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Generative adversarial networks with Monte Carlo dropout uncertainty quantification for structural health monitoring: Fibre Bragg grating data augmentation comparison in Hawk T1A aircraft

Alvaro Peiro, Marios Impraimakis

arXiv:2610.22436v1cs.LGeess.SP

TL;DR

Scarce labelled damage data complicate structural health monitoring, particularly for safety-critical aerospace systems. This work evaluates an uncertainty-aware conditional GAN on full-scale Hawk T1A measurements, finding dataset-dependent classification outcomes and an association between uncertainty and signal representativeness.

  • Problem

    Structural-health-monitoring datasets are biased toward healthy states because labelled damage data are costly, complex, and experimentally constrained, despite aerospace safety demands.

    Source: §1 · p. 1

  • Method

    An uncertainty-aware conditional GAN synthesizes class-conditional structural responses, with Monte Carlo dropout uncertainty estimation and evaluation across signal domains and classification.

    Source: §1 · p. 2, §3 · p. 4

  • Results

    Classification performance is dataset dependent, spanning 65% to 99%; strain datasets show larger variability reductions than acceleration, and white-noise cases have higher uncertainty than multisine cases.

    Source: §6 · p. 16

  • Takeaways & Limitations

    Lower-uncertainty datasets generally retain more experimental statistical variability, making uncertainty a practical indicator of confidence and signal representativeness for SHM use.

    Source: §6 · p. 14

    Reduced variability, overestimated high-frequency content, and class overlap limit distributional representation and are reflected in reduced classification performance.

    Source: §5 · p. 12

Abstract

from arXiv · show

The signal generation capabilities of a novel data augmentation framework are examined in aerospace structures. First, the framework learns class-conditional temporal and spectral characteristics of the measured structural responses. It uses conditional generative adversarial network training and Monte Carlo dropout uncertainty quantification as a Bayesian approximation. This step enables stochastic signal synthesis and uncertainty quantification. Second, the generated responses are rigorously compared against experimental measurements across time, frequency, uncertainty, variability, and feature domains to assess physical realism, statistical consistency, and distributional fidelity. Finally, the synthetic data are evaluated to determine whether they should be incorporated into a supervised damage classification workflow. The framework is validated on the full-scale benchmark dataset from a BAE Systems Hawk T1A aircraft tested at the University of Sheffield's Structural Dynamics Laboratory for Verification and Validation. The test involves acceleration, fibre Bragg grating strain, and nonlinear dynamic response measurements. The results demonstrate that the model accurately captures dominant structural dynamics, it guides on signal use for classification improvement based on uncertainty characteristics, and it provides meaningful uncertainty estimates linked to signal complexity and excitation characteristics. Importantly, the framework offers a realistic generative modelling plan as a robust digital twin component for data-driven structural health monitoring, supporting resilient decision-making for condition assessment in safety-critical aerospace systems.

1. Introduction

Damage detection in complex aerospace structures is constrained by scarce labelled damage data and demanding validation needs. This work tests uncertainty-aware conditional generative modelling on Hawk T1A measurements and evaluates synthetic signals for realism and classification use.

1. Introduction

  • Costly, complex, and practically constrained damage-data collection leaves structural-health-monitoring datasets heavily biased toward undamaged states.The challenge is especially consequential in aerospace, where safety requirements, complex loading, and variable operations increase monitoring demands.Source: §1 · p. 1
  • Physics-driven methods offer interpretability but struggle with structural complexity and environmental variability, while data-driven methods capture complex patterns but depend on representative data.Hybrid methods aim to balance those strengths; vibration-based methods also face damage-characterisation, processing, and validation challenges.Source: §1 · p. 1
  • Reconstruction-based LSTMs may reproduce observed sequences rather than learn full distributions, while VAEs can smooth away high-frequency detail relevant to subtle or localised damage.Conditional GANs are presented as an alternative suited to high-dimensional time series and adversarial optimisation of generation quality.Source: §1 · p. 2
  • The study evaluates uncertainty-aware conditional GAN augmentation on full-scale Hawk T1A data across signal domains and tests its impact on structural-state classification.The framework judges whether generated signals should be used, using physical-realism and statistical-consistency assessments across time, frequency, uncertainty, variability, and feature domains.Source: §1 · p. 2

2. The experimental design of the BAE Systems Hawk T1A aircraft

The study uses full-scale Hawk T1A vibration measurements across selected sensing, excitation, and damage conditions. Recordings are partitioned before windowing to avoid train-test leakage.

2. The experimental design of the BAE Systems Hawk T1A aircraft

  • 216 test configurations, repeated about ten times, provide approximately 139 synchronized channels spanning accelerometers, FBG strain gauges, force transducers, and environmental sensors.Conditions include healthy, pseudo-damaged states created by discrete mass additions, and physical damage introduced by port-wing panel removal.Source: §2 · p. 2
  • Healthy-state frequency response functions show dominant resonances within the primary 5–256 Hz excitation bandwidth.The figure presents representative FRFs for the investigated configurations.Source: §2 · p. 2, Figure 2 · p. 3
  • Tests use broadband white noise, pink noise, and odd random-phase multisine excitation over 5–256 Hz, sampled at 2048 Hz.Odd random-phase multisine excitation probes nonlinear behaviour through structured frequency content that can expose harmonic distortion and energy transfer to unexcited frequencies.Source: §2 · p. 2
  • White-noise and odd random-phase multisine tests pair one FBG strain sensor with one accelerometer across pseudo-damage and panel-removal scenarios.WN03 and ORPM02 provide the selected excitation configurations; the selected sensor and damage locations are PW_FB2, PW_ULE3, SW_TLE, and PW1.Source: §2 · p. 2, Figure 1 · p. 3, Table 2 · p. 3
  • Recording-level train-test splitting precedes segmentation into non-overlapping windows, yielding 788 healthy and 787 damaged samples truncated to 1201 time steps.This ordering is used to prevent leakage between training and testing data; signals are mean-centred and normalized using the global standard deviation.Source: §2 · p. 2, Table 3 · p. 3

3. Uncertainty-aware generative adversarial network modeling

The framework uses a conditional GAN to synthesize vibration signals for different structural conditions. Monte Carlo dropout makes generation stochastic and provides signal-level uncertainty estimates.

3. Uncertainty-aware generative adversarial network modeling

  • The model extends a conditional GAN architecture to learn class-dependent vibration characteristics under varying excitation and damage conditions.The generator and discriminator are trained adversarially to learn the joint distribution of vibration signals and structural states.Source: §3 · pp. 3–4
  • The generator maps latent noise and a structural-condition label to synthetic vibration signals, using transposed convolutions to form coherent outputs.The latent vector is sampled from a standard normal distribution; the label is embedded and concatenated with its representation before signal generation.Source: §3 · p. 4
  • Monte Carlo dropout at inference produces stochastic signals for fixed latent inputs and labels, enabling uncertainty estimation across repeated forward passes.The procedure computes time-step sample means and variances, then averages pointwise standard deviations into a global measure and normalizes it by mean absolute signal amplitude.Source: §3 · p. 4
  • The discriminator scores signal-label pairs as real or generated, converting its scalar output to a probability used in the adversarial loss.The class label is embedded, reshaped to the signal dimensions, and concatenated with the input signal along the channel dimension.Source: §3 · p. 4
  • Generator and discriminator updates compete iteratively: the generator produces signals conditioned on structural state, while the discriminator evaluates their consistency with real signal-label pairs.This interaction is used to learn the underlying data distribution.Source: §3 · pp. 5–6

4. Evaluation metrics

The section defines measures for checking adversarial training behavior and comparing generated signals with measured responses in the time, frequency, and feature domains.

4. Evaluation metrics

  • Bounded, gradually stabilising generator and discriminator scores indicate that neither network consistently dominated the optimisation process.The scores are average discriminator probabilities for generated and real samples; adversarial training does not inherently guarantee convergence.Source: §4 · p. 6, Figure 6 · p. 7
  • RMS amplitude and waveform comparisons assess whether generated signals reproduce measured amplitude behavior and temporal structure across conditions.RMS is computed for each signal and averaged per class.Source: §4 · p. 6
  • The coefficient of variation normalizes time-averaged signal dispersion by mean absolute amplitude, while PSD analysis assesses frequency-content fidelity.PSD RMSE compares mean spectra across 5–256 Hz and higher frequencies up to the 1024 Hz Nyquist limit; spectral-energy ratios compare generated and real signals.Source: §4 · p. 6
  • A 14-dimensional vector of spectral and time-domain features represents each signal for feature-space visualization.The first three principal components are examined, and an SVM evaluates classification accuracy, precision, recall, and F1-score.Source: §4 · pp. 6–7
  • Table 9 summarizes implementation settings for PCA, SVM classification, synthetic data generation, and hyperparameter selection.The provided text identifies the table's scope but gives no settings.Source: §4 · p. 7

5. Application to fibre Bragg grating strain, acceleration and nonlinear dynamic response measurements

Across four excitation–sensor configurations, the cGAN reproduces dominant time- and frequency-domain response structure, but generated signals often have reduced variability. Classification effects depend on dataset separability, while white-noise cases show higher uncertainty than multisine cases.

ORPM02-S strain

  • For ORPM02-S, generated signals overlap real signals in feature space and slightly improve SVM performance, despite a more compact distribution.The first three principal components capture 90.25% of total variance.Source: §5 · p. 8, Figure 8 · p. 9

ORPM02-A acceleration

  • For ORPM02-A, generated acceleration signals reproduce the dominant spectrum, with modest high-frequency error, and retain distinct healthy and damaged feature clusters.The first three principal components capture 98.15% of total variance.Source: §5 · p. 9, Table 13 · p. 9

Cross-configuration variability

  • Across reported comparisons, generated signals show reductions relative to real data: one case had inter-signal SD down approximately 60% and CV 47%, while another had mean SD down approximately 20% and CV 16%.A separate comparison reported an approximately 65% reduction in inter-signal standard deviation; the coefficient of variation also decreased, but to a lesser extent due to the higher mean amplitude of generated signals.Source: §5 · pp. 8, 11, 13

WN03-S strain

  • For WN03-S, generated strain signals reproduce dominant spectral structure but substantial class overlap accompanies a slight classification reduction, especially in recall and F1.The first three principal components retain 89.65% of total variance.Source: §5 · pp. 10–11, Table 16 · p. 11

Uncertainty

  • Normalized uncertainty is higher under white-noise excitation than multisine excitation across both sensor types, with small healthy–damaged differences within each case.Reported values are 0.521 and 0.524 for WN03-S, 0.434 and 0.464 for WN03-A, 0.327 and 0.342 for ORPM02-A, and 0.446 for both ORPM02-S states.Source: §5 · pp. 9, 12, 14

WN03-A acceleration

  • For WN03-A, generated data capture overall class structure despite minor inconsistencies; SVM performance on real signals remains exceptionally high across both training configurations, with a very small reduction and increased variability versus the ORPM case.Source: §5 · p. 14, Table 21 · p. 14

6. Discussion

The discussion treats uncertainty as an indicator of generated-signal confidence and representativeness, while emphasizing that fidelity and classification effects vary by dataset and sensor modality. Results favor preserving class-discriminative information over matching full response variability.

Uncertainty and variability

  • Lower uncertainty generally accompanies greater retention of experimental variability, while higher uncertainty is associated with stronger distribution compression.The authors propose uncertainty as a practical indicator of confidence and of whether generated signals are representative enough for SHM tasks.Source: §6 · p. 14, Figure 16 · p. 15

Frequency-domain interpretation

  • The model captures dominant structural dynamics but is less sensitive to fine-scale features, which may include subtle early damage or local defects.The discussion contrasts smoother, global acceleration responses with more localized, higher-order strain behavior.Source: §6 · p. 14

Classification and fidelity

  • Strain responses show larger variability reductions than acceleration responses, and augmentation’s classification effect is modest and dataset dependent.Substantial variability reductions do not necessarily correspond to equivalent classification reductions; retaining class-discriminative information matters more than preserving all dispersion.Source: §6 · pp. 14–15, Figure 17 · p. 15

Cross-dataset synthesis

  • The cross-dataset comparison reports higher uncertainty under white-noise than odd random-phase multisine excitation and recommends validation with fully Bayesian methods and more datasets and channels.The results span classification performance from 65% to 99%.Source: §6 · p. 16, Table 23 · p. 16

Additional sensor validation

  • Neighbouring FBG and accelerometer channels show consistent healthy-to-damaged amplification trends, supporting representativeness within the investigated wing region.Absolute response amplitudes differ among sensors.Source: §6 · p. 16, Figure 18 · p. 16, Table 24 · p. 16

7. Conclusion

The conclusion presents an uncertainty-aware conditional GAN validated on full-scale Hawk T1A measurements across sensor types, excitations, and damage scenarios. It positions the framework as a generative component for vibration-based SHM, with potential beyond aerospace where representative damage data are limited.

7. Conclusion

  • The framework enables class-conditional learning of long-range temporal and spectral characteristics, uncertainty quantification in generated signals and decisions, and assessment of augmentation consistency with classification performance.The conclusion also states applicability across sensor modalities and excitation types.Source: §7 · p. 16
  • The authors describe the framework as a practical generative component for vibration-based SHM, with potential generality to other complex engineering systems facing limited representative damage data..Source: §7 · p. 16

Declaration of competing interest

Data availability

The Hawk T1A aircraft data were provided by the University of Sheffield’s Structural Dynamics Laboratory for Verification and Validation.

Data availability

  • The University of Sheffield’s Structural Dynamics Laboratory for Verification and Validation provides the Hawk T1A aircraft data.Source: Data availability · p. 17

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