{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T16:18:33Z","timestamp":1772727513975,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,5,24]],"date-time":"2018-05-24T00:00:00Z","timestamp":1527120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2016YFB1200203"],"award-info":[{"award-number":["2016YFB1200203"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2017RC011"],"award-info":[{"award-number":["2017RC011"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005023","name":"State Key Laboratory of Rail Traffic Control and Safety","doi-asserted-by":"publisher","award":["Nos. RCS2016ZQ003 and RCS2016ZT018"],"award-info":[{"award-number":["Nos. RCS2016ZQ003 and RCS2016ZT018"]}],"id":[{"id":"10.13039\/501100005023","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Bogies are crucial for the safe operation of rail transit systems and usually work under uncertain and variable operating conditions. However, the diagnosis of bogie faults under variable conditions has barely been discussed until now. Thus, it is valuable to develop effective methods to deal with variable conditions. Besides, considering that the normal data for training are much more than the faulty data in practice, there is another problem in that only a small amount of data is available that includes faults. Concerning these issues, this paper proposes two new algorithms: (1) A novel feature parameter named spectral kurtosis entropy (SKE) is proposed based on the protrugram. The SKE not only avoids the manual post-processing of the protrugram but also has strong robustness to the operating conditions and parameter configurations, which have been validated by a simulation experiment in this paper. In this paper, the SKE, in conjunction with variational mode decomposition (VMD), is employed for feature extraction under variable conditions. (2) A new learning algorithm named weighted self-adaptive evolutionary extreme learning machine (WSaE-ELM) is proposed. WSaE-ELM gives each sample an extra sample weight to rebalance the training data and optimizes these weights along with the parameters of hidden neurons by means of the self-adaptive differential evolution algorithm. Finally, the hybrid method based on VMD, SKE, and WSaE-ELM is verified by using the vibration signals gathered from real bogies with speed variations. It is demonstrated that the proposed method of bogie fault diagnosis outperforms the conventional methods by up to 4.42% and 6.22%, respectively, in percentages of accuracy under variable conditions.<\/jats:p>","DOI":"10.3390\/s18061705","type":"journal-article","created":{"date-parts":[[2018,5,28]],"date-time":"2018-05-28T03:54:21Z","timestamp":1527479661000},"page":"1705","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Spectral Kurtosis Entropy and Weighted SaE-ELM for Bogie Fault Diagnosis under Variable Conditions"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3039-7582","authenticated-orcid":false,"given":"Zhipeng","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Lab of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China"},{"name":"National Engineering Laboratory for System Safety and Operation Assurance of Urban Rail Transit, Guangzhou 510000, China"},{"name":"Beijing Research Center of Urban Traffic Information Sensing and Service Technologies, Beijing Jiaotong University, Beijing 100044, China"}]},{"given":"Limin","family":"Jia","sequence":"additional","affiliation":[{"name":"State Key Lab of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China"},{"name":"National Engineering Laboratory for System Safety and Operation Assurance of Urban Rail Transit, Guangzhou 510000, China"},{"name":"Beijing Research Center of Urban Traffic Information Sensing and Service Technologies, Beijing Jiaotong University, Beijing 100044, China"}]},{"given":"Linlin","family":"Kou","sequence":"additional","affiliation":[{"name":"State Key Lab of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China"},{"name":"National Engineering Laboratory for System Safety and Operation Assurance of Urban Rail Transit, Guangzhou 510000, China"},{"name":"Beijing Research Center of Urban Traffic Information Sensing and Service Technologies, Beijing Jiaotong University, Beijing 100044, China"}]},{"given":"Yong","family":"Qin","sequence":"additional","affiliation":[{"name":"State Key Lab of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China"},{"name":"National Engineering Laboratory for System Safety and Operation Assurance of Urban Rail Transit, Guangzhou 510000, China"},{"name":"Beijing Research Center of Urban Traffic Information Sensing and Service Technologies, Beijing Jiaotong University, Beijing 100044, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Liu, J., Chen, A., and Zhao, N. (2018). An Intelligent Fault Diagnosis Method for Bogie Bearings of Metro Vehicles Based on Weighted Improved D-S Evidence Theory. Energies, 11.","DOI":"10.3390\/en11010232"},{"key":"ref_2","first-page":"30","article-title":"Condition Monitoring of Railway Track Systems by Using Acceleration Signals on Wheelset Axle-Boxes","volume":"33","author":"Chudzikiewicz","year":"2018","journal-title":"Transport"},{"key":"ref_3","unstructured":"Chudzikiewicz, A., Bogacz, R., and Kostrzewski, M. (2014, January 8\u201311). Using Acceleration Signals Recorded on a Railway Vehicle Wheelsets for Rail Track Condition Monitoring. Proceedings of the EWSHM\u20147th European Workshop on Structural Health Monitoring, Nantes, France."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2286","DOI":"10.4028\/www.scientific.net\/AMR.753-755.2286","article-title":"High Speed Train Bogie Fault Signal Analysis Based on Wavelet Entropy Feature","volume":"753\u2013755","author":"Qin","year":"2013","journal-title":"Adv. Mater. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"10991","DOI":"10.3390\/s150510991","article-title":"Faults Diagnostics of Railway Axle Bearings Based on IMF\u2019s Confidence Index Algorithm for Ensemble EMD","volume":"15","author":"Yi","year":"2015","journal-title":"Sensors"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1408","DOI":"10.1177\/0954409714560798","article-title":"Maintenance of bogie components through vibration inspection with intelligent wireless sensors: A case study on axle-boxes and wheel-sets using the empirical mode decomposition technique","volume":"230","author":"Trilla","year":"2016","journal-title":"Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.ifacol.2017.08.052","article-title":"Bogie Fault Identification Based on EEMD Information Entropy and Manifold Learning","volume":"50","author":"Qin","year":"2017","journal-title":"IFAC-PapersOnLine"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bustos, A., Rubio, H., Castej\u00f3n, C., and Garc\u00eda-Prada, C.J. (2018). EMD-Based Methodology for the Identification of a High-Speed Train Running in a Gear Operating State. Sensors, 18.","DOI":"10.3390\/s18030793"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational Mode Decomposition","volume":"62","author":"Dragomiretskiy","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wang, Z., Jia, L., and Qin, Y. (2018). Adaptive Diagnosis for Rotating Machineries Using Information Geometrical Kernel-ELM Based on VMD-SVD. Entropy, 20.","DOI":"10.3390\/e20010073"},{"key":"ref_11","unstructured":"Dwyer, R. (1983, January 14\u201316). Detection of non-Gaussian signals by frequency domain Kurtosis estimation. Proceedings of the ICASSP \u201983. IEEE International Conference on Acoustics, Speech, and Signal Processing, Boston, MA, USA."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.ymssp.2005.12.002","article-title":"Fast computation of the kurtogram for the detection of transient faults","volume":"21","author":"Antoni","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.ymssp.2012.10.003","article-title":"An enhanced Kurtogram method for fault diagnosis of rolling element bearings","volume":"35","author":"Wang","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"29363","DOI":"10.3390\/s151129363","article-title":"Early Fault Diagnosis of Bearings Using an Improved Spectral Kurtosis by Maximum Correlated Kurtosis Deconvolution","volume":"15","author":"Jia","year":"2015","journal-title":"Sensors"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1352","DOI":"10.1016\/j.ymssp.2008.07.019","article-title":"Application of spectral kurtosis for detection of a tooth crack in the planetary gear of a wind turbine","volume":"23","author":"Barszcz","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1016\/j.ymssp.2015.04.039","article-title":"Spectral kurtosis for fault detection, diagnosis and prognostics of rotating machines: A review with applications","volume":"66\u201367","author":"Wang","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.ymssp.2010.05.018","article-title":"A novel method for the optimal band selection for vibration signal demodulation and comparison with the Kurtogram","volume":"25","author":"Barszcz","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s10462-013-9405-z","article-title":"Extreme learning machine: Algorithm, theory and applications","volume":"44","author":"Ding","year":"2015","journal-title":"Artif. Intell. Rev."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.neunet.2014.10.001","article-title":"Trends in extreme learning machines: A review","volume":"61","author":"Huang","year":"2015","journal-title":"Neural Netw."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Rodriguez, N., Cabrera, G., Lagos, C., and Cabrera, E. (2017). Stationary Wavelet Singular Entropy and Kernel Extreme Learning for Bearing Multi-Fault Diagnosis. Entropy, 19.","DOI":"10.3390\/e19100541"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/s11063-012-9236-y","article-title":"Self-Adaptive Evolutionary Extreme Learning Machine","volume":"36","author":"Cao","year":"2012","journal-title":"Neural Process. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1109\/TEVC.2008.927706","article-title":"Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization","volume":"13","author":"Qin","year":"2009","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_23","unstructured":"Guang-Bin, H., Qin-Yu, Z., and Chee-Kheong, S. (2004, January 25\u201329). Extreme learning machine: A new learning scheme of feedforward neural networks. Proceedings of the 2004 IEEE International Joint Conference on Neural Networks, Budapest, Hungary."},{"key":"ref_24","first-page":"16","article-title":"Extreme learning machine with randomly assigned RBF kernels","volume":"11","author":"Huang","year":"2005","journal-title":"Int. J. Inf. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.neucom.2005.12.126","article-title":"Extreme learning machine: Theory and applications","volume":"70","author":"Huang","year":"2006","journal-title":"Neurocomputing"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.neucom.2012.08.010","article-title":"Weighted extreme learning machine for imbalance learning","volume":"101","author":"Zong","year":"2013","journal-title":"Neurocomputing"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/6\/1705\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:05:50Z","timestamp":1760195150000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/6\/1705"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,24]]},"references-count":26,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["s18061705"],"URL":"https:\/\/doi.org\/10.3390\/s18061705","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,24]]}}}