Abstract
In order to achieve accurate fault diagnosis of rolling bearing under random noise, a new fault diagnosis method based on wavelet packet-variational mode decomposition (WP-VMD) and kernel extreme learning machine (KELM) optimized by particle swarm optimization (PSO) is proposed in this paper. Firstly, the time–frequency domain feature vectors of the original rolling bearing fault signals are effectively obtained by preprocessing of WMD and decomposition and reconstruction of VMD. Then, the extracted two-dimensional feature vector is input into the KELM neural network for fault identification, and combined with PSO, KELM parameters were optimized. The experimental results show that the proposed method can effectively diagnose the rolling bearing under random noise, with the features of fast speed, stable performance and high accuracy. By comparison, this paper obtains better accuracy and real-time performance with fewer features, which provides a simple and efficient solution for fault diagnosis of rolling bearings.














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References
Abu AO (2017) Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations. Neural Comput 28(7):1591–1610. https://doi.org/10.1007/s00521-015-2110-x
Abu AO, Al-Smadi M, Momani S, Hayat T (2016) Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method. Soft Comput 20(8):3283–3302. https://doi.org/10.1007/s00500-015-1707-4
Arqub OA, Al-Smadi M (2020) Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions. Soft Comput 24(16):12501–12522. https://doi.org/10.1007/s00500-020-04687-0
Arqub OA, Al-Smadi M, Momani S, Hayat T (2017) Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft Comput 23:7191–7206. https://doi.org/10.1007/s00500-016-2262-3
Cao S, Xu F, Ma T (2021) Fault diagnosis of rolling bearing based on multiscale one-dimensional hybrid binary pattern. Measurement. https://doi.org/10.1016/j.measurement.2021.109552
Cheng J, Yang Y, Shao H, Pan H, Zheng J (2021) Enhanced periodic mode decomposition and its application to composite fault diagnosis of rolling bearings. ISA Trans 35:1–18. https://doi.org/10.1016/j.isatra.2021.07.014
Dragomiretskiy K, Zosso D (2014) Variational mode decomposition. IEEE Trans Signal Process 62(3):531–544
He Q, Wang XX, Zhou Q (2014) Vibration sensor data denoising using a time-frequency manifold for machinery fault diagnosis. Sensors 14(1):382–402
Huang BG (2014) An insight into extreme learning machines: random neurons, random features and kernels. Cogn Comput 6(3):376–390
Huang BG, Zhu QY, Siew CK (2016) Extreme learning machine: theory and applications. Neurocomputing 70(1):489–501. https://doi.org/10.1016/j.neucom.2005.12.126
Huang WT, Sun HJ, Luo NJ, Wang WJ (2019) Periodic feature oriented adapted dictionary free OMP for rolling element bearing incipient fault diagnosis. Mech Syst Signal Process 126:137–160
Jia HC, Pan DH, Yuan Y, Zhang WC (2015) Using a BP neural network for rapid assessment of populations with difficulties accessing drinking water because of drought. Hum Ecol Risk Assess Int J 21(1):100–116. https://doi.org/10.1080/10807039.2013.879025
Learned RE (1992) Wavelet packet based transient signal classification. Time-frequency and Time-scale Analysis, IEEE-SP International Symposium
Li JM, Yao XF, Zhang WH (2019) Periodic impulses extraction based on improved adaptive VMD and sparse code shrinkage denoising and its application in rotating machinery fault diagnosis. Mech Syst and Signal Process 126:568–589
Lian RJ (2013) Adaptive self-organizing fuzzy sliding-mode radial basis-function neural-network controller for robotic systems. IEEE Trans Ind Electron 61(3):1493–1503
Liang HL, Bressler SL, Desimone R, Fries P (2005) Empirical mode decomposition: a method for analyzing neural data. Neurocomputing 65:801–807. https://doi.org/10.1016/j.neucom.2004.10.077
Liu XF, Lin B, Luo HL (2015) Bearing faults diagnostics based on hybrid LS-SVM and EMD method. Measurement 59:145–166. https://doi.org/10.1016/j.measurement.2014.09.037
Liu Y, Zhao YL, Li JT, Ma H, Yang Q, Yan XX (2020) Application of weighted contribution rate of nonlinear output frequency response functions to rotor rub-impact. Mech Syst Signal Process 136:106518. https://doi.org/10.1016/j.ymssp.2019.106518
Madalena C, Goldberger AL, Peng CK (2007) Multiscale entropy analysis of complex physiologic time series. Phys Rev Lett 89(6):705–708
Madalena C, Goldberger AL, Peng CK (2005) Multiscale entropy analysis of biological signals. Phys Rev E Statist Nonlinear Soft Matter Phys 71:021906
Mao W, Feng W, Liang X (2019) A novel deep output kernel learning method for bearing fault structural diagnosis. Mech Syst and Signal Process 117:293–318. https://doi.org/10.1016/j.ymssp.2018.07.034
Meng L, Li CS, Zhang XY, Li RH, An XL (2016) Compound feature selection and parameter optimization of ELM for fault diagnosis of rolling element bearings. ISA Trans 65:556–566. https://doi.org/10.1016/j.isatra.2016.08.022
Qin B, Sun GD, Wang JG, Hu J (2017) Fault features extraction and identification based rolling bearing fault diagnosis. In: 12th International Conference on Damage Assessment of Structures, pp 1–14
Qin X, Guo J, Dong X, Guo Y (2020) The fault diagnosis of rolling bearing based on variational mode decomposition and iterative random forest. Shock Vib. https://doi.org/10.1155/2020/1576150
Qiu JB, Ji WQ, Rudas IJ, Gao HJ (2020) Asynchronous sampled-data filtering design for fuzzy-affine-model-based stochastic. IEEE Trans Cybern 51:1–11
Qiu JB, Ji WQ, Lam HK, Wang M (2020) Fuzzy-affine-model based sampled-data filtering design for stochastic nonlinear systems. IEEE Trans on Fuzzy Syst 29:1–13
Richman JS, Moorman JR (2000) Physiological time-series analysis using approximate entropy and sample entropy. Am J Physiol-Heart and Circul Physiol 278(6):2039–2049
Shao HD, Jiang JK, Wang F, Wang YN (2017) Rolling bearing fault diagnosis using adaptive deep belief network with dual-tree complex wavelet packet. ISA Trans 69:187–201. https://doi.org/10.1016/j.isatra.2017.03.017
Su H, Xiang L, Hu A, Yang X (2021) A novel hybrid method based on KELM with SAPSO for fault diagnosis of rolling bearing under variable operating conditions. Measurement 177:109276. https://doi.org/10.1016/j.measurement.2021.109276
Ting-ting X, Yan Z, Zong M, Xiao-lin G (2020) A fault diagnosis method of rolling bearing based on VMD Tsallis entropy and FCM clustering. Multim Tools Appl 79(39):30069–30085
Wang R, Jiang H, Li X, Liu S (2020) A reinforcement neural architecture search method for rolling bearing fault diagnosis. Measurement 154:107417. https://doi.org/10.1016/j.measurement.2019.107417
Wang Y, Xu GH, Liang L, Jiang KS (2015a) Detection of weak transient signals based on wavelet packet transform and manifold learning for rolling element bearing fault diagnosis. Mech Syst Signal Process 54:259–276
Wang YX, Markert R, Xiang JW, Zheng WG (2015b) Research on variational mode decomposition and its application in detecting rub-impact fault of the rotor system. Mech Syst Signal Process 60:243–251. https://doi.org/10.1016/j.ymssp.2015.02.020
Xu B, Zhou FX, Li HP, Yan BK (2019) Early fault feature extraction of bearings based on Teager energy operator and optimal VMD. ISA Trans 86:249–265
Yan XA, Jia MP, Zhang W, Zhu L (2018) Fault diagnosis of rolling element bearing utsing a new optimal scale morphology analysis method. ISA Trans 73:165–180. https://doi.org/10.1016/j.isatra.2018.01.004
Yao DC, Yang JW, Bai YL (2016) Railway rolling bearing fault diagnosis based on multi-scale intrinsic mode function permutation entropy and extreme learning machine classifier. Adv Mech Eng 54:168–176. https://doi.org/10.1177/1687814016676157
Yao DC, Yang JW, Pang ZF, Nie CM, Fang W (2018) Railway axle box bearing fault identification using LCD-MPE and ELM-AdaBoost. J Vibroeng 20(1):165–174. https://doi.org/10.21595/jve.2017.18502
Zhang Q, Gao J, Dong H, Mao Y (2018) WPD and DE/BBO-RBFNN for solution of rolling bearing fault diagnosis. Neurocomputing 312:27–33. https://doi.org/10.1016/j.neucom.2018.05.014
Zhang XX, Zhou GW, Li DD (2019) Application of variational mode decomposition and permutation entropy for rolling bearing fault diagnosis. Int J Acoust Vib 24:303–311
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by TJ, YL and SL. The first draft of the manuscript was written by TJ and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Jiang, T., Li, Y. & Li, S. Multi-fault diagnosis of rolling bearing using two-dimensional feature vector of WP-VMD and PSO-KELM algorithm. Soft Comput 27, 8175–8187 (2023). https://doi.org/10.1007/s00500-022-07704-6
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DOI: https://doi.org/10.1007/s00500-022-07704-6