GO-OSC and VASH: Geometry-Aware Representation Learning for Early Degradation Detection in Oscillatory Systems

TL;DR

This paper introduces GO-OSC, a geometry-aware framework for early detection of degradation in oscillatory systems, improving sensitivity and robustness over traditional energy-based methods.

Contribution

The paper proposes a novel geometry-aware representation learning approach with invariant probes, enabling earlier and more reliable degradation detection in oscillatory signals.

Findings

Geometry-aware representations improve early detection.

Invariant probes outperform energy-based statistics.

Method is robust to operating condition changes.

Abstract

Early-stage degradation in oscillatory systems often manifests as geometric distortions of the dynamics, such as phase jitter, frequency drift, or loss of coherence, long before changes in signal energy are detectable. In this regime, classical energy-based diagnostics and unconstrained learned representations are structurally insensitive, leading to delayed or unstable detection. We introduce GO-OSC, a geometry-aware representation learning framework for oscillatory time series that enforces a canonical and identifiable latent parameterization, enabling stable comparison and aggregation across short, unlabeled windows. Building on this representation, we define a family of invariant linear geometric probes that target degradation-relevant directions in latent space. We provide theoretical results showing that under early phase-only degradation, energy-based statistics have zero first-order detection power, whereas geometric probes achieve strictly positive sensitivity. Our analysis characterizes when and why linear probing fails under non-identifiable representations and shows how canonicalization restores statistical detectability. Experiments on synthetic benchmarks and real vibration datasets validate the theory, demonstrating earlier detection, improved data efficiency, and robustness to operating condition changes.