**6. Conclusions**

In this paper, a fault feature extraction of the rolling bearing signal under strong noise background is studied by using the combination of VMD optimized with information entropy and RobustICA. The conclusions were as follows.

(1) Although VMD can analyze the signal in the frequency domain, the effect is limited by the impact of modal component *k* and penalty factor *α*. This study used information entropy to optimize VMD to set initialization parameters. Compared with the way of setting parameters by experience, this method can search for a better combination of VMD parameters. This method can overcome the problems of modal aliasing and endpoint effect caused by impact component and noise interference in traditional EMD, LMD and EEMD, and has a good processing effect on the extraction of fault characteristic frequency of nonstationary and nonlinear signals. It can extract fault features more accurately. Compared with the traditional method, the experimental results show that this method can highlight the fault characteristic frequency and distinguish the fault.

(2) In this experiment, a typical simulation signal model is selected and Gaussian white noise is added on this basis to simulate the periodic impact signal caused by bearing fault under the condition of noise interference. Then, a signal component screening criterion based on correlation coefficient and kurtosis is established, and the optimal signal component is used to construct the observation signal channel of RobustICAalgorithm, so as to achieve the purpose of noise reduction.Through the in-depth analysis of the constructed simulation signal and the collected signal of the actual rolling bearing, it can be seen that compared with the traditional methods based on LMD–RobustICA, EMD–RobustICA, and EEMD–RobustICA, the method proposed in this paper can obtain better evaluation results of noise-reduction index, and the time–domain waveform of the signal after noise reduction is very similar to the waveform of the original signal.

(3) By comparing and analyzing the envelope demodulation results obtained by different methods, it can be seen that after the envelope spectrum analysis using the method proposed in this paper, the amplitude of fault characteristic frequency has been enhanced, and the surrounding interference will not affect the identification of fault fundamental frequency and frequency doubling, which is more convenient for fault diagnosis and analysis.

As an effective adaptive signal processing method, VMD has achieved good results in the field of fault diagnosis. However, the relevant parameters of this method need to be set in advance. In the process of parameter optimization, there is no theoretical basis for the definition of parameter search range. Therefore, in the next work, we will conduct in-depth research and further improve the parameter optimization method of VMD method.

**Author Contributions:** Conceptualization, J.Y.; Data curation, J.Y. and C.Z.; Formal analysis, C.Z. and X.L.; Funding acquisition, J.Y.; Methodology, J.Y.; Resources, J.Y.; Writing—original draft, J.Y.; Writing—review and editing, J.Y., C.Z., and X.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the Scientific research fund project of Baoshan University (Grant No. ZKMS202101), Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities' Association (Grant No. 202001BA070001-109), collaborative education project of industry university cooperation of the Ministry of Education (Grant No. 202102049026), 10th batches of Baoshan young and middle-aged leaders training project in academic and technical (Grant No. 202109), and the Ph.D. research startup foundation of Yunnan Normal University (Grant No.01000205020503131).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request.

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