment After a fault feature is defined, its robustness should be checked. Here, the term “robustness” corresponds to the evaluation whether the feature value extracted in a faulty state is always greater than or less than the one extracted in a healthy state. This a strong condition imposed to the quality of the feature because in practice statistical variance can lead to some overlap between the two sets. In this paper, we propose the use of radar plots for assessment and visualization of feature robustness and for determination of domain of validity. This way, the robustness of the feature can be visualized in one map and for several operating conditions. Each radius represents an operating condition obtained as a combination of speed and torque as illustrated for the example in Figure 3.

2.2

Method for feature thresholding

2.2.1 Why do we need thresholds? Condition monitoring activities result in definition of fault indicators or fault features. To distinguish healthy from faulty states, thresholds should be set for those indicators. The thresholds can be used for defining a

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Figure 3: Robustness assessment of a fault feature. kind of traffic light for warning the user or the operator of the machine. In vibration monitoring, some standards exist and provide guidance for evaluating vibration severity. The ISO 2372 (10816) standard gives such guidance for machines operating in the 10 to 200Hz (600 to 12,000 RPM) frequency range and categorized in different classes depending on the power of the machine and how it is fixed on its foundation (Figure 4). Because the ISO 10816 chart is defined on overall velocity level (RMS in the range 10-1000Hz), it cannot be used for diagnostic purpose but only for assessing the general health status of the machine. The difference with a diagnostic approach is that such a chart should exist for each machine component and for different fault features.

Figure 4: ISO 10816 chart. Different approaches are possible for determining threshold values including decision tree, logistic regression and method based on SPC (Statistical Process Control) methods. However, the first two methods require the existence of faulty feature values. This can be a serious limitation since one has to wait for or to artificially introduce fault occurrences to be able to set his thresholds. When physics-based model approach is used, fault can be virtually introduced into the model and enough data for a learning process can be generated from the model. The SPC method based only on healthy feature values was preferred since it is more suitable for practical situations.

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2.2.2 SPC-based method SPC method relies on the basic assumption that for a normal distribution more than 99% (99.7%) of the population are located in a range of 3 times of the standard deviation around the mean value. So if one assumes that a vibration feature value follows a Gaussian distribution, its healthy values lie between M − 3σ and M + 3σ, where M is the mean value and σ is the standard deviation of healthy population. The mean value M will be considered as the baseline (reference) value and each deviation from it larger than 3σ indicates a departure from healthy condition. However, the use of Gaussian distribution vibration data will be limited by the fact that fault features are hardly ever “nicely” normally distributed in practice. To deal with such practical situation, some authors have proposed the use of generalized extreme values (GEV) distribution due to the one-sided distribution shape of vibration data [10, 11]. The GEV distribution is mathematically described by the following expression: "  1  1#  1 x − µ −k x − µ −1− k y = p (x|k, µ, σ) = − 1+k 1+k (1) σ σ σ with 1+k x−µ σ > 0, k, σ and µ represent the shape parameter, the scale parameter and the location parameter, respectively. The shape parameter k governs the tail behavior of the distribution and leads to 3 families or 3 types of distributions (i.e. Gumbel family for k = 0 representing an unlimited shape, Frechet family with a lower limit and reversed Weibull with an upper limit) as shown in Figures 5 and 6:

Figure 5: Probability density function of GEV distribution types.

Figure 6: Cumulative distribution function of GEV distribution types.

Defining threshold by use of GEV distribution will be based on the following criteria: 1. The baseline is set at high percentile value of the fitted cumulative probability density of the healthy values. Typical values are in the range of 96-98%. In practice, one has to choose a value in this interval. 2. The warning threshold is set 3 db above the baseline 3. The alarm threshold is set 6 db above the baseline (double of the baseline value) Figures 7 and 8 illustrate the baseline and the threshold values for a fault feature. In these two figures, it’s also illustrated how the method is tested on data collected from a faulty state.

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1

Healthy Faulty Alarm Reference

0.9 0.8 0.7

0.6 U-

S 0.5 0.4

0.3 0.2 0.1

0.5

,

,

,

1

1.5

2

, 2.5

,

3

, 3.5

, 4

Feature Value

Figure 7: Representation of threshold value on feature data.

Figure 8: Reference and threshold values shown on CDF.

2.2.3 Thresholding by use of GEV The approach proposed for threshold determination using GEV can be summarized through 5 steps as shown in Figure 9. Operating condition filtering

Outlier removal

Distribution fitting

Reference value setting (Baseline)

Threshold setting

Figure 9: Thresholding process by use of GEV.

Filtering operating conditions. The illustrative example concerns 10 different operating conditions represented in Table 1. It is unrealistic to try to find a single threshold to use for all the possible operating condition. In some cases, extrapolation can be useful but its exploration was out of scope of this study. One has to define a threshold for each operating conditions. Filtering operating conditions consists of separating them before the thresholding process is applied. Speed [Hz] Load Low High

30 Regime 1 Regime 2

35 Regime 3 Regime 4

40 Regime 5 Regime 6

45 Regime 7 Regime 8

50 Regime 9 Regime 10

Table 1: Different operating conditions (regimes).

Outlier removal. An important processing step to carry out before the distribution fitting is outlier removal. In this step, one removes data points which appear to be inconsistent with the remainder of the dataset

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(outliers). Some algorithms for outlier removal are proposed in the reference [12]. We have proposed the Grubbs test because of its ease of use. The Grubbs test removes one outlier at a time. This outlier is expunged from the dataset and the test is iterated until no outliers are detected. The test assumes normal distribution of data. It consists in the following steps: 1. If the data series is X = {xi |i = 1, 2, . . . , N }, compute Ri = |xi − x ¯| /std(X), where x ¯ is the mean value. 2. Test if the maximum value is an outlier. The hypothesis of no outlier is rejected if v u t2(α/n,n−2) n − 1u t Rmax > √ n n − 2 + t2(α/n,n−2)

(2)

with t2(α/n,n−2) denoting the α/n percentile of a t-distribution with (n − 2) degrees of freedom. When applied on the regime 10 of the illustrative case, the result is represented on Figure 10. The left figure shows the dataset before outlier removal and the right figure shows the dataset after removal.

Figure 10: Outlier removal.

Distribution fitting It is necessary that the dataset used for threshold determination contains all possible variability that can be induced on vibration by factors such as small speed and load changes, temperature variation, etc. A sufficiently long historical data can contain a representative set of operating patterns. The illustrative dataset is cleaned from outliers. When we fit the GEV distribution on it, the result is shown on Figure 11. We have performed a study of vibration variability effect due to speed change, load change, temperature variation, oil level and assembly. The changes were manually induced on the lab setup and their effects on features were analyzed. We tried to keep most of the introduced changes in a range corresponding to real-life applications, but for the oil level we have exaggerated the quantity in the aim of modifying the transfer of the structure. Without a generalization aim, we noticed that each of these changes could introduce more or less variation in calculated features. However, in the range of the changes we introduced, this variability did not mask the distinction between faulty and healthy cases. Baseline and threshold setting. The baseline or reference value is set using a 96% percentile and the threshold is fixed at 6dB of the reference (see green and red line on Figure 11).

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Figure 11: Fitting GEV distribution.

2.3 Diagnostic agent with fuzzy logic Fuzzy logic can be used to perform diagnostics. It allows clustering feature dataset and leads directly to rules of the form:

If (Feature Value is High) Then (Condition is Faulty) which can be incorporated into a diagnostic decision rule base for fault classification [9]. A fuzzy logic system with 2 components is shown in Figure 12. The measured features are first classified into linguistic terms such as Low, High, etc. To accomplish this one needs membership functions. These inputs are mapped to outputs related to output membership functions giving the fault condition. The numerical values of the edge of an input membership function (corresponding to feature values) may be determined from historical date, expert knowledge or physical modeling.

State

Faulty

Healthy

Feature value Low

High

Figure 12: Fuzzy clustering. Fuzzy logic has been also used for the diagnostic agent. We have proposed the use of two membership functions to represent states of the features with respect to the threshold determined using GEV. The two membership functions correspond to “High” and “Low” level of the feature and were determined from the

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GEV distribution of feature values (see Section 2.2.3). The advantage of this approach is that these membership functions are based on the GEV distribution fitted from data.

3

Experimental methodology

To experimentally verify the proposed framework, vibration data have been collected from a gearbox dynamic simulator (GDS) setup with healthy and faulty states. The GDS is a dedicated test setup that enables one to simulate a healthy and faulty gearbox with different type of faults, namely localized bearing faults (i.e. inner race, outer race and rolling element faults) and gear faults (eccentricity, chipped tooth, missing tooth, cracked tooth, backlash, and profile error). The test setup and the experimental procedure are described in the forthcoming subsections.

3.1 Apparatus Figure 13 shows the photograph and the schematic-top-view of the test setup used in this study. The GDS consists of two gearboxes connected to each other, namely a parallel-shaft gearbox (3) and a perpendicularshaft gearbox (4). The input shaft (10) of the parallel-shaft gearbox is driven through a flexible coupling by an induction electric motor (2) which is controlled by a variable-frequency-drive (1). The shaft rotational speed of the motor can be varied from 0 to 3000 rpm, with either a stationary mode or a transient mode (run-up/run-down). The output shaft (13) of the perpendicular-shaft gearbox is coupled with a magneticparticle brake (5), where the torque applied to the output-shaft can be adjusted by the brake controller (8) from 0 to 50 Nm. The control signals to the motor drive (1) and to the brake controller (8) are sent out by a PC (7) using dedicated programs. Vibration signals in the axial (perpendicular to the gearboxes wall) and horizontal-radial directions are sensed by three triaxial piezoelectric (ICP type) accelerometers, which are mounted at different positions; two of them (A#1 and A#2) respectively on the drive side and non-drive side of the parallel-shaft gearbox and the third one (A#3) on the drive side of the perpendicular-shaft gearbox. The three accelerometers have the same sensitivity of 100 mV/g with ±5 % response deviation in the frequency range of 0.5 Hz to 5 kHz. An optical tachometer system is used to measure the shaft rotational speed of the motor where the light from the sensor head is directed to a reflective tape attached on the motor shaft, thus generating one pulse signal per revolution. All the signals are synchronously acquired by a National Instruments (NI) data acquisition system (6) and then stored to the PC with a Labview program. 2

12

11

10

5

3

L

1

B#2

G#2

A#2

B#1

G#1

B#3

13 M

5

1

B#4

Tach

2

G#3

B#8

G#5

B#6

B#5

A#1

G#6 G#4

B#7 A#3

9

7

3

6

4

8

4

NI DAQ

6

(a)

(b)

Figure 13: Experimental apparatus: (a) photograph and (b) schematic top view. The parallel-shaft gearbox (3) was designed and built with three parallel-shafts as seen in Figure 13(b). Four helical gears are arranged in the gearbox such that it has two-stage reductions. Two straight-bevel gears

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are assembled on their corresponding shaft, in the perpendicular-shaft gearbox, so there is only one-stage reduction. Some details of the gears assembled in the two gearboxes are summarized in Table 2. Note that the total reduction factor from the motor shaft to the output shaft of the perpendicular-shaft gearbox can be easily calculated based on the number of teeth of the gears, that is equal to (100/29) × (90/36) × (40/20) = 18.2.

Component

Number of teeth

Comment

G#1 G#2 G#3 G#4 G#5 G#6

29 100 36 90 20 40

Helical Helical Helical Helical Straight bevel Straight bevel

Table 2: Specifications of the assembled gears. Two different bearing types are assembled in the test setup, namely MB ER-14K and MB ER-16K. Two identical bearings (B#1 and B#2) of the former type are mounted in the parallel-shaft gearbox to support the input shaft (10) and the other bearings (from B#3 to B#8) of the latter type are mounted to support the other shafts, see Figure 13(b). They all are deep-groove ball bearings with the same geometrical specifications, thus the same theoretical fault frequencies.

3.2

Test Procedure

3.2.1 Operating condition In this study, the gearbox demonstrator was set at different stationary operating conditions. The shaft rotational speed of the electric motor of the gearbox setup and the brake torque were controlled at different conditions as listed in Table 1. 3.2.2 Measurement settings Prior to signal digitizing, each measured signal was low-pass filtered with an anti-aliasing filter embedded in each channel of the used NI data acquisition system. This way, potential aliasing problems resulting from high frequency noise can be avoided. With this data acquisition system, the cut-off frequency of the anti-aliasing filter is automatically selected depending on the used sampling frequency. Later on, the filtered signals were sampled at 51.2 kHz with a duration of a few seconds. Finally, the digital data were stored in the PC and then processed with the developed diagnostics system as will be discussed in the next section.

4

A Labview-based gearbox diagnostics system

A complete diagnostic system should comprise the following 4 functions: 1. A data organizer: this function aims at managing measurement data. It performs tasks like: • associate a measurement point or a specific data channel with a machine component • indicate from which channel a given feature is to be calculated • manage the configuration of the gearbox

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Developing a generic solution for this function was out of the scope. However, it is good to know that this can be done using relational database, as a solution among others. 2. A feature calculator: this function results in the calculation of fault features. In its generic part, this function provides, on the one hand, methods for development of new features and on the other hand, tools for the calculation of features for some specific faults. 3. A threshold generator: this function provides methods for feature thresholding, for instance the GEV thresholding method proposed in this study. When implemented, this function accesses an historical database of baseline data, filter the data by operating conditions and set a threshold for each operating condition following the proposed method. 4. A diagnostic agent: it aims at establishing and evaluating diagnostic rules. Methods to derive diagnostic rules can be based on technologies like Bayesian networks or fuzzy inference system.

Generic Tools

Figure 14 schematically shows how the aforementioned 4 functions and the generic results developed in this study are put together to develop a diagnostics system for a gearbox. The generic results correspond to functions 2 and 4, while functions 1 and 4 have been made for specific gearbox application.

Tools for feature calculation

Method for feature thresholding

Historical healthy data

Implementation

Incoming data source (sensors, files, channels)

Method for decision support

Determine thresholds for all possible operating conditions

Assign a data source to each component/ element

Calculate fault features

Evaluate diagnostic rules

Faults to evaluate for each component/ element

Gearbox physical configuration

Data organisation

Features calculator

Threshold generator

Diagnostic agent

Figure 14: Diagnostics system development. In order to show how tools developed in this study can be used to build a diagnostic system following the scheme proposed on Figure 14, we have implemented a Labview application demo for the gearbox demonstrator discussed in Section 3. This Labview application consists of three main panels, namely (1) General Settings, (2) Gearbox Status and (3) Rules Status. The General Settings panel is shown in Figure 15, wherein the measurement, acquisition and analysis can be set. Note that, this application can be run on-line on the lab setup or off-line on recorded dataset. Once analysis has been completed, the results are visualized as seen in Figure 16. If a component is in green, it indicates that the component is still in a good condition. On the other hand, the component is in a bad condition when it is in red. For more detailed analysis, one can also find possible root-causes of the components identified to be faulty by selecting the third panel. An example of the root-cause analysis is visually shown in Figure 17. The thresholding part has been implemented based on GEV methods and the diagnostic agent uses fuzzy logic as discussed in the previous section. The demo can diagnose successfully the fault we studied. Figures 15 to 17 show some snapshots from the implemented demonstrator.

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Figure 15: System configuration and data organization.

Figure 16: Graphical results visualization.

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Figure 17: Diagnostic rules visualization.

5

Conclusion

A framework for developing an automatic diagnostics system for gearboxes has been presented and discussed in this paper. The diagnostics system development was focused on detecting major faults typically occurring in gearboxes, i.e. bearing and gear faults. The developed framework comprises three levels, namely fault features development, thresholds setting and diagnostics report generation. Stress has been put on thresholding methods that can be used in absence of data recorded in faulty state. A statistics-based method using generalized extreme value (GEV) distribution was proposed and applied with encouraging results on developed fault features. It has also been demonstrated in this paper how the developed tools can be put together to develop a working gearbox diagnostic system. This demonstration on a laboratory gearbox setup can be used as a starting point to develop an envisaged diagnostics system for specific gearbox applications.

Acknowledgments The authors wish to thank the project partners, including NV Michel Van de Wiele, for their support.

References [1] B.-S. Yang, D.-S. Lim, A. C. C. Tan, VIBEX: an expert system for vibration fault diagnosis of rotating machinery using decision tree and decision table, Expert Systems with Applications, Vol. 28(4), 2005, pp. 735 - 742. [2] C. Emmanouilidis, E. Jantunen, J. MacIntyre Flexible software for condition monitoring, incorporating novelty detection and diagnostics, Computers in Industry, Vol. 57, 2006, pp. 516 - 527. [3] J. Rafiee, F. Arvani, A. Harifi, M.H. Sadeghi, Intelligent condition monitoring of a gearbox using artificial neural network, Mechanical Systems and Signal Processing, Vol. 21, Issue 4, May 2007, pp. 1746 - 1754. [4] A. Widodo, B.-S. Yang, Support vector machine in machine condition monitoring and fault diagnosis, Mechanical Systems and Signal Processing, Vol. 21(6), 2007, pp. 2560 - 2574. [5] W. Wang, An enhanced diagnostic system for gear system monitoring, IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, Vol. 38, No. 1, February 2008, pp. 102 - 112. [6] S. Ebersbach, Z. Peng, Expert system development for vibration analysis in machine condition monitoring, Expert Systems with Applications, Vol. 34, 2008, pp. 291 - 299.

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[7] M. Lebold, K. McClintic, R. Campbell, C. Byinton, K. Maynard Review of vibration analysis methods for gearbox diagnostics and prognostics, in R. Boone, editor, Proceedings of the 54th Meeting of the Society for Machinery Failure Prevention Technology, Virginia Beach, (VA) USA, 2000 May 1-4, pp. 623 - 634. [8] R. B. Randall, Vibration-based Condition Monitoring, John Wiley and Sons, 2011. [9] G. Vachtsevanos, F. Lewis, M. Roemer, A. Hess, B. Wu, Intelligent fault diagnosis and prognosis for engineering systems, John Wiley and Sons, 2006. [10] A. Jablonski, T. Barszcz, M. Bielecka, P. Breuhaus, Modeling of probability distribution functions for automatic threshold calculation in condition monitoring systems, Measurement, 2012. [11] C. Cempel, Simple condition forecasting techniques in vibroacoustical diagnostics, Mechanical Systems and Signal Processing, Vol. 1, 1987, pp. 75 - 82. [12] F.A.A Garcia, Tests to identify outliers in data series, Pontifical Catholic University of Rio de Janeiro, Industrial Engineering Department, Rio de Janeiro, Brazil, 2012.

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