A novel threshold segmentation instantaneous frequency calculation approach for fault diagnosis

Zhibo Liu; Yu Yuan; Ling Yu; Yingjie Li; Jiyou Fei; Zhibo Liu; Yu Yuan; Ling Yu; Yingjie Li; Jiyou Fei

doi:10.3934/mbe.2020291

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5395-5413. doi: 10.3934/mbe.2020291

Previous Article Next Article

Research article

A novel threshold segmentation instantaneous frequency calculation approach for fault diagnosis

1.
School of Mechanical Engineering, Dalian Jiaotong University, Dalian 116028, China
2.
School of Locomotive and Rolling Stock Engineering, Dalian Jiaotong University, Dalian 116028, China
3.
China Household Electric Appliance Research Institute, Beijing 100037, China
4.
SPIC Hubei New Energy CO., LTD, Wuhan 430077, China
5.
Traction Power State Key Laboratory of Southwest Jiaotong University, Chengdu 610031 China

Received: 15 June 2020 Accepted: 03 August 2020 Published: 12 August 2020

Instantaneous frequency can well track and reflect the transient information of signal, so it plays an important role in the analysis and processing of the non-stationary signal. In this paper, the single component signal is compared with the Second Order Differential Equation in polar coordinates. Based on this, a threshold segmentation instantaneous frequency calculation method is proposed. This method is mainly for characteristics of the non-stationary signal, use the change of the area around the signal and the x axis to determine the amplitude mutation point of each single component signal, and perform segmentation. Simulations, mathematical derivations and experimental tests are used to highlight the performance of the proposed method. It is not only simple in calculation, but also can reduce the unnecessary influence of non-stationary signal amplitude mutation on instantaneous frequency, and can effectively judge the fault of rolling bearing in fault diagnosis.
- rolling bearings,
- signal analysis,
- instantaneous frequency,
- fault diagnosis,
- performance
Citation: Zhibo Liu, Yu Yuan, Ling Yu, Yingjie Li, Jiyou Fei. A novel threshold segmentation instantaneous frequency calculation approach for fault diagnosis[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5395-5413. doi: 10.3934/mbe.2020291

Related Papers:

Abstract

Instantaneous frequency can well track and reflect the transient information of signal, so it plays an important role in the analysis and processing of the non-stationary signal. In this paper, the single component signal is compared with the Second Order Differential Equation in polar coordinates. Based on this, a threshold segmentation instantaneous frequency calculation method is proposed. This method is mainly for characteristics of the non-stationary signal, use the change of the area around the signal and the x axis to determine the amplitude mutation point of each single component signal, and perform segmentation. Simulations, mathematical derivations and experimental tests are used to highlight the performance of the proposed method. It is not only simple in calculation, but also can reduce the unnecessary influence of non-stationary signal amplitude mutation on instantaneous frequency, and can effectively judge the fault of rolling bearing in fault diagnosis.

References

[1]	J. Benali, M. Sayadi, F. Fnaiech, B. Morello, N. Zerhouni, Importance of the fourth and fifth intrinsic mode functions for bearing fault diagnosis, 14th international conference on Sciences and Techniques of Automatic control & computer engineering-STA'2013, 2013 (2013), 259-264.
[2]	J. Yu, Z. Guo, J. Zhao, Remaining useful life pre-diction of planet bearings based on conditional deep recurrent generative adversarial network and action discovery, J. Mech. Sci. Technol., 2020 (2020),1-9.
[3]	S. Nandi, H. A. Toliyat, X. Li, Condition monitoring and fault diagnosis of electrical motors-a review, IEEE T. Energy. Conver., 20 (2005), 719-729.
[4]	H. Zhao, H. Liu, J. Xu, W. Deng, Performance prediction using high-order differential mathematical morphology gradient spectrum entropy and extreme learning machine, IEEE T. Instrum. Meas., 69 (2020), 4165-4172.
[5]	T. Li, J. Shi, X. Li, J. Wu, F. Pan, Image encryption based on pixel-level diffusion with dynamic filtering and DNA-level permutation with 3D Latin cubes, Entropy, 21 (2019), 1-21.
[6]	Y. Xu, H. Chen, J. Luo, Q. Zhang, S. Jiao, X. Zhang, Enhanced Moth-flame optimizer with mutation strategy for global optimization, Inform. Sciences, 492 (2019), 181-203.
[7]	H. Zhao, J. Zheng, J. Xu, W. Deng, Fault diagnosis method based on principal component analysis and broad learning system, IEEE Access, 7 (2019), 99263-99272.
[8]	R. Chen, S. K. Guo, X. Z. Wang, T. Zhang, Fusion of multi-RSMOTE with fuzzy integral to classify bug reports with an imbalanced distribution, IEEE T. Fuzzy Syst., 27 (2019), 2406-2420.
[9]	H. Zhao, S. Zuo, M. Hou, W. Liu, L. Yu, A novel adaptive signal processing method based on enhanced empirical wavelet transform technology, Sensors, 18 (2018), 1-17.
[10]	Y. Liu, X. Wang, Z. Zhai, R. Chen, Y. Jiang, Timely daily activity recognition from headmost sensor events, ISA T., 94 (2019), 379-390.
[11]	H. Zhao, J. Zheng, W. Deng, Y. Song, Semi-supervised broad learning system based on manifold regularization and broad network, IEEE T. Circuits-I., 67 (2020), 983-994.
[12]	A. Rai, S. H. Upadhyay, A review on signal processing techniques utilized in the fault diagnosis of rolling element bearings, Tribol. Int., 96 (2016), 289-306.
[13]	J. H. Shin, H. B. Jun, On condition based maintenance policy, J. Comput. Des. Eng., (2015), 119-127.
[14]	T. Li, Z. Qian, T. He, Short-term load forecasting with improved CEEMDAN and GWO-based multiple kernel ELM, Complexity, 2020 (2020), 1-20.
[15]	W. Deng, H. Liu, J. Xu, H. Zhao, Y. Song, An improved quantum-inspired differential evolution algorithm for deep belief network, IEEE T. Instrum. Meas., 2020 (2020), 1-8.
[16]	D. Iatsenko, P. V. E. Mcclintock, A. Stefanovska, Extraction of instantaneous frequencies from ridges in time-frequency representations of signals, Signal Process., 125 (2016), 290-303.
[17]	B. Yu, Z. Yao, On Compution of the Instaneous Frequency of Complicated Signals, J. Southwest Uni. (Nat. Sci.), 34 (2012), 108-111.
[18]	M. Kowalski, A. Meynard, H. T. Wu, Convex Optimization approach to signals with fast varying instantaneous frequency, Appl. Comput. Harmon. A., 9 (2015), 1260-1267.
[19]	S. Lu, Q. He, J. Wang, A review of stochastic resonance in rotating machine fault detection, Mech. Syst. Signal Pr., 116 (2019), 230-260.
[20]	H. Zhao, D. Li, W. Deng, Research on vibration suppression method of alternating current motor based on fractional order control strategy, P. I. Mech. Eng. E-J. Pro., 231 (2017), 786-799.
[21]	W. Deng, J. Xu, Y. Song, H. Zhao, An effective improved co-evolution ant colony optimization algorithm with multi-strategies and its application, Int. J. Bio-Inspired Comput., 2020 (2020),1-10.
[22]	J. Li, L. Li, G.Q. Zhao, Y. Pan, Instantaneous frequency estimation of nonlinear frequency-modulated signals under strong noise environment, Circ. Syst. Signal. Pr., 35 (2016)), 3734-3744.
[23]	K. Czarnecki, The instantaneous frequency rate spectrogram. Mech. Syst. Signal Pr., 66-67 (2016), 361-373.
[24]	H. Shao, J. Cheng, H. Jiang, Y. Yang, Z. Wu, Enhanced deep gated recurrent unit and complex wavelet packet energy moment entropy for early fault prognosis of bearing, Knowl-Based Syst., 188 (2020), 1-14.
[25]	H. Chen, Q. Zhang, J. Luo, Y. Xu, X. Zhang, An enhanced Bacterial Foraging Optimization and its application for training kernel extreme learning machine, Appl. Soft Comput., 86 (2020), 1-24.
[26]	W. Deng, J. Xu, H. Zhao, An improved ant colony optimization algorithm based on hybrid strategies for scheduling problem, IEEE Access, 7 (2019), 20281-20292.
[27]	C. K. Chui, M. D. van der Walt, Signal analysis via instantaneous frequency estimation of signal components, GEM, 6 (2015), 1-42.
[28]	M. J. Afroni, D. Sutanto, D. Stirling, Analysis of nonstationary power-quality waveforms using iterative Hilbert Huang transform and SAX algorithm, IEEE T. Power Deliver., 28 (2013), 2134-2144.
[29]	Y. Liu, Y. Mu, K. Chen, Y. Li, J. Guo, Daily activity feature selection in smart homes based on pearson correlation coefficient, Neural Process. Lett., 51 (2020), 1771-1787.
[30]	Z. He, H. Shao, X. Zhang, J. Cheng, Y. Yang, Improved deep transfer auto-encoder for fault diagnosis of gearbox under variable working conditions with small training samples, IEEE Access, 7 (2019), 115368-115377.
[31]	W. Deng, W. Li, X. Yang, A novel hybrid optimization algorithm of computational intelligence techniques for highway passenger volume prediction, Expert Syst. Appl., 38 (2011), 4198-4205.
[32]	A. Baccigalupi, A. Liccardo, The Huang Hilbert transform for evaluating the instantaneous frequency evolution of transient signals in non-linear systems, Measurement, 86 (2016), 1-13.
[33]	A. Abutaleb, Instantaneous frequency estimation using stochastic calculus and bootstrapping, EURASIP J. Adv. Sig. Pr., 12 (2005), 1886-1901.
[34]	J. Zheng, Z. Dong, H. Pan, Q. Ni, J. Zhang, Composite multi-scale weighted permutation entropy and extreme learning machine based intelligent fault diagnosis for rolling bearing, Measurement, 143 (2019), 69-80.
[35]	J. Zheng, H. Pan, S. Yang, J. Cheng, Adaptive parameterless empirical wavelet transform based time-frequency analysis method and its application to rotor rubbing fault diagnosis, Signal Process, 130 (2017), 305-314.
[36]	S. Krishnan, A new approach for estimation of instantaneous mean frequency of a time-varying signal, EURASIP J. Adv. Sig. Pr., 17 (2005), 2848-2855.
[37]	A. Soualhi, K. Medjaher, N. Zerhouni, Bearing health monitoring based on Hilbert-Huang transform, support vector machine, and regression, IEEE T. Instrum. Meas., 64 (2014), 52-62.
[38]	J. Lerga, V. Sucic, B. Boashash, An efficient algorithm for instantaneous frequency estimation of nonstationary multicomponent signals in low SNR, EURASIP J. Adv. Sig. Pr., 2011 (2011), 1-16.
[39]	W. Deng, H. M. Zhao, L. Zou, G. Y. Li, X. H. Yang, D. Q. Wu, A novel collaborative optimization algorithm in solving complex optimization problems, Soft Comput., 21 (2017), 4387-4398.
[40]	N. E. Huang, Z. Wu, S. R. Long, On the frequency, Adv. Adapt. Data Anal., 1 (2009), 177-229.
[41]	J. D. Zheng, J. S. Cheng, Y. Yang, A new instantaneous frequency estimation approach-empirical envelope method, J. Sound Vib., 31 (2012), 86-90.
[42]	A. Cicone, J. F. Liu, H. M. Zhou, Adaptive local iterative filtering for signal decomposition and instantaneous frequency analysis, Appl. Comput. Harmon. A., 41 (2016), 384-411.
[43]	T. Y. Wu, C. H. Lai, D. C. Liu, Defect diagnostics of roller bearing using instantaneous frequency normalization under fluctuant rotating speed, J. Mech. Sci. Technol., 30 (2016), 1037-1048.
[44]	Z. Ji, Z. Wang, X. Deng, W. Huang, T. Wu, A new parallel algorithm to solve one classic water resources optimal allocation problem based on inspired computational model, Desalin. Water Treat., 160 (2019), 214-218.
[45]	W. Deng, R. Yao, H. M. Zhao, X. H. Yang, G.Y. Li, A novel intelligent diagnosis method using optimal LS-SVM with improved PSO algorithm, Soft Comput., 23 (2019), 2445-2462
[46]	Z. Wang, Z. Ji, X. Wang, T. Wu, W. Huang, A new parallel DNA algorithm to solve the task scheduling problem based on inspired computational model, BioSystems, 162 (2017), 59-65.
[47]	A. Cicone, H. M. Zhou, Multidimensional iterative filtering method for the decomposition of high-dimensional non-stationary signals, Numer. Math. Theory Me., 10 (2017), 278-298.
[48]	F. R. Sun, Y. D. Yao, G. Z. Li, W. Liu, Simulation of real gas mixture transport through aqueous nanopores during the depressurization process considering stress sensitivity, J. Petrol. Sci. Eng., 178 (2019), 829-837.
[49]	J. Yu, M. Bai, G. Wang, X. Shi, Fault diagnosis of planetary gearbox with incomplete information using assignment reduction and flexible naive Bayesian classifier, J. Mech. Sci. Technol., 32 (2018), 37-47.
[50]	Y. Xue, B. Xue, M. J. Zhang, Self-adaptive particle swarm optimization for large-scale feature selection in classification, ACM T. Knowl. Discov. D., 23 (2019), 50.
[51]	Y. Xu, H. Chen, A. A. Heidari, J. Luo, Q. Zhang, X. Zhao, et al, An efficient chaotic mutative moth-flame-inspired optimizer for global optimization tasks, Expert Syst. Appl., 129 (2019),135-155.
[52]	J. Yu, Y. Xu, K. Liu, Planetary gear fault diagnosis using stacked denoising autoencoder and gated recurrent unit neural network under noisy environment and time-varying rotational speed conditions, Meas. Sci. Technol., 30 (2019), 095003.
[53]	Z. Wang, X. Ren, Z. Ji, W. Huang, T. Wu, A novel bio-heuristic computing algorithm to solve the capacitated vehicle routing problem based on Adleman-Lipton model, Biosystems, 184 (2019), 103997.
[54]	H. L. Fu, M. M. Wang, P. Li, S. Jiang, M. Cao, Tracing knowledge development trajectories of the internet of things domain: A main path analysis, IEEE T. Ind. Inform., 15 (2019), 6531-6540.
[55]	A. Cicone, J. Liu, H. Zhou, Hyperspectral chemical plume detection algorithms based on multidimensional iterative filtering decomposition, Philos. T. R. Soc. A., 374 (2016), 20150196.
[56]	J. Luo, H. Chen, A. A. Heidari, Y. Xu, Q. Zhang, C. Li, Multi-strategy boosted mutative whale-inspired optimization approaches, Appl. Math. Model, 73 (2019),109-123.
[57]	J. Yu, Y. Xu, G. Yu, L. Liu, Fault severity identification of roller bearings using flow graph and Non-naive Bayesian inference, P. I. Mech. Eng. C-J. Mec., 233(2019), 5161-5171.
[58]	X. J. Liu, X. D. Liu, X. Luo, H. Fua, M. Wang, L. Lia, Impact of different policy instruments on diffusing energy consumption monitoring technology in public buildings: evidence from Xi'an, China, J. Clean. Prod., 251 (2020), 119693.
[59]	H. Chen, F. Miao, X. Shen, Hyperspectral remote sensing image classification with CNN based on quantum genetic-optimized sparse representation, IEEE Access, 8 (2020), 99900-99909.
[60]	J. Yu, Y. He, Planetary gearbox fault diagnosis based on data-driven valued characteristic multigranulation model with incomplete diagnostic information, J. Sound Vib., 429 (2018), 63-77.

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)