Mechanical fault diagnosis under time-varying conditions remains challenging due to speed fluctuations that induce signal nonstationarity. To address this issue, a multiscale correntropy matrix representation method is proposed. First, aligned Fourier decomposition is introduced to decompose multivariate sensor signals into structured multiscale components with consistent frequency alignment across sensors. Then, scale-aligned and scale-varied correntropy matrices are constructed to characterize cross-sensor coupling and within-sensor nonstationarity, respectively, capturing spatial coupling and nonstationary behavior. These matrices are mapped from a Riemannian manifold to Euclidean space via matrix logarithm operations and fused into a compact feature vector for joint signal representation. The effectiveness of the method is evaluated on bearing and gearbox datasets under time-varying and constant speed conditions. The results of comparative and ablation experiments demonstrate that the proposed approach achieves superior performance and practicality compared to existing methods.
ChenZDuanZQianH-M, et al. Unified health domain relation learning for train transmission systems fault detection under varying operating conditions. Struct Health Monit2026.
2.
JiangWWuJYangY, et al. Health evaluation techniques towards rotating machinery: a systematic literature review and implementation guideline. Reliab Eng Syst Safe2025; 260: 110924.
3.
ZhangZLiuYHanY, et al. An adaptive slope entropy combined with hierarchical entropy applied to rolling bearing fault diagnosis. Struct Health Monit2025; 24: 3543–3560.
4.
LvYLiuYLiS, et al. Enhancing marine shaft generator reliability through intelligent fault diagnosis of gearbox bearings via improved Bidirectional LSTM. Ocean Eng2025; 337: 121860.
5.
GuoJHeQGuF. DNOCNet: a novel end-to-end network for induction motor drive systems fault diagnosis under speed fluctuation condition. IEEE Trans Ind Inform2024; 20: 8284–8293.
6.
HeCShiHLiR, et al. Interpretable modulated differentiable STFT and physics-informed balanced spectrum metric for freight train wheelset bearing cross-machine transfer fault diagnosis under speed fluctuations. Adv Eng Inform2024; 62: 102568.
7.
SongCChengWChenX, et al. Identification and separation of coupled vibration sources in multi-rotor gas turbines under time-varying speed conditions. Mech Syst Signal Process2023; 188: 110037.
8.
WangJPengYQiaoW. Current-aided order tracking of vibration signals for bearing fault diagnosis of direct-drive wind turbines. IEEE Trans Ind Electron2016; 63(10): 6336–6346.
9.
SchmidtSHeynsPSde VilliersJP. A tacholess order tracking methodology based on a probabilistic approach to incorporate angular acceleration information into the maxima tracking process. Mech Syst Signal Process2018; 100: 630–646.
10.
SuYSunR-BChenH, et al. Broadening the application of angle-time cyclostationary analysis in bearing fault diagnosis using precise speed reconstruction. J Vib Control2026; 32: 702–715.
11.
ZhangMLiuYLiB, et al. Advanced self-tuning vibration modeling strategy for rotating machinery fault diagnosis. Mech Syst Signal Process2025; 241: 113498.
12.
PengLLiuFSunY, et al. Kurtosis-based spectral index-guided adaptive speed estimation for bearing fault diagnosis under nonstationary conditions. IEEE Trans Instrum Meas2025; 74: 1–11.
13.
TaoWSunZYangZ, et al. Transformer fault diagnosis technology based on AdaBoost enhanced transferred convolutional neural network. Expert Syst Appl2025; 264: 125972.
14.
YangCLiHCaoS, et al. CE-FFGAN: a feature fusion generative adversarial network with deep embedded category information for limited sample fault diagnosis of rotating machinery under speed variation. Adv Eng Inform2024; 62: 102605.
15.
ZhangJZhangMWangD, et al. Multi-scale convolutional sparse attention transformer: a lightweight fault diagnosis model for rotating machinery. Neurocomputing2025; 650: 130934.
16.
LinLZhangSFuS, et al. FD-LLM: large language model for fault diagnosis of complex equipment. Adv Eng Inform2025; 65: 103208.
17.
PengLLiuFLvZ, et al. Phoneme-inspired acoustic frame embedded lightweight transformer for rolling bearing fault diagnosis. Mech Syst Signal Process2026; 248: 114030.
18.
LiangPWangBJiangG, et al. Unsupervised fault diagnosis of wind turbine bearing via a deep residual deformable convolution network based on subdomain adaptation under time-varying speeds. Eng Appl Artif Intell2023; 118: 105656.
19.
ChenJChenJChenZ, et al. Hybrid augmented network with balance domain window for few-shot fault diagnosis under sharp speed variation. Mech Syst Signal Process2024; 207: 110944.
20.
DongYJiangHYaoR, et al. Rolling bearing intelligent fault diagnosis towards variable speed and imbalanced samples using multiscale dynamic supervised contrast learning. Reliab Eng Syst Saf2024; 243: 109805.
21.
ShaoHGaoYQuH, et al. A novel method for variable-speed mechanical fault diagnosis using sparse threshold graph and adaptive loss weighting. Adv Eng Inform2025; 67: 103588.
22.
QinYZhaoLChenY, et al. Learnable wavelet-driven physically interpretable networks for bearing fault diagnosis under variable speed. Mech Syst Signal Process2025; 237: 113121.
23.
LiYWangTXieJ, et al. A temporal cross-contrastive self-supervised learning framework for high-speed train bearing fault diagnosis: addressing limited labeling and speed variability. Eng Appl Artif Intell2025; 158: 111537.
24.
KimSLeeSLeeJ, et al. Multi-scale signal transformer with signal processing-based attention interpretation for fault diagnosis of rotating machinery under variable speed conditions. Reliab Eng Syst Saf2026; 271: 112243.
25.
WangCXuMLiY, et al. A novel two-stage fault diagnosis method with frequency-aware graph contrastive learning and multi-scale recursive graph networks for rotating machinery. Adv Eng Inform2026; 70: 104196.
26.
HanYJiaRCaiH, et al. Topological incremental fast Fourier transform on time–frequency domain feature extraction for equipment fault diagnosis. Chaos Soliton Fract2025; 199: 116761.
27.
LinTRenZZhuL, et al. A systematic review of multi-sensor information fusion for equipment fault diagnosis. IEEE Trans Instrum Meas2025; 74: 3507848.
28.
DengQZhangZTuX, et al. FDFNet: feature-decision dual fusion network for intelligent fault diagnosis of rotating machinery under varying speed conditions. Eng Appl Artif Intell2025; 162: 112423.
29.
SinghPJoshiSDPatneyRK, et al. The Fourier decomposition method for nonlinear and non-stationary time series analysis. Proc Math Phys Eng Sci2017; 473(2199): 20160871.
30.
FengZWuQYangS. Temporal local correntropy representation for fault diagnosis of machines. IEEE Trans Ind Inform2023; 19(12): 11868–11877.
31.
LiXZhongXShaoH, et al. Multisensor gearbox fault diagnosis by using feature-fusion covariance matrix and multi-Riemannian kernel ridge regression. Reliab Eng Syst Saf2021; 216: 108018.
32.
HeDZhangZJinZ, et al. RTSMFFDE-HKRR: a fault diagnosis method for train bearing in noise environment. Measurement2025; 239: 115417.
33.
JungWKimSYunS, et al. Vibration, acoustic, temperature, and motor current dataset of rotating machine under varying operating conditions for fault diagnosis. Data Brief2023; 48: 109049.
34.
KumarHSUpadhyayaG. Fault diagnosis of rolling element bearing using continuous wavelet transform and K- nearest neighbour. Mater Today Proc2023; 92: 56–60.
35.
RenY. Fault diagnosis of a gearbox under varying speed based on STFT and SVM. In: WangYYuTWangK (eds), Advanced manufacturing and automation XIII. Singapore: Springer Nature Singapore, 2024, pp. 736–744.
36.
HeCShiHSiJ, et al. Physics-informed interpretable wavelet weight initialization and balanced dynamic adaptive threshold for intelligent fault diagnosis of rolling bearings. J Manuf Syst2023; 70: 579–592.
37.
YanSShaoHWangJ, et al. LiConvFormer: a lightweight fault diagnosis framework using separable multiscale convolution and broadcast self-attention. Expert Syst Appl2024; 237: 121338.
38.
YangLWanJJiangG, et al. WCamba: lightweight fault diagnosis for aero-engine via wide-kernel convolution and state space modeling. Results Eng2025; 26: 107202.
39.
NguyenD-TNguyenV-Q-VTranT-T, et al. MLFork: bearing fault diagnosis via Mamba-powered few-shot learning model with multi-level architecture enhanced by spatial-wise and channel-wise local vector attention. Neurocomputing2025; 656: 131518.
40.
NguyenV-QTranT-TVuM-H, et al. Multiple local-global correlation-based deep neural network with selective kernel attention for bearing fault diagnosis. Cogn Comput2025; 17: 147.
41.
TruongG-BTranT-TThanN-L, et al. SC-MambaFew: few-shot learning based on Mamba and selective spatial-channel attention for bearing fault diagnosis. Comput Electr Eng2025; 123: 110004.
42.
JérômeG. Empirical wavelet transform. IEEE Trans Signal Process2013; 61(16): 3999–4010.
43.
ZhouWFengZXuYF, et al. Empirical Fourier decomposition: an accurate signal decomposition method for nonlinear and non-stationary time series analysis. Mech Syst Signal Process2022; 163: 108155.
44.
LiHLiZMoW. A time varying filter approach for empirical mode decomposition. Signal Process2017; 138: 146–158.
45.
DragomiretskiyKZossoD. Variational mode decomposition. IEEE Trans Signal Process2014; 62(3): 531–544.
46.
DuPLiFShaoJ. Multi-agent reinforcement learning clustering algorithm based on silhouette coefficient. Neurocomputing2024; 596: 127901.
