Fault Diagnosis of Outer Race of Rolling Bearings Based on Optimized VMD-CYCBD Method Under Variable Speed Conditions

Zhang, Xudong; Shi, Mengmeng; Song, Dongchen; Li, Hongyu; Li, Yanbin; Zhang, Dahai

doi:10.3390/aerospace13030219

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Open AccessArticle

Fault Diagnosis of Outer Race of Rolling Bearings Based on Optimized VMD-CYCBD Method Under Variable Speed Conditions

by

Xudong Zhang

^1,2,

Mengmeng Shi

¹,

Dongchen Song

¹,

Hongyu Li

¹,

Yanbin Li

¹ and

Dahai Zhang

^1,*

¹

School of Mechanical Engineering, Southeast University, Nanjing 211189, China

²

National Key Laboratory of Aerospace Flight Technology, Beijing 100074, China

^*

Author to whom correspondence should be addressed.

Aerospace 2026, 13(3), 219; https://doi.org/10.3390/aerospace13030219

Submission received: 29 December 2025 / Revised: 14 February 2026 / Accepted: 16 February 2026 / Published: 27 February 2026

(This article belongs to the Section Aeronautics)

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Abstract

This paper addresses the challenge of extracting weak early fault signals from rolling bearings under variable speed conditions, where strong background noise often obscures diagnostic features. We propose a novel fault diagnosis method that integrates variational mode decomposition (VMD) and maximum second-order cyclo-stationarity blind deconvolution (CYCBD). The proposed approach begins by converting non-stationary vibration signals into angular-domain stationary signals using computed order tracking (COT). Subsequently, the parameters of the VMD algorithm are optimized via the sine–cosine and Cauchy mutation sparrow search algorithm (SCSSA) to select the optimal modal components. A key contribution is the introduction of a composite index (CI), combining harmonic significance and the envelope spectrum crest factor, which serves as the fitness function for the SCSSA to optimize the critical parameters of CYCBD for enhanced feature enhancement. Finally, fault characteristics are extracted by analyzing the deconvolved signal with an order envelope spectrum. Both simulation and experimental results demonstrate the superior capability of the proposed VMD-CYCBD method in effectively identifying weak fault features submerged in strong noise under variable speed conditions.

Keywords: rolling element bearing; early weak fault; variable speed condition; variational mode decomposition; maximum second-order cyclo-stationarity blind deconvolution

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MDPI and ACS Style

Zhang, X.; Shi, M.; Song, D.; Li, H.; Li, Y.; Zhang, D. Fault Diagnosis of Outer Race of Rolling Bearings Based on Optimized VMD-CYCBD Method Under Variable Speed Conditions. Aerospace 2026, 13, 219. https://doi.org/10.3390/aerospace13030219

AMA Style

Zhang X, Shi M, Song D, Li H, Li Y, Zhang D. Fault Diagnosis of Outer Race of Rolling Bearings Based on Optimized VMD-CYCBD Method Under Variable Speed Conditions. Aerospace. 2026; 13(3):219. https://doi.org/10.3390/aerospace13030219

Chicago/Turabian Style

Zhang, Xudong, Mengmeng Shi, Dongchen Song, Hongyu Li, Yanbin Li, and Dahai Zhang. 2026. "Fault Diagnosis of Outer Race of Rolling Bearings Based on Optimized VMD-CYCBD Method Under Variable Speed Conditions" Aerospace 13, no. 3: 219. https://doi.org/10.3390/aerospace13030219

APA Style

Zhang, X., Shi, M., Song, D., Li, H., Li, Y., & Zhang, D. (2026). Fault Diagnosis of Outer Race of Rolling Bearings Based on Optimized VMD-CYCBD Method Under Variable Speed Conditions. Aerospace, 13(3), 219. https://doi.org/10.3390/aerospace13030219

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Fault Diagnosis of Outer Race of Rolling Bearings Based on Optimized VMD-CYCBD Method Under Variable Speed Conditions

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