SAMS-Net: A Smoothness-Anchored Monotone Neural Differential Equation Network for Failure-Only-Supervised Structural Health Indicator Construction.

Structural health monitoring (SHM) of fibre-reinforced composites requires a health indicator that is monotonically non-decreasing under the standard SHM assumption that no self-healing or maintenance-induced restoration event is active, derived from heterogeneous sliding-window observations of acoustic emission, strain, and fibre Bragg grating channels, with only the failure timestamp available per specimen. Conventional endpoint-supervised regressors attain high rank correlation with normalised life but produce jagged, non-monotone trajectories of limited engineering value. A method named SAMS-Net (Smoothness-Anchored Monotone Neural Differential Equation Network) is developed, in which a neural differential equation backbone is anchored by a two-level Pool-Adjacent-Violators (PAV) projection. A within-window projection is applied during training with a straight-through gradient, and an across-window projection is applied at inference, yielding a globally non-decreasing health indicator. A smoothness-stratified two-phase training schedule first trains on specimens whose per-specimen median local-smoothness coefficient exceeds 0.5, then fine-tunes on the full set. Across the present seventeen-specimen open-hole carbon-fibre dataset spanning two stress levels and six leave-one-specimen-out and cross-condition scenarios, SAMS-Net wins on every scenario on the canonical Prognostics and Health Management (PHM) Composite of monotonicity, trendability, and robustness, with margins of 0.22 to 0.48 against the strongest baseline, reproducible across three random seeds. Ablation reveals that the operative mechanism is the two-level PAV projection rather than the stochastic differential equation (SDE) inductive bias. A new control experiment in which the across-window PAV projection is applied at inference to the strongest baselines confirms that the projection accounts for a substantial share of the SAMS-Net margin, while the within-window training-time projection and a globally consistent prognosability metric retain a SAMS-Net advantage. Cross-site or cross-material transferability remains to be established in future work.