**4. Conclusions**

In this paper, a bearing fault detection method, based on a Resnet classifier with model-based data augmentation, is proposed. For our purpose, a four-DOFs dynamic model is constructed to describe the bearing system. The dynamic model was identified by comparing the simulation and experimental results. Then, a large number of data under different conditions could then be generated, based on which the training dataset was constructed, and the Resnet classifier was trained for the bearing state classification. Furthermore, to reduce the gap between the simulation data and the real data, the envelop signals were applied in the training process rather than the original signals. The proposed

method was testified by the real data from the Bearing Data Center of Case Western Reserve University. The trained Resnet classifier was able to identify the bearing states with 100% accuracy. The framework of the proposed method, based on data augmentation, which combines the theoretical model with the deep learning method, can be further used in other fields which have the deterministic model.

**Author Contributions:** For research articles with several authors, Conceptualization, L.Q. and X.Z.; methodology, L.Q. and Q.P.; software, Y.L.; validation, L.Q., Y.L. and X.Z.; formal analysis, Q.P.; investigation, L.Q.; resources, Y.L.; data curation, L.Q.; writing—original draft preparation, L.Q.; writing—review and editing, Y.L.; visualization, Q.P.; supervision, Y.L.; project administration, X.Z.; funding acquisition, X.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by [National Natural Science Foundation of China under Grant] gran<sup>t</sup> number [51905184, 72101194], [Open Research Fund of State Key Laboratory of High Performance Complex Manufacturing, Central South University] gran<sup>t</sup> number [Kfkt2020-12], [Humanities and Social Science Foundation of Ministry of Education of China] gran<sup>t</sup> number [20YJC630096].

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
