{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T22:13:40Z","timestamp":1773180820819,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,19]],"date-time":"2022-04-19T00:00:00Z","timestamp":1650326400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51565055"],"award-info":[{"award-number":["51565055"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the key research and development projects of Xinjiang Uygur Autonomous Region","award":["2020B02014"],"award-info":[{"award-number":["2020B02014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>To satisfy the requirements of the end-to-end fault diagnosis of rolling bearings, a hybrid model, based on optimal SWD and 1D-CNN, with the layer of multi-sensor data fusion, is proposed in this paper. Firstly, the BAS optimal algorithm is adopted to obtain the optimal parameters of SWD. After that, the raw signals from different channels of sensors are segmented and preprocessed by the optimal SWD, whose name is BAS-SWD. By which, the sensitive OCs with higher values of spectrum kurtosis are extracted from the raw signals. Subsequently, the improved 1D-CNN model based on VGG-16 is constructed, and the decomposed signals from different channels are fed into the independent convolutional blocks in the model; then, the features extracted from the input signals are fused in the fusion layer. Finally, the fused features are processed by the fully connected layers, and the probability of classification is calculated by the cross-entropy loss function. The result of comparative experiments, based on different datasets, indicates that the proposed model is accurate, effective, and has a good generalization ability.<\/jats:p>","DOI":"10.3390\/e24050573","type":"journal-article","created":{"date-parts":[[2022,4,19]],"date-time":"2022-04-19T22:07:26Z","timestamp":1650406046000},"page":"573","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Rolling Bearing Fault Diagnosis Using Multi-Sensor Data Fusion Based on 1D-CNN Model"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8598-2343","authenticated-orcid":false,"given":"Hongwei","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Xinjiang University, Urumqi 830047, China"}]},{"given":"Wenlei","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xinjiang University, Urumqi 830047, China"}]},{"given":"Li","family":"He","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xinjiang University, Urumqi 830047, China"}]},{"given":"Jianxing","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xinjiang University, Urumqi 830047, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ma, J., Li, Z., Li, C., Zhan, L., and Zhang, G. (2021). Rolling Bearing Fault Diagnosis Based on Refined Composite Multi-Scale Approximate Entropy and Optimized Probabilistic Neural Network. Entropy, 23.","DOI":"10.3390\/e23020259"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Yan, X., Xu, Y., She, D., and Zhang, W. (2022). Reliable Fault Diagnosis of Bearings Using an Optimized Stacked Variational Denoising Auto-Encoder. Entropy, 24.","DOI":"10.3390\/e24010036"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Luo, S., Yang, W., and Luo, Y. (2020). Fault Diagnosis of a Rolling Bearing Based on Adaptive Sparest Narrow-Band Decomposition and Refined Composite Multiscale Dispersion Entropy. Entropy, 22.","DOI":"10.3390\/e22040375"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TIM.2022.3216413","article-title":"Intelligent Fault Diagnosis Method for Gear Transmission Systems Based on Improved Multi-Scale Reverse Dispersion Entropy and Swarm Decomposition","volume":"71","author":"Wang","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.measurement.2017.08.036","article-title":"Early Fault Diagnosis of Bearing and Stator Faults of the Single-Phase Induction Motor Using Acoustic Signals","volume":"113","author":"Glowacz","year":"2018","journal-title":"Measurement"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Pang, B., Nazari, M., and Tang, G. (2022). Recursive Variational Mode Extraction and Its Application in Rolling Bearing Fault Diagnosis. Mech. Syst. Signal Process., 165.","DOI":"10.1016\/j.ymssp.2021.108321"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. Math. Phys. Eng. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S1793536909000047","article-title":"Ensemble empirical mode decomposition: A noise-assisted data analysis method","volume":"1","author":"Wu","year":"2009","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1142\/S1793536910000422","article-title":"Complementary Ensemble Empirical Mode Decomposition: A Novel Noise Enhanced Data Analysis Method","volume":"2","author":"Yeh","year":"2010","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1016\/j.measurement.2015.03.003","article-title":"A Novel Sensor Fault Diagnosis Method Based on Modified Ensemble Empirical Mode Decomposition and Probabilistic Neural Network","volume":"68","author":"Yu","year":"2015","journal-title":"Measurement"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Torres, M.E., Colominas, M.A., Schlotthauer, G., and Flandrin, P. (2011, January 22\u201327). A Complete Ensemble Empirical Mode Decomposition with Adaptive Noise. Proceedings of the 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic.","DOI":"10.1109\/ICASSP.2011.5947265"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.bspc.2014.06.009","article-title":"Improved Complete Ensemble EMD: A Suitable Tool for Biomedical Signal Processing","volume":"14","author":"Colominas","year":"2014","journal-title":"Biomed. Signal Process. Control"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational Mode Decomposition","volume":"32","author":"Dragomiretskiy","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.ymssp.2017.11.029","article-title":"A Parameter-adaptive VMD Method Based on Grasshopper Optimization Algorithm to Analyze Vibration Signals from Rotating Machinery","volume":"108","author":"Zhang","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.sigpro.2016.09.004","article-title":"Swarm Decomposition: A Novel Signal Analysis Using Swarm Intelligence","volume":"132","author":"Georgios","year":"2017","journal-title":"Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1016\/j.ymssp.2018.12.034","article-title":"Optimal Swarm Decomposition with Whale Optimization Algorithm for Weak Feature Extraction from Multicomponent Modulation Signal","volume":"122","author":"Miao","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1312","DOI":"10.1016\/j.renene.2020.04.041","article-title":"Mahalanobis Semi-Supervised Mapping and Beetle Antennae Search Based Support Vector Machine for Wind Turbine Rolling Bearings Fault Diagnosis","volume":"155","author":"Wang","year":"2020","journal-title":"Renew. Energy"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TIM.2021.3127641","article-title":"A New Interpretable Learning Method for Fault Diagnosis of Rolling Bearings","volume":"70","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Qin, X., Xu, D., Dong, X., Cui, X., and Zhang, S. (2021). The Fault Diagnosis of Rolling Bearing Based on Improved Deep Forest. Shock. Vib., 2021.","DOI":"10.1155\/2021\/9933137"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"87529","DOI":"10.1109\/ACCESS.2020.2992935","article-title":"Adaptive Multiscale Weighted Permutation Entropy for Rolling Bearing Fault Diagnosis","volume":"8","author":"Huo","year":"2020","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"31078","DOI":"10.1109\/ACCESS.2021.3059761","article-title":"Rolling Bearing Fault Diagnosis Based on One-Dimensional Dilated Convolution Network with Residual Connection","volume":"9","author":"Liang","year":"2021","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1007\/s11063-019-10137-2","article-title":"Intelligent Fault Diagnosis of Rolling Bearing Using Adaptive Deep Gated Recurrent Unit","volume":"51","author":"Zhao","year":"2020","journal-title":"Neural Process. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Hou, M., Pi, D., and Li, B. (2020). Similarity-Based Deep Learning Approach for Remaining Useful Life Prediction. Measurement, 159.","DOI":"10.1016\/j.measurement.2020.107788"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Xu, Y., Li, Z., Wang, S., Li, W., Sarkodie-Gyan, T., and Feng, S. (2021). A Hybrid Deep-Learning Model for Fault Diagnosis of Rolling Bearings. Measurement, 169.","DOI":"10.1016\/j.measurement.2020.108502"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Hao, S., Ge, F., and Li, Y. (2020). Multisensor Bearing Fault Diagnosis Based on One-Dimensional Convolutional Long Short-Term Memory Networks. Measurement, 159.","DOI":"10.1016\/j.measurement.2020.107802"},{"key":"ref_26","first-page":"1","article-title":"Fault Diagnosis of High-Speed Train Bogie Based on the Improved-CEEMDAN and 1-D CNN Algorithms","volume":"70","author":"Huang","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Xue, F., Zhang, W., Xue, F., Li, D., Xie, S., and Fleischer, J. (2021). A Novel Intelligent Fault Diagnosis Method of Rolling Bearing Based on Two-Stream Feature Fusion Convolutional Neural Network. Measurement, 176.","DOI":"10.1016\/j.measurement.2021.109226"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1109\/TII.2020.2979467","article-title":"Multidimensional Feature Fusion and Ensemble Learning-Based Fault Diagnosis for the Braking System of Heavy-Haul Train","volume":"17","author":"Liu","year":"2021","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Shang, Z., Li, W., Gao, M., Liu, X., and Yu, Y. (2021). An Intelligent Fault Diagnosis Method of Multi-Scale Deep Feature Fusion Based on Information Entropy. Chin. J. Mech. Eng., 34.","DOI":"10.1186\/s10033-021-00580-5"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.comcom.2021.04.016","article-title":"Multi-Feature Fusion for Fault Diagnosis of Rotating Machinery Based on Convolutional Neural Network","volume":"173","author":"Liu","year":"2021","journal-title":"Comput. Commun."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TIM.2021.3123218","article-title":"Novel Three-Stage Feature Fusion Method of Multimodal Data for Bearing Fault Diagnosis","volume":"70","author":"Wang","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Pan, L., Zhao, L., Song, A., She, S., and Wang, S. (2021). Research on Gear Fault Diagnosis Based on Feature Fusion Optimization and Improved Two Hidden Layer Extreme Learning Machine. Measurement, 177.","DOI":"10.1016\/j.measurement.2021.109317"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Wu, T., Zhuang, Y., Fan, B., Guo, H., Fan, W., Yi, C., and Xu, K. (2021). Multi Domain Feature Fusion for Varying Speed Bearing Diagnosis Using Broad Learning System. Shock. Vib., 2021.","DOI":"10.1155\/2021\/6627305"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Wang, X., Mao, D., and Li, X. (2021). Bearing Fault Diagnosis Based on Vibro-Acoustic Data Fusion and 1D-CNN Network. Measurement, 173.","DOI":"10.1016\/j.measurement.2020.108518"},{"key":"ref_35","first-page":"1","article-title":"BAS: Beetle Antennae Search Algorithm for Optimization Problems","volume":"1","author":"Jiang","year":"2017","journal-title":"Int. J. Robot. Control"},{"key":"ref_36","unstructured":"Simonyan, K., and Zisserman, A. (2014). Very Deep Convolutional Networks for Large-Scale Image Recognition. arXiv."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/5\/573\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:56:35Z","timestamp":1760136995000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/5\/573"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,19]]},"references-count":36,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["e24050573"],"URL":"https:\/\/doi.org\/10.3390\/e24050573","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,19]]}}}