GO-OSC and VASH: Geometry-Aware Representation Learning for Early Degradation Detection in Oscillatory Systems
Vashista Nobaub
TL;DR
This work tackles early degradation in oscillatory systems where energy-based diagnostics are insensitive to phase distortions. It introduces GO-OSC, a geometry-aware representation that enforces a canonical real--Schur gauge on the latent state $z_t \in \mathbb{R}^{2K}$, making latent coordinates identifiable and comparable across windows. Building on this, it defines a family of gauge-invariant linear geometric probes (e.g., GSI, PCC, DDI, FWR, MLL, LQF) and proves under a local asymptotic normality regime that phase-only degradation yields positive power for these probes while energy statistics have zero first-order power. Empirical results on synthetic and real vibration data confirm earlier detection, better data efficiency, and robustness to nuisance variation, with ablations showing canonicalization as essential. The paper reframes fault detection as a structured representation (non-identifiable embeddings are insufficient) and provides a principled blueprint for geometry-aware ML in physical systems.
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.