
@Article{cmes.2026.084403,
AUTHOR = {Safa Alsafari, Ayman Yafoz},
TITLE = {Few-Shot Bearing Fault Diagnosis under Joint Fault-Severity and Load Shift: A Leak-Free Cross-Domain Benchmark},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {},
YEAR = {},
NUMBER = {},
PAGES = {{pages}},
URL = {http://www.techscience.com/CMES/online/detail/27551},
ISSN = {1526-1506},
ABSTRACT = {Bearing fault diagnosis in industrial deployment must contend with two simultaneous distributional shifts: fault severity increases as damage progresses, and motors operate at loads unseen during training. We define this compound setting as the <i>double domain shift</i> and present a rigorous few-shot benchmark on the Case Western Reserve University (CWRU) and Paderborn University (PU) bearing datasets. Six architectures spanning distinct learning paradigms—a multilayer perceptron (MLP), a capsule network (CapsNet), a residual capsule network (ResCaps), a prototypical network (ProtoNet), a modified residual convolutional network (MRCN), and Deep Correlation Alignment (Deep CORAL)—are evaluated under a strict three-way split (support/validation/held-out test) that prevents the data-leakage patterns prevalent in prior CWRU protocols. Models are adapted using <mml:math id="mml-ieqn-1"><mml:mi>K</mml:mi><mml:mo>∈</mml:mo><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mn>5</mml:mn><mml:mo>,</mml:mo><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:mn>20</mml:mn><mml:mo fence="false" stretchy="false">}</mml:mo></mml:math> labelled target samples and assessed on three complementary metrics: accuracy, macro F1-score, and Cohen’s <mml:math id="mml-ieqn-2"><mml:mi>κ</mml:mi></mml:math>. A lightweight 1-D convolutional neural network (CNN) with a capsule routing head (CapsNet) leads on 15 of 18 CWRU conditions and on all PU conditions at <mml:math id="mml-ieqn-3"><mml:mi>K</mml:mi><mml:mtext> </mml:mtext><mml:mrow><mml:mo>≥</mml:mo></mml:mrow><mml:mtext> </mml:mtext><mml:mn>10</mml:mn></mml:math> (with MRCN leading at PU Target-A <mml:math id="mml-ieqn-4"><mml:mi>K</mml:mi><mml:mo>=</mml:mo><mml:mn>5</mml:mn></mml:math>), achieving macro F1 of <mml:math id="mml-ieqn-5"><mml:mn>0.860</mml:mn></mml:math> and <mml:math id="mml-ieqn-6"><mml:mi>κ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.818</mml:mn></mml:math> at <mml:math id="mml-ieqn-7"><mml:mi>K</mml:mi><mml:mo>=</mml:mo><mml:mn>5</mml:mn></mml:math> on the harder CWRU target—with 18,624 parameters (roughly one-third of the MLP baseline) and without any distribution-alignment objective. The multi-metric evaluation reveals findings invisible to accuracy alone: several baselines fall below moderate agreement (<mml:math id="mml-ieqn-8"><mml:mi>κ</mml:mi><mml:mtext> </mml:mtext><mml:mrow><mml:mo>&lt;</mml:mo></mml:mrow><mml:mtext> </mml:mtext><mml:mn>0.60</mml:mn></mml:math>) at low <mml:math id="mml-ieqn-9"><mml:mi>K</mml:mi></mml:math>, and MRCN’s accuracy–F1 gap of <mml:math id="mml-ieqn-10"><mml:mn>5.3</mml:mn></mml:math> percentage points (pp) at <mml:math id="mml-ieqn-11"><mml:mi>K</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn></mml:math> exposes class-selective failure that accuracy conceals. On PU, a macro F1 of <mml:math id="mml-ieqn-12"><mml:mn>0.443</mml:mn></mml:math> at <mml:math id="mml-ieqn-13"><mml:mi>K</mml:mi><mml:mo>=</mml:mo><mml:mn>5</mml:mn></mml:math> on the real inner-race target quantifies the artificial-to-real fatigue transfer gap, and all models produce <mml:math id="mml-ieqn-14"><mml:mi>κ</mml:mi><mml:mtext> </mml:mtext><mml:mrow><mml:mo>&lt;</mml:mo></mml:mrow><mml:mtext> </mml:mtext><mml:mn>0.06</mml:mn></mml:math> on the outer-race target at <mml:math id="mml-ieqn-15"><mml:mi>K</mml:mi><mml:mo>=</mml:mo><mml:mn>5</mml:mn></mml:math>, establishing a realistic lower bound for future work. Wilcoxon signed-rank tests confirm the CapsNet advantage is statistically significant against the weaker baselines in nearly all conditions. Capsule output norms provide interpretable, per-class confidence-like activation scores without requiring post-hoc attribution methods.},
DOI = {10.32604/cmes.2026.084403}
}



