Semi-supervised and unsupervised learning for health indicator extraction from guided waves in aerospace composite structures

AI summary

Overview

• Research area: Machine learning for prognostics and health management (PHM), specifically guided-wave structural health monitoring (SHM) of aerospace composite structures.
• Technical level: Advanced — assumes familiarity with semi-supervised anomaly detection, variational autoencoders, signal processing transforms, and prognostic evaluation metrics.
• Scope in one sentence: The paper compares a semi-supervised model (augmented Diversity-DeepSAD) and an unsupervised model (a degradation-trend-constrained variational autoencoder, DTC-VAE) for extracting health indicators from guided-wave data measured on five single-stiffener composite panels under fatigue loading, then fuses per-frequency health indicators by unsupervised ensemble learning.

What This Paper Is About

Health indicators (HIs) — numbers that quantify how damaged a structure is — are essential for deciding when to repair an aircraft composite part, but no true HI labels exist, so models cannot simply be trained in a supervised way. This paper builds a data-driven framework that learns HIs from guided-wave sensor signals without ground-truth labels, using a semi-supervised method with continuous "damage proxy" labels and an unsupervised method with a built-in monotonicity constraint. The goal is an HI that behaves physically, degrading consistently in a way that satisfies three prognostic criteria: monotonicity, prognosability, and trendability.

Key Contributions

1. Continuous auxiliary labels for Diversity-DeepSAD. The authors extend Diversity-DeepSAD by replacing binary ±1 auxiliary labels with continuous labels in the range [1, −1], computed by a linear function y~_j = 1 − 2(t_j/t_N) applied only across the first and last quarters of the lifetime. This is intended to capture intermediate fatigue states that binary labelling ignores — a particular problem in composites, where the severely damaged phase may contain only a single measurement at failure.
2. The DTC-VAE architecture with an explicit monotonicity constraint. A degradation-trend-constrained variational autoencoder is developed in which the monotonicity criterion is embedded directly in the latent space via an explicit trend constraint, enforcing consistent HI evolution for guided-wave monitoring of aerospace composites.
3. Prognostic-metric-guided Bayesian hyperparameter optimisation. Hyperparameters are tuned using a composite fitness score built from monotonicity, prognosability and trendability, which requires constructing complete run-to-failure HI trajectories for all training and validation units.
4. Frequency-agnostic HI fusion. Per-frequency HIs are combined with an unsupervised ensemble learning mechanism weighted by the composite fitness score, offering a principled alternative to picking a single guided-wave excitation frequency.

The paper also reports a comparison of semi-supervised and unsupervised models for generating history-independent HIs, and uses rectified evaluation criteria (Mo_test, Pr_test) rather than only training-set fitness, to reduce bias toward well-matched training units.

Main Findings

• Best signal-processing route used FFT features. Using fast Fourier transform features, the models reached fitness scores of 81.6% for Diversity-DeepSAD and 92.3% for DTC-VAE, which the authors describe as improved monotonicity and consistency over existing baselines.
• DTC-VAE outperformed the semi-supervised approach in this study. On the same FFT-based features, the unsupervised DTC-VAE scored higher than the augmented Diversity-DeepSAD (92.3% versus 81.6% fitness).
• Per-criterion breakdowns are not reported in the available content. The abstract states overall fitness percentages only; individual monotonicity, prognosability and trendability values for the two proposed models on this dataset are not reported in the text available here.
• Frequency fusion addresses frequency dependence. Because each guided-wave measurement is taken at six excitation frequencies, the authors fuse per-frequency HIs through fitness-weighted unsupervised ensembling to mitigate frequency dependence and reduce variance.
• The dataset is harder than typical benchmark datasets of this type. The authors cite coefficients of variation of 51% for guided-wave data from five single-stiffener composite panels and 87% for acoustic emission data from 12 specimens, compared with 24% for the thermal spray coating dataset used in earlier Diversity-DeepSAD work.
• Prior Diversity-DeepSAD results were dataset-dependent. The paper reports that on the PHME2010 milling dataset Diversity-DeepSAD achieved 99% Mo, 99% Tr and 94% Pr, while on thermal spray coating monitoring it achieved 91% Mo and 72% Pr, with Tr not reported.
• Related prior work on comparable structures. A multi-layer LSTM semi-supervised approach reached a fitness score of 93% under leave-one-out cross-validation; CEEMDAN-based semi-supervised ensemble deep learning reached 91.3%; the Hilbert transform semi-supervised CNN (HT-SSCNN) reached 93% on history-independent guided-wave data; and the same semi-supervised inductive learning approach applied to PHME2010 by another group reached 96%.

Methodology in Plain English

Five single-stiffener composite panels (IM7/8552 carbon fibre-reinforced epoxy prepreg, with layups [±45/0/45/90/−45/0]_S and [±45/0/±45]_S) were loaded in compression until failure under the ReMAP-H2020 project. Eight piezoelectric transducers (PZTs), acting in turn as actuators and sensors, produced 56 actuator-sensor paths; measurements were taken every 5000 cycles at six excitation frequencies: 50, 100, 125, 150, 200 and 250 kHz. Each sample is a 56 × 6 × 2000 data tensor. Some specimens had a pre-applied impact load or disbond, and the models were not told about these uncertainties, broken sensors or impacts.

The workflow has four stages. First, data are pre-processed. Second, time-domain signals are transformed using FFT, short-time Fourier transform (STFT), empirical mode decomposition (EMD), and the Hilbert transform (HT). Third, statistical features are extracted: 19 time-domain features (features 1–19), 14 frequency-domain features (20–33), 19 HT features (34–52), 19 EMD features (53–71) and 68 time-frequency features from STFT (72–139), giving 139 features per timestep after averaging across paths and frequencies. Features whose fitness exceeds the mean fitness of all features for that transform are kept, which selects the best-performing signal-processing method. Fourth, the selected features are fed to the two AI models, with Bayesian optimisation of hyperparameters, and the per-frequency HIs are fused by unsupervised ensembling before evaluation.

Data were split into 5 folds using a leave-one-unit-out strategy: one specimen tested, the remaining four used for training. Inputs were Z-score normalised using training statistics only, and model outputs were min-max normalised so HIs run from approximately 0 in the healthy state to approximately 1 at failure. HI quality was scored with monotonicity (modified Mann-Kendall), prognosability (spread of HI values at failure), and trendability (minimum pairwise Pearson correlation between units), combined with equal weights into fitness scores F_all and F_test on a [0, 3] scale; reported percentages are these scores normalised by 3.

Why This Matters

Impact on research. The work targets a well-known bottleneck in prognostics: no true health labels exist for real structures, so supervised learning is not directly applicable. It shows how continuous damage-proxy labels and an explicitly constrained latent space can be used to produce HIs that satisfy physics-inspired criteria, and it moves Diversity-DeepSAD and DTC-VAE into a domain — guided-wave monitoring of aerospace composites — where neither had previously been applied.

Real-world applications:

• Condition-based maintenance scheduling for composite aircraft components, where a reliable HI signals when intervention is needed before failure.
• Remaining useful life (RUL) prediction, since the HI is intended as the input trajectory for forecasting failure.
• In-service monitoring of composite structures around impact-prone areas, where damage from events such as bird strikes or manufacturing disbonds may not be observable directly.
• Reduction of reliance on a single excitation frequency, since measured HI quality varies with frequency and the framework fuses across frequencies instead.

Industry relevance. Aerospace operators and manufacturers benefit from a history-independent HI — one that uses only the current measured state and does not require a recorded baseline from the same unit — because it is more practical for fleets where historical records are inconsistent. The authors also emphasise that earlier evaluation practice can be biased toward training units, and that reporting test-unit-focused metrics (Mo_test, Pr_test) gives a fairer picture of field performance.

Future Directions

• Validate generalisation beyond five specimens. With only five single-stiffener panels, the leave-one-unit-out test is stringent but small; a larger set of structures would test whether the 92.3% and 81.6% fitness scores hold across more units.
• Extend to other structures and damage modes. The authors position the framework for aeronautical composite structures generally, but this study covers a single stiffener geometry under compressive fatigue; multi-stiffener panels, different layups, and other damage modes remain untested here.
• Investigate alternative auxiliary label functions and label counts. The paper notes that many functions were considered for continuous auxiliary labels and that the linear function applied over the first and last quarters performed best, leaving open how other label shapes or proportions of labelled data behave.
• Connect the HI to prognostic outcomes. The stated motivation is diagnostics and prognostics; the reported results concern HI quality metrics, and how these HIs translate into RUL accuracy is not established in the available content.

Target Audience

Researchers and graduate students in structural health monitoring, prognostics and health management, and applied machine learning for engineering systems; aerospace engineers working on composite structure monitoring and condition-based maintenance; and machine learning practitioners interested in semi-supervised and unsupervised methods where ground-truth labels are unavailable. Readers should already be comfortable with deep anomaly detection, variational autoencoders, guided-wave physics, and signal processing transforms.

Authors’ abstract

Health indicators (HIs) are central to diagnosing and prognosing the condition of aerospace composite structures, enabling efficient maintenance and operational safety. However, extracting reliable HIs remains challenging due to variability in material properties, stochastic damage evolution, and diverse damage modes. Manufacturing defects (e.g., disbonds) and in-service incidents (e.g., bird strikes) further complicate this process. This study presents a comprehensive data-driven framework that learns HIs via two learning approaches integrated with multi-domain signal processing. Because ground-truth HIs are unavailable, a semi-supervised and an unsupervised approach are proposed: (i) a diversity deep semi-supervised anomaly detection (Diversity-DeepSAD) approach augmented with continuous auxiliary labels used as hypothetical damage proxies, which overcomes the limitation of prior binary labels that only distinguish healthy and failed states while neglecting intermediate degradation, and (ii) a degradation-trend-constrained variational autoencoder (DTC-VAE), in which the monotonicity criterion is embedded via an explicit trend constraint. Guided waves with multiple excitation frequencies are used to monitor single-stiffener composite structures under fatigue loading. Time, frequency, and time-frequency representations are explored, and per-frequency HIs are fused via unsupervised ensemble learning to mitigate frequency dependence and reduce variance. Using fast Fourier transform features, the augmented Diversity-DeepSAD model achieved 81.6% performance, while DTC-VAE delivered the most consistent HIs with 92.3% performance, outperforming existing baselines.