First-author paper · Interactive deep dive

Reading machine health from vibration.

Rotating machinery usually fails at its bearings, and the vibration signal carries the warning. The paper compares deep-learning approaches for telling bearing faults apart when the machine’s load and speed keep changing, then asks how the best models behave under heavy noise and what they would cost to deploy.

Each chapter lets you explore one step of the study. Every number comes from the published paper, and anything illustrative is labelled as such.

Read the paperdoi:10.1038/s41598-026-42592-y

Venue: Scientific Reports · Nature Portfolio
Published: 11 April 2026 · Vol. 16, Art. 16892
Role: First author
Status: Published, peer-reviewed

Authors: Pratyush Vishal, Rohith Nair, Jonathan Jacob, Narendiranath Babu T., M. Pandiyan

01The rig

45 ways for a bearing to run.

Defects were cut into deep-groove ball bearings with a diamond-tipped tool, then each bearing was run at three speeds and three loads while an accelerometer recorded vibration at 12.8 kHz. Five health states × three speeds × three loads gives 45 recorded conditions. Pick one.

Operating conditions

Condition 14 of 45

Select a recorded condition: health state, speed and load
	1000 rpm			1500 rpm			2000 rpm
	0 g	6 g	12 g	0 g	6 g	12 g	0 g	6 g	12 g
HB
IRF
ORF
BF
CF

Every combination was recorded as its own file of roughly 420,000 samples at 12,800 Hz (about 33 s of vibration), more than 18.9 million points in all.

IRF · 1500 rpm · 6 g

Inner race fault

Seeded defect: 1.5 mm span, 1.2 mm wide, 0.5 mm deep
Shaft speed: 1500 rpm = 25.00 Hz
Load: Light (6 g)
Expected signature: Inner race (BPFI): 123.8 Hz

Frequencies are the theoretical values from the paper’s Table 3 factors × shaft speed. The paper confirms envelope-spectrum peaks close to them in the recorded data.

Setup from Tables 1–2 and the dataset description

02The physics

Each defect has a frequency, and it moves with speed.

A defect on the outer race, the inner race or a ball is struck at a characteristic rate set by the bearing’s geometry and the shaft speed. That is why variable speed makes diagnosis hard: the signature the model needs to find never sits still.

Fault frequencies vs speed

1500 rpm · 25.00 Hz shaft

Shaft speed1500 rpm

Bearing condition

Linear frequency axisspacing stretches

Logarithmic (constant-Q) axisshape is preserved

Drag the speed. On the linear axis the comb of harmonics stretches and its spacing changes, so a model that memorised fixed frequencies would have to relearn every speed. On the logarithmic axis the same comb keeps its shape and only slides, because a change of speed multiplies every frequency by the same ratio. That is one intuition for why a constant-Q representation, whose bins are spaced geometrically, suits variable-speed data. Faint ticks show the 1500 rpm pattern for comparison.

Show data table

Theoretical fault frequencies at 1500 rpm
Family	1×	2×	3×	4×
Outer race (BPFO)	76.3 Hz	152.5 Hz	228.7 Hz	305.0 Hz
Inner race (BPFI)	123.8 Hz	247.5 Hz	371.3 Hz	495.0 Hz
Rolling element (BSF)	49.8 Hz	99.5 Hz	149.3 Hz	199.0 Hz

Factors from Table 3: BPFO 3.05×, BPFI 4.95×, BSF 1.99× shaft frequency · harmonics 1–4 · theoretical values

03Signal to image

Choosing how the model sees the signal.

Vibration from rotating machinery is non-stationary, so neither the time domain nor the frequency domain alone is enough. The study turned each signal window into a time–frequency image, compared four ways of doing it, and measured how well each kept the fault classes apart.

Signal-to-image transforms

Spectral-kurtosis features

Class separabilityhigher is better

Intra-class variancelower is better

CQ-NSGT

Constant-Q non-stationary Gabor transform

Geometrically spaced frequency bins keep resolution at both low and high frequencies, so fault harmonics stand out. Lowest intra-class variance by a wide margin.

CWT edges out CQ-NSGT on separability (0.0630 vs 0.0585), but its classes are four times as spread out. CQ-NSGT gives the best balance: nearly the highest separability with by far the tightest clusters, so it became the model input.

Show data table

Time–frequency transform comparison (Table 5)
Transform	Separability	Intra-class variance
CQ-NSGT	0.0585	70.110
STFT	0.0408	260.025
CWT	0.0630	282.621
WPT	0.0170	205.295

Values from Table 5 · spectrograms compared at 1500 rpm, 6 g

04The model

Freeze what is general, train what is specific.

Three pretrained networks were each used as a frozen feature extractor, followed by custom residual blocks and a shared classification head. Try unfreezing part of the backbone to see the experiment that justified keeping it frozen.

Hybrid transfer-learning model

As published: frozen backbone

CQ-NSGT spectrogram

224 × 224 image

EfficientNetB0

pretrained on large image datasets

frozen: feature extractor only

Residual blocks

custom · skip connections

always trainable

Classification head

shared by all three backbones

5 classes

HB · IRF · ORF · BF · CF

Training time, relative to the frozen model

Frozen

177 s

25% unfrozen

+50%

Validation accuracy: 99.9%
Inference: 0.59 GFLOPS
Latency (CPU): 12.214 ms
Parameter memory: 24.623 MB

The pretrained backbone stays frozen as a general-purpose feature extractor, and only the custom residual blocks and head learn the bearing-specific patterns. EfficientNetB0 trained in 177 s.

Architecture and fine-tuning results from the Methodology and partial fine-tuning sections; cost from Tables 14–16

05Validation

Is it real, or a lucky split?

Every model was trained five times, each time holding out a different fifth of the data. Consistency across folds matters as much as the average: look at how tightly each model’s five results cluster.

Fivefold cross-validation

Accuracy per fold, no noise

Fold 1: train on four fifths, test on the fifth

testtraintraintraintrain

Stratified: each fold has a balanced share of all five classes and every speed and load. Windows do not overlap, so near-identical fragments can’t leak across folds.

fold accuracy mean (value at right)

Friedman test

χ²(4) = 20.00, p = 0.0005

Effect size

η² = 1.00

The ranking (EfficientNetB0, MobileNetV2, InceptionV3, CNN, ViT) was identical in every fold of the grouped evaluation, so the differences are systematic rather than luck of the split.

Show data table

Per-fold accuracy by model (Tables 7–11)
Model	F1	F2	F3	F4	F5	Mean
EfficientNetB0	99.80%	99.50%	100.00%	100.00%	100.00%	99.9%
MobileNetV2	97.70%	99.10%	99.30%	99.10%	99.50%	99.0%
InceptionV3	97.70%	98.40%	98.20%	97.70%	99.10%	98.2%
Base CNN	97.00%	93.00%	86.00%	94.00%	94.00%	92.8%
ViT	75.34%	85.11%	82.89%	81.34%	90.22%	83.0%

Per-fold values from Tables 7–11 · statistics from Table 17

06Under noise

What 98.8% at 1 dB actually means.

Factory floors are noisy. The study added white Gaussian noise at 5, 3 and 1 dB signal-to-noise ratio and re-tested every model. Step through the noise levels to see the signal degrade and the models respond.

Noise stress test

Additive white Gaussian noise

Synthetic signal · 60 msSNR 1 dB

Illustration, not paper data: outer-race impacts at 76.25 Hz (1500 rpm) plus white Gaussian noise scaled to the selected SNR. At 1 dB, the noise carries almost as much power as the signal.

EfficientNetB0: 98.8%
MobileNetV2: 95.2%
InceptionV3: 90.0%
Base CNN: 83.8%
ViT: 73.3%

Accuracy as noise increases (Table 12)

EfficientNetB0 loses just 1.1 points at 1 dB. The CNN and ViT baselines drop sharply and then fluctuate, rather than degrading smoothly.

With simulated speed fluctuation

EfficientNetB099.90% → 99.83%
MobileNetV299.00% → 98.23%
InceptionV398.20% → 95.07%

Grey dot: steady speed · filled dot: with fluctuation · axis 94–100%

Show data table

Accuracy by model and noise level (Table 12)
Model	No noise	5 dB	3 dB	1 dB
EfficientNetB0	99.9%	99.6%	99.2%	98.8%
MobileNetV2	99.0%	98.4%	97.4%	95.2%
InceptionV3	98.2%	95.2%	92.2%	90.0%
Base CNN	92.8%	83.6%	81.6%	83.8%
ViT	83.0%	69.0%	74.4%	73.3%

Accuracy from Table 12 · speed fluctuation from Table 13

The paper frames additive noise as a lower-bound robustness check rather than a model of every mechanical disturbance; speed fluctuation was tested separately.

07Deployment

The best model isn’t always the one you ship.

Accuracy is one axis. For predictive maintenance on edge hardware, compute, latency and memory matter too. Switch the cost metric to see where each model lands.

Accuracy vs cost

Up and to the left is better

MobileNetV2 and EfficientNetB0 need 0.50 and 0.59 GFLOPS per image; InceptionV3, ViT and the baseline CNN need roughly five to eight times as much, for lower accuracy.

Show data table

Accuracy and cost by model (Tables 6, 14–16)
Model	Accuracy	GFLOPS	Training (s)	Latency (ms)	Memory (MB)
EfficientNetB0	99.9%	0.59	177	12.214	24.623
MobileNetV2	99.0%	0.5	121.4	8.167	17.788
InceptionV3	98.2%	3.47	230.5	20.735	96.096
Base CNN	92.8%	4.05	195.5	–	–
ViT	83.0%	3.26	213.6	–	–

Accuracy from Table 6 · compute from Table 15

Read the full paper

Scientific Reports, 2026

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