Condition Monitoring of Slow-speed Gear Wear using a Transmission Error-based Approach with Automated Feature Selection
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Published
Aug 17, 2021
Stefan Sendlbeck
Alexander Fimpel
Benedikt Siewerin
Michael Otto
Karsten Stahl
Abstract
Gear flank changes caused by wear do not only affect the dynamic behavior of gear systems, but they can also compromise the load-carrying capacity of gear teeth up to critical failure. To help avoid unintended consequences like downtime or safety risks, a condition monitoring system needs to be able to estimate the current wear during operation based on available sensor measurements. While many condition monitoring approaches in research rely on vibrational analysis with manual feature engineering, gearboxes running at slow speed do not reveal much excitation information for this purpose. We therefore introduce an approach for slow-speed gear wear monitoring that is based on the dynamic gear transmission error and that contains an automated feature selection process. For this purpose, we extract a large set of features from the preprocessed transmission error samples. Applying combined filter and embedded feature selection methods enables us to automatically identify and remove features with low relevance. The selection process consists of filtering features with no statistical dependence on the target wear value, removing redundant features with a correlation analysis and a recursive feature elimination process with cross-validation based on a random forest regressor. The remaining relevant set of features is the basis for model training and subsequent wear estimation. For this, the present research employed two independent ensemble models, random forest regression and gradient boosted regression trees. To train and test the proposed approach, we conducted slow-speed gear experiments with developing gear wear on a single-stage spur gear test rig setup. The results of both models show good gear wear estimation performance compared to the actual wear mass loss, even for small quantities. Hence, the proposed transmission error-based approach with automated feature selection is able to quantify the degree of slow-speed wear and offers a possible way for condition monitoring and fault diagnosis.
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Keywords
Gears, Condition Monitoring, Feature Selection, Slow-speed Gear Wear
References
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Benjamini, Y., & Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics, 29, 1165–1188.
Brecher, C., Gorgels, C., Hesse, J., & Hellmann, M. (2011). Dynamic transmission error measurements of a drive train. Production Engineering, 5(3), 321–327. https://doi.org/10.1007/s11740-011-0310-5
Breiman, L. (2001). Random Forests. Machine Learning, 45(1), 5–32. https://doi.org/10.1023/A:1010933404324
Caruana, R., & Niculescu-Mizil, A. (2006). An empirical comparison of supervised learning algorithms. Proceedings of the 23rd International Conference on Machine Learning, 161–168. https://doi.org/10.1145/1143844.1143865
Cerrada, M., Zurita, G., Cabrera, D., Sánchez, R.-V., Artés, M., & Li, C. (2016). Fault diagnosis in spur gears based on genetic algorithm and random forest. Mechanical Systems and Signal Processing, 70-71, 87–103. https://doi.org/10.1016/j.ymssp.2015.08.030
Chin, Z. Y., Smith, W. A., Borghesani, P., Randall, R. B., & Peng, Z. (2021). Absolute transmission error: A simple new tool for assessing gear wear. Mechanical Systems and Signal Processing, 146, 107070. https://doi.org/10.1016/j.ymssp.2020.107070
Choy, F. K., Polyshchuk, V., Zakrajsek, J. J., Handschuh, R. F., & Townsend, D. P. (1996). Analysis of the effects of surface pitting and wear on the vibration of a gear transmission system. Tribology International, 29(1), 77–83. https://doi.org/10.1016/0301-679X(95)00037-5
Christ, M., Braun, N., Neuffer, J., & Kempa-Liehr, A. W. (2018). Time Series FeatuRe Extraction on basis of Scalable Hypothesis tests (tsfresh – A Python package). Neurocomputing, 307, 72–77. https://doi.org/10.1016/j.neucom.2018.03.067
Christ, M., Kempa-Liehr, A. W., & Feindt, M. (2017). Distributed and parallel time series feature extraction for industrial big data applications. ArXiv E-Prints.
DIN ISO 14635-1 (2006). DIN ISO 14635-1:2006-05: Zahnräder - FZG-Prüfverfahren - Teil1: FZG-Prüfverfahren A/8,3 /90 zur Bestimmung der relativen Fresstragfähigkeit von Schmierölen (ISO 14635-1:2000), Gears - FZG test procedures - Part 1: FZG test method A/8,3/90 for relative scuffing load-carrying capacity of oils.
Ding, H., & Kahraman, A. (2007). Interactions between nonlinear spur gear dynamics and surface wear. Journal of Sound and Vibration, 307(3-5), 662–679. https://doi.org/10.1016/j.jsv.2007.06.030
Feng, Z., & Zuo, M. J. (2012). Vibration signal models for fault diagnosis of planetary gearboxes. Journal of Sound and Vibration, 331(22), 4919–4939. https://doi.org/10.1016/j.jsv.2012.05.039
Fernández-Delgado, M., Cernadas, E., Barro, S., & Amorim, D. (2014). Do We Need Hundreds of Classifiers to Solve Real World Classification Problems? J. Mach. Learn. Res., 15(1), 3133–3181.
Friedman, J. H. (2001). Greedy function approximation: A gradient boosting machine. The Annals of Statistics, 29(5), 1189–1232. https://doi.org/10.1214/aos/1013203451
Fromberger, M., Weinberger, U., Kohn, B., Utakapan, T., Otto, M., & Stahl, K. (2016). Condition Monitoring by Position Encoders. In W. Kropp (Ed.), Proceedings of the Inter-Noise 2016: 45th International Congress and Exposition on Noise Control Engineering : Towards a quiter future : August 21-24, 2016, Hamburg. Berlin: Deutsche Gesellschaft für Akustik e.V.
Fulcher, B. D. (2017). Feature-based time-series analysis. ArXiv E-Prints.
Fulcher, B. D., & Jones, N. S. (2014). Highly Comparative Feature-Based Time-Series Classification. IEEE Transactions on Knowledge and Data Engineering, 26(12), 3026–3037. https://doi.org/10.1109/TKDE.2014.2316504
Guyon, I., & Elisseeff, A. (2000). 10.1162/153244303322753616. CrossRef Listing of Deleted DOIs, 1, 1157–1182. https://doi.org/10.1162/153244303322753616
Guyon, I., Weston, J., Barnhill, S., & Vapnik, V. (2002). Gene Selection for Cancer Classification using Support Vector Machines. Machine Learning, 46(1/3), 389–422. https://doi.org/10.1023/A:1012487302797
Han, T., Jiang, D., Zhao, Q., Wang, L., & Yin, K. (2018). Comparison of random forest, artificial neural networks and support vector machine for intelligent diagnosis of rotating machinery. Transactions of the Institute of Measurement and Control, 40(8), 2681–2693. https://doi.org/10.1177/0142331217708242
Hu, C., Smith, W. A., Randall, R. B., & Peng, Z. (2016). Development of a gear vibration indicator and its application in gear wear monitoring. Mechanical Systems and Signal Processing, 76-77, 319–336. https://doi.org/10.1016/j.ymssp.2016.01.018
Janssens, O., Slavkovikj, V., Vervisch, B., Stockman, K., Loccufier, M., Verstockt, S., . . . van Hoecke, S. (2016). Convolutional Neural Network Based Fault Detection for Rotating Machinery. Journal of Sound and Vibration, 377, 331–345. https://doi.org/10.1016/j.jsv.2016.05.027
Kaggle (2019). Kaggle's State of Data Science and Machine Learning 2019: Enterprise Executive Summary.
Kuang, J. H., & Lin, A. D. (2001). The Effect of Tooth Wear on the Vibration Spectrum of a Spur Gear Pair. Journal of Vibration and Acoustics, 123(3), 311–317. https://doi.org/10.1115/1.1379371
Lee, K., Kim, J.-K. K., Kim, J., Hur, K., & Kim, H. (2018). Stacked Convolutional Bidirectional LSTM Recurrent Neural Network for Bearing Anomaly Detection in Rotating Machinery Diagnostics. 1st International Conference on Knowledge Innovation and Invention, 98–101.
Lei, Y., Jia, F., Lin, J., Xing, S., & Ding, S. X. (2016). An Intelligent Fault Diagnosis Method Using Unsupervised Feature Learning Towards Mechanical Big Data. IEEE Transactions on Industrial Electronics, 63(5), 3137–3147. https://doi.org/10.1109/TIE.2016.2519325
Louppe, G. (2014). Understanding Random Forests: From Theory to Practice. Dissertation: Université de Liège.
Mark, W. D. (2015). Time-synchronous-averaging of gear-meshing-vibration transducer responses for elimination of harmonic contributions from the mating gear and the gear pair. Mechanical Systems and Signal Processing, 62-63, 21–29. https://doi.org/10.1016/j.ymssp.2015.03.006
McFadden, P. D. (1986). Detecting Fatigue Cracks in Gears by Amplitude and Phase Demodulation of the Meshing Vibration. Journal of Vibration and Acoustics, 108(2), 165–170. https://doi.org/10.1115/1.3269317
Murphy, K. P. (2012). Machine learning: A probabilistic perspective. Cambridge, MA: MIT Press. Retrieved from https://ebookcentral-proquest-com.eaccess.ub.tum.de/lib/munchentech/detail.action?docID=3339490
Niemann, G., & Winter, H. (2003). Getriebe allgemein, Zahnradgetriebe - Grundlagen, Stirnradgetriebe: Band 2: Getriebe allgemein, Zahnradgetriebe - Grundlagen, Stirnradgetriebe (2., völlig neubearb. Aufl., 2. berichtigter Nachdr., korrigierter Nachdr). Maschinenelemente: / G. Niemann; H. Winter ; Bd. 2. Berlin: Springer. https://doi.org/10.1007/978-3-662-11873-3
Olson, R. S., La Cava, W., Mustahsan, Z., Varik, A., & Moore, J. H. (2018). Data-driven advice for applying machine learning to bioinformatics problems. Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing, 23, 192–203.
Pacheco, F., Valente de Oliveira, J., Sánchez, R.-V., Cerrada, M., Cabrera, D., Li, C., . . . Artés, M. (2016). A statistical comparison of neuroclassifiers and feature selection methods for gearbox fault diagnosis under realistic conditions. Neurocomputing, 194, 192–206. https://doi.org/10.1016/j.neucom.2016.02.028
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., . . . Duchesnay, E. (2011). Scikit-learn: Machine Learning in Python. Journal of Machine Learning Research, 12, 2825–2830.
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., . . . Duchesnay, E. (2020, October 14). sklearn.preprocessing.robust_scale — scikit-learn 0.23.2 documentation. Retrieved from https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.robust_scale.html
Randall, R. B. (2011). Vibration-based condition monitoring: Industrial, aerospace, and automotive applications. Chichester, UK: John Wiley & Sons. Retrieved from http://lib.myilibrary.com?id=310092 https://doi.org/10.1002/9780470977668
Samanta, B. (2004). Gear fault detection using artificial neural networks and support vector machines with genetic algorithms. Mechanical Systems and Signal Processing, 18(3), 625–644. https://doi.org/10.1016/S0888-3270(03)00020-7
Samuel, P. D., & Pines, D. J. (2005). A review of vibration-based techniques for helicopter transmission diagnostics. Journal of Sound and Vibration, 282(1-2), 475–508. https://doi.org/10.1016/j.jsv.2004.02.058
Scheffer, C., & Girdhar, P. (2004). Practical machinery vibration analysis and predictive maintenance. Oxford, UK: Newnes. Retrieved from http://ebookcentral.proquest.com/lib/munchentech/detail.action?docID=293533
Schultheiss, H., Tobie, T., Michaelis, K., Höhn, B.-R., & Stahl, K. (2014). The Slow-Speed Wear Behavior of Case-Carburized Gears Lubricated with NLGI 00 Grease under Boundary Lubrication Conditions. Tribology Transactions, 57(3), 524–532. https://doi.org/10.1080/10402004.2014.883005
Sharma, V., & Parey, A. (2016). A Review of Gear Fault Diagnosis Using Various Condition Indicators. Procedia Engineering, 144, 253–263. https://doi.org/10.1016/j.proeng.2016.05.131
Shen, C., Wang, D., Kong, F., & Tse, P. W. (2013). Fault diagnosis of rotating machinery based on the statistical parameters of wavelet packet paving and a generic support vector regressive classifier. Measurement, 46(4), 1551–1564. https://doi.org/10.1016/j.measurement.2012.12.011
Siewerin, B. J., Dobler, A., Tobie, T., & Stahl, K. (2020). Applicability of an Oil Based Calculation Approach for Wear Risk and Wear Lifetime to Grease Lubricated Gear Pairings. In ASME (Ed.), Print proceedings of the international design engineering technical conferences & computers and information in engineering conference. AMER SOC OF MECH ENGINEER. https://doi.org/10.1115/DETC2019-97439
Soualhi, A., Hawwari, Y., Medjaher, K., Guy, C., Razik, H., & Guillet, F. (2018). PHM survey: Implementation of signal processing methods for monitoring bearings and gearboxes. International Journal of Prognostics and Health Management, 9.
Wu, S., Zuo, M. J., & Parey, A. (2008). Simulation of spur gear dynamics and estimation of fault growth. Journal of Sound and Vibration, 317(3-5), 608–624. https://doi.org/10.1016/j.jsv.2008.03.038
Yan, R., Gao, R. X., & Chen, X. (2014). Wavelets for fault diagnosis of rotary machines: A review with applications. Signal Processing, 96, 1–15. https://doi.org/10.1016/j.sigpro.2013.04.015
Yang, R., Huang, M., Lu, Q., & Zhong, M. (2018). Rotating Machinery Fault Diagnosis Using Long-short-term Memory Recurrent Neural Network. IFAC-PapersOnLine, 51(24), 228–232. https://doi.org/10.1016/j.ifacol.2018.09.582
Zhao, R., Yan, R., Wang, J., & Mao, K. (2017). Learning to Monitor Machine Health with Convolutional Bi-Directional LSTM Networks. Sensors, 17(2). https://doi.org/10.3390/s17020273
Zhu, J., Nostrand, T., Spiegel, C., & Morton, B. (2014). Survey of condition indicators for condition monitoring systems. PHM 2014 - Proceedings of the Annual Conference of the Prognostics and Health Management Society 2014, 635–647.
Albon, C. (2018). Machine learning with Python cookbook: Practical solutions from preprocessing to deep learning (1st edition). Sebastopol, CA: O'Reilly Media.
Benjamini, Y., & Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics, 29, 1165–1188.
Brecher, C., Gorgels, C., Hesse, J., & Hellmann, M. (2011). Dynamic transmission error measurements of a drive train. Production Engineering, 5(3), 321–327. https://doi.org/10.1007/s11740-011-0310-5
Breiman, L. (2001). Random Forests. Machine Learning, 45(1), 5–32. https://doi.org/10.1023/A:1010933404324
Caruana, R., & Niculescu-Mizil, A. (2006). An empirical comparison of supervised learning algorithms. Proceedings of the 23rd International Conference on Machine Learning, 161–168. https://doi.org/10.1145/1143844.1143865
Cerrada, M., Zurita, G., Cabrera, D., Sánchez, R.-V., Artés, M., & Li, C. (2016). Fault diagnosis in spur gears based on genetic algorithm and random forest. Mechanical Systems and Signal Processing, 70-71, 87–103. https://doi.org/10.1016/j.ymssp.2015.08.030
Chin, Z. Y., Smith, W. A., Borghesani, P., Randall, R. B., & Peng, Z. (2021). Absolute transmission error: A simple new tool for assessing gear wear. Mechanical Systems and Signal Processing, 146, 107070. https://doi.org/10.1016/j.ymssp.2020.107070
Choy, F. K., Polyshchuk, V., Zakrajsek, J. J., Handschuh, R. F., & Townsend, D. P. (1996). Analysis of the effects of surface pitting and wear on the vibration of a gear transmission system. Tribology International, 29(1), 77–83. https://doi.org/10.1016/0301-679X(95)00037-5
Christ, M., Braun, N., Neuffer, J., & Kempa-Liehr, A. W. (2018). Time Series FeatuRe Extraction on basis of Scalable Hypothesis tests (tsfresh – A Python package). Neurocomputing, 307, 72–77. https://doi.org/10.1016/j.neucom.2018.03.067
Christ, M., Kempa-Liehr, A. W., & Feindt, M. (2017). Distributed and parallel time series feature extraction for industrial big data applications. ArXiv E-Prints.
DIN ISO 14635-1 (2006). DIN ISO 14635-1:2006-05: Zahnräder - FZG-Prüfverfahren - Teil1: FZG-Prüfverfahren A/8,3 /90 zur Bestimmung der relativen Fresstragfähigkeit von Schmierölen (ISO 14635-1:2000), Gears - FZG test procedures - Part 1: FZG test method A/8,3/90 for relative scuffing load-carrying capacity of oils.
Ding, H., & Kahraman, A. (2007). Interactions between nonlinear spur gear dynamics and surface wear. Journal of Sound and Vibration, 307(3-5), 662–679. https://doi.org/10.1016/j.jsv.2007.06.030
Feng, Z., & Zuo, M. J. (2012). Vibration signal models for fault diagnosis of planetary gearboxes. Journal of Sound and Vibration, 331(22), 4919–4939. https://doi.org/10.1016/j.jsv.2012.05.039
Fernández-Delgado, M., Cernadas, E., Barro, S., & Amorim, D. (2014). Do We Need Hundreds of Classifiers to Solve Real World Classification Problems? J. Mach. Learn. Res., 15(1), 3133–3181.
Friedman, J. H. (2001). Greedy function approximation: A gradient boosting machine. The Annals of Statistics, 29(5), 1189–1232. https://doi.org/10.1214/aos/1013203451
Fromberger, M., Weinberger, U., Kohn, B., Utakapan, T., Otto, M., & Stahl, K. (2016). Condition Monitoring by Position Encoders. In W. Kropp (Ed.), Proceedings of the Inter-Noise 2016: 45th International Congress and Exposition on Noise Control Engineering : Towards a quiter future : August 21-24, 2016, Hamburg. Berlin: Deutsche Gesellschaft für Akustik e.V.
Fulcher, B. D. (2017). Feature-based time-series analysis. ArXiv E-Prints.
Fulcher, B. D., & Jones, N. S. (2014). Highly Comparative Feature-Based Time-Series Classification. IEEE Transactions on Knowledge and Data Engineering, 26(12), 3026–3037. https://doi.org/10.1109/TKDE.2014.2316504
Guyon, I., & Elisseeff, A. (2000). 10.1162/153244303322753616. CrossRef Listing of Deleted DOIs, 1, 1157–1182. https://doi.org/10.1162/153244303322753616
Guyon, I., Weston, J., Barnhill, S., & Vapnik, V. (2002). Gene Selection for Cancer Classification using Support Vector Machines. Machine Learning, 46(1/3), 389–422. https://doi.org/10.1023/A:1012487302797
Han, T., Jiang, D., Zhao, Q., Wang, L., & Yin, K. (2018). Comparison of random forest, artificial neural networks and support vector machine for intelligent diagnosis of rotating machinery. Transactions of the Institute of Measurement and Control, 40(8), 2681–2693. https://doi.org/10.1177/0142331217708242
Hu, C., Smith, W. A., Randall, R. B., & Peng, Z. (2016). Development of a gear vibration indicator and its application in gear wear monitoring. Mechanical Systems and Signal Processing, 76-77, 319–336. https://doi.org/10.1016/j.ymssp.2016.01.018
Janssens, O., Slavkovikj, V., Vervisch, B., Stockman, K., Loccufier, M., Verstockt, S., . . . van Hoecke, S. (2016). Convolutional Neural Network Based Fault Detection for Rotating Machinery. Journal of Sound and Vibration, 377, 331–345. https://doi.org/10.1016/j.jsv.2016.05.027
Kaggle (2019). Kaggle's State of Data Science and Machine Learning 2019: Enterprise Executive Summary.
Kuang, J. H., & Lin, A. D. (2001). The Effect of Tooth Wear on the Vibration Spectrum of a Spur Gear Pair. Journal of Vibration and Acoustics, 123(3), 311–317. https://doi.org/10.1115/1.1379371
Lee, K., Kim, J.-K. K., Kim, J., Hur, K., & Kim, H. (2018). Stacked Convolutional Bidirectional LSTM Recurrent Neural Network for Bearing Anomaly Detection in Rotating Machinery Diagnostics. 1st International Conference on Knowledge Innovation and Invention, 98–101.
Lei, Y., Jia, F., Lin, J., Xing, S., & Ding, S. X. (2016). An Intelligent Fault Diagnosis Method Using Unsupervised Feature Learning Towards Mechanical Big Data. IEEE Transactions on Industrial Electronics, 63(5), 3137–3147. https://doi.org/10.1109/TIE.2016.2519325
Louppe, G. (2014). Understanding Random Forests: From Theory to Practice. Dissertation: Université de Liège.
Mark, W. D. (2015). Time-synchronous-averaging of gear-meshing-vibration transducer responses for elimination of harmonic contributions from the mating gear and the gear pair. Mechanical Systems and Signal Processing, 62-63, 21–29. https://doi.org/10.1016/j.ymssp.2015.03.006
McFadden, P. D. (1986). Detecting Fatigue Cracks in Gears by Amplitude and Phase Demodulation of the Meshing Vibration. Journal of Vibration and Acoustics, 108(2), 165–170. https://doi.org/10.1115/1.3269317
Murphy, K. P. (2012). Machine learning: A probabilistic perspective. Cambridge, MA: MIT Press. Retrieved from https://ebookcentral-proquest-com.eaccess.ub.tum.de/lib/munchentech/detail.action?docID=3339490
Niemann, G., & Winter, H. (2003). Getriebe allgemein, Zahnradgetriebe - Grundlagen, Stirnradgetriebe: Band 2: Getriebe allgemein, Zahnradgetriebe - Grundlagen, Stirnradgetriebe (2., völlig neubearb. Aufl., 2. berichtigter Nachdr., korrigierter Nachdr). Maschinenelemente: / G. Niemann; H. Winter ; Bd. 2. Berlin: Springer. https://doi.org/10.1007/978-3-662-11873-3
Olson, R. S., La Cava, W., Mustahsan, Z., Varik, A., & Moore, J. H. (2018). Data-driven advice for applying machine learning to bioinformatics problems. Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing, 23, 192–203.
Pacheco, F., Valente de Oliveira, J., Sánchez, R.-V., Cerrada, M., Cabrera, D., Li, C., . . . Artés, M. (2016). A statistical comparison of neuroclassifiers and feature selection methods for gearbox fault diagnosis under realistic conditions. Neurocomputing, 194, 192–206. https://doi.org/10.1016/j.neucom.2016.02.028
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., . . . Duchesnay, E. (2011). Scikit-learn: Machine Learning in Python. Journal of Machine Learning Research, 12, 2825–2830.
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., . . . Duchesnay, E. (2020, October 14). sklearn.preprocessing.robust_scale — scikit-learn 0.23.2 documentation. Retrieved from https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.robust_scale.html
Randall, R. B. (2011). Vibration-based condition monitoring: Industrial, aerospace, and automotive applications. Chichester, UK: John Wiley & Sons. Retrieved from http://lib.myilibrary.com?id=310092 https://doi.org/10.1002/9780470977668
Samanta, B. (2004). Gear fault detection using artificial neural networks and support vector machines with genetic algorithms. Mechanical Systems and Signal Processing, 18(3), 625–644. https://doi.org/10.1016/S0888-3270(03)00020-7
Samuel, P. D., & Pines, D. J. (2005). A review of vibration-based techniques for helicopter transmission diagnostics. Journal of Sound and Vibration, 282(1-2), 475–508. https://doi.org/10.1016/j.jsv.2004.02.058
Scheffer, C., & Girdhar, P. (2004). Practical machinery vibration analysis and predictive maintenance. Oxford, UK: Newnes. Retrieved from http://ebookcentral.proquest.com/lib/munchentech/detail.action?docID=293533
Schultheiss, H., Tobie, T., Michaelis, K., Höhn, B.-R., & Stahl, K. (2014). The Slow-Speed Wear Behavior of Case-Carburized Gears Lubricated with NLGI 00 Grease under Boundary Lubrication Conditions. Tribology Transactions, 57(3), 524–532. https://doi.org/10.1080/10402004.2014.883005
Sharma, V., & Parey, A. (2016). A Review of Gear Fault Diagnosis Using Various Condition Indicators. Procedia Engineering, 144, 253–263. https://doi.org/10.1016/j.proeng.2016.05.131
Shen, C., Wang, D., Kong, F., & Tse, P. W. (2013). Fault diagnosis of rotating machinery based on the statistical parameters of wavelet packet paving and a generic support vector regressive classifier. Measurement, 46(4), 1551–1564. https://doi.org/10.1016/j.measurement.2012.12.011
Siewerin, B. J., Dobler, A., Tobie, T., & Stahl, K. (2020). Applicability of an Oil Based Calculation Approach for Wear Risk and Wear Lifetime to Grease Lubricated Gear Pairings. In ASME (Ed.), Print proceedings of the international design engineering technical conferences & computers and information in engineering conference. AMER SOC OF MECH ENGINEER. https://doi.org/10.1115/DETC2019-97439
Soualhi, A., Hawwari, Y., Medjaher, K., Guy, C., Razik, H., & Guillet, F. (2018). PHM survey: Implementation of signal processing methods for monitoring bearings and gearboxes. International Journal of Prognostics and Health Management, 9.
Wu, S., Zuo, M. J., & Parey, A. (2008). Simulation of spur gear dynamics and estimation of fault growth. Journal of Sound and Vibration, 317(3-5), 608–624. https://doi.org/10.1016/j.jsv.2008.03.038
Yan, R., Gao, R. X., & Chen, X. (2014). Wavelets for fault diagnosis of rotary machines: A review with applications. Signal Processing, 96, 1–15. https://doi.org/10.1016/j.sigpro.2013.04.015
Yang, R., Huang, M., Lu, Q., & Zhong, M. (2018). Rotating Machinery Fault Diagnosis Using Long-short-term Memory Recurrent Neural Network. IFAC-PapersOnLine, 51(24), 228–232. https://doi.org/10.1016/j.ifacol.2018.09.582
Zhao, R., Yan, R., Wang, J., & Mao, K. (2017). Learning to Monitor Machine Health with Convolutional Bi-Directional LSTM Networks. Sensors, 17(2). https://doi.org/10.3390/s17020273
Zhu, J., Nostrand, T., Spiegel, C., & Morton, B. (2014). Survey of condition indicators for condition monitoring systems. PHM 2014 - Proceedings of the Annual Conference of the Prognostics and Health Management Society 2014, 635–647.
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