Geometry-Aware Visual Representation for Remaining Useful Life Prediction

Accurate Remaining Useful Life (RUL) prediction is funda-mental to Prognostics and Health Management, yet remains challeng-ing due to stochastic degradation and non-stationary vibration patterns.Existing image-based approaches predominantly rely on time–frequencyrepresentations (e.g., spectrograms or wavelet transforms), which cap-ture spectral energy variations but overlook the intrinsic geometric struc-ture of system dynamics. In this work, we reformulate RUL predictionthrough a phase-space-inspired visual representation. We introduce thePhase Space Density Image (PSDI), a novel representation that encodesthe spatial density of time-delay embedded trajectories. Unlike spectralheatmaps, PSDI characterizes degradation as a progressive geometric dis-persion of the system attractor, revealing structural transitions invisibleto conventional representations. To ensure that these geometric changesreflect true degradation rather than coordinate drift, we further proposea Globally Anchored Reconstruction strategy that enforces consistentphase-space alignment across samples and time. We evaluate the effec-tiveness of the proposed representation across multiple vision architec-tures and integrate it with a compact knowledge distillation frameworkthat transfers useful visual priors while reducing prediction jitter throughtemporal aggregation. Experiments on benchmark datasets demonstratethat PSDI achieves competitive and robust performance compared withclassical signal representations and state-of-the-art time-series models,supporting phase-space density maps as an effective visual representa-tion for vibration-based degradation tracking.