Bearing fault diagnosis via topological data analysis: Strategic feature selection and algorithm-dependent performance under sample-size constraints

Vibration-based bearing fault diagnosis under severe sample-size constraints (n < 100) presents fundamental challenges in feature extraction and classification. This work develops a systematic methodology combining topological data analysis (TDA) with classical time-domain features, validated on laboratory (n=51, 30 kHz, SKF 6206) and industrial (Paderborn, 64 kHz, FAG 6203) datasets under strict bearing-wise generalization. Strategic 8-dimensional Classical+H 0 feature selection achieves perfect classification (100.0% ± 0.0%) on the laboratory dataset using Support Vector Machines with radial basis function kernel, significantly improving over classical features alone (94.2%, p = 0 . 046 , Cohen’s d = 1 . 21 ). Cross-dataset validation confirms consistent performance trends, with SVM achieving 73.3% accuracy under industrial conditions, outperforming metric learning (Metric LDA: 46.7%) and tree-based ensembles. Kernel ablation experiments demonstrate algorithm-dependent exploitation of topological features, with nonlinear kernels achieving up to 40% higher accuracy than linear classifiers. Correlation analysis quantifies partial redundancy between classical and topological features ( r = − 0 . 883 ), yet residual geometric information remains discriminative under nonlinear projection. Multi-window extraction stabilizes feature estimation, reducing classification variance by 14 × . Results establish practical deployment strategies for small-sample diagnostics, demonstrating that topological features provide complementary geometric invariants exploitable by appropriate nonlinear classifiers.