Diagnosing rolling-element bearing faults from vibration is a canonical physical-sensing task and a widely used benchmark for domain adaptation under operating-condition shift. Accuracies above 99 percent are commonly reported, but under evaluation splits that place the same physical bearing in both training and test. We revisit the task under a held-out-bearing protocol, assigning every bearing unit entirely to either the training or the test set, and find that source-only transfer is far weaker than such numbers suggest: on a change of shaft speed it reaches only 0.36, against a target-supervised ceiling of 0.97. We then study what governs transfer. Treating computed order tracking, a shaft-angle resampling that places fault frequencies at fixed shaft orders independent of running speed, as a controlled change of representation, we find that a Fourier Neural Operator raises source-only transfer from 0.36 to 0.61 on the speed shift, where the fault peaks move, while a convolutional network of matched feature dimension stays near chance in both representations. The representation also decides whether unsupervised alignment can work: with the same normalized RBF-MMD loss and no target labels, the operator reaches 0.71 in the frequency domain but 0.95 in the order domain, within 0.02 of the target-supervised ceiling and above 0.86 on every held-out bearing fold. Once the representation is right, a small label budget adds little. These results indicate that, for this task, the input representation rather than the alignment method decides whether adaptation helps. A second dataset, whose held-out units are fault diameters rather than bearings, shows that the same protocol exposes failures that even a target-supervised model cannot avoid.
Figures & tables
Figure 1: Overview. Raw vibration is reduced to a common envelope, expressed in either the frequency (Hz) or the order domain, classified by a Fourier Neural Operator or a convolutional network of the same feature size, and adapted across operating conditions under a held-out-bearing protocol.
Figure 2: Preprocessing. Top: each window is band-passed around the bearing resonance, demodulated to its Hilbert envelope, decimated to 2 kHz, and either kept in the Hz domain or resampled against shaft angle to the order domain. Bottom: envelope spectrum of the outer-race fault at the source and target speeds. In the Hz domain the fault peak moves with speed; after order tracking it falls at the same shaft order (near 3.05 orders for the 6203).
Model
Shift
B1 (Hz)
B1 (order)
Δ
Oracle (Hz)
Oracle (order)
FNO
speed
0.36
0.61
+0.25
0.97
0.97
FNO
torque
0.95
0.94
−0.01
0.95
0.95
FNO
load
0.93
0.93
+0.00
0.97
1.00
CNN
speed
0.38
0.43
+0.06
0.65
0.75
CNN
torque
0.81
0.91
+0.10
0.81
0.83
CNN
load
0.78
0.78
+0.00
0.78
0.69
Table 1: PU: source-only transfer (B1) and target-supervised ceiling (oracle) under the frequency (Hz) and order representations. Order tracking lifts the neural operator on the shift that moves the fault frequencies and is benign elsewhere; the convolutional network is largely unchanged. Means over nine runs (three seeds × three held-out-bearing folds); standard deviations and source-validation accuracy in Appendix 7.1 . Δ is order minus Hz.
Model
Alignment ( f=0 )
Hz
Order
FNO
none (source-only)
0.36±0.04
0.61±0.13
CORAL
0.63±0.27
0.76±0.36
DANN
0.55±0.16
0.76±0.26
MMD (linear)
0.44±0.14
0.60±0.36
MMD (RBF, normalized)
0.71±0.33
0.95±0.06
oracle
0.97±0.03
0.97±0.04
Table 2: Unsupervised alignment ( f=0 ) on the PU speed shift, mean ± standard deviation over nine runs. For the operator, every stable loss transfers better in the order domain, and normalized RBF-MMD reaches the oracle only there. For the convolutional network no loss helps in either domain. Source-only (no alignment) and oracle rows are references.
B1
Oracle
Held-out class recall (outer / inner)
Fold (held-out diameter)
Hz
Order
Hz
Order
B1 (order)
Oracle (order)
1 ( 0.007 in.)
0.52±0.06
0.91±0.10
0.87±0.20
1.00±0.00
1.00 / 0.95
1.00 / 1.00
2 ( 0.014 in.)
0.37±0.20
0.61±0.06
0.47±0.19
0.57±0.00
0.09 / 1.00
0.00 / 1.00
3 ( 0.021 in.)
0.55±0.08
0.50±0.08
0.86±0.22
0.75±0.24
0.99 / 0.01
0.98 / 0.44
Table 3: CWRU per fold (neural operator; mean ± std over three loads × three seeds). Each fold holds out one fault diameter for testing. Fold 1 is a transfer test across the load shift: the operator’s frequency-domain deficit there is confined to the inner-race class and persists at doubled bandwidth (see text). Folds 2 and 3 are unseen-geometry tests that the target-supervised oracle also fails on the held-out class. Zero standard deviations are real: on these small test folds every run makes the same predictions (Section 5 ).
Figure 3: Target accuracy against the target-label fraction f on the PU speed shift, in the order domain, with model selection on source validation only. Dashed lines are the source-only baseline (gray) and the oracle (black). For the operator, f=0.03 closes most of the gap and by f≈0.2 the stable alignment methods are indistinguishable. Error bars: one standard deviation over the nine runs.
Model
Shift
B1 (Hz)
B1 (order)
Oracle (Hz)
Oracle (order)
Src. val. (B1)
FNO
speed
0.36±0.04
0.61±0.13
0.97±0.03
0.97±0.04
1.00
FNO
torque
0.95±0.11
0.94±0.10
0.95±0.11
0.95±0.10
1.00
FNO
load
0.93±0.13
0.93±0.13
0.97±0.06
1.00±0.01
1.00
CNN
speed
0.38±0.16
0.43±0.16
0.65±0.16
0.75±0.13
1.00
CNN
torque
0.81±0.17
0.91±0.12
0.81±0.16
0.83±0.13
1.00
CNN
load
0.78±0.16
0.78±0.14
0.78±0.13
0.69±0.08
1.00
Table 4: PU source-only (B1) and oracle accuracy, mean ± standard deviation over nine runs, under both representations, with the source-validation accuracy of the source-only model.
Comparison
Mean Δ
95% interval
Wins
p
FNO source-only: order − Hz
+0.25
[+0.15,+0.33]
8/9
0.012
CNN source-only: order − Hz
+0.06
[−0.07,+0.18]
4/9
0.65
FNO order: RBF-MMD ( f=0 ) − source-only
+0.34
[+0.28,+0.40]
9/9
0.004
FNO RBF-MMD ( f=0 ): order − Hz
+0.24
[+0.05,+0.42]
4/9
0.16
FNO DANN ( f=0 ): order − Hz
+0.21
[+0.03,+0.40]
5/9
0.11
FNO CORAL ( f=0 ): order − Hz
+0.13
[−0.06,+0.33]
4/9
0.44
Table 5: Paired differences over the nine matched (fold, seed) runs of the PU speed shift. The last three rows are the duration control (Appendix 7.5 ): matching physical duration alone does not change transfer, while matching shaft revolutions recovers the order-domain result.
Configuration
Src. val.
Oracle
Source-only (B1)
CNN, best oracle (width 32, depth 5)
0.99
0.80±0.20
0.40±0.22
CNN, default (width 48, depth 4)
1.00
0.75±0.13
0.43±0.16
CNN, worst oracle (width 64, depth 4, lr 3×10−3 )
0.99
0.64±0.19
0.39±0.16
FNO (reference)
1.00
0.97±0.04
0.61±0.13
Table 6: Convolutional-network grid search, PU speed shift, order domain. Oracle and source-only (B1) accuracy, mean ± std over nine runs, with the mean source-validation accuracy of each configuration. The operator is shown for reference.
Source-only (B1)
Oracle
Ablated band (orders)
acc
outer / inner
acc
outer / inner
none
0.61
0.74 / 0.84
0.97
0.98 / 0.92
BPFO 2.90 – 3.20
0.48
0.33 / 0.87
0.96
0.89 / 1.00
2× BPFO 5.95 – 6.25
0.60
0.72 / 0.84
0.97
0.98 / 0.92
BPFI 4.80 – 5.10
0.60
0.74 / 0.83
0.94
0.98 / 0.84
2× BPFI 9.75 – 10.05
0.61
0.74 / 0.84
0.97
0.98 / 0.91
Table 7: Mode ablation on the PU speed shift (order domain, neural operator; mean over nine runs). Zeroing a fault-order band affects only its own class; control bands are inert. The outer class depends on the BPFO fundamental while the inner class survives removal of its fundamental, matching the concentrated-versus-sideband structure of the two fault types.
Assumed-rate error
−5%
−2%
−1%
0
+1%
+2%
+5%
B1 accuracy
0.34±0.10
0.35±0.04
0.51±0.14
0.61±0.12
0.62±0.11
0.62±0.10
0.62±0.11
Table 8: Sensitivity of source-only order-domain accuracy to an erroneous assumed shaft rate (PU speed shift, neural operator, mean ± std over nine runs). Negative perturbations displace every order by the stated fraction and are the faithful model of a real rate error of either sign; positive perturbations change only the sampling density and leave the orders on their bins, serving as a control.
Vibration-based health monitoring of rotating machinery requires reliable fault diagnosis under operational data constraints, yet condition assessment remains challenged by structural scarcity of fault events and heterogeneous sim-to-real gaps in digital twin-generated signals. Each fault type generates impulses with distinct periodicity, amplitude modulation, and spectral character, making feature-space discrepancies fundamentally heterogeneous across fault classes. Existing domain adaptation methods apply a class-agnostic global transformation that cannot close all fault-specific gaps without distorting inter-class separability, while uniform source-target mixing introduces distributional noise into the data-abundant Normal class. These limitations stem from treating a sequential, state-dependent alignment problem as a one-shot optimization. Each corrective transformation simultaneously reshapes all class distributions, creating state dependencies that static gradient descent cannot resolve. We formulate feature alignment as a continuous-action Markov decision process solved via Proximal Policy Optimization, where the learned policy issues fault-type-specific affine corrections responsive to the current feature-space configuration, with a dual-objective reward balancing gap minimization against separability preservation. An asymmetry-aware strategy reserves real data for the Normal class while augmenting fault classes with policy-aligned simulated samples. Validation across XJTU-SY, CWRU, and a self-built slewing bearing testbed confirms the dominant gain from reinforcement learning-driven alignment, and cross-equipment linear probing achieves 92.8% without encoder retraining, demonstrating transferable monitoring capability.
Jinghan Wang, Yanjun Chen, Wei Zhang +3
a Harbin Institute of Technology, China · b Eastern Institute of Technology, China
Bearing fault diagnosis faces critical challenges when dataset heterogeneity, operating condition variations, and limited labeled data occur simultaneously in industrial environments. Existing approaches address these issues in isolation and rely on implicit feature alignment, limiting effectiveness under concurrent challenges. This paper proposes a knowledge-guided two-stage transfer learning framework that employs a lightweight GPT-2-style Transformer with causal self-attention for hierarchical feature extraction from vibration signals, establishing explicit pathways where pre-trained encoder weights and fault prototype embeddings serve as knowledge carriers from multi-source pre-training to target adaptation. The framework addresses the dual-shift challenge through multi-source learning for generalizable representations, prototype-based knowledge modulation for target adaptation, and taxonomy-adaptive classification for seamless transfer across heterogeneous fault categories. Experimental validation on four real-world datasets demonstrates 92.61% average accuracy with only 10% labeled target data, outperforming state-of-the-art methods by 17.24 percentage points, establishing a practical pathway toward cost-effective predictive maintenance in Industry 4.0 applications.
Jinghan Wang, Feng Cheng, Wentao Wu +3
School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, China
To address the degradation of bearing fault diagnosis accuracy under strong noise, this paper proposes a time-frequency dual-domain multi-scale convolutional neural network. The time-domain branch employs three parallel convolutional kernels to capture multi-scale impulse features, while the frequency-domain branch applies the Fast Fourier Transform to extract noise-robust spectral structure information. Features from both branches are fused for fault classification, yielding a compact model of 110,122 parameters. Experiments on the CWRU bearing dataset across seven signal-to-noise ratio levels demonstrate that the proposed method achieves 99.75% accuracy under clean conditions and maintains 92.50% at -4 dB SNR, representing a 7.25 percentage-point improvement over the single-domain baseline with monotonically increasing gains under stronger noise. Ablation experiments validate the independent performance contributions of the time-domain multi-scale branch and the frequency-domain branch. Comparative experiments against WDCNN, DRSN-CW, MCNN, and 1D-LeNet confirm the superiority of the proposed method under strong noise conditions.
Yanxi Ding, Tingyue Jia
School of Engineering China University of Petroleum-Beijing at Karamay Campus Karamay, China