A quantum-inspired spectral encoding framework for rolling-element bearing fault diagnosis

Bearing fault diagnosis requires compact representations that remain discriminative under operating variability, noise, and fault-severity changes while avoiding evaluation leakage. This work investigates a quantum-inspired, classically simulated framework based on Partitioned Amplitude Quantum Encoding (PAQE), a shallow variational quantum circuit, and Pauli expectation-value readout. Ordered spectral band-magnitude coefficients are mapped to computational-basis amplitudes and transformed into a compact 2q−1-dimensional representation. For the principal q=4 configuration, only seven expectation-value features are used. The measured observables are shown to correspond to parameterized quadratic forms rather than direct physical frequency-band products, and classical first- and second-order controls are included to assess the role of generic nonlinear structure. Group-disjoint evaluation on the Paderborn, CWRU, and MFPT benchmarks yields accuracies of 0.963±0.024, 0.934–0.962, and 0.929±0.023, respectively. Across these conditions, OPT-VQC exceeds CNN-1D by 3.4–10.5 percentage points, whereas differences relative to ResNet-1D are smaller and condition‑dependent. In the fixed-load CWRU domain-alignment experiment, second-moment alignment increases target accuracy from 0.891±0.028 to 0.949±0.023, corresponding to a 5.8‑percentage‑point improvement. These findings support OPT-VQC as a compact quantum-inspired spectral representation that uses variational-circuit parameterisation to learn structured second-order interactions for leakage-controlled bearing-fault diagnosis.