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Gear and bearing fault classification under different load and speed by using Poincaré plot features and SVM

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Abstract

This paper describes two algorithms for feature extraction from the Poincaré plot which is constructed with the vibration signals measured in roller bearings and gearboxes. The extracted features are used for classifying 10 types of fault conditions in a gearbox and 7 types of fault conditions a roller bearings. Both vibration signal datasets were acquired at different loads and speeds. The feature extraction using Algorithm 1 performs the feature calculation from the Poincaré plot constructed with the raw vibration signals. In contrast, the Algorithm 2 requires an additional stage where the vibration signal is pre-processed for identifying the peaks of the signal. This peak sequence is equivalent to a non-uniform sub-sampling of the vibration signal that retains relevant information useful for fault classification. The fault classification is attained by using a multi-class Support Vector Machine. The proposed method is tested using the tenfold cross-validation. Results show that both algorithms could attain classification accuracies as high as 99.3% for the gearbox dataset and 100% for the roller bearings. The results are compared to other classification approaches performed on the same datasets by using other different features. The comparison shows that the approach in this paper has a performance as good as obtained by using well-known statistical features.

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Abbreviations

PHM:

Prognostics and health management

CD:

Correlation dimension

LLE:

Larger Lyapunov exponent

LZC:

Lempel–Ziv complexity

SampEn:

Sample entropy

ApEn:

Approximate entropy

SVM:

Support vector machines

ANN:

Artificial neural networks

ECOC:

Error-correcting output codes

NI:

National instruments

A/D:

Analog to digital converter

HP:

Horse power

RBF:

Radial basis function

FNR:

False negative rate

FN:

False negative

TP:

True positive

FPR:

False positive rate

FP:

False positive

TN:

True negative

TPR:

True positive rate

TNR:

True negative rate

P:

Precision

SN:

Sensitivity

SP:

Specificity

ROC:

Receiver operator curve

KNN:

K nearest neighbors

RF:

Random forest

MDSVC:

Multi-modal deep support vector Classification

GDBM:

Gaussian–Bernoulli deep Boltzmann machine

References

  • Aherwar, A. (2012). An investigation on gearbox fault detection using vibration analysis techniques: A review. Australian Journal of Mechanical Engineering, 10(2), 169–183.

    Google Scholar 

  • Ali, S., & Smith-Miles, K. A. (2006). A meta-learning approach to automatic kernel selection for support vector machines. Neurocomputing, 70(1–3), 173–186.

    Google Scholar 

  • Alligood, K. T., Sauer, T. D., & Yorke, J. A. (1997). Chaos: An introduction to dynamical systems. Berlin: Springer.

    Google Scholar 

  • Aly, M. (2005). Survey on multiclass classification methods. Neural Networks, 19, 1–9.

    Google Scholar 

  • Anguita, D., Ghelardoni, L., Ghio, A., Oneto, L., & Ridella, S. (2012). The’k’in k-fold cross validation. In 2012 proceedings of the European symposium on artificial neural networks, computational intelligence and machine learning (pp. 25–27).

  • Bajric, R., Sprecic, D., & Zuber, N. (2011). Review of vibration signal processing techniques towards gear pairs damage identification. International Journal of Engineering and Technology, 11(4), 124–128.

    Google Scholar 

  • Bangalore, P., & Tjernberg, L. B. (2015). An artificial neural network approach for early fault detection of gearbox bearings. IEEE Transactions on Smart Grid, 6(2), 980–987.

    Google Scholar 

  • Blum, A., Kalai, A., Langford, J. (1999). Beating the hold-out: Bounds for k-fold and progressive cross-validation. In Proceedings of the twelfth annual conference on computational learning theory (pp. 203–208). ACM.

  • Brennan, M., Palaniswami, M., & Kamen, P. (2001). Do existing measures of poincare plot geometry reflect nonlinear features of heart rate variability? IEEE Transactions on Biomedical Engineering, 48(11), 1342–1347.

    Google Scholar 

  • Burges, C. J. (1998). A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2(2), 121–167.

    Google Scholar 

  • Cerrada, M., Macancela, J. C., Cabrera, D., Estupiñan, E., Sánchez, R. V., & Medina, R. (2020). Reciprocating compressor multi-fault classification using symbolic dynamics and complex correlation measure. Applied Sciences, 10(7), 2512.

    Google Scholar 

  • Cerrada, M., Sánchez, R. V., Pacheco, F., Cabrera, D., Zurita, G., & Li, C. (2016a). Hierarchical feature selection based on relative dependency for gear fault diagnosis. Applied Intelligence, 44(3), 687–703.

    Google Scholar 

  • Cerrada, M., Zurita, G., Cabrera, D., Sánchez, R. V., Artés, M., & Li, C. (2016b). Fault diagnosis in spur gears based on genetic algorithm and random forest. Mechanical Systems and Signal Processing, 70, 87–103.

    Google Scholar 

  • Cheng, S., Azarian, M. H., & Pecht, M. G. (2010). Sensor systems for prognostics and health management. Sensors, 10(6), 5774–5797.

    Google Scholar 

  • Cui, L., Qian, Z. (2010). Study on dynamic properties of roller bearing with nonlinear vibration. In 2010 International conference on mechanic automation and control engineering (MACE) (pp. 2723–2726). IEEE .

  • Daw, C. S., Finney, C. E. A., & Tracy, E. R. (2003). A review of symbolic analysis of experimental data. Review of Scientific instruments, 74(2), 915–930.

    Google Scholar 

  • De Berg, M., Cheong, O., Van Kreveld, M., & Overmars, M. (2008). Computational geometry: Introduction. Berlin: Springer.

    Google Scholar 

  • Doguer, T., Strackeljan, J. (2009). Vibration analysis using time domain methods for the detection of small roller bearing defects. In SIRM 2009-8th international conference on vibrations in rotating machines (pp. 23–25).

  • Escalera, S., Pujol, O., & Radeva, P. (2010). On the decoding process in ternary error-correcting output codes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(1), 120–134.

    Google Scholar 

  • Fraser, A. M., & Swinney, H. L. (1986). Independent coordinates for strange attractors from mutual information. Physical Review A, 33(2), 1134.

    Google Scholar 

  • Goyal, D., & Pabla, B. (2016). The vibration monitoring methods and signal processing techniques for structural health monitoring: A review. Archives of Computational Methods in Engineering, 23(4), 585–594.

    Google Scholar 

  • Goyal, D., Choudhary, A., Pabla, B., & Dhami, S. (2020). Support vector machines based non-contact fault diagnosis system for bearings. Journal of Intelligent Manufacturing, 31, 1275–1289.

    Google Scholar 

  • Hiroaki, E., & Nader, S. (2012). Gearbox simulation models with gear and bearing faults. In Mechanical engineering. InTech.

  • Hoshi, R. A., Pastre, C. M., Vanderlei, L. C. M., & Godoy, M. F. (2013). Poincaré plot indexes of heart rate variability: Relationships with other nonlinear variables. Autonomic Neuroscience, 177(2), 271–274.

    Google Scholar 

  • Hossin, M., & Sulaiman, M. (2015). A review on evaluation metrics for data classification evaluations. International Journal of Data Mining and Knowledge Management Process, 5(2), 1–11. https://doi.org/10.5121/ijdkp.2015.5201.

    Article  Google Scholar 

  • Huang, W., Kong, F., & Zhao, X. (2018). Spur bevel gearbox fault diagnosis using wavelet packet transform and rough set theory. Journal of Intelligent Manufacturing, 29(6), 1257–1271.

    Google Scholar 

  • Igba, J., Alemzadeh, K., Durugbo, C., & Eiriksson, E. T. (2016). Analysing rms and peak values of vibration signals for condition monitoring of wind turbine gearboxes. Renewable Energy, 91, 90–106.

    Google Scholar 

  • Janjarasjitt, S., Ocak, H., & Loparo, K. (2008). Bearing condition diagnosis and prognosis using applied nonlinear dynamical analysis of machine vibration signal. Journal of Sound and Vibration, 317(1), 112–126.

    Google Scholar 

  • Jáuregui, J. C. (2011). Phase diagram analysis for predicting nonlinearities and transient responses. In Recent advances in vibrations analysis. InTech.

  • Jedliński, Ł., & Jonak, J. (2015). Early fault detection in gearboxes based on support vector machines and multilayer perceptron with a continuous wavelet transform. Applied Soft Computing, 30, 636–641.

    Google Scholar 

  • Kahraman, A. (1992). On the response of a preloaded mechanical oscillator with a clearance: Period-doubling and chaos. Nonlinear Dynamics, 3(3), 183–198.

    Google Scholar 

  • Kahraman, A., & Blankenship, G. W. (1997). Experiments on nonlinear dynamic behavior of an oscillator with clearance and periodically time-varying parameters. Journal of Applied Mechanics, 64(1), 217–226.

    Google Scholar 

  • Kedadouche, M., Thomas, M., Tahan, A., & Guilbault, R. (2015). Nonlinear parameters for monitoring gear: Comparison between lempel-ziv, approximate entropy, and sample entropy complexity. Shock and Vibration. https://doi.org/10.1155/2015/959380.

  • Kohavi, R., et al. (1995). A study of cross-validation and bootstrap for accuracy estimation and model selection (Vol. 14, pp. 1137–1145). Montreal: Ijcai.

    Google Scholar 

  • Landgrebe, T. C., & Duin, R. P. (2008). Efficient multiclass roc approximation by decomposition via confusion matrix perturbation analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 30(5), 810–822.

    Google Scholar 

  • Li, B., Zhang, X., & Wu, T. (2018). Measurement of instantaneous angular displacement fluctuation and its applications on gearbox fault detection. ISA Transactions, 74, 245–260.

    Google Scholar 

  • Li, C., Liang, M., & Wang, T. (2015a). Criterion fusion for spectral segmentation and its application to optimal demodulation of bearing vibration signals. Mechanical Systems and Signal Processing, 64, 132–148.

    Google Scholar 

  • Li, C., Sanchez, R. V., Zurita, G., Cerrada, M., Cabrera, D., & Vásquez, R. E. (2015b). Multimodal deep support vector classification with homologous features and its application to gearbox fault diagnosis. Neurocomputing, 168, 119–127.

    Google Scholar 

  • Li, C., de Oliveira, J. V., Cerrada, M., Pacheco, F., Cabrera, D., Sanchez, V., et al. (2016a). Observer-biased bearing condition monitoring: From fault detection to multi-fault classification. Engineering Applications of Artificial Intelligence, 50, 287–301.

    Google Scholar 

  • Li, C., Sánchez, R. V., Zurita, G., Cerrada, M., & Cabrera, D. (2016b). Fault diagnosis for rotating machinery using vibration measurement deep statistical feature learning. Sensors, 16(6), 895.

    Google Scholar 

  • Liqin, W., Li, C., Dezhi, Z., & Le, G. (2008). Nonlinear dynamics behaviors of a rotor roller bearing system with radial clearances and waviness considered. Chinese Journal of Aeronautics, 21(1), 86–96.

    Google Scholar 

  • Liu, Z., He, Z., Guo, W., & Tang, Z. (2016). A hybrid fault diagnosis method based on second generation wavelet de-noising and local mean decomposition for rotating machinery. ISA Transactions, 61, 211–220.

    Google Scholar 

  • Loutridis, S. (2008). Self-similarity in vibration time series: Application to gear fault diagnostics. Journal of Vibration and Acoustics, 130(3), 031004.

    Google Scholar 

  • Luo, J., Huang, J., & Li, H. (2020). A case study of conditional deep convolutional generative adversarial networks in machine fault diagnosis. Journal of Intelligent Manufacturing. https://doi.org/10.1007/s10845-020-01579-w.

  • Luts, J., Ojeda, F., Van de Plas, R., De Moor, B., Van Huffel, S., & Suykens, J. A. (2010). A tutorial on support vector machine-based methods for classification problems in chemometrics. Analytica Chimica Acta, 665(2), 129–145.

    Google Scholar 

  • Medina, R., Alvarez, X., Jadán, D., Cerrada, M., Sánchez, R.V., & Macancela, J.C. (2017). Poincaré plot features from vibration signal for gearbox fault diagnosis. In 2017 IEEE Second Ecuador Technical Chapters Meeting (ETCM) (pp. 1–6). https://doi.org/10.1109/ETCM.2017.8247500.

  • Medina, R., Macancela, J. C., Lucero, P., Cabrera, D., Cerrada, M., Sánchez, R. V., et al. (2019). Vibration signal analysis using symbolic dynamics for gearbox fault diagnosis. The International Journal of Advanced Manufacturing Technology, 104(5–8), 2195–2214.

    Google Scholar 

  • Mevel, B., & Guyader, J. L. (2008). Experiments on routes to chaos in ball bearings. Journal of Sound and Vibration, 318(3), 549–564.

    Google Scholar 

  • Motahar, H., Samani, F. S., & Molaie, M. (2016). Nonlinear vibration of the bevel gear with teeth profile modification. Nonlinear Dynamics, 83(4), 1875–1884.

    Google Scholar 

  • Moumene, I., & Ouelaa, N. (2012). Gears and bearings combined faults detection using hilbert transform and wavelet multiresolution analysis. In T. Fakhfakh, W. Bartelmus, F. Chaari, R. Zimroz, & M. Haddar (Eds.), Condition monitoring of machinery in non-stationary operations (pp. 319–328). Berlin: Springer.

    Google Scholar 

  • Pacheco, F., de Oliveira, J. V., Sánchez, R. V., Cerrada, M., Cabrera, D., Li, C., et al. (2016). A statistical comparison of neuroclassifiers and feature selection methods for gearbox fault diagnosis under realistic conditions. Neurocomputing, 194, 192–206.

    Google Scholar 

  • Patil, M., Mathew, J., & RajendraKumar, P. (2008). Bearing signature analysis as a medium for fault detection: A review. Journal of Tribology, 130(1), 014001.

    Google Scholar 

  • Randall, R. B., & Antoni, J. (2011). Rolling element bearing diagnostics—A tutorial. Mechanical Systems and Signal Processing, 25(2), 485–520.

    Google Scholar 

  • Repo, J. (2010). Condition monitoring of machine tools and machining processes using internal sensor signals. Ph.D thesis, School of Industrial Engineering and Management, KTH Royal Institute of Technology, Sweden.

  • Rocha, R., Andrucioli, G. L., & Medrano-T, R. O. (2010). Experimental characterization of nonlinear systems: A real-time evaluation of the analogous chua’s circuit behavior. Nonlinear Dynamics, 62(1–2), 237–251.

    Google Scholar 

  • Sait, A. S., & Sharaf-Eldeen, Y. I. (2011). A review of gearbox condition monitoring based on vibration analysis techniques diagnostics and prognostics. Rotating Machinery, Structural Health Monitoring, Shock and Vibration, 5, 307–324.

    Google Scholar 

  • Sánchez, R. V., Lucero, P., Macancela, J. C., Cerrada, M., Vásquez, R. E., & Pacheco, F. (2017). Multi-fault diagnosis of rotating machinery by using feature ranking methods and svm-based classifiers. In 2017 International conference on sensing, diagnostics, prognostics, and control (SDPC) (pp. 105–110). IEEE.

  • Sánchez, R. V., Lucero, P., Vásquez, R. E., Cerrada, M., Macancela, J. C., & Cabrera, D. (2018). Feature ranking for multi-fault diagnosis of rotating machinery by using random forest and knn. Journal of Intelligent and Fuzzy Systems, 34(6), 3463–3473.

    Google Scholar 

  • Sharma, V., & Parey, A. (2016). A review of gear fault diagnosis using various condition indicators. Procedia Engineering, 144, 253–263.

    Google Scholar 

  • Sokolova, M., & Lapalme, G. (2009). A systematic analysis of performance measures for classification tasks. Information Processing and Management, 45(4), 427–437.

    Google Scholar 

  • Soleimani, A., & Khadem, S. (2015). Early fault detection of rotating machinery through chaotic vibration feature extraction of experimental data sets. Chaos, Solitons and Fractals, 78, 61–75.

    Google Scholar 

  • Sun, C., Wang, P., Yan, R., & Gao, R. X. (2016). A sparse approach to fault severity classification for gearbox monitoring. In 2016 19th international conference on information fusion (FUSION) (pp. 2303–2308).

  • Sun, Y. (2012). Fault detection in dynamic systems using the largest lyapunov exponent. Ph.D. thesis, Texas A & M University, USA.

  • Szuminski, P., & Kapitaniak, T. (2012). Nonlinear control and chaotic vibrations of perturbed trajectories of manipulators. Copyright (c) 2012 Annual Review of Chaos Theory, Bifurcations and Dynamical Systems (ARCTBDS) ISSN 2253-0371 All Rights Reserved www arctbds com (p. 32).

  • Takens, F. (1981). Detecting strange attractors in turbulence. In Dynamical systems and turbulence, Warwick 1980 (pp. 366–381). Berlin: Springer.

  • Tharwat, A. (2018). Classification assessment methods. Applied Computing and Informatics. https://doi.org/10.1016/j.aci.2018.08.003.

  • Trendafilova, I., & Manoach, E. (2012). Vibration-based methods for structural and machinery fault diagnosis based on nonlinear dynamics tools. In G. Rigatos (Ed.), Fault diagnosis in robotic and industrial systems. New York: IConcept Press LTD.

    Google Scholar 

  • Tucker, W. (2002). Computing accurate poincaré maps. Physica D: Nonlinear Phenomena, 171(3), 127–137.

    Google Scholar 

  • Von Oertzen, T., & Boker, S. M. (2010). Time delay embedding increases estimation precision of models of intraindividual variability. Psychometrika, 75(1), 158–175.

    Google Scholar 

  • Wang, C., Gan, M., et al. (2017). Intelligent fault diagnosis of rolling element bearings using sparse wavelet energy based on overcomplete dwt and basis pursuit. Journal of Intelligent Manufacturing, 28(6), 1377–1391.

    Google Scholar 

  • Wang, J., Li, R., & Peng, X. (2003). Survey of nonlinear vibration of gear transmission systems. Applied Mechanics Reviews, 56(3), 309–329.

    Google Scholar 

  • Wang, Z., & Xue, X. (2014). Multi-class support vector machine. In Support vector machines applications (pp. 23–48). Berlin: Springer.

  • Wang, Z., Han, Z., Gu, F., Gu, J. X., & Ning, S. (2015). A novel procedure for diagnosing multiple faults in rotating machinery. ISA Transactions, 55, 208–218.

    Google Scholar 

  • Wu, S. T., Campos, S. P., & de Aguiar, M. A. (1998). Scientific visualization of poincarémaps. Computers and Graphics, 22(2–3), 209–216.

    Google Scholar 

  • Xia, Z., Xia, S., Wan, L., & Cai, S. (2012). Spectral regression based fault feature extraction for bearing accelerometer sensor signals. Sensors, 12(10), 13694–13719.

    Google Scholar 

  • Yan, R., & Gao, R. X. (2004). Complexity as a measure for machine health evaluation. IEEE Transactions on Instrumentation and Measurement, 53(4), 1327–1334.

    Google Scholar 

  • Yin, Z., & Hou, J. (2016). Recent advances on svm based fault diagnosis and process monitoring in complicated industrial processes. Neurocomputing, 174, 643–650.

    Google Scholar 

  • Zhou, Q., Yan, P., Liu, H., & Xin, Y. (2019). A hybrid fault diagnosis method for mechanical components based on ontology and signal analysis. Journal of Intelligent Manufacturing, 30(4), 1693–1715.

    Google Scholar 

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Authors and Affiliations

  1. CIBYTEL-Engineering School, Universidad de Los Andes, Mérida, 5101, Venezuela

    Rubén Medina

  2. GIDTEC, Universidad Politécnica Salesiana, 010105, Cuenca, Ecuador

    Jean Carlo Macancela, Pablo Lucero, Diego Cabrera, René-Vinicio Sánchez & Mariela Cerrada

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  1. Rubén Medina
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  2. Jean Carlo Macancela
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  3. Pablo Lucero
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  6. Mariela Cerrada
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Correspondence to Mariela Cerrada.

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Medina, R., Macancela, J.C., Lucero, P. et al. Gear and bearing fault classification under different load and speed by using Poincaré plot features and SVM. J Intell Manuf 33, 1031–1055 (2022). https://doi.org/10.1007/s10845-020-01712-9

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