# American Institute of Mathematical Sciences

## EMD and GNN-AdaBoost fault diagnosis for urban rail train rolling bearings

 1 State Key Lab of Rail Traffic Control & safety, Beijing Jiaotong University, Beijing 100044, China 2 School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China 3 Institute of Computing Technology, China Academy of Railway Sciences Corporation Limited, Beijing 100081, China

* Corresponding author: Guoqiang Cai

Received  July 2017 Revised  January 2018 Published  November 2018

Rolling bearings are the most prone components to failure in urban rail trains, presenting potential danger to cities and their residents. This paper puts forward a rolling bearing fault diagnosis method by integrating empirical mode decomposition (EMD) and genetic neural network adaptive boosting (GNN-AdaBoost). EMD is an excellent tool for feature extraction and during which some intrinsic mode functions (IMFs) are obtained. GNN-AdaBoost fault identification algorithm, which uses genetic neural network (GNN) as sub-classifier of the boosting algorithm, is proposed in order to address the shortcomings in classification when only using a GNN. To demonstrate the excellent performance of the approach, experiments are performed to simulate different operating conditions of the rolling bearing, including high speed, low speed, heavy load and light load. For de-nosing signal, by EMD decomposition is applied to obtain IMFs, which is used for extracting the IMF energy feature parameters. The combination of IMF energy feature parameters and some time-domain feature parameters are selected as the input vectors of the classifiers. Finally, GNN-AdaBoost and GNN are applied to experimental examples and the identification results are compared. The results show that GNN-AdaBoost offers significant improvement in rolling bearing fault diagnosis for urban rail trains when compared to GNN alone.

Citation: Guoqiang Cai, Chen Yang, Yue Pan, Jiaojiao Lv. EMD and GNN-AdaBoost fault diagnosis for urban rail train rolling bearings. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2019101
##### References:
 [1] S. Abbasion, A. Rafsanjani, A. Farshidianfar and N. Irani, Rolling element bearings multi-fault classification based on the wavelet denoising and support vector machine, Mechanical Systems & Signal Processing, 21 (2007), 2933-2945. [2] A. Ahadi and A. Dehghan, The inapproximability for the (0, 1)-additive number, Discrete Mathematics and Theoretical Computer Science, 17 (2016), 217-226. [3] M. Y. Asr, M. M. Ettefagh, R. Hassannejad and S. N. Razavi, Diagnosis of combined faults in rotary machinery by non-naive bayesian approach, Mechanical Systems & Signal Processing, 85 (2017), 56-70. [4] I. S. Bozchalooi and M. Liang, A smoothness index-guided approach to wavelet parameter selection in signal de-noising and fault detection, Journal of Sound & Vibration, 308 (2007), 246-267. [5] G. Chen, J. Chen and G. M. Dong, Chirplet wigner-ville distribution for time-frequency representation and its application, Mechanical Systems & Signal Processing, 41 (2013), 1-13. [6] J. Cheng, Y. Yang and Y. Yang, A rotating machinery fault diagnosis method based on local mean decomposition, Digital Signal Processing, 22 (2012), 356-366. doi: 10.1016/j.dsp.2011.09.008. [7] A. Figueiredo and M. Nave, Time-frequency analysis of nonstationary fusion plasma signals: A comparison between the choi-williams distribution and wavelets, Review of scientific instruments, 75 (2004), 4268-4270. [8] Y. Freund and R. Schapire, A decision-theoretic generalization of on-line learning and an application to boosting, Journal of Computer and System Sciences, 55 (1997), 119-139. doi: 10.1006/jcss.1997.1504. [9] S. Gholizadeh, E. Salajegheh and P. Torkzadeh, Structural optimization with frequency constraints by genetic algorithm using wavelet radial basis function neural network, Journal of Sound & Vibration, 312 (2008), 316-331. [10] N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, W. Zheng, N. Yen, C. C. Tung, H. H. Liu and N. C. Yen, The empirical mode decomposition method and the hilbert spectrum for non-stationary time series analysis, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 454 (1998), 903-995. doi: 10.1098/rspa.1998.0193. [11] M. C. Kim and C. H. Choi, A new weight initialization method for the mlp with the bp in multiclass classification problems, Neural Processing Letters, 6 (1997), 11-23. [12] R. Klein, D. Ingman and S. Braun, Non-stationary signals: Phase-energy approach-theory and simulations, Mechanical Systems & Signal Processing, 15 (2001), 1061-1089. [13] L. I. Kuncheva and C. J. Whitaker, Using Diversity with Three Variants of Boosting: Aggressive, Conservative, and Inverse, In: International Workshop on Multiple Classifier Systems, 2002: Springer, 2002. [14] B. Li, M. Y. Chow, Y. Tipsuwan and J. C. Hung, Neural-network-based motor rolling bearing fault diagnosis, IEEE Transactions on Industrial Electronics, 47 (2002), 1060-1069. [15] X. Li, L. Wang and E. Sung, A study of adaboost with svm based weak learners, IEEE International Joint Conference on Neural Networks, 2005. IJCNN '05. Proceedings, 1 (2005), 196-201. [16] X. Li, L. Wang and E. Sung, Adaboost with svm-based component classifiers, Engineering Applications of Artificial Intelligence, 21 (2008), 785-795. [17] H. Liu, J. Zhang, Y. Cheng and C. Lu, Fault diagnosis of gearbox using empirical mode decomposition and multi-fractal detrended cross-correlation analysis, Journal of Sound & Vibration, 385 (2016), 350-371. [18] C. Meshram and S. A. Meshram, Constructing id-based cryptographic technique for ifp and gdlp based cryptosystem, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 1121-1134. doi: 10.1080/09720529.2015.1032621. [19] C. C. Peck and A. P. Dhawan, Genetic algorithms as global random search methods: An alternative perspective, Evolutionary Computation, 3 (2014), 39-80. [20] Z. K. Peng, P. W. Tse and F. L. Chu, An improved hilbert-huang transform and its application in vibration signal analysis, Journal of Sound & Vibration, 286 (2005), 1151-1153. doi: 10.1016/j.jsv.2004.01.049. [21] B. Samanta and K. R. Al-Balushi, Artificial neural network based fault diagnostics of rolling element bearings using time-domain features, Mechanical Systems & Signal Processing, 17 (2003), 317-328. [22] R. E. Schapire and Y. Singer, Improved Boosting Algorithms Using Confidence-rated Predictions, vol. 37, Machine Learning, 1999. [23] Z. Y. Shi, S. S. Law and X. Xu, Identification of linear time-varying mdof dynamic systems from forced excitation using hilbert transform and emd method, Journal of Sound & Vibration, 321 (2009), 572-589. [24] H. Wang and P. Chen, Intelligent diagnosis method for rolling element bearing faults using possibility theory and neural network, Computers & Industrial Engineering, 60 (2011), 511-518. [25] M. Weinfeld, Integrated Artificial Neural Networks: Components for Higher Level Architectures with New Properties, Springer Berlin Heidelberg, 1990. [26] Y. Xiang, J. Lu and Y. Y. Huang, A fast wave superposition spectral method with complex radius vector combined with two-dimensional fast fourier transform algorithm for acoustic radiation of axisymmetric bodies, Journal of Sound and Vibration, 331 (2012), 1441-1454.

show all references

##### References:
 [1] S. Abbasion, A. Rafsanjani, A. Farshidianfar and N. Irani, Rolling element bearings multi-fault classification based on the wavelet denoising and support vector machine, Mechanical Systems & Signal Processing, 21 (2007), 2933-2945. [2] A. Ahadi and A. Dehghan, The inapproximability for the (0, 1)-additive number, Discrete Mathematics and Theoretical Computer Science, 17 (2016), 217-226. [3] M. Y. Asr, M. M. Ettefagh, R. Hassannejad and S. N. Razavi, Diagnosis of combined faults in rotary machinery by non-naive bayesian approach, Mechanical Systems & Signal Processing, 85 (2017), 56-70. [4] I. S. Bozchalooi and M. Liang, A smoothness index-guided approach to wavelet parameter selection in signal de-noising and fault detection, Journal of Sound & Vibration, 308 (2007), 246-267. [5] G. Chen, J. Chen and G. M. Dong, Chirplet wigner-ville distribution for time-frequency representation and its application, Mechanical Systems & Signal Processing, 41 (2013), 1-13. [6] J. Cheng, Y. Yang and Y. Yang, A rotating machinery fault diagnosis method based on local mean decomposition, Digital Signal Processing, 22 (2012), 356-366. doi: 10.1016/j.dsp.2011.09.008. [7] A. Figueiredo and M. Nave, Time-frequency analysis of nonstationary fusion plasma signals: A comparison between the choi-williams distribution and wavelets, Review of scientific instruments, 75 (2004), 4268-4270. [8] Y. Freund and R. Schapire, A decision-theoretic generalization of on-line learning and an application to boosting, Journal of Computer and System Sciences, 55 (1997), 119-139. doi: 10.1006/jcss.1997.1504. [9] S. Gholizadeh, E. Salajegheh and P. Torkzadeh, Structural optimization with frequency constraints by genetic algorithm using wavelet radial basis function neural network, Journal of Sound & Vibration, 312 (2008), 316-331. [10] N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, W. Zheng, N. Yen, C. C. Tung, H. H. Liu and N. C. Yen, The empirical mode decomposition method and the hilbert spectrum for non-stationary time series analysis, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 454 (1998), 903-995. doi: 10.1098/rspa.1998.0193. [11] M. C. Kim and C. H. Choi, A new weight initialization method for the mlp with the bp in multiclass classification problems, Neural Processing Letters, 6 (1997), 11-23. [12] R. Klein, D. Ingman and S. Braun, Non-stationary signals: Phase-energy approach-theory and simulations, Mechanical Systems & Signal Processing, 15 (2001), 1061-1089. [13] L. I. Kuncheva and C. J. Whitaker, Using Diversity with Three Variants of Boosting: Aggressive, Conservative, and Inverse, In: International Workshop on Multiple Classifier Systems, 2002: Springer, 2002. [14] B. Li, M. Y. Chow, Y. Tipsuwan and J. C. Hung, Neural-network-based motor rolling bearing fault diagnosis, IEEE Transactions on Industrial Electronics, 47 (2002), 1060-1069. [15] X. Li, L. Wang and E. Sung, A study of adaboost with svm based weak learners, IEEE International Joint Conference on Neural Networks, 2005. IJCNN '05. Proceedings, 1 (2005), 196-201. [16] X. Li, L. Wang and E. Sung, Adaboost with svm-based component classifiers, Engineering Applications of Artificial Intelligence, 21 (2008), 785-795. [17] H. Liu, J. Zhang, Y. Cheng and C. Lu, Fault diagnosis of gearbox using empirical mode decomposition and multi-fractal detrended cross-correlation analysis, Journal of Sound & Vibration, 385 (2016), 350-371. [18] C. Meshram and S. A. Meshram, Constructing id-based cryptographic technique for ifp and gdlp based cryptosystem, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 1121-1134. doi: 10.1080/09720529.2015.1032621. [19] C. C. Peck and A. P. Dhawan, Genetic algorithms as global random search methods: An alternative perspective, Evolutionary Computation, 3 (2014), 39-80. [20] Z. K. Peng, P. W. Tse and F. L. Chu, An improved hilbert-huang transform and its application in vibration signal analysis, Journal of Sound & Vibration, 286 (2005), 1151-1153. doi: 10.1016/j.jsv.2004.01.049. [21] B. Samanta and K. R. Al-Balushi, Artificial neural network based fault diagnostics of rolling element bearings using time-domain features, Mechanical Systems & Signal Processing, 17 (2003), 317-328. [22] R. E. Schapire and Y. Singer, Improved Boosting Algorithms Using Confidence-rated Predictions, vol. 37, Machine Learning, 1999. [23] Z. Y. Shi, S. S. Law and X. Xu, Identification of linear time-varying mdof dynamic systems from forced excitation using hilbert transform and emd method, Journal of Sound & Vibration, 321 (2009), 572-589. [24] H. Wang and P. Chen, Intelligent diagnosis method for rolling element bearing faults using possibility theory and neural network, Computers & Industrial Engineering, 60 (2011), 511-518. [25] M. Weinfeld, Integrated Artificial Neural Networks: Components for Higher Level Architectures with New Properties, Springer Berlin Heidelberg, 1990. [26] Y. Xiang, J. Lu and Y. Y. Huang, A fast wave superposition spectral method with complex radius vector combined with two-dimensional fast fourier transform algorithm for acoustic radiation of axisymmetric bodies, Journal of Sound and Vibration, 331 (2012), 1441-1454.
The process flow for applying the GNN-AdaBoost algorithm
Procedure for rolling bearing fault diagnosis based on EMD and GNN-AdaBoost
Simulator stand for rolling bearing faults
Different health conditions of the rolling bearing: (a) normal; (b) inner-race fault; (c) outer-race fault; (d) rolling ball fault
Time-domain waveform figures of four rolling bearing states under the working condition of 6 r/s speed and light load: (a) normal; (b) inner-race fault; (c) outer-race fault and (d) rolling ball fault.
Diagram of the 13 IMF components
Total error and weight changes
Error variations and iterations of GNN-AdaBoost
The testing results of GNN-AdaBoost and GNN under different working conditions: (a) 6 r/s and light load; (b) 6 r/s and heavy load; (c) 8 r/s and light load (d) 8 r/s and heavy load
Expected output code
 Fault type Expected output code Normal (1 0 0 0) Inner-race fault (0 1 0 0) Outer-race fault (0 0 1 0) Rolling ball fault (0 0 0 1)
 Fault type Expected output code Normal (1 0 0 0) Inner-race fault (0 1 0 0) Outer-race fault (0 0 1 0) Rolling ball fault (0 0 0 1)
Accuracy comparisons between GNN-AdaBoost and GNN under different working conditions
 Experimental condition GNN-AdaBoost GNN Right Wrong Accuracy (%) Right Wrong Accuracy (%) Speed 6 r/s, light load 77 3 96.25 71 9 88.75 Speed 6 r/s, heavy load 78 2 97.5 74 6 92.5 Speed 8 r/s, light load 78 2 97.5 73 7 91.25 Speed 8 r/s, heavy load 79 1 98.75 76 4 95
 Experimental condition GNN-AdaBoost GNN Right Wrong Accuracy (%) Right Wrong Accuracy (%) Speed 6 r/s, light load 77 3 96.25 71 9 88.75 Speed 6 r/s, heavy load 78 2 97.5 74 6 92.5 Speed 8 r/s, light load 78 2 97.5 73 7 91.25 Speed 8 r/s, heavy load 79 1 98.75 76 4 95
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