Vibration Signal Generation for Straddle-Monorail Train Gearboxes Using a Physics-Conditioned VQ-VAE Model

Table 1. Hyperparameter Configuration for PC-VQVAE Model Training

Parameter Category	Hyperparameter	Value	Rationale
Optimization Parameters	Optimizer	Adam	A standard adaptive learning rate optimization algorithm, widely used for training deep neural networks.
Optimization Parameters	Learning Rate	2e-04	A common initial learning rate for the Adam optimizer, selected to accelerate convergence during the initial phase of training.
Optimization Parameters	Batch Size	128	A larger batch size helps provide a more stable gradient estimation and fully utilizes the parallel computing capabilities of modern GPUs.
Optimization Parameters	Training Epochs	200	A sufficient number of epochs ensures that the model can fully learn and converge under complex physical constraints.
Data Signal Parameters	Sequence Length	2048	Balances the capture of key fault features with the control of computational resource consumption, allowing for larger batch sizes.
Data Signal Parameters	Sampling Rate	25.6 kHz / 10.24 kHz	Matches typical industrial sensor specifications and satisfies the Nyquist theorem to capture the high-frequency vibration components of the gearbox.
Model Architecture	Encoder Hidden Channels	128	Ensures sufficient feature extraction capability while avoiding excessive computational overhead.
Model Architecture	Codebook Size	512	A moderately sized codebook, capable of capturing diverse signal primitives while mitigating the risk of codebook collapse.
Model Architecture	Embedding Dimension	64	Balances the representational power of the latent vectors with the overall complexity of the model.
Loss Function	Commitment Loss Weight	0.25	Controls the influence of the encoder output on codebook updates, preventing drastic fluctuations in the codebook vectors.
Loss Function	Physical Consistency Loss Weight	0.1	As shown in Eq. (23), used to balance the data-driven reconstruction term with the physics-based regularization term.

Table 2. Details on the selection of SEU-GB, SQ bearing dataset, CWRU dataset, XJTU-SY bearing dataset, and DGLC dataset.

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Dataset Selection Strategy (Stratified Sampling)

The datasets were selected using a stratified sampling strategy to ensure representativeness across two key dimensions:

1. Fault Modes
2. Operating Conditions (Speed/Load)

This selection is not random. Instead, it is designed to verify that the proposed model remains robust across the entire operational envelope, rather than overfitting to a single condition.

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Table I (Ablation Study)

Selected Datasets

• Dataset 39: Normal State (1500 rpm, medium load)
• Dataset 81: Assembly Error (1500 rpm, medium load)
• Dataset 202: Inner Ring Failure (2000 rpm, high speed)
• Dataset 308: Fatigue Wear / Spalling (500 rpm, low speed)

Rationale

As detailed in the Supplementary Material (DGLC Dataset Details), these four datasets strictly correspond to the four distinct gearbox health states. This design ensures that the ablation study validates the contribution of physical modules (e.g., dual-path injection) across all major failure mechanisms, covering both high-speed and low-speed dynamics.

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Table II (Comparative Analysis)

Selected Datasets

• Dataset 48: Normal State (1000 rpm)
• Dataset 99: Assembly Error (2000 rpm)
• Dataset 202: Inner Ring Failure (2000 rpm, high speed)
• Dataset 320: Fatigue Wear (1000 rpm)

Rationale

We intentionally selected different datasets (with different speed/load combinations compared to Table I) for the comparative evaluation. For example:

• Dataset 99 represents a high-speed assembly error
• Dataset 320 represents a medium-speed fatigue-wear fault

This design demonstrates that PC-VQVAE consistently outperforms baseline models (GANs/Diffusion) under variable operating conditions, ensuring the comparison is fair and not biased toward specific easy-to-learn samples.

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Table IV (CWRU Bearing Dataset)

Selected Datasets

• Dataset 97
• Dataset 98
• Dataset 99
• Dataset 100

Rationale

In the public CWRU bearing dataset, these file IDs correspond to the standard “Normal Baseline” recordings under four different motor loads:

• 0 hp, 1 hp, 2 hp, and 3 hp

Selecting these specific files is a standard practice in the fault diagnosis literature, enabling direct and fair benchmarking against state-of-the-art methods that adopt the same standard split.

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Dataset	Field	Value
SEU-GB	Condition	Chipped tooth, Missing tooth, Root fault, Surface fault, Health working state
SEU-GB	RF-Load	20 Hz–0 V / 30 Hz–2 V

Dataset	SF (kHz)	RF (Hz)	Classes
SQ	25.6	9, 19, 29, 39	Inner_1 → Inner_3, Outer_1 → Outer_3, Normal
Dataset	SF (kHz)	Operating point	Theoretical rpm
---------------	--------	---------------	---------------
XJTU-SY Bearing	25.6	35 Hz 12 kN	2100
XJTU-SY Bearing	25.6	37.5 Hz 11 kN	2250
XJTU-SY Bearing	25.6	40 Hz 10 kN	2400

Dataset	SF (kHz)	File/ID	Motor speed (rpm)
CWRU	12/48	97	1797
CWRU	12/48	98	1772
CWRU	12/48	99	1750
CWRU	12/48	100	1730

Dataset	Condition	Number	Theoretical rpm	Actual rpm	Load (N·m)
DGLC	Normal	39	1500	1468	668
DGLC	Normal	48	1000	973	1002
DGLC	Normal	60	1418	1380	707
DGLC	Assembly Error	81	1500	1460	501
DGLC	Assembly Error	99	2000	variable	504
DGLC	Assembly Error	108	500	variable	1480
DGLC	Inner Ring Failure	202	2000	1945	375
DGLC	Inner Ring Failure	216	1000	974	501
DGLC	Inner Ring Failure	236	1500	variable	none
DGLC	Fatigue Wear	308	500	500	334
DGLC	Fatigue Wear	320	1000	1000	848
DGLC	Fatigue Wear	336	800	800	variable