Abstract
Deep learning methods recently have gained growing interests and are extensively applied in the data-driven bearing fault diagnosis. However, current deep learning methods perform the bearing fault diagnosis in the form of deterministic classification, which overlook the uncertainties that inevitably exist in actual practice. To tackle this issue, in this research, we develop a probabilistic fault diagnosis framework that can account for the uncertainty effect in prediction, which bears practical significance. This framework uses the Gaussian process classifier (GPC) as the mainstay, which fundamentally is built upon the Bayesian inference. To establish the high-fidelity GPC, the tailored feature extraction method can be adaptively determined through the cross validation-based grid search upon a prespecified method pool consisting of various kernel principal component analysis (KPCA) methods and stacked autoencoder. This adaptive strategy can ensure the adequate GPC model training to accurately characterize the complex nonlinear relations between the data features and respective faults. Systematic case studies using the publicly accessible experimental rolling bearing dataset, i.e., CWRU bearing dataset are carried out to validate this new framework. The results clearly illustrate the unique capability of this framework in handling uncertainties. It is also found that this framework outperforms other well-established machine learning and deep learning models in terms of accuracy and robustness. Moreover, the sensor fusion that combines the spatial vibration measurements appears to be an effective technique to further enhance the fault diagnosis performance. By fully leveraging the probabilistic feature of the framework, the future research endeavor, such as the extended fault diagnosis using limited fault labels will be facilitated.
This is a preview of subscription content, access via your institution.












References
Attoui I, Oudjani B, Boutasseta N, Fergani N, Bouakkaz M-S, Bouraiou A (2020) Novel predictive features using a wrapper model for rolling bearing fault diagnosis based on vibration signal analysis. Int J Adv Manuf Technol 106:3409–3435. https://doi.org/10.1007/s00170-019-04729-4
Wang H, Chen J, Zhou Y, Ni G (2020) Early fault diagnosis of rolling bearing based on noise-assisted signal feature enhancement and stochastic resonance for intelligent manufacturing. Int J Adv Manuf Technol 107:1017–1023. https://doi.org/10.1007/s00170-019-04333-6
Wei Y, Li Y, Xu M, Huang W (2019) A review of early fault diagnosis approaches and their applications in rotating machinery. Entropy 21:409. https://doi.org/10.3390/e21040409
Zhou K, Tang J (2021) Harnessing fuzzy neural network for gear fault diagnosis with limited data labels. Int J Adv Manuf Technol 115:1005–1019. https://doi.org/10.1007/s00170-021-07253-6
Barusu MR, Deivasigamani M (2021) Non-invasive vibration measurement for diagnosis of bearing faults in 3-phase squirrel cage induction motor using microwave sensor. IEEE Sens J 21:1026–1039. https://doi.org/10.1109/JSEN.2020.3004515
Li C, Sánchez R-V, Zurita G, Cerrada M, Cabrera D (2016) Fault diagnosis for rotating machinery using vibration measurement deep statistical feature learning. Sensors 16:895. https://doi.org/10.3390/s16060895
Zhang J, Wu J, Hu B, Tang J (2020) Intelligent fault diagnosis of rolling bearings using variational mode decomposition and self-organizing feature map. J Vib Control 26:1886–1897. https://doi.org/10.1177/1077546320911484
Wang Z, Wang C, Li N (2021) Bearing fault diagnosis method based on similarity measure and ensemble learning. Meas Sci Technol 32:055005. https://doi.org/10.1088/1361-6501/abda97
Goyal D, Choudhary A, Pabla BS, Dhami SS (2020) Support vector machines based non-contact fault diagnosis system for bearings. J Intell Manuf 31:1275–1289. https://doi.org/10.1007/s10845-019-01511-x
Wang Z, Yao L, Cai Y, Zhang J (2020) Mahalanobis semi-supervised mapping and beetle antennae search based support vector machine for wind turbine rolling bearings fault diagnosis. Renew Energy 155:1312–1327. https://doi.org/10.1016/j.renene.2020.04.041
Zhang W, Li C, Peng G, Chen Y, Zhang Z (2018) A deep convolutional neural network with new training methods for bearing fault diagnosis under noisy environment and different working load. Mech Syst Signal Process 100:439–453. https://doi.org/10.1016/j.ymssp.2017.06.022
Liang M, Cao P, Tang J (2021) Rolling bearing fault diagnosis based on feature fusion with parallel convolutional neural network. Int J Adv Manuf Technol 112:819–831. https://doi.org/10.1007/s00170-020-06401-8
Xu F, Tse YL (2018) Roller bearing fault diagnosis using stacked denoising autoencoder in deep learning and Gath–Geva clustering algorithm without principal component analysis and data label. Appl Soft Comput 73:898–913. https://doi.org/10.1016/j.asoc.2018.09.037
Shao H, Jiang H, Zhang X, Niu M (2015) Rolling bearing fault diagnosis using an optimization deep belief network. Meas Sci Technol 26:115002. https://doi.org/10.1088/0957-0233/26/11/115002
Pandarakone SE, Masuko M, Mizuno Y, Nakamura H (2018) Deep neural network based bearing fault diagnosis of induction motor using fast Fourier transform analysis. In 2018 IEEE Energy Convers Congr Expo IEEE 3214–3221. https://doi.org/10.1109/ECCE.2018.8557651
Xu G, Liu M, Jiang Z, Söffker D, Shen W (2019) Bearing fault diagnosis method based on deep convolutional neural network and random forest ensemble learning. Sensors 19:1088. https://doi.org/10.3390/s19051088
Yu W, Lu Y, Wang J (2021) Application of small sample virtual expansion and spherical mapping model in wind turbine fault diagnosis. Expert Syst Appl 183:115397. https://doi.org/10.1016/j.eswa.2021.115397
Zhao J, Yang S, Li Q, Liu Y, Gu X, Liu W (2021) A new bearing fault diagnosis method based on signal-to-image mapping and convolutional neural network. Measurement 176:109088. https://doi.org/10.1016/j.measurement.2021.109088
Luo J, Huang J, Li H (2021) A case study of conditional deep convolutional generative adversarial networks in machine fault diagnosis. J Intell Manuf 32:407–425. https://doi.org/10.1007/s10845-020-01579-w
Liu S, Jiang H, Wu Z, Li X (2021) Rolling bearing fault diagnosis using variational autoencoding generative adversarial networks with deep regret analysis. Measurement 168:108371. https://doi.org/10.1016/j.measurement.2020.108371
Liu S, Jiang H, Wu Z, Li X (2022) Data synthesis using deep feature enhanced generative adversarial networks for rolling bearing imbalanced fault diagnosis. Mech Syst Signal Process 163:108139. https://doi.org/10.1016/j.ymssp.2021.108139
Yang B, Lei Y, Jia F, Xing S (2019) An intelligent fault diagnosis approach based on transfer learning from laboratory bearings to locomotive bearings. Mech Syst Signal Process 122:692–706. https://doi.org/10.1016/j.ymssp.2018.12.051
Zhang R, Tao H, Wu L, Guan Y (2017) Transfer learning with neural networks for bearing fault diagnosis in changing working conditions. IEEE Access 5:14347–14357. https://doi.org/10.1109/ACCESS.2017.2720965
Li H, Zhang Q, Qin X, Yuantao S (2020) Raw vibration signal pattern recognition with automatic hyper-parameter-optimized convolutional neural network for bearing fault diagnosis. Proc Inst Mech Eng Part C J Mech Eng Sci 234:343–360. https://doi.org/10.1177/0954406219875756
Guo C, Li L, Hu Y, Yan J (2020) A deep learning based fault diagnosis method with hyperparameter optimization by using parallel computing. IEEE Access 8:131248–131256. https://doi.org/10.1109/ACCESS.2020.3009644
Kochenderfer MJ, Reynolds HJD (2015) Decision making under uncertainty: theory and application. MIT Press
Theodoridis S (2020) Machine learning: a Bayesian and optimization perspective. Elsevier Science
Zhou K, Hegde A, Cao P, Tang J (2016) Design optimization toward alleviating forced response variation in cyclically periodic structure using Gaussian process. J Vib Acoust 139. https://doi.org/10.1115/1.4035107
Zhou K, Tang J (2018) Uncertainty quantification in structural dynamic analysis using two-level Gaussian processes and Bayesian inference. J Sound Vib 412:95–115. https://doi.org/10.1016/j.jsv.2017.09.034
Zhou K, Tang J (2020) Uncertainty quantification of mode shape variation utilizing multi-level multi-response Gaussian process. J Vib Acoust 143. https://doi.org/10.1115/1.4047700
Zhou K, Tang J (2021) Structural model updating using adaptive multi-response Gaussian process meta-modeling. Mech Syst Signal Process 147:107121. https://doi.org/10.1016/j.ymssp.2020.107121
Wan H-P, Ren W-X (2015) A residual-based Gaussian process model framework for finite element model updating. Comput Struct 156:149–159. https://doi.org/10.1016/j.compstruc.2015.05.003
Wan H-P, Mao Z, Todd MD, Ren W-X (2014) Analytical uncertainty quantification for modal frequencies with structural parameter uncertainty using a Gaussian process metamodel. Eng Struct 75:577–589. https://doi.org/10.1016/j.engstruct.2014.06.028
Ringdahl B (2019) Gaussian process multiclass classification: Evaluation of binarization techniques and likelihood functions
Rasmussen CE, Williams CK (2006) Gaussian processes for machine learning. MIT press
Xiao Y, He Y (2011) A novel approach for analog fault diagnosis based on neural networks and improved kernel PCA. Neurocomputing 74:1102–1115. https://doi.org/10.1016/j.neucom.2010.12.003
Xiao Y, Feng L (2012) A novel linear ridgelet network approach for analog fault diagnosis using wavelet-based fractal analysis and kernel PCA as preprocessors. Measurement 45:297–310. https://doi.org/10.1016/j.measurement.2011.11.018
Oyedotun OK, Khashman A (2017) Deep learning in vision-based static hand gesture recognition. Neural Comput Appl 28:3941–3951. https://doi.org/10.1007/s00521-016-2294-8
Amrouche F, Lagraa S, Frank R, State R (2020) Intrusion detection on robot cameras using spatio-temporal autoencoders: a self-driving car application. In 2020 IEEE 91st Veh Technol Conf IEEE 1–5. https://doi.org/10.1109/VTC2020-Spring48590.2020.9129461
Deng J, Zhang Z, Eyben F, Schuller B (2014) Autoencoder-based unsupervised domain adaptation for speech emotion recognition. IEEE Signal Process Lett 21:1068–1072. https://doi.org/10.1109/LSP.2014.2324759
Zabalza J, Ren J, Zheng J, Zhao H, Qing C, Yang Z, Du P, Marshall S (2016) Novel segmented stacked autoencoder for effective dimensionality reduction and feature extraction in hyperspectral imaging. Neurocomputing 185:1–10. https://doi.org/10.1016/j.neucom.2015.11.044
Sun M, Wang H, Liu P, Huang S, Fan P (2019) A sparse stacked denoising autoencoder with optimized transfer learning applied to the fault diagnosis of rolling bearings. Measurement 146:305–314. https://doi.org/10.1016/j.measurement.2019.06.029
Wen L, Li X, Gao L (2020) A transfer convolutional neural network for fault diagnosis based on ResNet-50. Neural Comput Appl 32:6111–6124. https://doi.org/10.1007/s00521-019-04097-w
Zhang X, Zhang M, Wan S, He Y, Wang X (2021) A bearing fault diagnosis method based on multiscale dispersion entropy and GG clustering. Measurement 185:110023. https://doi.org/10.1016/j.measurement.2021.110023
Smith WA, Randall RB (2015) Rolling element bearing diagnostics using the Case Western Reserve University data: a benchmark study. Mech Syst Signal Process 64–65:100–131. https://doi.org/10.1016/j.ymssp.2015.04.021
Nickisch H, Rasmussen CE (2008) Approximations for binary Gaussian process classification. J Mach Learn Res 9:2035–2078
Rosipal R, Girolami M, Trejo LJ, Cichocki A (2001) Kernel PCA for feature extraction and de-noising in nonlinear regression. Neural Comput Appl 10:231–243. https://doi.org/10.1007/s521-001-8051-z
Wang Q (2012) Kernel principal component analysis and its applications in face recognition and active shape models. http://arxiv.org/abs/1207.3538
Katuwal R, Suganthan PN (2019) Stacked autoencoder based deep random vector functional link neural network for classification. Appl Soft Comput 85:105854. https://doi.org/10.1016/j.asoc.2019.105854
Dai J, Song H, Sheng G, Jiang X (2017) Cleaning method for status monitoring data of power equipment based on stacked denoising autoencoders. IEEE Access 5:22863–22870. https://doi.org/10.1109/ACCESS.2017.2740968
Liu Q, Wang H-P (2001) A case study on multisensor data fusion for imbalance diagnosis of rotating machinery. Artif Intell Eng Des Anal Manuf AIEDAM 15:203–210. https://doi.org/10.1017/S0890060401153011
Kadilar C, Cingi H (2003) Ratio estimators in stratified random sampling. Biometrical J 45:218–225. https://doi.org/10.1002/bimj.200390007
Krizhevsky A, Sutskever I, Hinton GE (2012) ImageNet classification with deep convolutional neural networks. In Adv Neural Inf Process Syst 1097–1105
Cao P, Zhang S, Tang J (2018) Preprocessing-free gear fault diagnosis using small datasets with deep convolutional neural network-based transfer learning. IEEE Access 6:26241–26253. https://doi.org/10.1109/ACCESS.2018.2837621
Funding
The authors appreciate the startup funding support from Michigan Technological University.
Author information
Authors and Affiliations
Contributions
M. Liang and K. Zhou worked together to generate the conception of the work. M. Liang and K. Zhou carried out algorithm development and data analysis and interpretation, as well as drafted the paper. K. Zhou also provided critical revision of the paper.
Corresponding author
Ethics declarations
Ethics approval
Not applicable.
Consent to participate
Not applicable.
Consent to publication
Not applicable.
Conflicts of interest
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Liang, M., Zhou, K. Probabilistic bearing fault diagnosis using Gaussian process with tailored feature extraction. Int J Adv Manuf Technol 119, 2059–2076 (2022). https://doi.org/10.1007/s00170-021-08392-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-021-08392-6
Keywords
- Rolling bearings
- Probabilistic fault diagnosis
- Gaussian process classifier (GPC)
- Kernel principal component analysis (KPCA)
- Stacked autoencoder
- Sensor fusion