The vibration signals of rolling bearings usually show significant nonstationarity and low SNR, which makes it difficult to extract fault characteristics effectively by traditional methods. As a new signal analysis method, feature mode decomposition (FMD) has excellent performance in fault diagnosis, but it has the problem of artificial parameter setting. Besides, its objective function correlated kurtosis (CK) was unstable under nonstationary conditions. To solve these problems, this study proposes a two-stage parameter optimization FMD method. First, the original fault signal is denoised using complete ensemble empirical mode decomposition with adaptive noise, and its frequency domain signal-to-noise ratio is evaluated. Second, designed a slope kurtosis error ratio (SKER) index. By combining short-time kurtosis error and slope entropy, the traditional CK is replaced. Third, a two-stage parameter adaptive optimization strategy is proposed, an improved tornado optimizer with Coriolis force is used to search the optimal filter parameters globally, aiming at minimizing SKER. Meanwhile, by combining energy ratio, CK gain, and envelope harmonic ratio, a comprehensive scoring function was constructed to dynamically determine the number of modes. Finally, the envelope spectrum of each mode component is calculated to realize the fault identification of rolling bearings. The effectiveness of this method in fault diagnosis is verified by the experimental analysis of single fault signal and compound fault signal. At the same time, the superiority and robustness of this method in fault diagnosis are further proved by comparing with variational mode decomposition and FMD.
DingLJiJLiY, et al. A novel weak feature extraction method for rotating machinery: link dispersion entropy. IEEE Trans Instrum Meas2023; 72: 1–12.
2.
ZhengKLiTSuZ, et al. Sparse elitist group lasso denoising in frequency domain for bearing fault diagnosis. IEEE Trans Ind Inform2020; 17(7): 4681–4691.
3.
ZhangWChenDXiaoY, et al. Semi-supervised contrast learning based on multiscale attention and multitarget contrast learning for bearing fault diagnosis. IEEE Trans Ind Inform2023; 19(10): 10056–10068.
4.
PengJZhaoYZhangX, et al. An adaptive reweighted-Kurtogram for bearing fault diagnosis under strong external impulse noise. Struct Health Monit2024; 23(6): 3336–3351.
5.
LuanXZhongCZhaoF, et al. Bearing fault damage degree identification method based on SSA-VMD and Shannon entropy–exponential entropy decision. Struct Health Monit2024; 23(5): 3105–3133.
6.
VashishthaGChauhanSSehriM, et al. A roadmap to fault diagnosis of industrial machines via machine learning: a brief review. Measurement2025; 242: 116216.
7.
MiaoYShiHLiC, et al. Period-refined CYCBD using time synchronous averaging for the feature extraction of bearing fault under heavy noise. Struct Health Monit2024; 23(2): 1071–1088.
8.
HuoCXuWJiangQ, et al. An unsupervised transfer learning approach for rolling bearing fault diagnosis based on dual pseudo-label screening. Struct Health Monit2024; 23(4): 2288–2309.
9.
YiCTaoYTangJ, et al. Adaptive cyclic content ratiogram: a new signal decomposition method for bearing concurrent fault diagnosis. Struct Health Monit2024; 24(3): 1564–1585.
10.
DaiJSoH.Group-sparsity learning approach for bearing fault diagnosis. IEEE Trans Ind Inform2021; 18(7): 4566–4576.
11.
MiaoYHuSLiuY, et al. Angle-domain feature mode decomposition for fault diagnosis under speed-varying condition. IEEE Trans Instrum Meas2025; 74: 3506909.
12.
ChengJPanHZhengJ.Maximum Ramanujan spectrum signal-to-noise ratio deconvolution method: algorithm and applications. IEEE Trans Ind Inform2024; 20(10): 11977–11986.
13.
AntoniJ.The spectral kurtosis: a useful tool for characterising non-stationary signals. Mech Syst Signal Process2006; 20(2): 282–307.
14.
AntoniJ.Fast computation of the kurtogram for the detection of transient faults. Mech Syst Signal Process2007; 21(1): 108–124.
15.
McDonaldGZhaoQZuoM.Maximum correlated Kurtosis deconvolution and application on gear tooth chip fault detection. Mech Syst Signal Process2012; 33: 237–255.
16.
ZhangBMiaoYLinJ, et al. Adaptive maximum second-order cyclostationarity blind deconvolution and its application for locomotive bearing fault diagnosis. Mech Syst Signal Process2021; 158(12): 107736.
17.
LiHLiuTWuX, et al. A bearing fault diagnosis method based on enhanced singular value decomposition. IEEE Trans Ind Inform2020; 17(5): 3220–3230.
18.
ZhuDLiuGWuX, et al. An enhanced empirical Fourier decomposition method for bearing fault diagnosis. Struct Health Monit2024; 23(2): 903–923.
19.
ZhouPChenSHeQ, et al. Rotating machinery fault-induced vibration signal modulation effects: a review with mechanisms, extraction methods and applications for diagnosis. Mech Syst Signal Process2023; 200: 110489.
20.
XuYWangLHuA, et al. Time-extracting S-transform algorithm and its application in rolling bearing fault diagnosis. Sci China Technol Sci2022; 65(4): 932–942.
21.
HuaLWuXLiuT, et al. The methodology of modified frequency band envelope kurtosis for bearing fault diagnosis. IEEE Trans Ind Inform2022; 19(3): 2856–2865.
22.
ChengJYangYWuZ, et al. Ramanujan Fourier mode decomposition and its application in gear fault diagnosis. IEEE Trans Ind Inform2021; 18(9): 6079–6088.
23.
YanZXuYZhangK, et al. Adaptive synchroextracting transform and its application in bearing fault diagnosis. ISA Trans2023; 137: 574–589.
24.
VashishthaGChauhanSZimrozR.Fault detection of the rotating machines through optimized orthogonal matching pursuit by golden jackal optimization. Struct Health Monit2025. DOI: 10.1177/14759217251342197.
25.
SunBLiHWangC, et al. Optimized weights time-frequency analysis: a novel method for fault diagnosis in rotating machinery under time-varying speeds. Mech Syst Signal Process2025; 226: 112345.
26.
LiMLiuYWangT, et al. Adaptive synchronous demodulation transform with application to analyzing multicomponent signals for machinery fault diagnostics. Mech Syst Signal Process2023; 191: 110208.
27.
JiangWJiangHYaoR, et al. A weighted frequency domain energy operator spectral method based on soft thresholding fast iterative filtering for rolling bearing incipient fault feature extraction. Struct Health Monit2025. DOI: 10.1177/14759217241306723.
28.
WangJDuGZhuZ, et al. Fault diagnosis of rotating machines based on the EMD manifold. Mech Syst Signal Process2020; 135: 106443.
29.
GuoJLiuYLiJ, et al. Rotating machinery fault detection using a new version of intrinsic time-scale decomposition. IEEE Sens J2023; 24(2): 1905–1918.
30.
GaoZZhengJPanH, et al. Adaptive generalized empirical wavelet transform and its application to fault diagnosis of rolling bearing. Measurement2025; 249: 116958.
31.
MaPZhangHWangC.Adaptive dynamic mode decomposition and its application in rolling bearing compound fault diagnosis. Struct Health Monit2023; 22(1): 398–416.
32.
YuMGuoGFangM, et al. Intershaft bearing compound faults identification by using VMD and a new index: the activity parameter in Hjorth parameters. Nonlinear Dyn2022; 110(3): 2657–2672.
33.
WangAQinPSunX M, et al. An automatic parameter setting variational mode decomposition method for vibration signals. IEEE Trans Ind Inform2023; 20(2): 2053–2062.
34.
VashishthaGChauhanSSinghM, et al. Bearing defect identification by swarm decomposition considering permutation entropy measure and opposition-based slime mould algorithm. Measurement2021; 178: 109389.
35.
MiaoYZhangBLiC, et al. Feature mode decomposition: new decomposition theory for rotating machinery fault diagnosis. IEEE Trans Ind Electron2022; 70(2): 1949–1960.
36.
ChauhanSVashishthaGKumarR, et al. An adaptive feature mode decomposition based on a novel health indicator for bearing fault diagnosis. Measurement2024; 226: 114191.
37.
YanXJiaM.Bearing fault diagnosis via a parameter-optimized feature mode decomposition. Measurement2022; 203: 112016.
38.
YanXYanW JXuY, et al. Machinery multi-sensor fault diagnosis based on adaptive multivariate feature mode decomposition and multi-attention fusion residual convolutional neural network. Mech Syst Signal Process2023; 202: 110664.
39.
ZuoJMiaoYZhangB, et al. Cyclostationary feature mode decomposition and its application in fault diagnosis of planetary gearboxes via built-in information. IEEE Sens J2023; 24(2): 1129–1139.
40.
MengTJiangXSongQ, et al. Modified feature mode decomposition guided by spectral structure information for machinery fault diagnosis. IEEE Trans Instrum Meas2024; 73: 3525810.
41.
TorresMColominasMSchlotthauerG, et al. A complete ensemble empirical mode decomposition with adaptive noise. In: 2011 IEEE international conference on acoustics, speech and signal processing (ICASSP), Prague, Czech Republic, 22–27 May 2011, pp. 4144–4147. IEEE.
42.
ChauhanSVashishthaGKaurP.An effective approach to rotatory fault diagnosis combining CEEMDAN and feature-level integration. Algorithms2025; 18(10): 644.
43.
ChenBChengYZhangW, et al. Optimal frequency band selection using blind and targeted features for spectral coherence-based bearing diagnostics: a comparative study. ISA Trans2022; 127: 395–414.
44.
BraikMAl-HiaryHAlzoubiH, et al. Tornado optimizer with Coriolis force: a novel bio-inspired meta-heuristic algorithm for solving engineering problems. Artif Intell Rev2025; 58(4): 1–99.
45.
ChengYWangSChenB, et al. An improved envelope spectrum via candidate fault frequency optimization-gram for bearing fault diagnosis. J Sound Vib2022; 523: 116746.
46.
KennedyJEberhartR.Particle swarm optimization. In: Proceedings of ICNN’95–international conference on neural networks, Perth, WA, Australia, 27 November01 December 1995, vol. 4, pp. 1942–1948. IEEE.
47.
BaiXSongXWangZ, et al. Fault diagnosis in rotation motor bearings: novel interpretable indicator and improved snow ablation optimizer. Meas Sci Technol2025; 36(3): 036109.
48.
ZhangZLiuYHanY, et al. An adaptive slope entropy combined with hierarchical entropy applied to rolling bearing fault diagnosis. Struct Health Monit2024; 24(6): 3543–3560.
49.
ChenSXieBWangY, et al. Non-stationary harmonic summation: a novel method for rolling bearing fault diagnosis under variable speed conditions. Struct Health Monit2023; 22(3): 1554–1580.
50.
WangBLeiYLiN, et al. Multiscale convolutional attention network for predicting remaining useful life of machinery. IEEE Trans Ind Electron2020; 68(8): 7496–7504.
51.
VashishthaGChauhanSSehriM, et al. Advancing machine fault diagnosis: a detailed examination of convolutional neural networks. Meas Sci Technol2024; 36(2): 022001.
52.
GuoJWangZLiH, et al. A hybrid prognosis scheme for rolling bearings based on a novel health indicator and nonlinear Wiener process. Reliab Eng Syst Saf2024; 245: 110014.
53.
DingWLiJMaoW, et al. Rolling bearing remaining useful life prediction based on dilated causal convolutional DenseNet and an exponential model. Reliab Eng Syst Saf2023; 232: 109072.
54.
YaoDTangBYangJ, et al. Patch ModernTCN-Mixer: a dual-task temporal convolutional network framework for hybrid implementation of first prediction time detection and remaining useful life prognosis. Meas Sci Technol2024; 35(11): 116011.
55.
ZhaoCZioEShenW.Domain generalization for cross-domain fault diagnosis: an application-oriented perspective and a benchmark study. Reliab Eng Syst Saf2024; 245: 109964.
56.
WuHChengJHuN, et al. Quaternion empirical Ramanujan Fourier decomposition and its application in gear fault diagnosis. Struct Health Monit2024; 23(5): 2713–2736.
